  Extrapolation of perturbative nucleon spin fluctuation rates seems to suggest
a strong suppression of weak interactions in supernova cores. We derive a new
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 emission rates increase somewhat slower than the lowest
order emissivities towards the center of a hot supernova core.
