Medium Effect in S-shell Double- $$\Lambda $$ Hypernuclei and Hyperon Superfluidity in Neutron Star Cores

The effective $$\Lambda $$ - $$\Lambda $$ interaction energies in s-shell double- $$\Lambda $$ hypernuclei, $$^{6}_{\Lambda \Lambda }\text {He}$$ , $$^{5}_{\Lambda \Lambda }\text {He}$$ and $$^{5}_{\Lambda \Lambda }\text {H}$$ have been investigated by solving three-body system ( $$\Lambda $$ + $$\Lambda $$ + 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 $$\Lambda $$ - $$\Lambda $$ interaction. By taking into account the medium effects, it was adjusted to fit the experimental $$\Lambda $$ - $$\Lambda $$ interaction energies of $$^{6}_{\Lambda \Lambda }\text {He}$$ (0.67 ± 0.17 MeV). The effective $$\Lambda $$ - $$\Lambda $$ interaction energies of $$^{5}_{\Lambda \Lambda }\text {He}$$ are 0.92 MeV, 0.88 MeV, 0.86 MeV for each potential model and that of $$^{5}_{\Lambda \Lambda }\text {H}$$ is 0.6 MeV for all potential modes. Moreover, the $$\Lambda $$ -superfludity in the neutron star cores which is related to cooling process has also been investigated by applying our constructed effective $$\Lambda $$ - $$\Lambda $$ NSC97e potential of $$^{6}_{\Lambda \Lambda }\text {He}$$ . It is found that $$\Lambda $$ superfludity begins to appear when the interaction strength is 1.5 times more attractive than our constructed interaction. The $$\Lambda $$ -superfluidity in the neutron star cores might occur at the hyperon percentage $$Y_\Lambda $$ (1%–5%), and vanish at $$Y_\Lambda $$ (15%– 20%).