Realistic Calculations of Hyperon-Mixed Phase and Neutron Stars at Birth and at Evolved Stage

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(A) The effective ΛN and ΛΛ interactions applicable to the Y-mixing problem are constructed from the G-matrix calculations by paying particular attention to the use of YN and YY interactions compatible with hypernuclear data. Similarly, the effective Σ^-N and Σ^-Σ^- interactions are constructed.(B) The Y-mixing problem in neutron star cores is investigated by an efffective interaction approach based on (A). It is found that ∧ and Σ^- begin to mix in neutron star matter at the total baryon density ρ〜3ρ_0 (ρ_0 being the nuclear density) and the mixing ratio y_Y increases with ρ, with hyperons becoming components comparable to nucleons (N) (e.g., y_Λ〜20%, y_Σ-〜15%, y_p〜15%, y_n〜50% at ρ=6ρ_0). Of particular interest is the fact that the Y-mixing effects soften the EOS dramatically and thereby the maximum mass M_<max> sustained by the EOS cannot exceed the observed mass M_<obs>=1.44M_<【of sun】> for PSR1913+16, leading to a serious problem contradicting observations. The mechanism of such a dramatic softening is analyzed, showing up the characterisics of Y-mixing effects.(C) It is stressed that M_<max><M_<obs> is of special interest, suggesting the necessity of "Extra Repulsion" in hypernuclear systems. It is pointed out that such a repulsion as in the three- body force currently introduced in nuclear systems could be one of the candidates for "Extra Repulsion".(D) The existence of Λ- and Σ^-- superfluids (and also Ξ^--superfluid) in neutron star cores is shown by using three kinds of YY interaction models. The limited density region for Λ-superfluid interestingly restricts the mass of neutron stars with the "hyperon cooling".