Second-forbidden nonunique β− decays of 59,60Fe:possible candidates for gA 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 59Fe(3/2−)→59Co(7/2−) and 60Fe(0+)→60Co(2+) in the framework of the nuclear shell model. We have computed the involved wave functions by carrying out a complete 0ℏω 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-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 gA. By comparing these computed shapes with the measured spectral shapes allows then to extract the effective value of gA for these decay transitions. This procedure, coined the spectrum-shape method (SSM) in several earlier studies, complements the method of determining the value of gA 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, VM(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.