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

Abstract

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 $^{56}\mathrm{Fe}$ and $^{82}\mathrm{Ge}$, 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 ${E}_{\ensuremath{\nu}}\ensuremath{\lesssim}20$ 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 $^{56}\mathrm{Fe}$ we also compare the Skyrme-TQRPA results to those obtained earlier from a hybrid approach that combines shell-model and RPA calculations.