  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.
