Cross-sections for neutral-current neutrino-nucleus interactions: applications for $^{12}$C and $^{16}$O

We calculate cross sections for neutral current quasi-elastic neutrino-nucleus scattering within a continuum RPA model, based on a Green's function approach. As residual interaction a Skyrme force is used. The unperturbed single particle wave functions are generated using either a Woods-Saxon potential or a Hartree-Fock calculation. These calculations have interesting applications. Neutrinos play an important role in supernova nucleosynthesis. To obtain more information about these processes, cross sections are folded with a Fermi-Dirac distribution with temperatures of approximately 10$^9$ K