Nucleon superfluidity in a core of neutron stays.

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Coexistence of nucleon superfluidity with "new phases" (i.e., pion-condensed, kaon-condensed, large proton-mixing phases and so on) which lead to a rapid cooling scenario is suggested from recent surface-temperature observations for neutron stars. In this research project, we aim to investigate systematically whether nucleon superfluid can coexist with these new phases, intending to check what is a true candidate for the rapid cooling in terms of the compatibility of a new phase with superfluidity.(1) Kaon-condensed and (2) Large proton-mixing phases : We have found that these phases are unlikely to have nucleon superfluidity, mainly due to the small effective-mass of nucleons relevant to these phases. This means that the "kaon cooling" and the "direct URCA cooling" would be excluded from the rapid cooling scenario.(3) Charged pion (pi^C) -condensed phase : We have extended the BCS theory into the case applicable to quasi-particle (eta composed of n and p) superfluidity under pi^C condensation, and found that the ^3P_2 pairing interaction between eta's is not so different from the case without pion condensation, leading to the result that eta-superfluid exists up to about 3rho_0 (rho_0 being the standard nuclear density).(4) Neutral pion (pi^0) -condensed phase : In this phase, nucleon system takes a layred structure accompained by a spin-ordering (called ALS structure) and poses a new problem to treat a low-dimensional superfluid in nuclear system. We have presented a formulation suitable to the ALS state and made it applicable to the case including the isobar DELTA (1232) in the light of SU (4) quark model. We have found that due to the DELTA effects, the existence of superfluid is extended at least up to 4 rho_0.On the basis of these studies, we can say that the "pion cooling" is most promising for the rapid cooling scenario. The superfluidity under pi^0 pi^C combined condensate is a forthcoming subject, to which studies in (3) and (4) serve as an important step.