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

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 − + ν ̄ e , 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. We have adopted a Gaussian energy distribution function with the axial-vector weak coupling constant g A = 1, as well as a new set of the adjustable parameter σ N related to the standard deviation for the Gamow-Teller resonance, 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 calculation without the inclusion of the antineutrino mass with that adopting a really overestimated value of 50 keV for it to illustrate the effect on the decay rates. We have shown that they are improved only by approximately one per thousand in this case. We conclude that the effect of the antineutrino mass on decay rates is not relevant.