Nuclear effects on neutrino emissivities from nucleon-nucleon bremsstrahlung

The rates of neutrino pair emission by nucleon-nucleon (NN) bremsstrahlung are calculated with the inclusion of the full contribution from a nuclear one pion exchange potential (OPEP). We compute the contributions from the neutron-neutron (nn), proton-proton (pp), and neutron-proton (np) processes for physical conditions encountered in supernovae and neutron stars, both in the degenerate (D) and nondegenerate (ND) limits. We find a significant reduction of these rates, especially for the nn and pp processes, in comparison with the case when the whole nuclear contribution was replaced by constants, representing the high-momentum limits of the expressions of the nuclear potential. Furthermore, we also perform the calculations by including contributions due to the rho meson exchange between nucleons, in the OPEP. This may be relevant for processes produced in the inner core of neutron stars, where the density may exceed several times the standard nuclear density, and the short-range part of the NN interaction should be taken into account. These corrections lead to an additional suppression of the neutrino emission rates between (8 and 36)%, depending on the process [nn (pp) or np] and physical conditions (temperature and degeneracy of the nucleons).