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Simple Woods-Saxon type form for $Ωα$ and $Ξα$ interactions using Folding Model

We derive a simple Woods-Saxon type form for the potentials between $Y=Ξ, Ω$ and $α$ by using a single-folding potential method, based on a separable $Y$-nucleon potential. Accordingly, the potentials $Ξ+α$ and $Ω+α$ are obtained using the ESC08c Nijmegens $ΞN$ potential (in $^{3}S_{1}$ channel) and HAL QCD Collaboration $ΩN$ interactions (in lattice QCD), respectively. In deriving the potential between $Y$ and $α$, the same potential between $Y$ and $N$ is used. Binding energy, scattering length and effective range of $Y$ particle on the alpha particle are approximated by the resultant potentials. The depths of the potentials in $Ωα$ and $Ξα$ systems are obtained $-61$ and $-24.4$ MeV, respectively. In the case of $Ξα$ potential, a fairly good agreement is observed between the single-folding potential method and the phenomenological potential of Dover-Gal model. These potentials can be used in 3-,4- and 5-body cluster structures of $ Ω$ and $Ξ$ hypernuclei.