Neutrino emission due to Cooper pairing of protons in cooling neutron stars: Collective effects

The process of neutrino-pair radiation due to formation and breaking of Cooper pairs of protons in superconducting cores of neutron stars is considered with taking into account of the electromagnetic coupling of protons to ambient electrons. It is shown that plasma polarization strongly modifies the effective vector weak current of protons. Collective response of ambient electrons to the proton quantum transition contributes coherently to the complete interaction with the neutrino field and enhances the rate of neutrino-pair production by two orders of magnitude.