  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. It
is shown that collective response of electrons to the proton quantum transition
contributes coherently to the complete interaction with a neutrino field and
enhances the neutrino-pair production. 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. We show domains
of these parameters where the neutrino radiation, caused by a singlet-state
pairing of protons is dominating.
