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

## TL;DR

This paper develops a microscopic, thermodynamically consistent method using thermal quasiparticle RPA with Skyrme interactions to calculate stellar electron capture rates, accounting for thermal effects and comparing with shell-model results.

## Contribution

It introduces a novel approach combining TQRPA and multipole expansion to compute electron capture rates in hot stellar environments, including thermal unblocking effects.

## Key findings

- TQRPA rates can exceed shell-model rates due to Brink-Axel hypothesis violation.
- Thermal unblocking significantly enhances electron capture on $^{56}$Fe and $^{78}$Ni.
- Both allowed and forbidden transitions are thermally unblocked, increasing capture rates.

## Abstract

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 semi-leptonic 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 RPA (TQRPA) with the Skyrme effective interaction. Three different Skyrme parametrizations (SkM$^*$, SGII and SLy4) are used to investigate thermal effects on EC for $^{56}$Fe and $^{78}$Ni. For $^{56}$Fe, the impact of thermally unblocked 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 $^{78}$Ni 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 favour EC.