Calculation of nuclear matrix elements for 0 ν β β decay of Sn 124 using the nonclosure approach in the nuclear shell model

Le résumé fourni par la source

In this study, we calculate the nuclear matrix elements (NMEs) for the light neutrino-exchange mechanism of neutrinoless double beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) of $^{124}\mathrm{Sn}$ within the framework of the interacting nuclear shell model, using the effective shell model Hamiltonian GCN5082. The NMEs are calculated employing both closure and nonclosure approaches. For the intermediate nucleus $^{124}\mathrm{Sb}$, effects of energy of 100 states for each ${J}_{k}^{\ensuremath{\pi}}={0}^{+}$ to ${11}^{+}$ and ${2}^{\ensuremath{-}}$ to ${9}^{\ensuremath{-}}$ ($\mathrm{\ensuremath{\Delta}}{J}_{k}=1)$ are explicitly included in the nonclosure approach. The optimal closure energy, which reproduces nonclosure NMEs using the closure approach, is found to be $\ensuremath{\approx}$ 3 MeV for $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{124}\mathrm{Sn}$. The NMEs for $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{124}\mathrm{Sn}$ did not fully converge with 100 intermediate states for each spin-parity of $^{124}\mathrm{Sb}$. A comparison of NMEs and lower limits of ${T}_{1/2}^{0\ensuremath{\nu}}$ with some of the recent calculations is presented. Further, to gain a comprehensive understanding of the role of nuclear structure on the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay, the dependence of NMEs on the spin-parity of the intermediate states, coupled spin-parity of neutrons and protons, and the number of intermediate states, is explored. The estimated lower limit on the half-life ${T}_{1/2}^{0\ensuremath{\nu}}\ensuremath{\approx}7.49\ifmmode\times\else\texttimes\fi{}{10}^{26}$ yr provides valuable input for the experimental investigations of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{124}\mathrm{Sn}$ in India and elsewhere.

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