Impurity effects of $\Lambda$ hyperons on $p_{\Lambda }$ orbitals

Abstract

Based on the deformed Skyrme–Hartree–Fock (DSHF) approach, impurity effects of the $\Lambda$ hyperons occupying $p_{\Lambda }$ orbitals are studied systematically in this work. Properties of $\Lambda$ and double-$\Lambda$ hypernuclei with both even and odd numbers of nucleons, from light to heavy nuclear mass regions, are investigated. In our calculation, the Skyrme force, SkI4, is used for the NN interaction, while, for the $N\Lambda$ interaction, two kinds of density-dependent forces are used, which are NSC89 and SLL4, respectively. In general, compared to observed binding energies, a Skyrme-type SLL4 interaction gives better predictions for p-shell region hypernuclei and heavy ones, while the microscopic NSC89 interaction is suitable for sd-shell hypernuclei for the $s_{\Lambda }$ state and the $p_{\Lambda }$ states. Through analysis of the density distributions and the energy curves of different configurations, we find that the $\Lambda$ hyperons occupying the $s_{\Lambda }$ orbital, $[000]1/2^{+}$, make the density of nucleons more concentrated at the center and reduce the deformation of the nuclear core for light hypernuclei. It is also found that the $\Lambda$ hyperons occupying the two $p_{\Lambda }$ orbitals $[110]1/2^{-}$ and $[101]3/2^{-}$ drive the shapes of nuclear cores toward the prolate side and the oblate side, respectively, which is caused by the different distributions of the $\Lambda$ hyperons on these two orbitals. The B(E2) values extracted from the DSHF calculation also support such conclusions. However, for the heavy hypernuclei, hyperons located on both $s_{\Lambda }$ and $p_{\Lambda }$ make little change on the nuclear core due to the saturation of its density distribution.