Baryonic 3P2-dominant superfluidity under combined pion condensation with Δ isobar.: II -: Properties of pairing interaction and numerical results

According to the formulation developed in I, we calculate energy gaps of the baryonic P-3(2)- dominant superfluidity under the combined pion condensation with Delta-mixing at moderately high density in neutron star interior. Adopting a baryon-baryon potential extended from a "root" NN potential to be workable in the N + Delta space, we obtain the concrete form of the pairing interaction matrix elements between the quasi-baryon pairs, which constitute a two-dimensional angular-momentum stretched state and a charge triplet. With use of OPEG-B as a "root" NN potential and an available set of the parameters representing the combined pion condensation, we study the properties of two-dimensional pairing potentials and the matrix elements of pairing interaction. We find that the strong attraction of pairing interaction for the quasi-neutron pairs is brought about by the spin-orbit potential and the spin- and isospin-dependent core terms of the central potential, whose effects are enhanced due to the pion condensation. The quasi-neutron pair plays a decisive role to bring about meaningful energy gaps, while the coupling between different. quasi-baryon pairs plays no important role, as a consequence of a unique feature of the combined pion condensation we adopt. We numerically solve the energy gap equation for baryon density of (2 - 6) times the nuclear density and clarify substantial aspects of resulting superfluid energy gaps, and discuss related problems by taking into account possible change in the factors affecting the energy gaps, such as baryon-baryon potentials, some of the pion condensation parameters and an effective mass of the quasi-particle. Standing on these results, we can say that the P-3(2)-dominant superfluid is realized with the critical temperatures T. of the order of 10(9) K, equivalent to the energy gaps of the order of 0.1 MeV, under the combined pion condensation in neutron star matter. The key point of the recognition lies in the aspects that the A-mixing provides the additional pairing attraction of short range, although the attenuation of the pairing attraction due to the charged-pion condensation comes about in the whole interaction range. This means that the superfluid of this type can provide the meaningful suppression on the emissivity of the pion direct Urca process, which makes the pion cooling scenario of neutron stars available.