Nucleon Spin Fluctuations and Neutrino-Nucleon Energy Transfer in Supernovae

The formation of neutrino spectra in a supernova depends crucially on strength and inelasticity of weak interactions in hot nuclear matter. Neutrino interactions with nonrelativistic nucleons are mainly governed by the dynamical structure function for the nucleon spin density which describes its fluctuations. It has recently been shown that these fluctuations give rise to a new mode of energy transfer between neutrinos and nucleons which inside the neutrinosphere is of comparable or greater importance than ordinary recoil. We calculate numerically the spin density structure function in the limit of a dilute, non-degenerate medium from exact two-nucleon wave functions for some representative nuclear interaction potentials. We show that spectrum and magnitude of the energy transfer can deviate significantly from those based on the Born approximation. They are, however, rather insensitive to the particular nuclear potential as long as it reproduces experimental nucleon scattering phase shifts at energies up to a few tens of MeV. We also compare with calculations based on a one-pion exchange potential in Born approximation and briefly comment on their applicability near the center of a supernova core. Our study is relevant for numerical simulations of the neutrino spectra emerging from type-II supernovae.