Spectrum-shape method and the next-to-leading-order terms of theβ-decay shape factor

Abstract

Effective values of the axial-vector coupling constant ${g}_{\mathrm{A}}$ have lately attracted much attention due to the prominent role of ${g}_{\mathrm{A}}$ in determining the half-lives of double $\ensuremath{\beta}$ decays, in particular their neutrinoless mode. The half-life method, i.e., comparing the calculated half-lives to the corresponding experimental ones, is the most widely used method to access the effective values of ${g}_{\mathrm{A}}$. The present paper investigates the possibilities offered by a complementary method: the spectrum-shape method (SSM). In the SSM, comparison of the shapes of the calculated and measured $\ensuremath{\beta}$ electron spectra of forbidden nonunique $\ensuremath{\beta}$ decays yields information on the magnitude of ${g}_{\mathrm{A}}$. In parallel, we investigate the impact of the next-to-leading-order terms of the $\ensuremath{\beta}$-decay shape function and the radiative corrections on the half-life method and the SSM by analyzing the fourfold forbidden decays of $^{113}\mathrm{Cd}$ and $^{115}\mathrm{In}$ by using three nuclear-structure theory frameworks; namely, the nuclear shell model, the microscopic interacting boson-fermion model, and the microscopic quasiparticle-phonon model. The three models yield a consistent result, ${g}_{\mathrm{A}}\ensuremath{\approx}0.92$, when the SSM is applied to the decay of $^{113}\mathrm{Cd}$ for which $\ensuremath{\beta}$-spectrum data are available. At the same time the half-life method yields results which are in tension with each other and the SSM result.