Gross theory of β decay by considering the spin-orbit splitting from relativistic Hartree-Bogoliubov theory

Abstract

Nuclear $\ensuremath{\beta}$-decay half-lives are predicted with the so-called gross theory, which is improved by including the spin-orbit splitting from relativistic Hartree-Bogoliubov theory. The calculated differences between the Gamow-Teller and Fermi transition energies are in excellent agreement with experimental data for Zr, Sn, and Pb isotopes. The influences of the $Q$ value and the integrated Fermi function on the calculations of $\ensuremath{\beta}$-decay half-lives are carefully studied. Based on the mass predictions of the latest Weizs\"acker-Skyrme model, the half-lives from Ca to Pb isotopes are systematically calculated. It is found that the Weizs\"acker-Skyrme model well reproduces the experimental data with accuracy better than that of quasiparticle random-phase approximation approaches. When extrapolated to the unknown region, our results are generally close to those from the Skyrme finite-amplitude method. This improved gross theory can be employed to calculate half-lives based on mass predictions of various models and hence can provide relatively consistent half-life inputs for the $r$-process studies.