Neutrino emission due to Cooper-pair recombination in neutron stars reexamined

Neutrino emission in processes of breaking and formation of neutron and proton Cooper pairs is calculated within the Larkin-Migdal-Leggett approach for a superfluid Fermi liquid. We demonstrate explicitly that the Fermi-liquid renormalization respects the Ward identity and ensures the weak vector-current conservation. The systematic expansion of the emissivities for small temperatures and nucleon Fermi velocity vF,i,i=n,p, is performed. Both neutron and proton processes are mainly controlled by the axial-vector current contributions, which are not strongly changed in the superfluid matter. Thus, compared to earlier calculations, the total emissivity of processes on neutrons paired in the 1S₀ state is suppressed by a factor of (0.9-1.2)vF,n². A similar suppression factor (~vF,p²) arises for processes on protons.