Calculations of two-neutrino double- β decay for fpg shell nuclei

Abstract

In this paper, we calculate the properties of two-neutrino double-$\ensuremath{\beta}$ ($2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decays for nuclei within $fpg$ ($1{p}_{3/2},\phantom{\rule{0.16em}{0ex}}0{f}_{5/2},\phantom{\rule{0.16em}{0ex}}1{p}_{1/2},\phantom{\rule{0.16em}{0ex}}0{g}_{9/2}$) shell model space systematically under the framework of the nuclear shell model. Both of the decays on the ${\ensuremath{\beta}}^{\ensuremath{-}}$ side ($2\ensuremath{\nu}2{\ensuremath{\beta}}^{\ensuremath{-}}$) and the mixed ${\ensuremath{\beta}}^{+}$ and electron capture types ($2\ensuremath{\nu}2{\ensuremath{\beta}}^{+},\phantom{\rule{0.28em}{0ex}}2\ensuremath{\nu}{\ensuremath{\beta}}^{+}\mathrm{EC}$, and $2\ensuremath{\nu}\mathrm{ECEC}$) are taken into consideration. Results of the calculated half lives, nuclear matrix elements (NMEs), phase space factors, and branching ratios are shown. Good agreements between theory and experiments have been reached. Accumulations of the NMEs are also analyzed which do not support the single-state dominance hypothesis. The half lives of the nuclei $^{86}\mathrm{Kr},\phantom{\rule{0.28em}{0ex}}^{70}\mathrm{Zn}$, and $^{84}\mathrm{Sr}$ are predicted to be $4.2\ifmmode\times\else\texttimes\fi{}{10}^{22},\phantom{\rule{0.28em}{0ex}}1.4\ifmmode\times\else\texttimes\fi{}{10}^{23}$, and $1.9\ifmmode\times\else\texttimes\fi{}{10}^{23}$ years respectively which appears attractive for future experimental probing.