Bound states of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi mathvariant="normal">Ω</mml:mi> </mml:math> baryons in light nuclei

We investigate bound states of light $Ω_{3x}$-clusters ($x = s, c$), motivated by the $Ω_{3s}N$ potential recently developed by the HAL QCD collaboration. To regularize this potential, we remove the deeply attractive core at $r < 0.4~\mathrm{fm}$ and parametrize the long-range component ($r > 0.4~\mathrm{fm}$) using a two-range Gaussian form. This procedure preserves the relevant two-body bound state energy while having a negligible effect on the $Ω_{3s}NN$ and $Ω_{3s}Ω_{3s}N$ systems. An effective $Ω_{3s}α$ potential is then constructed by fitting a two-range Gaussian function to the long-range component of the folding potential, enabling calculations of the bound state energies of the $Ω_{3s}α$, $Ω_{3s}αα$, and $Ω_{3s}Ω_{3s}α$ systems. The regularization procedure leads to a substantial reduction in bound state energies compared to those obtained with the original potential. We further extend the analysis to $Ω_{3c}$-cluster systems by introducing an $Ω_{3c}N$ interaction, derived by comparing the existing $Ω_{3s}Ω_{3s}$ and $Ω_{3c}Ω_{3c}$ potentials. Our results suggest that several parametrizations predict bound states in $Ω_{3c}$-containing clusters. Finally, the $Ω_{3s}Ω_{3s}$ interaction is described using a contact-like potential approach, motivated by the effective field theory.