Forbidden non-unique $\beta^{-}$ transitions and $g_A$-sensitive electron spectral-shapes

TL;DR

This study systematically analyzes forbidden non-unique beta-minus decay spectral-shapes in nuclei with mass 85-123, exploring the sensitivity to axial-vector coupling constants using shell model calculations and various effective interactions.

Contribution

It provides a comprehensive shell model analysis of spectral-shapes and their dependence on $g_A$ for multiple nuclei, including relativistic matrix element constraints.

Findings

Spectral-shapes are highly sensitive to $g_A$ in most cases.

The second forbidden transition in $^{93}$Zr shows insensitivity to $g_A$.

Shell model calculations with different interactions effectively reproduce experimental features.

Abstract

In the present work, we have done a systematic study of beta decay properties such as electron spectral-shapes, shape factors, and log$ft$ values for the higher forbidden non-unique $\beta^{-}$ transitions in the mass region A=85-123. We have performed the nuclear shell model (SM) calculations to explore the sensitivity of the electron spectral-shapes for different axial-vector coupling constants $g_{A}=0.8-1.27$. The effective interactions GWBXG, G-matrix, SNET and SN100PN are used for different model spaces. In the present work, we have computed the electron spectral-shapes of $^{85}$Br, $^{87}$Rb, $^{93}$Zr, $^{97}$Zr, $^{101}$Mo, $^{115}$Cd, $^{117}$Cd, $^{119}$In, $^{123}$Sn and $^{135}$Cs by constraining the small relativistic nuclear matrix element from conserved vector-current hypothesis (CVC). We have found that the electron spectral-shapes are strongly dependent on $g_{A}$ except the second forbidden non-unique $\beta^{-}$ transition $^{93}$Zr.