SUPERNOVA NEUTRINO SCATTERING RATES REDUCED BY NUCLEON SPIN FLUCTUATIONS - PERTURBATIVE LIMIT

In a nuclear medium, spin-dependent forces cause the nucleon spins to fluctuate with a rate Gamma(sigma). We have previously shown that as a consequence the effective axial-vector current neutrino-nucleon scatt ering cross section is reduced. Here, we calculate this reduction expl icitly in the perturbative limit Gamma(sigma)much less than T. By virt ue of an exact sum rule of the spin-density structure function, we exp ress the modified cross section in terms of the matrix element for neu trino-nucleon scattering in the presence of a spin-dependent nuclear p otential. This representation allows for a direct comparison with, and confirmation of, Sawyer's related perturbative result. In a supernova core with a typical temperature T=10 MeV, the perturbative limit is r elevant for densities rho less than or similar to 10(13) g cm(-3) and thus applies around the neutrino sphere. There, the cross-section redu ction is of order a few percent and thus not large; however, a new mod e of energy transfer between neutrinos and nucleons is enabled which m ay be important for neutrino spectra formation. We derive an analytic perturbative expression for the rate of energy transfer.