Thermal quasiparticle random-phase approximation with Skyrme interactions and supernova neutral-current neutrino-nucleus reactions

The thermal quasiparticle random-phase approximation is combined with the Skyrme energy density functional method (Skyrme-TQRPA) to study the response of a hot nucleus to an external perturbation. For the sample nuclei Fe-56 and Ge-82, the Skyrme-TQRPA is applied to analyze thermal effects on the strength function of charge-neutral Gamow-Teller transitions, which dominate neutrino-nucleus reactions at E-v less than or similar to 20 MeV. For the relevant supernova temperatures we calculate the cross sections for inelastic neutrino scattering. We also apply the method to examine the rate of neutrino-antineutrino pair emission by hot nuclei. The cross sections and rates are compared with those obtained earlier from the TQRPA calculations based on the phenomenological quasiparticle-phonon model Hamiltonian. For inelastic neutrino scattering on Fe-56 we also compare the Skyrme-TQRPA results to those obtained earlier from a hybrid approach that combines shell-model and RPA calculations.