Spectrum-shape method and the next-to-leading-order terms of the (ss)-decay shape factor

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