Large-scale shell-model investigation of $2ν$ECEC in $^{132}$Ba and $^{78}$Kr

Abstract

We present a theoretical investigation of two-neutrino double electron capture ($2ν$ECEC) in $^{132}$Ba and $^{78}$Kr based on large-scale shell-model calculations. The nuclear matrix elements (NMEs) for the $2ν$ECEC process in $^{132}$Ba and $^{78}$Kr are calculated using the SN100PN and GWBXG effective interactions, respectively. The reliability of the employed interactions is first examined through a comparison of the calculated and experimental spectroscopic properties of the parent, intermediate, and granddaughter nuclei involved in the decay. We also examine the cumulative contribution of the $2ν$ECEC NME with respect to the $1^+$ state energies in the intermediate nuclei. The present results provide an updated and improved shell-model estimate of the $2ν$ECEC NME and half-life for $^{78}$Kr relative to earlier studies, and a baseline theoretical prediction for $^{132}$Ba that may assist future experimental efforts in constraining this rare decay mode.