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Neutrino emissivity of $^{3}P_{2}$-$^{3}F_{2}$ superfluid cores in neutron stars

The influence of the admixture of the $^{3}F_{2}$ state onto collective spin oscillations and neutrino emission processes in the triplet superfluid neutron liquid is studied in the BCS approximation. The eigen mode of spin oscillations with $ω\simeq\sqrt{58/35}Δ$ is predicted to exist in the triplet superfluid neutron condensate besides the already known mode $ω\simeqΔ/\sqrt{5}$. Excitation of the high-frequency spin oscillations in the condensate occurs through the tensor interactions between quasiparticles. Neutrino energy losses through neutral weak currents are found to consist of three separate contributions caused by a recombination of broken Cooper pairs and by weak decays of the collective modes of spin oscillations. Neutrino decays of the low-frequency spin waves can play an important role in the cooling scenario of neutron stars. Weak decays of the high-frequency oscillations that occur only if the tensor forces are taken into account in the pairing interactions does not modify substantially the total energy losses. Simple expressions are suggested for the total neutrino emissivity.