  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 find that, in the densest parts of the inner crust
of a neutron star, neutrino emission at temperatures of about $2\times 10^9$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
important for neutron star thermal evolution than was previously thought.
