Calculation of stellar electron-capture cross sections on nuclei based on microscopic Skyrme functionals

TL;DR

This paper introduces a self-consistent microscopic framework based on Skyrme functionals for calculating stellar electron-capture cross sections, integrating finite-temperature Hartree-Fock and RPA methods.

Contribution

It develops a novel, fully self-consistent approach combining finite-temperature Skyrme Hartree-Fock and RPA to evaluate nuclear weak-interaction rates in astrophysical environments.

Findings

Calculated electron-capture cross sections for iron-group nuclei.

Applied the model to neutron-rich Ge isotopes.

Demonstrated consistency across different Skyrme functionals.

Abstract

A fully self-consistent microscopic framework for evaluation of nuclear weak-interaction rates at finite temperature is introduced, based on Skyrme functionals. The single-nucleon basis and the corresponding thermal occupation factors of the initial nuclear state are determined in the finite-temperature Skyrme Hartree-Fock model, and charge-exchange transitions to excited states are computed using the finite-temperature RPA. Effective interactions are implemented self-consistently: both the finite-temperature single-nucleon Hartree-Fock equations and the matrix equations of RPA are based on the same Skyrme energy density functional. Using a representative set of Skyrme functionals, the model is applied in the calculation of stellar electron-capture cross sections for selected nuclei in the iron mass group and for neutron-rich Ge isotopes.