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

Abstract

We present a theoretical investigation of two-neutrino double electron capture ($2\nu$ECEC) in ${}^{132}$Ba and ${}^{78}$Kr based on large-scale shell-model calculations. The nuclear matrix elements (NMEs) for the $2\nu$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 $2\nu$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 $2\nu$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.

Comments: 11 pages, 7 figures (Accepted for publication in EPJA)