Medium Effect in S-shell Double-Λ Hypernuclei and Hyperon Superfluidity in Neutron Star Cores

The effective Λ-Λ interaction energies in s-shell double-Λ hypernuclei, ⁶_ΛΛHe, ⁵_ΛΛHe and ⁵_ΛΛH have been investigated by solving three-body system (Λ + Λ + core) within the framework of coupled rearrangement channel Gaussian basis treatment. The Nijmegen soft-core potential models, NSC97d, NSC97e and NSC97f, have been applied for free-space Λ-Λ interaction. By taking into account the medium effects, it was adjusted to fit the experimental Λ-Λ interaction energies of ⁶_ΛΛHe (0.67 ± 0.17 MeV). The effective Λ-Λ interaction energies of ⁵_ΛΛHe are 0.92 MeV, 0.88 MeV, 0.86 MeV for each potential model and that of ⁵_ΛΛH is 0.6 MeV for all potential modes. Moreover, the Λ-superfluidity in the neutron star cores which is related to cooling process has also been investigated by applying our constructed effective Λ-Λ NSC97e potential of ⁶_ΛΛHe. It is found that Λ superfluidity begins to appear when the interaction strength is 1.5 times more attractive than our constructed interaction. The Λ-superfluidity in the neutron star cores might occur at the hyperon percentage Y_Λ (1%–5%), and vanish at Y_Λ (15%– 20%). (author)