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

Effective values of the axial-vector coupling constant gA have lately attracted much attention due to the prominent role of gA in determining the half-lives of double β 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 gA. 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 β electron spectra of forbidden nonunique β decays yields information on the magnitude of gA. In parallel, we investigate the impact of the next-to-leading-order terms of the β-decay shape function and the radiative corrections on the half-life method and the SSM by analyzing the fourfold forbidden decays of 113Cd and 115In 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, gA≈0.92, when the SSM is applied to the decay of 113Cd for which β-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.