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

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 $J^pi = 0^{pm}$, $ 1^{pm}$, $2^{pm}$ charge-exchange transitions are determined in the finitetemperature 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.

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