  Neutrino scattering and absorption rates of relevance to supernovae and
neutron star mergers are obtained from nuclear matter dynamical structure
functions that encode many-body effects from nuclear mean fields and
correlations. We employ nuclear interactions from chiral effective field theory
to calculate the density, spin, isospin, and spin-isospin response functions of
warm beta-equilibrium nuclear matter. We include corrections to the
single-particle energies in the mean field approximation as well as vertex
corrections resummed in the random phase approximation (RPA), including, for
the first time, both direct and exchange diagrams. We find that correlations
included through the RPA redistribute the strength of the response to higher
energy for neutrino absorption and lower energy for antineutrino absorption.
This tends to suppress the absorption rate of electron neutrinos across all
relevant energy scales. In contrast, the inclusion of RPA correlations enhances
the electron antineutrino absorption rate at low energy and supresses the rate
at high energy. These effects are especially important at high-density and in
the vicinity of the neutrino decoupling region. Implications for heavy element
nucleosynthesis, electromagnetic signatures of compact object mergers,
supernova dynamics, and neutrino detection from galactic supernovae are
discussed briefly.
