Excitation of nuclear giant resonances in neutrino scattering off nuclei

The cross sections for neutrino scattering off the 12C and 16O nuclei are calculated within the framework of the continuum Random Phase Approximation. A model to consider also the final state interactions is developed. Total charge-conserving and charge-exchange cross sections for both electron neutrinos and antineutrinos have been calculated up to projectile energies of 100 MeV. The sensitivity of the cross sections to the residual interaction and to the final state interactions is investigated. A direct comparison between neutrino and electron scattering cross sections calculated under the same kinematic conditions is presented. We found remarkable differences between electromagnetic and weak nuclear responses. The model is applied to describe cross sections of neutrinos produced by muon decay at rest and in supernovae explosions.