Neutrino propagation and spin zero sound in hot neutron matter with Skyrme interactions

We present microscopic calculations of neutrino propagation in hot neutron matter above nuclear density within the framework of the Random Phase Approximation . Calculations are performed for non- degenerate neutrinos using various Skyrme effective interactions. We find that for densities just above nuclear density, spin zero sound is present at zero temperature for all Skyrme forces considered. However it disappears rapidly with increasing temperature due to a strong Landau damping. As a result the mean-free path is given, to a good approximation, by the mean field value. Because of the renormalization of the bare mass in the mean field, the medium is more transparent as compared to the free case. We find, in contrast, that at several times nuclear density, a new type of behavior sets in due to the vicinity of a magnetic instability. It produces a strong reduction of the mean free path. The corresponding transition density however occurs in a region where inputs from more realistic calculations are necessary for the construction of a reliable Skyrme type parametrization.Comment: 17 pages, 4 figure