Closed-shell effect in two-neutrino double- β decay for fp shell nuclei

Abstract

Large scheme shell-model calculations are conducted for the two-neutrino double-$\ensuremath{\beta}$ $(2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta})$ decay of the $fp$ $(0{f}_{7/2},0{f}_{5/2},1{p}_{3/2},1{p}_{1/2})$ shell nuclei. 25 $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ processes are considered, of which seven $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ processes are either observed or candidates. The calculated half-lives, nuclear matrix elements (NMEs), strength function (SF) distributions, and phase space factors are shown. The calculated results agree with the experimental data and reveal that for the transitions involving a doubly, semimagic nucleus or only the nonmagic nuclei, the SF distributions are visibly different. This outcome indicates that the NMEs of the $2\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ processes are significantly influenced by the closed-shell effect.