Neutral-current supernova-neutrino cross sections for 204,206,208Pb calculated by Skyrme quasiparticle random-phase approximation

The present work constitutes a detailed study of neutral-current (NC) supernova-neutrino scattering off the stable even-even lead isotopes Pb-204,Pb-206,Pb-208. This is a continuation of our previous work [Almosly et al., Phys. Rev. C. 94, 044614 (2016)] where we investigated charged-current processes on the same nuclei. As in the previous work, we have adopted the quasiparticle random-phase approximation (QRPA) as the theory framework and use three different Skyrme interactions to build the involved nuclear wave functions. We test the Skyrme forces by computing the location of the lowest-order isovector spin-multipole giant resonances and comparing with earlier calculations. We have computed the NC cross sections for (anti)neutrino energies up to 100 MeV and estimated the nuclear responses to supernova (anti)neutrinos by folding the obtained cross sections by suitably parametrized Fermi-Dirac distributions of energies of the incoming (anti)neutrinos. We compare our results with results of earlier studies in the case of Pb-208, which is the only lead isotope where earlier calculations are available.