Effects of Many-body Interactions in the Hyperon with Skyrme and KIDS Functionals for Finite Nuclei and Nuclear Matter

We investigate $\Lambda$ hyperon effects on finite $\Lambda$-hypernuclei and neutron star matter using an effective nuclear density functional theory, which is based on the chiral effective field theory and has proper multiple density dependence for the effective many-body interactions. Starting from the effective density functional for nucleons, we determine the parameters for the many-body and two-body $\Lambda$ interactions added to the nucleon energy functional by fitting to some experimental $\Lambda$-hypernuclear data. The results turn out to properly explain the data relevant to hypernuclei due to the effective many-body interaction apart from a few data in light hypernuclei. This hyperon functional is exploited to the neutron star. $\Lambda$ hyperon in the functional shows up in the relatively high density compared to other models including the $\Lambda$ hyperon. Equation of states and mass radius relations of the hyperonic neutron stars are discussed with the role of the effective interaction for the $\Lambda$ hyperon beyond the two body interaction.