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.