Large-scale shell-model study of two-neutrino double-beta decay of ${}^{82}$Se, ${}^{94}$Zr, ${}^{108}$Cd, ${}^{124}$Sn, ${}^{128}$Te, ${}^{130}$Te, ${}^{136}$Xe, and ${}^{150}$Nd

Abstract

Large-scale shell-model calculations have been performed for the study of two neutrino double-beta ($2\nu \beta \beta$) decay in ${}^{82}$Se, ${}^{94}$Zr, ${}^{108}$Cd, ${}^{124}$Sn, ${}^{128}$Te, ${}^{130}$Te, ${}^{136}$Xe, and ${}^{150}$Nd. We have employed JUN45 interaction to calculate the nuclear matrix element (NME) for $2\nu \beta \beta$ decay in ${}^{82}$Se. In the case of ${}^{94}$Zr, the glekpn effective interaction is used. For ${}^{108}$Cd, we have used a realistic effective interaction derived through the G-matrix approach. In the case of ${}^{124}$Sn, ${}^{128,130}$Te and ${}^{136}$Xe, the sn100pn effective interaction is employed. For ${}^{150}$Nd, we have used KHHE effective interaction based on holes in a ${}^{208}$Pb core. We have extracted the half-lives of these nuclei for the $2\nu \beta \beta$ decay with the help of calculated NME. Our results are consistent with the available experimental half-lives. The variation of cumulative $2\nu \beta \beta$ NME with respect to the excitation energy of the intermediate $1^{+}$ states is also shown, and in all cases, it is ensured that their values are almost saturated. In the present work we have calculated more intermediate $1^{+}$ states as much as possible in comparison to results available in the literature.

Comments: 17 pages, 2 figures, 2 tables