Neutrino-Neutron Scattering Opacities in Supernova Matter

We compute the static density and spin structure factors in the long wavelength limit for pure neutron matter at subsaturation densities relevant to core-collapse supernovae within the Brueckner-Hartree-Fock (BHF) approach. The BHF results are reliable at high densities, extending beyond the validity of the virial expansion. Motivated by the similarities between the dilute neutron gas and a unitary gas, we propose a phenomenological approach to derive the static structures with finite momentum transfer as well as the dynamic ones with simple analytical expressions, based on the computed static structures in the long wavelength limit. We also compare the in-medium neutrino-neutron scattering cross sections using different structure factors. Our study emphasizes the importance of accurately computing the static structure factors theoretically and utilizing the full dynamic structure factors in core-collapse supernova simulations.