Abstract
Light hypernuclei with an $\alpha$ cluster substructure of the core nucleus are studied using an accurate cluster approach (the Hyper-THSR wave function) in combination with a density-dependent $\Lambda$ hyperon-nuclear interaction derived from chiral SU(3) effective field theory. This interaction includes important two-pion exchange processes involving $\Sigma N$ intermediate states and associated three-body mechanisms as well as effective mass and surface terms arising in a derivative expansion of the in-medium $\Lambda$ self-energy. Applications and calculated results are presented and discussed for $_\Lambda^9$Be and $^{13}_\Lambda$C. Furthermore, the result of the lightest $\alpha$ clustered hypernucleus, $^5_{\Lambda}$He using realistic $ab initio$ four nucleon density is shown.
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