Bound states of ^9_Be and ^6_He with ++ and ++ cluster models

We investigate the ^9_Be and ^6_He hypernuclei within the framework of the three-body cluster model %specifically as the ++ and ++ systems, using the Faddeev formalism in configuration space. The - potential is determined through a folding procedure of the HAL QCD -N interaction in the ⁴S₃/₂ channel with the matter distribution of ⁴He. The phenomenological - and - potentials are taken from the literature. Additionally, we construct a Wood-Saxon (WS) type interaction to simulate the - potential, also taken from the literature, based on an effective Lagrangian approach that includes KK meson loops in the -meson self-energy. A comparison of binding energies obtained for both types of the - interactions reveals qualitative agreement. %between the obtained approaches. We predict the binding energy for the ^9_Be and ^6_He hypernuclei as the mirror ++ and ++ systems in the range of 1-11 MeV and 3-10 MeV, respectively. The range of values of the binding energies relies on the choice of the WS - interaction parameters.