Effects of many-body interactions in hypernuclei with Korea-IBS-Daegu-SKKU functionals

Abstract

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 ${}_\Lambda ^{16}\hbox {O}$ to ${}_\Lambda ^{208}\hbox {Pb}$. 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 $^{124-136}_{\Lambda } \hbox {Sn}$ 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.