Neutrino emission due to Cooper pairing of nucleons in cooling neutron stars

. The neutrino energy emission rate due to formation of Cooper pairs of neutrons and protons in the superfluid cores of neutron stars is studied. The cases of singlet-state pairing with isotropic superfluid gap and triplet-state pairing with anisotropic gap are analysed. The neutrino emission due to the singlet-state pairing of protons is found to be greatly suppressed with respect to the cases of singlet- or triplet-state pairings of neutrons. The neutrino emission due to pairing of neutrons is shown to be very important in the superfluid neutron--star cores with the standard neutrino luminosity and with the luminosity enhanced by the direct Urca process. It can greatly accelerate both, standard and enhanced, cooling of neutron stars with superfluid cores. This enables one to interpret the data on surface temperatures of six neutron stars, obtained by fitting the observed spectra with the hydrogen atmosphere models, by the standard cooling with moderate nucleon superfluidity. Key wor..