$^7_\Lambda$He bound state within three-body approach

The $^7_\Lambda$He hypernucleus is studied within the cluster model $^5_{\Lambda}\rm He+\rm n+\rm n$, using configuration space Faddeev formalism. Intrinsic structure of the core nucleus is taken into account by the folding procedure applied to construct the $^5_{\Lambda}\rm He-\rm n$ interaction. The OBE simulating potential of the NSC97f model for $\Lambda \rm n$ and phenomenological $\alpha\Lambda$ potential are used. Singlet and triplet components of the folding potential are adjusted to reproduce the $2^-$ excitation energy $E_x$($^6_\Lambda$He) of the $^6_\Lambda$He hypernucleus. A correlation between $E_x$($^6_\Lambda$He) and hyperon binding energy $B_\Lambda$($^7_\Lambda$He) of $^7_\Lambda$He is established. We use this correlation to evaluate $B_\Lambda$($^7_\Lambda$He) taking into account results of our calculation for $E_x$($^6_\Lambda$He) within the three-body model $\alpha+\Lambda+n$. The value obtained for $E_x$($^6_\Lambda$He) is 0.18~MeV. With this value our evaluation for $B_\Lambda$($^7_\Lambda$He) yields 5.69~MeV, which is close to the recently reported experimental data (5.68~MeV).