Weak interactions in hot nucleon matter

Abstract

The reaction rates for electron capture, neutrino absorption, and neutrino scattering in hot asymmetric nuclear matter are calculated with two-body effective interactions and one-body effective weak operators obtained from realistic models of nuclear forces by use of correlated basis theory. The infinite system is modeled in a box with periodic boundary conditions, and the one-quasiparticle quasi-hole response functions are calculated with a large microcanonical sample and the Tamm-Dancoff approximation. Results for matter at a temperature of 10 MeV, proton fraction 0.4, and densities $\ensuremath{\rho}=(\frac{1}{2},1,\frac{3}{2}){\ensuremath{\rho}}_{0}$, where ${\ensuremath{\rho}}_{0}$ is the equilibrium density of symmetric nuclear matter, are presented to illustrate the method. In general, the strength of the response is shifted to higher-energy transfers when compared with that of a noninteracting Fermi gas. The shift in the response and the weakness of effective operators as compared with the bare operators significantly reduce the cross sections for electron capture and neutrino scattering by factors of $~2.5$--$3.5$. In contrast, the symmetry energy enhances the neutrino absorption reaction rate relative to the Fermi gas. However, this reaction rate is still quite small because of Pauli blocking.