Neutrino absorption mean free path in hot and dense nuclear matter within the random phase approximation

The neutrino absorption mean free path in warm and dilute nuclear matter is derived from response functions calculated within the random phase approximation starting from realistic chiral effective field theory nuclear potentials. For comparison we discuss also the density and spin response functions including mean field and vertex corrections at only first order in perturbation theory. Under certain conditions, the first-order perturbative response functions lead to unphysical neutrino absorption cross sections, while in contrast the RPA diagrammatic resummation always produces physical cross sections. In general, the RPA vertex corrections act opposite to nuclear mean fields and lead to an overall increase in the neutrino mean free path compared to the noninteracting response.