Neutrino-pair bremsstrahlung by electrons in neutron star crusts

Neutrino-pair bremsstrahlung by relativistic degenerate electrons in a neutron-star crust at densities (10^9 - 1.5x10^{14}) g/cm^3 is analyzed. The processes taken into account are neutrino emission due to Coulomb scattering of electrons by atomic nuclei in a Coulomb liquid, and electron-phonon scattering and Bragg diffraction (the static-lattice contribution) in a Coulomb crystal. The static-lattice contribution is calculated including the electron band-structure effects for cubic Coulomb crystals of different types and also for the liquid crystal phases composed of rod- and plate-like nuclei in the neutron-star mantle (at 10^{14} - 1.5x10^{14} g/cm^3). The phonon contribution is evaluated with proper treatment of the multi-phonon processes which removes a jump in the neutrino bremsstrahlung emissivity at the melting point obtained in previous works. Below 10^{13} g/cm^3, the results are rather insensitive to the nuclear form factor, but results for the solid state near the melting point are affected significantly by the Debye-Waller factor and multi-phonon processes. At higher densities, the nuclear form factor becomes more significant. A comparison of the various neutrino generation mechanisms in neutron star crusts shows that electron bremsstrahlung is among the most important ones.