Eeects of Electron Band Structure on Neutrino Pair Bremsstrahlung in Neutron Star Crusts Typeset Using Revt E X 2

We calculate the rate of energy emission by bremsstrahlung of neutrino pairs by electrons moving in the crystalline lattice of ions in dense matter in the crust of a neutron star. Since the periodic potential in the solid gives rise to electronic band gaps which can be as large as about 1 MeV, it is necessary in estimating the bremsstrahlung rate at low temperatures to take into account band structure in detail. We nd that, in the densest parts of the inner crust of a neutron star, neutrino emission at temperatures of about 2 10 9 K or less is much suppressed compared with earlier estimates that treated the electron-lattice interaction perturbatively, and conclude that neutrino pair bremsstrahlung by electrons in the crusts of neutron stars is much less impor-1 tant for neutron star thermal evolution than was previously thought.