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Double-Lambda hypernuclei within a Skyrme-Hartree-Fock approach

We extend our Skyrme-Hartree-Fock (SHF) approach, which was used earlier to describe successfully the single-$Λ$ hypernuclei, to investigate the binding and the $ΛΛ$ bond energies of the double-$Λ$ hypernuclei. The nucleon-nucleon ($NN$) and $Λ$-nucleon ($ΛN$) interactions are taken from our previous study. For the $ΛΛ$ force several Skyrme-like potentials available in the literature have been used. We discuss the sensitivity of the calculated $ΛΛ$ binding and bond energies to the $ΛΛ$ and $ΛN$ force parameters. It is found that the existing $ΛΛ$ hypernuclear data do not allow to distinguish between various $ΛΛ$ force parameter sets used by us. However, they show some selectivity for a particular set of the $ΛN$ potential determined in our previous work.