Thermal quasiparticle random-phase approximation calculations of stellar electron capture rates with the Skyrme effective interaction

A microscopic thermodynamically consistent approach is applied to compute electron capture (EC) rates and cross sections on nuclei in hot stellar environments. The cross-section calculations are based on the Donnelly-Walecka multipole expansion method for treatment of semileptonic processes in nuclei. To take into account thermal effects, we express the electron capture cross section in terms of temperature- and momentum-dependent spectral functions for respective multipole charge-changing operators. The spectral functions are computed by employing the self-consistent thermal quasiparticle random-phase approximation (TQRPA) with the Skyrme effective interaction. Three different Skyrme parametrizations (SkM*, SGII, and SLy4) are used to investigate thermal effects on EC for Fe-56 and Ni-78. For Fe-56, the impact of thermally unblocked Gamow-Teller GT(+) transitions on EC is discussed and the results are compared with those from shell-model calculations. In particular, it is shown that for some temperature and density regimes the TQRPA rates exceed the shell-model rates due to violation of the Brink-Axel hypothesis within the TQRPA. For neutron-rich Ni-78, the full momentum dependence of multipole transition operators is considered and it is found that not only thermally unblocked allowed 1(+) transitions but also thermally unblocked first-forbidden 1(-) and 2(-) transitions favor EC.