  The neutrino emission due to formation and breaking of Cooper pairs of protons in superconducting cores of neutron stars is considered with taking into account the electromagnetic coupling of protons to ambient electrons. Our calculation shows that the contribution of the vector weak current to the $\nu\bar\nu$ emissivity of protons is much larger than that calculated by different authors without taking into account the plasma effects. Partial contribution of the pairing protons to the total neutrino radiation from the neutron star core is very sensitive to the critical temperatures for the proton and neutron pairing and can dominate in some domains of these parameters. 
Plasma effects in neutrino-pair emission due to Cooper pairing of   protons in superconducting neutron stars