  Based on the shell model for Gamow-Teller and the Random Phase Approximation
for forbidden transitions, we have calculated reaction rates for inelastic
neutrino-nucleus scattering (INNS) under supernova (SN) conditions, assuming a
matter composition given by Nuclear Statistical Equilibrium. The rates have
been incorporated into state-of-the-art stellar core-collapse simulations with
detailed energy-dependent neutrino transport. While no significant effect on
the SN dynamics is observed, INNS increases the neutrino opacities noticeably
and strongly reduces the high-energy tail of the neutrino spectrum emitted in
the neutrino burst at shock breakout. Relatedly the expected event rates for
the observation of such neutrinos by earthbound detectors are reduced by up to
about 60%.
