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

Abstract

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