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

TL;DR

The paper performs large-scale shell-model calculations of $2ν$ECEC for $^{132}$Ba and $^{78}$Kr using SN100PN and GWBXG interactions, respectively, validating the interactions by reproducing spectroscopic data across parent, intermediate, and granddaughter nuclei. It presents two half-life formulations: GT-only and GT+Fermi, and analyzes the cumulative NMEs as functions of intermediate-state energies, including the impact of the effective axial coupling $g_A^{eff}$. For $^{132}$Ba, the lowest $1^+$ state dominates the GT NME and the total NME shows modest sensitivity to $g_A^{eff}$, yielding $T_{1/2}^{2ν}$ in the range $(2.2$–$7.3) imes10^{24}$ yr (GT only) and similar scales when Fermi terms are included; for $^{78}$Kr, an extended model space raises the GT NME to 0.2311 (GT) and 0.2083 (GT+Fermi), predicting $T_{1/2}^{2ν}$ around $1.7 imes10^{22}$ yr (and higher for quenched $g_A^{eff}$), with improved agreement to recent measurements. The results provide precise theoretical benchmarks for upcoming experiments and illustrate how including cross-shell neutron excitations and Fermi contributions refines $2ν$ECEC predictions in this mass region. Overall, the work strengthens the reliability of shell-model NMEs in the $A ilde{ }$130 region and informs future experimental and theoretical efforts on $2ν$ECEC decay channels.

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 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 $2ν$ECEC in $^{78}$Kr compared to previous studies and offer a precise theoretical benchmark for future experimental investigations in $^{132}$Ba.

Figures (8)

• Figure 1: Nuclear level and decay scheme for $2\nu$ECEC process in $^{78}$Kr (left panel) and $^{132}$Ba (right panel).
• Figure 2: Comparison between the theoretical and experimental NNDC energy levels in the $^{132}$Ba, $^{132}$Cs and $^{132}$Xe.
• Figure 3: Variation of the cumulative NME for the GT (upper panel) and Fermi transitions (lower panel) with respect to the $1^+$ and $0^+$ state energies in the intermediate nucleus $^{132}$Cs, respectively.
• Figure 4: Dependence of the total NME, including GT and Fermi contributions as defined in Eq. (\ref{['GT+Fermi:NME']}), on the $g_{\rm A}^{\rm eff}$ for $^{132}$Ba.
• Figure 5: Comparison between the theoretical and experimental NNDC energy levels in the $^{78}$Kr, $^{78}$Br and $^{78}$Se.