  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.
