We have evaluated the electron capture rates on $^{20}$Ne, $^{20}$F, $^{24}$Mg, $^{24}$Na and the $beta$ decay rates for $^{20}$F and $^{24}$Na at temperature and density conditions relevant for the late-evolution stages of stars with $M=8$-12 M$_odo
t$. The rates are based on recent experimental data and large-scale shell model calculations. We show that the electron capture rates on $^{20}$Ne, $^{24}$Mg and the $^{20}$F, $^{24}$Na $beta$-decay rates are based on data in this astrophysical range, except for the capture rate on $^{20}$Ne, which we predict to have a dominating contribution from the second-forbidden transition between the $^{20}$Ne and $^{20}$F ground states in the density range $log rho Y_e (mathrm{g~cm}^{-3}) = 9.3$-9.6. The dominance of a few individual transitions allows us to present the various rates by analytical expressions at the relevant astrophysical conditions. We also derive the screening corrections to the rates.
We have performed shell-model calculations of the half-lives and neutron-branching probabilities of the r-process waiting point nuclei at the magic neutron number N=82. These new calculations use a larger model space than previous shell model studies
and an improved residual interaction which is adjusted to recent spectroscopic data around A=130. Our shell-model results give a good account of all experimentally known half-lives and $Q_beta$-values for the N=82 r-process waiting point nuclei. Our half-life predictions for the N=82 nuclei with Z=42--46 agree well with recent estimates based in the energy-density functional method.
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%.
