  We perform an extensive study of the correlations between the
neutrino-nucleon inverse mean free paths (IMFPs) and the underlying equation of
states (EoSs). Strong interaction uncertainties in the neutrino mean free path
are investigated in different density regimes. The nucleon effective mass, the
nucleon chemical potentials, and the residual interactions in the medium play
an important role in determining neutrino-nucleon interactions in a
density-dependent manner. We study how the above quantities are constrained by
an EoS consistent with (i) nuclear mass measurements, (ii) proton-proton
scattering phase shifts, and (iii) neutron star observations. We then study the
uncertainties of both the charged current and the neutral current
neutrino-nucleon inverse mean free paths due to the variation of these
quantities, using Hartree-Fock+random phase approximation method. Finally, we
calculate the Pearson correlation coefficients between (i) the EoS-based
quantities and the EoS-based quantities; (ii) the EoS-based quantities and the
IMFPs; (iii) the IMFPs and the IMFPs. We find a strong impact of residual
interactions on neutrino opacity in the spin and spin-isospin channels, which
are not well constrained by current nuclear modelings.
