Folding procedure for $\Omega$-$\alpha$ potential

TL;DR

This paper employs a folding procedure to analyze the $ ext{Ω}+ ext{α}$ system's bound state, confirming previous findings and validating the method through comparison with $ ext{Ξ}+ ext{α}$ potentials.

Contribution

It introduces a detailed folding procedure for the $ ext{Ω}+ ext{α}$ potential and compares it with $ ext{Ξ}+ ext{α}$ potentials, providing new insights into these bound states.

Findings

The $ ext{Ω}+ ext{α}$ potential fits a Woods-Saxon form.

The binding energy aligns with previous studies.

The $ ext{Ξ}+ ext{α}$ potential comparison validates the folding approach.

Abstract

Using the folding procedure, we investigate the bound state of the $\Omega$+$\alpha$ system based on $\Omega$-$N$ ($^{5}S_{2}$) HAL QCD potential. 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, and the central HAL QCD $\Omega$-$N$ potential, 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.