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.