Theoretical estimates of supernova-neutrino cross sections for the stable even-even lead isotopes: Charged-current reactions

A detailed study of the charged-current supernova electron neutrino and electron antineutrino scattering off the stable even-mass lead isotopes A=204, 206, and 208 is reported in this work. The proton-neutron quasiparticle random-phase approximation (pnQRPA) is adopted to construct the nuclear final and initial states. Three different Skyrme interactions are tested for their isospin and spin-isospin properties and then applied to produce (anti)neutrino-nucleus scattering cross sections for (anti)neutrino energies below 80 MeV. Realistic estimates of the nuclear responses to supernova (anti)neutrinos are computed by folding the computed cross sections with a two-parameter Fermi-Dirac distribution of the electron (anti)neutrino energies. The computed cross sections are compared with earlier calculations and the analyses are extended to take into account the effects coming from the neutrino oscillations.