The structure of hypernuclei and hyperon mixing in neutron-star matter

We review our recent studies of the structure of Λ hypernuclei within the framework of the Gaussian expansion method for s- and p-shell hypernuclei and the mean-field approach for sd-shell hypernuclei. Specifically, we focus on the structures of (i) the energy splittings of the $3/2^{+}$–$5/2^{+}$ and $3/2^{-}$–$1/2^{-}$ levels in ${}_{\Lambda }^9$Be and ${}_{\Lambda }^{13}C$ within the framework of $2\alpha +\Lambda$ and $3\alpha +\Lambda$, three- and four-body cluster models for the hyperon–nucleon (Y–N) spin–orbit force; (ii) the ${}_{\Lambda }^{3}n$ system for $\Lambda N-\Sigma N$ coupling; (iii) the weakly bound states or resonant states of neutron-rich Λ hypernuclei such as ${}_{\Lambda }^{6}H$ and ${}_{\Lambda }^7$He within the framework of $t+\Lambda +n+n$ and $\alpha +\Lambda +n+n$ four-body models; and (iv) the tensor correlation effect and super-deformation structure of Λ hypernuclei based on sd-shell nuclei with mass $20⩽A⩽40$ using the deformed Skyrme–Hartree–Fock model and the antisymmetrized molecular dynamics model. As an extreme limit of nuclei including multiple hyperons, we review hyperon effects in neutron-star matter in the high-density region using recent Y–N interactions. (invited comment)