Effects of Antineutrino mass on β−-Decay Rates Calculated Within the Gross Theory of Beta Decay

Abstract

We analyze the effect of the antineutrino mass over the β −-decay rates calculated within the scheme of the Gross Theory of Beta Decay (GTBD). We give a non null value to the mass of the antineutrino participating in β −-decay, (A, Z) → (A, Z + 1) + e − + ¯νe, which is usually neglected because we know it is small compared with electron mass. We have slightly modified the GTDB by inserting the antineutrino mass in the formalism, and we have adopted a Gaussian energy distribution function with the axial-vector weak coupling constant gA = 1, as well as new sets of parameters and updated experimental mass defects and also an improved approximation for the Fermi function. Our sample consists of a set of 94 nuclei of interest in the pre-supernova phase, which have experimental data in terrestrial conditions available in the Letter of Nuclide. We have compared the calculations with and without the inclusion of the antineutrino mass, and we have shown that the decay rates are improved by approximately one per thousand when antineutrino mass effects are added. We conclude that the effect of the antineutrino mass on decay rates is not relevant.