Mean field approaches for $Ξ^-$ hypernuclei and current experimental data

Motivated by the recently observed hypernucleus (Kiso event) $^{15}_Ξ$C ($^{14}$N$+Ξ^-$), we identify the state of this system theoretically within the framework of the relativistic-mean-field and Skyrme-Hartree-Fock models. The $ΞN$ interactions are constructed to reproduce the two possibly observed $Ξ^-$ removal energies, $4.38\pm 0.25$ MeV or $1.11\pm 0.25$ MeV. The present result is preferable to be $^{14}{\rm N}({\rm g.s.})+Ξ^-(1p)$, corresponding to the latter value.

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