  We calculate the neutrino mean free path and the Equation of State of pure
neutron matter at finite temperature within a selfconsistent scheme based on
the Brueckner--Hartree--Fock approximation. We employ the nucleon-nucleon part
of the recent realistic baryon-baryon interaction (model NSC97e) constructed by
the Nijmegen group. The temperatures considered range from 10 to 80 MeV. We
report on the calculation of the mean field, the residual interaction and the
neutrino mean free path including short and long range correlations given by
the Brueckner--Hartree--Fock plus Random Phase Approximation (BHF+RPA)
framework. This is the first fully consistent calculation in hot neutron matter
dedicated to neutrino mean free path. We compare systematically our results to
those obtain with the D1P Gogny effective interaction, which is independent of
the temperature. The main differences between the present calculation and those
with nuclear effective interactions come from the RPA corrections to BHF (a
factor of about 8) while the temperature lack of consistency accounts for a
factor of about 2.
