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Four-Body Systems at Large Cutoffs in Effective Field Theory

Published 12 Apr 2023 in nucl-th | (2304.06172v4)

Abstract: Four-body systems are studied using an effective field theory with two- and three-body contact interactions. A method to systematically address deep trimers (three-body bound states that are more tightly bound than four-body bound/resonant states) in four-body calculations is developed using a diagrammatic approach. Previous calculations were limited by the existence of deep trimers, which this work overcomes. For cold $4$He atoms, binding energies of 526.1(5)~mK and 128.517(1)~mK are obtained at leading order for the tetramer ground and excited states, respectively, where errors come from the truncation of three-body partial waves. Tetramer binding energies and decay widths are also computed approaching the unitary limit. In the unitary limit, there are two tetramers associated with each trimer of binding energy $B_3{(0)}$. The binding energy and decay width for the associated tetramer ground state are $E_4{(0)} = 4.60(1)B_3{(0)}$ and $\Gamma_4{(0)}/2 = 0.0160(1)B_3{(0)}$, respectively, and for the associated tetramer excited state, $E_4{(1)} = 1.0022(3)B_3{(0)}$ and $\Gamma_4{(1)}/2 = 2.57(2)\times 10{-4}B_3{(0)}$, respectively. This calculation is a gateway to higher-order and/or more-body calculations in nuclear and atomic systems.

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  1. D. B. Kaplan, M. J. Savage, and M. B. Wise, A new expansion for nucleon-nucleon interactions, Physics Letters B 424, 390 (1998a).
  2. D. B. Kaplan, M. J. Savage, and M. B. Wise, Two-nucleon systems from effective field theory, Nuclear Physics B 534, 329 (1998b).
  3. E. Braaten and H.-W. Hammer, Universality in few-body systems with large scattering length, Physics Reports 428, 259 (2006).
  4. P. Bedaque, H.-W. Hammer, and U. van Kolck, The three-boson system with short-range interactions, Nuclear Physics A 646, 444 (1999a).
  5. P. F. Bedaque, H.-W. Hammer, and U. van Kolck, Renormalization of the three-body system with short-range interactions, Physical Review Letters 82, 463 (1999b).
  6. P. Bedaque, H.-W. Hammer, and U. van Kolck, Effective theory of the triton, Nuclear Physics A 676, 357 (2000).
  7. H.-W. Hammer and L. Platter, Efimov states in nuclear and particle physics, Annual Review of Nuclear and Particle Science 60, 207 (2010).
  8. H.-W. Hammer, S. König, and U. van Kolck, Nuclear effective field theory: Status and perspectives, Reviews of Modern Physics 92, 10.1103/revmodphys.92.025004 (2020).
  9. L. Platter, H. W. Hammer, and U.-G. Meissner, The Four boson system with short range interactions, Phys. Rev. A 70, 052101 (2004), arXiv:cond-mat/0404313 .
  10. O. A. Yakubovsky, On the Integral equations in the theory o N particle scattering, Sov. J. Nucl. Phys. 5, 937 (1967).
  11. D. Blume and C. H. Greene, Monte carlo hyperspherical description of helium cluster excited states, Journal of Chemical Physics 112, 8053 (2000).
  12. R. A. Aziz and M. J. Slaman, An examination of ab initio results for the helium potential energy curve, The Journal of Chemical Physics 94, 8047 (1991), https://doi.org/10.1063/1.460139 .
  13. R. Lazauskas and J. Carbonell, Description of He4superscriptHe4{}^{4}\mathrm{He}start_FLOATSUPERSCRIPT 4 end_FLOATSUPERSCRIPT roman_He tetramer bound and scattering states, Phys. Rev. A 73, 062717 (2006).
  14. H. W. Hammer and L. Platter, Universal properties of the four-body system with large scattering length, The European Physical Journal A 32, 113 (2007).
  15. J. von Stecher, J. P. D’Incao, and C. H. Greene, Signatures of universal four-body phenomena and their relation to the Efimov effect, Nature Physics 5, 417 (2009).
  16. A. Deltuva, Efimov physics in bosonic atom-trimer scattering, Phys. Rev. A 82, 040701 (2010), arXiv:1009.1295 [physics.atm-clus] .
  17. T. Frederico and M. Gattobigio, Universal tetramer limit-cycle at the unitarity limit (2023), arXiv:2303.14952 [physics.atm-clus] .
  18. L. Platter, H.-W. Hammer, and U.-G. Meißner, On the correlation between the binding energies of the triton and the α𝛼\alphaitalic_α-particle, Physics Letters B 607, 254 (2005).
  19. J. A. Tjon, Bound states of 4 He with local interactions, Phys. Lett. B 56, 217 (1975).
  20. J. Kirscher, Zero-energy neutron-triton and proton-Helium-3 scattering with EFT/πabsent𝜋/\!\!\!\pi/ italic_π, Phys. Lett. B 721, 335 (2013), arXiv:1105.3763 [nucl-th] .
  21. L. D. Blokhintsev and I. M. Narodetsky, SELECTED TOPICS ON THE NONRELATIVISTIC DIAGRAM TECHNIQUE,   (1983).
  22. J. von Stecher, Weakly bound cluster states of efimov character, Journal of Physics B: Atomic, Molecular and Optical Physics 43, 101002 (2010).
  23. E. Hiyama and M. Kamimura, Variational calculation of 44{}^{4}start_FLOATSUPERSCRIPT 4 end_FLOATSUPERSCRIPThe tetramer ground and excited states using a realistic pair potential, Phys. Rev. A 85, 022502 (2012).
  24. M. Gattobigio, A. Kievsky, and M. Viviani, Energy spectra of small bosonic clusters having a large two-body scattering length, Physical Review A 86, 10.1103/physreva.86.042513 (2012).
  25. B. Bazak, M. Eliyahu, and U. van Kolck, Effective Field Theory for Few-Boson Systems, Phys. Rev. A 94, 052502 (2016), arXiv:1607.01509 [cond-mat.quant-gas] .
  26. Rapid reaction task force: The systematic treatment of the coulomb interaction in few-body systems.
  27. F. Gabbiani, P. F. Bedaque, and H. W. Griesshammer, Higher partial waves in an effective field theory approach to nd scattering, Nucl. Phys. A 675, 601 (2000), arXiv:nucl-th/9911034 .
  28. C. Ji and D. R. Phillips, Effective field theory analysis of three-boson systems at next-to-next-to-leading order, Few-Body Systems 54, 2317 (2013).
  29. J. Vanasse, Triton charge radius to next-to-next-to-leading order in pionless effective field theory, Physical Review C 95, 10.1103/physrevc.95.024002 (2017).
  30. C. Ji, D. R. Phillips, and L. Platter, The three-boson system at next-to-leading order in an effective field theory for systems with a large scattering length, Annals of Physics 327, 1803 (2012).
  31. H. Kamada and W. Glöckle, Solutions of the yakubovsky equations for four-body model systems, Nuclear Physics A 548, 205 (1992).
  32. W. Gloeckle and H. Kamada, On the inclusion of 3N-forces into the 4N-Yakubovsky equations, Nucl. Phys. A 560, 541 (1993).
  33. S. Weinberg, Systematic solution of multiparticle scattering problems, Phys. Rev. 133, B232 (1964).
  34. J. Qin and J. Vanasse, Effective-field-theory analysis of boson-trimer bond lengths to next-to-leading order, Physical Review A 103, 10.1103/physreva.103.023333 (2021).
  35. L. W. Bruch, W. Schöllkopf, and J. P. Toennies, The formation of dimers and trimers in free jet 4he cryogenic expansions, The Journal of Chemical Physics 117, 1544 (2002), https://doi.org/10.1063/1.1486442 .
  36. K. T. Tang, J. P. Toennies, and C. L. Yiu, Accurate analytical he-he van der waals potential based on perturbation theory, Phys. Rev. Lett. 74, 1546 (1995).
  37. V. Roudnev and S. Yakovlev, Investigation of 4he3 trimer on the base of faddeev equations in configuration space, Chemical Physics Letters 328, 97 (2000).
  38. E. A. Kolganova, A. K. Motovilov, and W. Sandhas, The 4he trimer as an efimov system, Few-Body Systems 51, 249 (2011).
  39. V. Roudnev, Ultra-low energy elastic scattering in a system of three he atoms, Chemical Physics Letters 367, 95 (2003).
  40. M. Lewerenz, Structure and energetics of small helium clusters: Quantum simulations using a recent perturbational pair potential, The Journal of Chemical Physics 106, 4596 (1997), https://doi.org/10.1063/1.473501 .
  41. P. Grassberger and W. Sandhas, Systematical treatment of the non-relativistic n-particle scattering problem, Nuclear Physics B 2, 181 (1967).
  42. S. K. Adhikari, T. Frederico, and I. D. Goldman, Perturbative renormalization in quantum few-body problems, Phys. Rev. Lett. 74, 487 (1995).
  43. M. R. Hadizadeh, private communication .
  44. J. P. D’Incao, Few-body physics in resonantly interacting ultracold quantum gases, Journal of Physics B: Atomic, Molecular and Optical Physics 51, 043001 (2018).
  45. W. Glöckle, The quantum mechanical few-body problem, Texts and monographs in physics (Springer, Berlin, 1983).

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