Neutrino scattering from hydrodynamic modes in hot and dense neutron matter

We calculate the scattering rate of low-energy neutrinos in hot and dense neutron matter encountered in neutrons stars and supernovae in the hydrodynamic regime. We find that the Brillouin peak, associated with the sound mode, and the Rayleigh peak, associated with the thermal diffusion mode, dominate the dynamic structure factor. Although the total scattering cross section is constrained by the compressibility sum rule, the differential cross section calculated using the hydrodynamic response function differs from results obtained in approximate treatments often used in astrophysics such as random phase approximations. We identified these differences and discuss their implications for neutrino transport in supernovae.