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