Reduction of Weak Interaction Rates in Neutron Stars by Nucleon Spin Fluctuations: Degenerate Case

Nucleon spin fluctuations in a dense medium reduce the ``naive'' values of weak interaction rates (neutrino opacities, neutrino emissivities). We extend previous studies of this effect to the degenerate case which is appropriate for neutron stars a few ten seconds after formation. If neutron-neutron interactions by a one-pion exchange potential are the dominant cause of neutron spin fluctuations, a perturbative calculation of weak interaction rates is justified for $T\alt 3m/(4\pi\alpha_\pi^2)\approx 1 MeV$, where $m$ is the neutron mass and $\alpha_\pi\approx15$ the pion fine-structure constant. At higher temperatures, the application of Landau's theory of Fermi liquids is no longer justified, i.e. the neutrons cannot be viewed as simple quasiparticles in any obvious sense.