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$A$--Dependence of $ΛΛ$ Bond Energies in Double---$Λ$ Hypernuclei

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