Second-forbidden nonunique decays of Fe:possible candidates for sensitive electron spectral-shape measurements

Anil Kumar; Praveen C. Srivastava; Jouni Suhonen

doi:10.1140/epja/s10050-021-00540-6

2024 Impact factor 2.8

Hadrons and Nuclei

Eur. Phys. J. A (2021) 57: 225
https://doi.org/10.1140/epja/s10050-021-00540-6

Regular Article - Theoretical Physics

Second-forbidden nonunique $β^{-}$ $\beta ^-$ decays of $^{59, 60}$ $^{59,60}$ Fe:possible candidates for $g_{A}$ $g_{\mathrm{A}}$ sensitive electron spectral-shape measurements

Anil Kumar¹, Praveen C. Srivastava¹^b and Jouni Suhonen²

¹ Department of Physics, Indian Institute of Technology Roorkee, 247667, Roorkee, India
² Department of Physics, University of Jyvaskyla, P.O. Box 35 (YFL), 40014, Jyvaskyla, Finland

^b praveen.srivastava@ph.iitr.ac.in

Received: 6 January 2021
Accepted: 28 June 2021
Published online: 8 July 2021

Abstract

In this work, we present a theoretical study of the electron spectral shapes for the second-forbidden nonunique $β^{-}$ $\beta ^-$ -decay transitions $^{59} Fe (3 / 2^{-}) \to^{59} Co (7 / 2^{-})$ $^{59}\text {Fe}(3/2^-)\rightarrow \,^{59}\text {Co}(7/2^-)$ and $^{60} Fe (0^{+}) \to^{60} Co (2^{+})$ $^{60}\text {Fe}(0^+)\rightarrow \,^{60}\text {Co}(2^+)$ in the framework of the nuclear shell model. We have computed the involved wave functions by carrying out a complete $0 ħ ω$ $0\hbar \omega$ calculation in the full fp model space using the KB3G and GXPF1A effective interactions. When compared with the available data, these interactions predict the low-energy spectra and electromagnetic properties of the involved nuclei quite successfully. This success paves the way for the computations of the $β$ $\beta$ -decay properties, and comparison with the available data. We have computed the electron spectral shapes of the mentioned decay transitions as functions of the value of the weak axial coupling $g_{A}$ $g_{\mathrm{A}}$ . By comparing these computed shapes with the measured spectral shapes allows then to extract the effective value of $g_{A}$ $g_{\mathrm{A}}$ for these decay transitions. This procedure, coined the spectrum-shape method (SSM) in several earlier studies, complements the method of determining the value of $g_{A}$ $g_{\mathrm{A}}$ by reproducing the (partial) half-lives of decay transitions. Here we have enhanced the original SSM by constraining the value of the relativistic vector matrix element, $^{V} M_{K K - 11}^{(0)}$ $^V{\mathcal {M}}^{(0)}_{KK-11}$ , using the conserved vector-current hypothesis (CVC) as a starting point. We hope that this finding would be a strong incentive to measure the spectral shapes in the future.