Neutrino-nucleon scattering rate in proto neutron star matter

We present a calculation of the neutrino-nucleon scattering cross section which takes into account the nuclear correlations in the relativistic random phase approximation. Our approach is based on a quantum hadrodynamics model with exchange of $\sigma$, $\omega$, $\pi$, $\rho$ and $\delta$ mesons. In view of applications to neutrino transport in the final stages of supernova explosion and protoneutron star cooling, we study the evolution of the neutrino mean free path as a function of density, proton-neutron asymmetry and temperature. Special attention was paid to the issues of renormalization of the Dirac sea, residual interactions in the tensor channel and meson mixing. It is found that RPA corrections, with respect to the mean field approximation, amount to only 10% to 15% at high density.