Neutrino-pair bremsstrahlung in a neutron star crust

Based on the formalism by Kaminker et al. (Astron. Astrophys., 343 (1999) 1009) we derive an analytic approximation for neutrino-pair bremsstrahlung emissivity due to scattering of electrons by atomic nuclei in a neutron star crust of any realistic composition. The emissivity is expressed through the generalized Coulomb logarithm which we fit by introducing an effective potential of electron-nucleus scattering. In addition, we study the conditions at which the neutrino bremsstrahlung in the crust is affected by strong magnetic fields. The results can be applied for modelling of many phenomena in neutron stars, such as thermal relaxation in young isolated neutron stars and in accreting neutron stars with overheated crust in soft X-ray transients.