Within the framework of the Faddeev equations in configuration space, we examine the ${\mathrm{\Omega }}^{-}np$ system, employing strongly attractive lattice HAL QCD and Yukawa-type meson exchange potentials for the $\mathrm{\Omega }N$ interaction. Our formalism incorporates the attractive Coulomb force between the ${\mathrm{\Omega }}^{-}$ and proton, treating the system as three nonidentical particle pairs (the $ABC$ model). In this study, we assess the impact of the Coulomb interaction on the system and compare our results with recent $\mathrm{\Omega }NN$ ($AAC$ model) calculations, obtained using various approaches. The $ABC$ model yields low-energy characteristics for the $\mathrm{\Omega }NN$ system that differ from previous calculations. The Coulomb potential has a marginal perturbative effect on the $AAC$ system, shifting the three-body binding energy by the Coulomb energy of the two-body $BC$ subsystem, but only slightly deviating the spatial configuration from isosceles triangle symmetry. These effects are primarily driven by the strong $\mathrm{\Omega }N$ interaction. We demonstrate that the large binding energy of the ${\mathrm{\Omega }}^{-}np$ system arises from the short-range behavior of the $\mathrm{\Omega }N$ potentials.

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• Few-body systems
• Hypernuclei & mesic nuclei