We studied possible modifications of the neutrino - nucleon scattering rate
due to the nucleon - nucleon collisions in the hot dense matter which we find
in the supernova core. We show that the finite width of the nucleon spectral
function induced by the nucleon collisions leads to broadening of the dynamical
spin structure function of the nucleon, resulting in the reduction of the rate
of neutrino - nucleon scattering via the axial vector current and making the
energy exchange between neutrinos and nucleons easier. The reduction rate is
relatively large (about 0.6) even at density of about 10^{13}g/cm^{3} and could
have a significant impact on the dynamics of the collapse-driven supernova as
well as the cooling of the proto neutron star.Comment: 10pages, 7figures, submitted to NP
