Baryonic ^3P_2Dominant Superfluidity under Combined Pion Condensation with Δ Isobar. II : Properties of Pairing Interaction and Numerical Results
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Abstract
According to the formulation developed in I, we calculate energy gaps of the baryonic ^3P_2dominant superfluidity under the combined pion condensation with Δmixing at moderately high density in neutron star interior. Adopting a baryonbaryon potential extended from a "root" NN potential to be workable in the N+Δ space, we obtain the concrete form of the pairing interaction matrix elements between the quasibaryon pairs, which constitute a twodimensional angularmomentum stretched state and a charge triplet. With use of OPEGB as a "root" NN potential and an available set of the parameters representing the combined pion condensation, we study the properties of twodimensional pairing potentials and the matrix elements of pairing interaction. We find that the strong attraction of pairing interaction for the quasineutron pairs is brought about by the spinorbit potential and the spin and isospindependent core terms of the central potential, whose effects are enhanced due to the pion condensation. The quasineutron pair plays a decisive role to bring about meaningful energy gaps, while the coupling between different quasibaryon 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 (26) 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 baryonbaryon potentials, some of the pion condensation parameters and an effective mass of the quasiparticle. Standing on these results, we can say that the ^3P_2dominant superfluid is realized with the critical temperatures T_c 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 Δmixing provides the additional pairing attraction of short range, although the attenuation of the pairing attraction due to the chargedpion 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 Urea process, which makes the pion cooling scenario of neutron stars available.
Journal

 Progress of Theoretical Physics

Progress of Theoretical Physics 117(5), 861901, 20070525
Published for the Yukawa Institute for Theoretical Physics and the Physical Society of Japan