  In this paper, we calculate the diffusion coefficients that are related to
the neutrino opacities considering the formation of nuclear pasta and
homogeneous matter at low densities. Our results show that the mean free paths
are significantly altered by the presence of nuclear pasta in stellar matter
when compared with the results obtained with homogeneous matter. These
differences in neutrino opacities certainly influence the Kelvin-Helmholtz
phase of protoneutron stars and consequently the results of supernova explosion
simulations.

Nuclear Theory;High Energy Astrophysical Phenomena