Influence of the Axial-Vector Coupling Constant and the Energy Distribution Function on β-Decay Rates Within the Gross Theory of Beta Decay

Abstract

We evaluate the β-decay rates within the gross theory of beta decay (GTBD) and compare the results for different values of the axial-vector coupling constant, gA = 0.76, gA = 0.88, gA = 1, gA = 1.13, and gA = 1.26, and also different energy distribution functions like Gaussian, exponential, Lorentzian, and modified Lorentzian ones. We use new sets of parameters as well as updated experimental mass defects and also an improved approximation for the Fermi function. We compare our calculated results for a set of 94 nuclei of interest in pre-supernova phase, with experimental data in terrestrial conditions and also with other theoretical models like the QRPA, the shell model (SM), and different versions of the GTBD. We show that best results are obtained with gA = 1 using Gaussian and Lorentzian distributions, being the rates for the 74 and 80% of our sample, respectively, of the same order of magnitude that of experimental data. Finally, we show that the present results within the GTBD are better than those within the QRPA model and also older versions of the GTBD for the isotopes of cobalt and iron families, and comparable with SM for some elements.