Large-scale shell-model study of 2$\hat{I}½$ECEC process in ${}^{78}$Kr

Abstract

In this work, we present the systematic study of $2\hat{I}½$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 $2\hat{I}½$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$+β^+$ and $β^-$-channels are also discussed.

14 pages, 4 figures, Focus on Nuclear Science-ISNS-24, Physica Scripta 100, 015303 (2025)