Numerical evaluation of the folding Ω-α potential

Using the folding procedure, we construct the nuclear interaction in the Ωα system. Previous theoretical analyses have hinted at the existence of a deeply bound state [1], which is ascribed to the strong Ω-nucleon (N) interaction. By harnessing well-established parameterizations of nucleon density within the alpha particle and the lattice HAL QCD Ω-N model, we perform numerical calculations for the folding Ω-α potential. Our results demonstrate that the V_Ω-α(r) potential can be accurately fitted by a Woods-Saxon function, which incorporates a phenomenological parameter R = 1.1A^(1/3) ≈1.74 fm (A = 4), in the asymptotic region where the Ω-α inter-cluster distance r falls between 2 < r < 3 fm. The corresponding numerical procedure, implemented in Python, is presented in detail. Notably, our evaluation provides a lower bound for the binding energy of the Ωα system.



[1] F. Etminan and M. M. Firoozabadi, Chin. Phys. C 44, 054106 (2020).