Forbidden nonunique β decays and effective values of weak coupling constants

Forbidden nonunique 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(V) for the vector part and g(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 (beta spectra). As examples we study the fourth-forbidden nonunique ground-state-to-ground-state beta(-) decay branches of Cd-113 and In-115 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 beta spectrum is quite sensitive to the values of g(V) and g(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 beta transitions within two different nuclear-structure frameworks. While the SSM seems to confine the g(V) values close to the canonical value g(V) = 1.0, the values of g(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 gA in the future.