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Study of $Ξ^-$ hypernuclei in the Skyrme-Hartree-Fock approach

The properties of $Ξ^-$ hypernuclei are studied systematically using a two-dimensional Skyrme-Hartree-Fock approach combined with three different $ΞN$ Skyrme forces fitted to reproduce the existing data. We explore the impurity effect of a single $Ξ^-$ hyperon on the radii, deformations, and density distributions of the nuclear core and point out qualitative differences between the different forces. We find that the $Ξ^-$ removal energy of $^{\hskip0.10em13}_{Ξp}$B [$^{12}$C(g.s.)+ $Ξ^-$(1p)] calculated by the SLX3 force is 0.7 MeV, which is in good agreement with a possible value of $0.82\pm0.17\;$MeV from the KEK E176 experiment. The theoretical prediction for this weakly bound state depends strongly on the deformation of the nuclear core, which is analyzed in detail.