Investigation of $2\nu$ECEC in $^{132}$Ba and revisited for $^{78}$Kr

TL;DR

This paper uses large-scale shell-model calculations to study two-neutrino double electron capture in $^{132}$Ba and $^{78}$Kr, providing improved predictions for nuclear matrix elements and half-lives to guide future experiments.

Contribution

It offers the first comprehensive shell-model analysis of $2 u$ECEC in these isotopes, including assessment of effective interactions and detailed NME calculations.

Findings

Improved NME and half-life predictions for $^{78}$Kr.

Assessment of effective interactions' reliability.

Detailed analysis of intermediate nuclear state contributions.

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 have been calculated using the SN100PN and GWBXG effective interactions, respectively. The reliability of these interactions is first assessed by reproducing the spectroscopic properties of the parent, intermediate, and granddaughter nuclei of the decay. Two different formulations are employed to estimate the half-lives. We also examine the cumulative contribution of $1^+$ and $0^+$ states in the intermediate nuclei to the NMEs associated with the Gamow-Teller (GT) and Fermi transitions, respectively. Our results provide an improved prediction of the NME and half-life for $2\nu$ECEC in $^{78}$Kr compared to previous studies and offer a precise theoretical benchmark for future experimental investigations in $^{132}$Ba.