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 $v_{\mathrm{F},i},i=n,p,$ 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 $1S_0$ state is suppressed by a factor of $\simeq (0.9\text{−}1.2)v_{\mathrm{F},n}^2$. A similar suppression factor ($~v_{\mathrm{F},p}^2$) arises for processes on protons.

• Received 12 February 2008

DOI:https://doi.org/10.1103/PhysRevC.77.065808