Second-forbidden nonunique $β^-$ decays of ${}^{59,60}$Fe: Possible candidates for $g_A$ sensitive electron spectral-shape measurements

Abstract

In this work, we present a theoretical study of the electron spectral shapes for the second-forbidden nonunique $β^-$-decay transitions ${}^{59}\text{Fe}(3/2^{-})\to {}^{59}\text{Co}(7/2^{-})$ and ${}^{60}\text{Fe}(0^{+})\to {}^{60}\text{Co}(2^{+})$ in the framework of the nuclear shell model. We have computed the involved wave functions by carrying out a complete $0\hslash \ddot{I}‰$ 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 ${\hat{I}}^2$-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 $g_{\mathrm{A}}$. By comparing these computed shapes with the measured spectral shapes allows then to extract the effective value of $g_{\mathrm{A}}$ for these decay transitions. This procedure, coined the spectrum-shape method (SSM) in several earlier studies, complements the method of determining the value of $g_{\mathrm{A}}$ 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, ${}^V{\mathcal{M}}_{KK-11}^{(0)}$, 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.

18 pages, 10 figures and 6 tables. Accepted for publication in the European Physical Journal A