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Ab initio investigation of the $^7$Li($p,e^+e^-$)$^8$Be process and the X17 boson (2308.13751v3)

Published 26 Aug 2023 in nucl-th, hep-ph, and nucl-ex

Abstract: Observations of anomalies in the electron-positron angular correlations in high-energy decays in $4$He, $8$Be, and ${12}$C have been reported recently by the ATOMKI collaboration. These could be explained by the creation and subsequent decay of a new boson with a mass of ${\sim}17$ MeV. Theoretical understanding of pair creation in the proton capture reactions used in these experiments is important for the interpretation of the anomalies. We apply the ab initio No-Core Shell Model with Continuum (NCSMC) to the proton capture on $7$Li. The NCSMC describes both bound and unbound states in light nuclei in a unified way with chiral two- and three-nucleon interactions as the only input. We investigate the structure of $8$Be, the $p+7$Li elastic scattering, the $7$Li($p,\gamma$)$8$Be cross section and the internal pair creation $7$Li($p,e+ e-$)$8$Be. We discuss the impact of a proper treatment of the initial scattering state on the electron-positron angular correlation spectrum and compare our results to available ATOMKI data sets. Finally, we calculate $7$Li($p,X$)$8$Be cross sections for several proposed models of the hypothetical X17 particle.

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  31. A property of spherical tensor operators: ℛ⁢𝒪j⁢m⁢ℛ†=∑m′𝒪j⁢m′⁢Dm′⁢mj.ℛsubscript𝒪𝑗𝑚superscriptℛ†subscriptsuperscript𝑚′subscript𝒪𝑗superscript𝑚′subscriptsuperscript𝐷𝑗superscript𝑚′𝑚\mathcal{R}\mathcal{O}_{jm}\mathcal{R}^{\dagger}=\sum_{m^{\prime}}\mathcal{O}_% {jm^{\prime}}D^{j}_{m^{\prime}m}\;.caligraphic_R caligraphic_O start_POSTSUBSCRIPT italic_j italic_m end_POSTSUBSCRIPT caligraphic_R start_POSTSUPERSCRIPT † end_POSTSUPERSCRIPT = ∑ start_POSTSUBSCRIPT italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT caligraphic_O start_POSTSUBSCRIPT italic_j italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT italic_D start_POSTSUPERSCRIPT italic_j end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT italic_m end_POSTSUBSCRIPT . .
  32. The product of D𝐷Ditalic_D and D*superscript𝐷D^{*}italic_D start_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT is a D𝐷Ditalic_D matrix: Dm⁢kj⁢Dm′⁢k′j′⁣*=superscriptsubscript𝐷𝑚𝑘𝑗superscriptsubscript𝐷superscript𝑚′superscript𝑘′superscript𝑗′absent\displaystyle D_{mk}^{j}D_{m^{\prime}k^{\prime}}^{j^{\prime}*}=italic_D start_POSTSUBSCRIPT italic_m italic_k end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_j end_POSTSUPERSCRIPT italic_D start_POSTSUBSCRIPT italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT italic_k start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_j start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT * end_POSTSUPERSCRIPT = ∑J=|j−j′|j+j′(−)m′−k′⁢(j⁢m⁢j′−m′|J⁢(m−m′))superscriptsubscript𝐽𝑗superscript𝑗′𝑗superscript𝑗′superscriptsuperscript𝑚′superscript𝑘′𝑗𝑚superscript𝑗′conditionalsuperscript𝑚′𝐽𝑚superscript𝑚′\displaystyle\sum_{J=\left|j-j^{\prime}\right|}^{j+j^{\prime}}\left(-\right)^{% m^{\prime}-k^{\prime}}\left(jmj^{\prime}-m^{\prime}|J(m-m^{\prime})\right)∑ start_POSTSUBSCRIPT italic_J = | italic_j - italic_j start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT | end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_j + italic_j start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUPERSCRIPT ( - ) start_POSTSUPERSCRIPT italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT - italic_k start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUPERSCRIPT ( italic_j italic_m italic_j start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT - italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT | italic_J ( italic_m - italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) ) ×(j⁢k⁢j′−k′|J⁢(k−k′))⁢D(m−m′)⁢(k−k′)Jabsent𝑗𝑘superscript𝑗′conditionalsuperscript𝑘′𝐽𝑘superscript𝑘′superscriptsubscript𝐷𝑚superscript𝑚′𝑘superscript𝑘′𝐽\displaystyle\times\left(jkj^{\prime}-k^{\prime}|J(k-k^{\prime})\right)D_{(m-m% ^{\prime})(k-k^{\prime})}^{J}× ( italic_j italic_k italic_j start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT - italic_k start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT | italic_J ( italic_k - italic_k start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) ) italic_D start_POSTSUBSCRIPT ( italic_m - italic_m start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) ( italic_k - italic_k start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ) end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_J end_POSTSUPERSCRIPT .
  33. (j1⁢m1⁢j2⁢m2|j⁢m)=(−)j1−m1⁢j^j^2⁢(j⁢m⁢j1−m1|j2⁢m2)conditionalsubscript𝑗1subscript𝑚1subscript𝑗2subscript𝑚2𝑗𝑚superscriptsubscript𝑗1subscript𝑚1^𝑗subscript^𝑗2𝑗𝑚subscript𝑗1conditionalsubscript𝑚1subscript𝑗2subscript𝑚2\left(j_{1}m_{1}j_{2}m_{2}|jm\right)=\left(-\right)^{j_{1}-m_{1}}\frac{\hat{j}% }{\hat{j}_{2}}\left(jmj_{1}-m_{1}|j_{2}m_{2}\right)( italic_j start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_j start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT | italic_j italic_m ) = ( - ) start_POSTSUPERSCRIPT italic_j start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_m start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUPERSCRIPT divide start_ARG over^ start_ARG italic_j end_ARG end_ARG start_ARG over^ start_ARG italic_j end_ARG start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT end_ARG ( italic_j italic_m italic_j start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_m start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT | italic_j start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ) .
  34. (−)j1+j2+j3+j⁢j12^⁢j23^⁢{j1j2j12j3jj23}⁢(j1⁢m1⁢j23⁢m23|j⁢m)=superscriptsubscript𝑗1subscript𝑗2subscript𝑗3𝑗^subscript𝑗12^subscript𝑗23subscript𝑗1subscript𝑗2subscript𝑗12subscript𝑗3𝑗subscript𝑗23conditionalsubscript𝑗1subscript𝑚1subscript𝑗23subscript𝑚23𝑗𝑚absent\displaystyle\left(-\right)^{j_{1}+j_{2}+j_{3}+j}\hat{j_{12}}\hat{j_{23}}\left% \{\begin{array}[]{ccc}j_{1}&j_{2}&j_{12}\\ j_{3}&j&j_{23}\end{array}\right\}\left(j_{1}m_{1}j_{23}m_{23}|jm\right)=( - ) start_POSTSUPERSCRIPT italic_j start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT + italic_j start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT + italic_j start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT + italic_j end_POSTSUPERSCRIPT over^ start_ARG italic_j start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT end_ARG over^ start_ARG italic_j start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT end_ARG { start_ARRAY start_ROW start_CELL italic_j start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_CELL start_CELL italic_j start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT end_CELL start_CELL italic_j start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT end_CELL end_ROW start_ROW start_CELL italic_j start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT end_CELL start_CELL italic_j end_CELL start_CELL italic_j start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT end_CELL end_ROW end_ARRAY } ( italic_j start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_j start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT | italic_j italic_m ) = ∑m2(j1⁢m1⁢j2⁢m2|j12⁢m12)⁢(j12⁢m12⁢j3⁢m3|j⁢m)⁢(j2⁢m2⁢j3⁢m3|j23⁢m23)subscriptsubscript𝑚2conditionalsubscript𝑗1subscript𝑚1subscript𝑗2subscript𝑚2subscript𝑗12subscript𝑚12conditionalsubscript𝑗12subscript𝑚12subscript𝑗3subscript𝑚3𝑗𝑚conditionalsubscript𝑗2subscript𝑚2subscript𝑗3subscript𝑚3subscript𝑗23subscript𝑚23\displaystyle\sum_{m_{2}}\left(j_{1}m_{1}j_{2}m_{2}|j_{12}m_{12}\right)\left(j% _{12}m_{12}j_{3}m_{3}|jm\right)\left(j_{2}m_{2}j_{3}m_{3}|j_{23}m_{23}\right)∑ start_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT end_POSTSUBSCRIPT ( italic_j start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_j start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT | italic_j start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT ) ( italic_j start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 12 end_POSTSUBSCRIPT italic_j start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT | italic_j italic_m ) ( italic_j start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT italic_j start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT | italic_j start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT italic_m start_POSTSUBSCRIPT 23 end_POSTSUBSCRIPT ) .
  35. P. Descouvemont, Theoretical Models for Nuclear Astrophysics (Nova Science, Hauppauge NY, 2003).
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