Eur. Phys. J. A (2025) 61: 265
https://doi.org/10.1140/epja/s10050-025-01740-0

Regular Article - Theoretical Physics

Comprehensive shell model study of ${\beta }^{+}$/EC-decay properties for $f_{5/2}p{g}_{9/2}$ space nuclei

¹ Department of Physics, Institute of Science, Banaras Hindu University, 221 005, Varanasi, India
² Department of Physics, University of Jyväskylä, P.O. Box 35 (YFL), 40014, Jyvaskyla, Finland
³ International Centre for Advanced Training and Research in Physics (CIFRA), P.O. Box MG12, 077125, Bucharest-Măgurele, Romania

^a vikasphysics@bhu.ac.in

Received: 3 June 2025
Accepted: 4 November 2025
Published online: 21 November 2025

Abstract

In this study, we investigate the half-lives of the allowed combined ${\beta }^{+}$ and electron-capture (${\beta }^{+}$/EC) decays of nuclei with $Z=31-40$ and $A=60-89$ employing shell-model calculations within the $f_{5/2}p{g}_{9/2}$ valence space using the JUN45 interaction. Using the quenching factor $q=0.71\pm 0.01$ for the weak axial coupling $g_A,$ obtained from the analysis of pure Gamow–Teller ${\beta }^{-}$ and ${\beta }^{+}$ decay processes in nuclei with $Z=31-40$ and $A=61-87,$ the transition strengths and branching ratios for the ${\beta }^{+}$/EC decays are evaluated. The experimental $\beta$-decay half-lives are found to be rather well explained by the shell-model calculations. We investigate also the isospin mixing in the ground states of $_{}^{64}$Ge, $_{}^{70}$Se, and $_{}^{78}$Rb nuclei for non-analog $0^{+}\to 0^{+}$$(\Delta T\ne 0)$$\beta$ transitions from $_{}^{64}$Ge, $_{}^{70}$Se, and $_{}^{78}$Rb. A comprehensive study of the ${\beta }^{+}$/EC-decay processes in nuclei in this region is done for the first time in the present work. Though the model space has a limitation due to the lack of its $f_{7/2}$ and $g_{7/2}$ spin-orbit partners, the results obtained can be considered reasonable.