Neutrino-pair bremsstrahlung in dense stars. IV. Phonon contribution in the crystalline lattice phase

Phonon contributions to the neutrino-pair bremsstrahlung in the crystalline lattice phase are calculated in the framework of the Weinberg-Salam theory for the dense matter relevant to the interior of white dwarfs and neutron stars. The frequency moment sum rules for the pure Coulomb bcc lattice are used to derive the neutrino energy loss rate. It is found that the phonon contribution to the neutrino-pair bremsstrahlung is comparable to that of the static lattice near the melting temperature. Numerical results are parameterized in the form of accurate analytic fitting formulae