$A$--Dependence of $\Lambda\Lambda$ Bond Energies in Double---$\Lambda$ Hypernuclei

The $A$-dependence of the bond energy $\Delta B_{\Lambda\Lambda}$ of the ${\Lambda\Lambda}$ hypernuclear ground states is calculated in a three-body ${\Lambda + \Lambda + {^{A}Z}}$ model and in the Skyrme-Hartree-Fock approach. Various ${\Lambda\Lambda}$ and $\Lambda$-nucleus or ${\Lambda N}$ potentials are used and the sensitivity of $\Delta B_{\Lambda\Lambda}$ to the interactions is discussed. It is shown that in medium and heavy ${\Lambda\Lambda}$ hypernuclei, $\Delta B_{\Lambda\Lambda}$ is a linear function of $r_{\Lambda}^{-3}$, where $r_\Lambda$ is rms radius of the hyperon orbital. It looks unlikely that it will be possible to extract ${\Lambda\Lambda}$ interaction from the double-$\Lambda$ hypernuclear energies only, the additional information about the $\Lambda$-core interaction, in particular, on $r_{\Lambda}$ is needed.