Investigating three-body resonances in $\alpha \alpha \Omega /{\Omega }_{ccc}$ clusters within the ${}_{\Omega /{\Omega }_{ccc}}^9\mathrm{Be}$ nucleus

Abstract

We investigate the bound and resonant states of the $\alpha +\alpha +\Omega$ and $\alpha +\alpha +{\Omega }_{ccc}$ three-body systems, corresponding to ${}_{\Omega }^9\mathrm{Be}$ and ${}_{{\Omega }_{ccc}}^9\mathrm{Be}$, within the Gaussian expansion method combined with the complex scaling method. The $\alpha \Omega$ and $\alpha {\Omega }_{ccc}$ interactions are constructed by folding the $N\Omega$ and $N{\Omega }_{ccc}$ potentials obtained from lattice QCD calculations by the HAL QCD Collaboration with the nucleon density distribution of the $\alpha$ particle. The uncertainty associated with the $\alpha$-particle matter radius is also examined. For the $\Omega$ sector, the strong $N\Omega$ attraction generates deeply bound $0_1^{+}$, $2_1^{+}$, and $4_1^{+}$ states in ${}_{\Omega }^9\mathrm{Be}$, accompanied by a pronounced contraction of the $\alpha \alpha$ core, demonstrating a strong gluelike effect of the $\Omega$ baryon. An unconventional inversion between the $0_1^{+}$ and $4_1^{+}$ levels is also predicted. In contrast, the ${\Omega }_{ccc}$ baryon produces considerably weaker attraction: the $0_1^{+}$ state of ${}_{{\Omega }_{ccc}}^9\mathrm{Be}$ is weakly bound, whereas the $2_1^{+}$ and $4_1^{+}$ states remain resonances. Their resonance energies and widths exhibit a clear dependence on the strength of the $\alpha {\Omega }_{ccc}$ interaction. These results reveal qualitatively different gluelike behaviors of the $\Omega$ and ${\Omega }_{ccc}$ baryons and provide predictions for the spectroscopy of exotic multistrange and triply charmed hypernuclei.

Comments: 13 pages, 6 figures and 3 tables