Forbidden nonuniqueβdecays and effective values of weak coupling constants

Abstract

Forbidden nonunique $\ensuremath{\beta}$ decays feature shape functions that are complicated combinations of different nuclear matrix elements and phase-space factors. Furthermore, they depend in a very nontrivial way on the values of the weak coupling constants, ${g}_{\mathrm{V}}$ for the vector part and ${g}_{\mathrm{A}}$ for the axial-vector part. In this work we include also the usually omitted second-order terms in the shape functions to see their effect on the computed decay half-lives and electron spectra ($\ensuremath{\beta}$ spectra). As examples we study the fourth-forbidden nonunique ground-state-to-ground-state ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay branches of $^{113}\mathrm{Cd}$ and $^{115}\mathrm{In}$ using the microscopic quasiparticle-phonon model and the nuclear shell model. A striking new feature that is reported in this paper is that the calculated shape of the $\ensuremath{\beta}$ spectrum is quite sensitive to the values of ${g}_{\mathrm{V}}$ and ${g}_{\mathrm{A}}$ and hence comparison of the calculated with the measured spectrum shape opens a way to determine the values of these coupling constants. This article is designed to show the power of this comparison, coined spectrum-shape method (SSM), by studying the two exemplary $\ensuremath{\beta}$ transitions within two different nuclear-structure frameworks. While the SSM seems to confine the ${g}_{\mathrm{V}}$ values close to the canonical value ${g}_{\mathrm{V}}=1.0$, the values of ${g}_{\mathrm{A}}$ extracted from the half-life data and by the SSM emerge contradictory in the present calculations. This calls for improved nuclear-structure calculations and more measured data to systematically employ SSM for determination of the effective value of ${g}_{\mathrm{A}}$ in the future.