Effects of Many-body Interactions in Hypernuclei with Korea-IBS-Daegu-SKKU Functionals

We investigate the properties of \(\Lambda\) hyperon in \(\Lambda\)-hypernuclei using an effective nuclear density functional theory which is based on the low-energy effective field theory. It expands the energy density in the power of Fermi momentum, and consequently has multiple density dependence for the effective many-body interactions. Starting from the effective density functional for nucleons, we determine the parameters for the two- and many-body \(\Lambda\)-\(N\) interactions added to the nucleon energy density functional by fitting to \(\Lambda\)-hypernuclear data. The experimental data consist of the energy levels of a \(\Lambda\) hyperon in the \(p\)-, and \(d\)-states as well as \(s\)-state of \(\Lambda\)-hypernuclei in the mass range from \(_\Lambda^{16}\)O to \(_\Lambda^{208}\)Pb. The results turn out to properly explain the data relevant to hypernuclei owing to the effective many-body interaction apart from a few data in light hypernuclei. This hyperon functional is applied to study the \(\Lambda\) hyperon binding energy of the neutron-rich \(^{124-136}_\Lambda\)Sn isotopes which are under consideration for the measurement at J-PARC. Our results are shown to be insensitive to the density dependence of symmetry energy. We also examine the nuclear matter including \(\Lambda\) hyperon. We note that the hyperon threshold density depends on the nuclear matter properties.