Large-scale shell-model study of 2$\nu$ECEC process in $^{78}$Kr

TL;DR

This study employs large-scale shell-model calculations to analyze the two-neutrino double electron capture process in krypton-78, validating the model against experimental data and estimating the half-life with good accuracy.

Contribution

The paper provides a comprehensive shell-model analysis of the $2 u$ECEC process in $^{78}$Kr, including validation of the interaction and detailed NME calculations, which are novel for this isotope.

Findings

Shell-model predictions agree with experimental energy spectra.

Estimated half-life matches experimental measurements.

Analysis of Gamow-Teller transitions provides insight into decay channels.

Abstract

In this work, we present the systematic study of $2\nu$ECEC process in the $^{78}$Kr using large-scale shell-model calculations with the GWBXG effective interaction. We first validate the efficiency of the utilized interaction by comparing the theoretical low-lying energy spectra, the kinematic moment of inertia, and reduced transition probabilities with the experimental data for both the parent and grand-daughter nuclei $^{78}$Kr and $^{78}$Se, respectively. Additionally, we examine the shell-model level densities of the $1^+$ states in the intermediate nucleus $^{78}$Br, comparing them with the predictions from the Back-shifted Fermi gas model. We analyze the variation of cumulative nuclear matrix elements (NMEs) for the $2\nu$ECEC process in $^{78}$Kr as a function of $1^+$ state energies in the intermediate nucleus $^{78}$Br up to the saturation level. Our estimated half-life for $^{78}$Kr, extracted from the shell-model predicted NMEs, shows good agreement with the experimental value. The Gamow-Teller transitions from the lowest $1^+$ state of $^{78}$Br via both the EC$+\beta^+$ and $\beta^-$-channels are also discussed.