Folding Procedure for \(\Omega \)-\(\alpha \) Potential

Using the folding procedure, we investigate the bound state of the \(\Omega \) $\mathrm{\Omega }$ + \(\alpha \) $\alpha$ system. Previous theoretical analyses have indicated the existence of a deeply bound ground state, which is attributed to the strong \(\Omega \) $\mathrm{\Omega }$ -nucleon interaction. By employing well-established parameterizations of nucleon density within the alpha particle, we performed numerical calculations for the folding \(\Omega \) $\mathrm{\Omega }$ - \(\alpha \) $\alpha$ potential. Our results show that the \(V_{\Omega \alpha }(r)\) $V_{\mathrm{\Omega }\alpha }(r)$ potential can be accurately fitted using a Woods-Saxon function, with a phenomenological parameter \(R = 1.1A^{1/3} \approx 1.74\) $R=1.1A^{1/3}\approx 1.74$ fm ( \(A=4\) $A=4$ ) in the asymptotic region where \(2< r < 3\) $2<r<3$ fm. We provide a thorough description of the corresponding numerical procedure. Our evaluation of the binding energy of the \(\Omega \) $\mathrm{\Omega }$ + \(\alpha \) $\alpha$ system within the cluster model is consistent with both previous and recent reported findings. To further validate the folding procedure, we also calculated the \(\Xi \) $\mathrm{\Xi }$ - \(\alpha \) $\alpha$ folding potential based on a simulation of the ESC08c Y-N Nijmegen model. A comprehensive comparison between the \(\Xi \) $\mathrm{\Xi }$ - \(\alpha \) $\alpha$ folding and \(\Xi \) $\mathrm{\Xi }$ - \( \alpha \) $\alpha$ phenomenological potentials is presented and discussed.