Neutrino Emission by the "Urca" Process in Neutron Stars

The neutrino emission rate due to the reaction $n+n\to n+p+e^{-}+\overline{v}$, occurring in the interior of a neutron star, is calculated numerically. A highly degenerate Fermi-Dirac distribution is assumed for the neutrons and electrons; collective effects are ignored. The calculation is done relativistically, and for several values of the temperature and density. The results are in rough agreement with the estimates of other authors.