Weak Interactions in Supernova Cores and Saturation of Nucleon Spin Fluctuations

Extrapolation of perturbative nucleon spin fluctuation rates seems to suggest a strong suppression of weak interactions in supernova cores. We derive a generalized f sum rule for the dynamical spin-density structure function which relates the spin fluctuation rate to the average nuclear interaction energy. For a bremsstrahlung-like structure function profile we show that, instead of strongly decreasing, the neutrino scattering cross section is roughly density independent, and axion emissivities increase somewhat slower than the lowest order rates toward the center of a hot supernova core.