Neutrino cross section and mean free path in neutron stars in the framework of the Dirac-Hartree-Fock approximation

Abstract

A study of the neutral current reactions of neutrinos with the dense matter existing in the late cooling stages of protoneutron stars is carried out. The zero-temperature approximation is assumed at this stage and nondegenerate neutrinos are considered. The matter consists of neutrons, protons, electrons, and muons. The fraction of each component is determined once the charge neutrality and beta equilibrated neutrino-free matter conditions are fulfilled. Several nuclear models are used, all inside a Dirac-Hartree or Dirac-Hartree-Fock approximations. These are a \ensuremath{\sigma}-\ensuremath{\omega} model and three \ensuremath{\sigma}-\ensuremath{\omega}-\ensuremath{\pi}-\ensuremath{\rho} models that differ in the coupling forms used for the $\ensuremath{\pi}N$ and $\ensuremath{\sigma}N$ interactions. The neutrino mean free path is decreased in the Dirac-Hartree-Fock approximation from that obtained in the Dirac-Hartree approach by about 2--3 times at high densities. Some kind of consensus is found for the various models considered in the Dirac-Hartree-Fock approach in spite of their different foundations. Neutrino propagation is quite sensitive to the behavior of the relativistic nucleon effective mass. The dependence on the compression modulus and symmetry energy is also investigated.