2000 character limit reached
Shape of 12C (2403.05287v2)
Published 8 Mar 2024 in nucl-th and nucl-ex
Abstract: We have examined the hypothesis by Bijker and Iachello who asserted that 12C has an internal structure with three alpha particles arranged in a triangular shape, leading to the formation of the ground rotational band consisting of 0+, 2+, 3-, 4$\pm$ and 5- states. Following this idea, we reconstructed the intrinsic shape of 12C using experimental electron scattering data with minimal theoretical assumption. Our sole assumption was that the observed 0+, 2+, 3-, and 4+ states share a common internal structure, forming a rotational spectrum. The reconstructed intrinsic density showed a beautiful triangular shape with three peaks implying alpha cluster formation in the ground band.
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Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Wakasa, E. Ihara, K. Fujita, Y. Funaki, K. Hatanaka, H. Horiuchi, M. Itoh, J. Kamiya, G. Röpke, H. Sakaguchi, N. Sakamoto, Y. Sakemi, P. Schuck, Y. Shimizu, M. Takashina, S. Terashima, A. Tohsaki, M. Uchida, H. Yoshida, M. Yosoi, New candidate for an alpha cluster condensed state in at 400 MeV. Physics Letters B 653, 173–177 (2007). 10.1016/j.physletb.2007.08.016. URL http://linkinghub.elsevier.com/retrieve/pii/S0370269307009690 [9] Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. 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URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. 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Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Wakasa, E. Ihara, K. Fujita, Y. Funaki, K. Hatanaka, H. Horiuchi, M. Itoh, J. Kamiya, G. Röpke, H. Sakaguchi, N. Sakamoto, Y. Sakemi, P. Schuck, Y. Shimizu, M. Takashina, S. Terashima, A. Tohsaki, M. Uchida, H. Yoshida, M. Yosoi, New candidate for an alpha cluster condensed state in at 400 MeV. Physics Letters B 653, 173–177 (2007). 10.1016/j.physletb.2007.08.016. URL http://linkinghub.elsevier.com/retrieve/pii/S0370269307009690 [9] Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. 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Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. 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URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. 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Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. 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Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. 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URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. 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Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Wakasa, E. Ihara, K. Fujita, Y. Funaki, K. Hatanaka, H. Horiuchi, M. Itoh, J. Kamiya, G. Röpke, H. Sakaguchi, N. Sakamoto, Y. Sakemi, P. Schuck, Y. Shimizu, M. Takashina, S. Terashima, A. Tohsaki, M. Uchida, H. Yoshida, M. Yosoi, New candidate for an alpha cluster condensed state in at 400 MeV. Physics Letters B 653, 173–177 (2007). 10.1016/j.physletb.2007.08.016. URL http://linkinghub.elsevier.com/retrieve/pii/S0370269307009690 [9] Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. 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Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. 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URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Akimune, M. Fujiwara, U. Garg, T. Kawabata, K. Kawase, T. Murakami, K. Nakanishi, Y. Nakatsugawa, H. Sakaguchi, S. Terashima, M. Uchida, Y. Yasuda, M. Yosoi, J. Zenihiro, Nature of 10 MeV state in 12 C. Journal of Physics: Conference Series 436(1), 012006 (2013). 10.1088/1742-6596/436/1/012006. URL http://stacks.iop.org/1742-6596/436/i=1/a=012006?key=crossref.66f3eb5d27716d2a8697b3dd2ef6d8d0 [8] T. Wakasa, E. Ihara, K. Fujita, Y. Funaki, K. Hatanaka, H. Horiuchi, M. Itoh, J. Kamiya, G. Röpke, H. Sakaguchi, N. Sakamoto, Y. Sakemi, P. Schuck, Y. Shimizu, M. Takashina, S. Terashima, A. Tohsaki, M. Uchida, H. Yoshida, M. Yosoi, New candidate for an alpha cluster condensed state in at 400 MeV. Physics Letters B 653, 173–177 (2007). 10.1016/j.physletb.2007.08.016. URL http://linkinghub.elsevier.com/retrieve/pii/S0370269307009690 [9] Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. 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Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Wakasa, E. Ihara, K. Fujita, Y. Funaki, K. Hatanaka, H. Horiuchi, M. Itoh, J. Kamiya, G. Röpke, H. Sakaguchi, N. Sakamoto, Y. Sakemi, P. Schuck, Y. Shimizu, M. Takashina, S. Terashima, A. Tohsaki, M. Uchida, H. Yoshida, M. Yosoi, New candidate for an alpha cluster condensed state in at 400 MeV. Physics Letters B 653, 173–177 (2007). 10.1016/j.physletb.2007.08.016. URL http://linkinghub.elsevier.com/retrieve/pii/S0370269307009690 [9] Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. 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URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. 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Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. 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Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. 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Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. 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Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. 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Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. 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Sakemi, P. Schuck, Y. Shimizu, M. Takashina, S. Terashima, A. Tohsaki, M. Uchida, H. Yoshida, M. Yosoi, New candidate for an alpha cluster condensed state in at 400 MeV. Physics Letters B 653, 173–177 (2007). 10.1016/j.physletb.2007.08.016. URL http://linkinghub.elsevier.com/retrieve/pii/S0370269307009690 [9] Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. 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Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. 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Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Wakasa, E. Ihara, K. Fujita, Y. Funaki, K. Hatanaka, H. Horiuchi, M. Itoh, J. Kamiya, G. Röpke, H. Sakaguchi, N. Sakamoto, Y. Sakemi, P. Schuck, Y. Shimizu, M. Takashina, S. Terashima, A. Tohsaki, M. Uchida, H. Yoshida, M. Yosoi, New candidate for an alpha cluster condensed state in at 400 MeV. Physics Letters B 653, 173–177 (2007). 10.1016/j.physletb.2007.08.016. URL http://linkinghub.elsevier.com/retrieve/pii/S0370269307009690 [9] Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. 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Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. 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Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. 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URL http://linkinghub.elsevier.com/retrieve/pii/S0370269307009690 [9] Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. 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Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. 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Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. 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Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. 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Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. 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Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. 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Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. 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Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, T. Yamada, H. Horiuchi, G. Röpke, P. Schuck, A. Tohsaki, α𝛼\alphaitalic_α -Particle Condensation in O 16 Studied with a Full Four-Body Orthogonality Condition Model Calculation. Physical Review Letters 101, 082502 (2008). 10.1103/PhysRevLett.101.082502. URL http://link.aps.org/doi/10.1103/PhysRevLett.101.082502 [10] Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
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URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Funaki, Container evolution for cluster structures in O 16. Physical Review C 97(2), 021304 (2018). 10.1103/PhysRevC.97.021304 [11] S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. 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Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, T. Kawabata, K. Minomo, T. Kadoya, N. Yokota, H. Akimune, T. Baba, H. Fujimura, M. Fujiwara, Y. Funaki, T. Furuno, T. Hashimoto, K. Hatanaka, K. Inaba, Y. Ishii, M. Itoh, C. Iwamoto, K. Kawase, Y. Maeda, H. Matsubara, Y. Matsuda, H. Matsuno, T. Morimoto, H. Morita, M. Murata, T. Nanamura, I. Ou, S. Sakaguchi, Y. Sasamoto, R. Sawada, Y. Shimizu, K. Suda, A. Tamii, Y. Tameshige, M. Tsumura, M. Uchida, T. Uesaka, H.P. Yoshida, S. Yoshida, Systematic analysis of inelastic <math> <mi>α𝛼\alphaitalic_α</mi> </math> scattering off self-conjugate <math> <mrow> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>n</mi> </mrow> </math> nuclei. Physical Review C 97(1), 014601 (2018). 10.1103/PhysRevC.97.014601. URL https://link.aps.org/doi/10.1103/PhysRevC.97.014601 [12] S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. 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Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. 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De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 S. Adachi, Y. Fujikawa, T. Kawabata, H. Akimune, T. Doi, T. Furuno, T. Harada, K. Inaba, S. Ishida, M. Itoh, C. Iwamoto, N. Kobayashi, Y. Maeda, Y. Matsuda, M. Murata, S. Okamoto, A. Sakaue, R. Sekiya, A. Tamii, M. Tsumura, Candidates for the 5α𝛼\alphaitalic_α condensed state in 20Ne. Physics Letters B 819, 136411 (2021). 10.1016/j.physletb.2021.136411. URL https://linkinghub.elsevier.com/retrieve/pii/S0370269321003518 [13] B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Zhou, Y. Funaki, H. Horiuchi, Y.G. Ma, G. Röpke, P. Schuck, A. Tohsaki, T. Yamada, The 5alpha condensate state in 20Ne. Nature Communications 14(1), 8206 (2023). 10.1038/s41467-023-43816-9. URL https://www.nature.com/articles/s41467-023-43816-9 [14] E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, D. Lee, U.G. Meißner, Ab-initio calculation of the Hoyle state. Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. 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Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Physical Review Letters 106(19), 192501 (2011). 10.1103/PhysRevLett.106.192501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.192501 [15] E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 E. Epelbaum, H. Krebs, T.A. Lähde, D. Lee, U.G. Meißner, U.G. Meiner, Structure and Rotations of the Hoyle State. Physical Review Letters 109(25), 252501 (2012). 10.1103/PhysRevLett.109.252501. URL https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.109.252501https://link.aps.org/doi/10.1103/PhysRevLett.109.252501 [16] A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Lovato, S. Gandolfi, J. Carlson, S.C. Pieper, R. Schiavilla, Electromagnetic Response of 12C : A First-Principles Calculation. Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. 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Physical Review Letters 117(8), 082501 (2016). 10.1103/PhysRevLett.117.082501. URL https://link.aps.org/doi/10.1103/PhysRevLett.117.082501 [17] T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. 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Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 T. Otsuka, T. Abe, T. Yoshida, Y. Tsunoda, N. Shimizu, N. Itagaki, Y. Utsuno, J. Vary, P. Maris, H. Ueno, α𝛼\alphaitalic_α-Clustering in atomic nuclei from first principles with statistical learning and the Hoyle state character. Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. 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Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. 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Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Nature Communications 13(1), 2234 (2022). 10.1038/s41467-022-29582-0. URL https://www.nature.com/articles/s41467-022-29582-0 [18] G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Stellin, L. Fortunato, A. Vitturi, Electromagnetic selection rules in the triangular α𝛼\alphaitalic_α -cluster model of 12 C. Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Journal of Physics G: Nuclear and Particle Physics 43(8), 085104 (2016). 10.1088/0954-3899/43/8/085104. URL https://iopscience.iop.org/article/10.1088/0954-3899/43/8/085104 [19] P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. 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Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- P.O. Hess, 12C within the Semimicroscopic Algebraic Cluster Model. The European Physical Journal A 54(3), 32 (2018). 10.1140/epja/i2018-12468-7. URL http://link.springer.com/10.1140/epja/i2018-12468-7 [20] A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Vitturi, J. Casal, L. Fortunato, E.G. Lanza, Transition densities and form factors in the triangular α𝛼\alphaitalic_α-cluster model of C12. Physical Review C 101(1), 014315 (2020). 10.1103/PhysRevC.101.014315. URL https://link.aps.org/doi/10.1103/PhysRevC.101.014315 [21] J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J. Casal, L. Fortunato, E.G. Lanza, A. Vitturi, Alpha-induced inelastic scattering and alpha-transfer reactions in12C and 16O within the Algebraic Cluster Model. The European Physical Journal A 57(1), 33 (2021). 10.1140/epja/s10050-021-00347-5. URL http://link.springer.com/10.1140/epja/s10050-021-00347-5 [22] R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. 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URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster states in nuclei as representations of a U(nu+1) group. Physical Review C 61(6), 067305 (2000). 10.1103/PhysRevC.61.067305. URL https://journals.aps.org/prc/abstract/10.1103/PhysRevC.61.067305https://link.aps.org/doi/10.1103/PhysRevC.61.067305 [23] R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Bijker, F. Iachello, Cluster structure of light nuclei. Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. 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Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Progress in Particle and Nuclear Physics 110, 103735 (2020). 10.1016/j.ppnp.2019.103735 [24] D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 D.J. Marín-Lámbarri, R. Bijker, M. Freer, M. Gai, T. Kokalova, D.J. Parker, C. Wheldon, Evidence for Triangular D3h Symmetry in C12. Physical Review Letters 113(1), 012502 (2014). 10.1103/PhysRevLett.113.012502. URL https://link.aps.org/doi/10.1103/PhysRevLett.113.012502 [25] A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. 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Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Nakada, Y. Torizuka, Y. Horikawa, Determination of the Deformation in 12C from Electron Scattering. Physical Review Letters 27(11), 745–748 (1971). 10.1103/PhysRevLett.27.745. URL https://link.aps.org/doi/10.1103/PhysRevLett.27.745 [26] M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Kamimura, Transition densities between states in 12C derived from the three-alpha resonating-group wave functions. Nuclear Physics A 351, 456–480 (1981) [27] J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. 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Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. 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URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
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URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
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URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. 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Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- J.H. Fregeau, Elastic and Inelastic Scattering of 187-Mev Electrons from Carbon-12. Physical Review 104(1), 225–236 (1956). 10.1103/PhysRev.104.225. URL https://link.aps.org/doi/10.1103/PhysRev.104.225 [28] H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H.L. Crannell, T.A. Griffy, Determination of Radiative Transition C12. Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Physical Review 136(6B), B1580–B1584 (1964). 10.1103/PhysRev.136.B1580. URL https://link.aps.org/doi/10.1103/PhysRev.136.B1580 [29] H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- H. Crannell, Elastic and Inelastic Electron Scattering from C12 and O16. Physical Review 148(3), 1107–1118 (1966). 10.1103/PhysRev.148.1107. URL https://link.aps.org/doi/10.1103/PhysRev.148.1107 [30] P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 P. Strehl, T. Schucan, Study of monopole transitions in 12C, 24Mg, 28Si, 32S and 40Ca by inelastic electron scattering. Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Physics Letters B 27(10), 641–643 (1968). 10.1016/0370-2693(68)90303-1. URL https://linkinghub.elsevier.com/retrieve/pii/0370269368903031 [31] I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 I. Sick, J. McCarthy, Elastic electron scattering from 12C and 16O. Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Nuclear Physics A 150(3), 631–654 (1970). 10.1016/0375-9474(70)90423-9. URL https://linkinghub.elsevier.com/retrieve/pii/0375947470904239 [32] F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 F. Kline, H. Crannell, J.T. O’Brien, J. McCarthy, R. Whitney, Elastic electron scatterring from 14C. Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Nuclear Physics A 209(2), 381–395 (1973). 10.1016/0375-9474(73)90585-X. URL https://linkinghub.elsevier.com/retrieve/pii/037594747390585X [33] W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Reuter, G. Fricke, K. Merle, H. Miska, Nuclear charge distribution and rms radius of C12 from absolute elastic electron scattering measurements. Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Physical Review C 26(3), 806–818 (1982). 10.1103/PhysRevC.26.806. URL https://link.aps.org/doi/10.1103/PhysRevC.26.806 [34] H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. De Vries, C. De Jager, C. De Vries, Nuclear charge-density-distribution parameters from elastic electron scattering. Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Atomic Data and Nuclear Data Tables 36(3), 495–536 (1987). 10.1016/0092-640X(87)90013-1. URL https://linkinghub.elsevier.com/retrieve/pii/0092640X87900131 [35] A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 A. Bohr, B. Mottelson, Nuclear Structure Vol. 2 (Benjamin Inc., New York, 1975) [36] R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- R. Imai, T. Tada, M. Kimura, Real-time evolution method and its application to the 3α𝛼\alphaitalic_α cluster system. Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Physical Review C 99, 064327 (2019) [37] B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even–even nuclei. Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Atomic Data and Nuclear Data Tables 107, 1–139 (2016). 10.1016/j.adt.2015.10.001. URL https://linkinghub.elsevier.com/retrieve/pii/S0092640X15000406 [38] H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 H. Crannell, T. Griffy, L. Suelzle, M. Yearian, A determination of the transition widths of some excited states in 12C. Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Nuclear Physics A 90(1), 152–158 (1967). 10.1016/0375-9474(67)90745-2. URL https://linkinghub.elsevier.com/retrieve/pii/0375947467907452 [39] W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 W. Vermeer, M. Esat, J. Kuehner, R. Spear, A. Baxter, S. Hinds, Electric quadrupole moment of the first excited state of 12C. Physics Letters B 122(1), 23–26 (1983). 10.1016/0370-2693(83)91160-7. URL https://linkinghub.elsevier.com/retrieve/pii/0370269383911607 [40] G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 G. Ripka, in Advances in Nuclear Physics (Springer US, Boston, MA, 1968), pp. 183–259. 10.1007/978-1-4757-0103-6_3. URL http://link.springer.com/10.1007/978-1-4757-0103-6_3 [41] Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics. Physical Review Letters 81, 5291–5293 (1998) [42] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. 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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
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Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
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Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Structure of the Hoyle State in C 12. Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Physical Review Letters 98, 032501 (2007) [43] M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 M. Chernykh, H. Feldmeier, T. Neff, P. von Neumann-Cosel, A. Richter, Pair Decay Width of the Hoyle State and its Role for Stellar Carbon Production. Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Physical Review Letters 105(2), 022501 (2010). 10.1103/PhysRevLett.105.022501. URL https://link.aps.org/doi/10.1103/PhysRevLett.105.022501 [44] Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Y. Kanada-En’yo, The Structure of Ground and Excited States of 12C. Progress of Theoretical Physics 117(4), 655–680 (2007). 10.1143/PTP.117.655. URL https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.117.655 [45] B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 B. Foris, C.N. Papanicolas, Electron Scattering and Nuclear Structure. Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Annual Review of Nuclear and Particle Science 37(1), 133–176 (1987). 10.1146/annurev.ns.37.120187.001025. URL https://www.annualreviews.org/doi/10.1146/annurev.ns.37.120187.001025 [46] L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388 L.S. Cardman, D.H. Dowell, R.L. Gulbranson, D.G. Ravenhall, R.L. Mercer, Coupled-channel analysis of high-energy electron scattering by 152Sm. Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
- Physical Review C 18(3), 1388–1417 (1978). 10.1103/PhysRevC.18.1388. URL https://link.aps.org/doi/10.1103/PhysRevC.18.1388
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