Stellar electron-capture rates on nuclei based on a microscopic Skyrme functional

Abstract

We compute electron-capture rates for ${}^{54,56}$Fe and Ge isotopes using a self-consistent microscopic approach. The single-nucleon basis and the occupation factors in the target nucleus are calculated in the finite-temperature Skyrme Hartree-Fock model, and the ${J}^{\ensuremath{\pi}}={0}^{\ifmmode\pm\else\textpm\fi{}}$, ${1}^{\ifmmode\pm\else\textpm\fi{}}$, ${2}^{\ifmmode\pm\else\textpm\fi{}}$ charge-exchange transitions are determined in the finite-temperature random-phase approximation (RPA). The scheme is self-consistent; i.e., both the Hartree-Fock and the RPA equations are based on the same Skyrme functional. Several interactions are used in order to provide a theoretical uncertainty on the electron-capture rates for different astrophysical conditions. Comparing electron-capture rates obtained either with different Skyrme sets or with different available models indicates that differences up to one to two orders of magnitude can arise.