Self-consistent microscopic calculations for electron captures on nuclei in core-collapse supernovae

Calculations for electron capture rates on nuclei with atomic numbers between $Z=20$ and $Z=52$ are performed in a self-consistent finite-temperature covariant energy density functional theory within the relativistic quasiparticle random-phase approximation. Electron captures on these nuclei contribute most to reducing the electron fraction during the collapse phase of core-collapse supernovae. The rates include contributions from allowed (Gamow-Teller) and first-forbidden (FF) transitions, and it is shown that the latter become dominant at high stellar densities and temperatures. Temperature-dependent effects such as Pauli unblocking and transitions from thermally excited states are also included. The new rates are implemented in a spherically symmetric 1D simulation of the core-collapse phase. The results indicate that the increase in electron capture rates, due to inclusion of FF transitions, leads to reductions of the electron fraction at nuclear saturation density, the peak neutrino luminosity, and enclosed mass at core bounce. The new rates reaffirm that the most relevant nuclei for the deleptonization situate around the $N = 50$ and $82$ shell closures, but compared to previous simulations, nuclei are less proton rich. The new rates developed in this work are available, and will be of benefit to improve the accuracy of multi-dimensional supernova simulations.