Superfluid response and the neutrino emissivity of baryon matter: Fermi-liquid effects

The linear response of a nonrelativistic superfluid baryon system on an external weak field is investigated while taking into account of the Fermi-liquid interactions. We generalize the theory developed by Leggett for a superfluid Fermi-liquid at finite temperature to the case of timelike momentum transfer typical of the problem of neutrino emission from neutron stars. A space-like kinematics is also analysed for completeness and compared with known results. We use the obtained response functions to derive the neutrino energy losses caused by recombination of broken pairs in the electrically neutral superfluid baryon matter. We find that the dominant neutrino radiation occurs through the axial-vector neutral currents. The emissivity is found to be of the same order as in the BCS approximation, but the details of its temperature dependence are modified by the Fermi-liquid interactions. The role of electromagnetic correlations in the pairing case of protons interacting with the electron background is discussed in the conclusion.