The possible bound state of the ${}_{c\overline{c}}{}^9\mathrm{Be}$, a charmonium-nucleus system, is investigated. The analysis is carried out within a three-cluster model, where its binary subsystems are represented as $c\overline{c}\text{+}\alpha$ and $\alpha +\alpha$. The hyperspherical harmonics method is employed to facilitate a convenient description of this three-cluster configuration. The calculations are done by employing the effective $c\overline{c}\text{−}\alpha$ potentials. These potentials were derived recently based on state-of-the-art lattice QCD calculations by HAL collaboration, which provided interactions for the spin-3/2 $J/\psi N$, spin-1/2 $J/\psi N$, spin-1/2 ${\eta }_{c}N$, and spin-averaged $J/\psi N$ interactions, all obtained with nearly physical pion masses. The Coulomb interaction was also incorporated into the current calculations. It is determined that, despite neither the ${}_{c\overline{c}}{}^5\mathrm{He}$ nor the ${}^8\mathrm{Be}$ binary subsystems being bound, a bound state of the $c\overline{c}\text{−}\alpha \alpha$ nuclear system could potentially exist. The maximum central binding energy is found to be approximately 1.71 MeV, based on the spin-1/2 $J/\psi N$ interaction, while a minimum value of about 0.56 MeV is obtained from calculations involving the spin-1/2 ${\eta }_{c}N$ interaction.

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• Binding energy & masses
• Few-body systems
• Lattice QCD
• Particle interactions
• Charm quark
• Quarkonia
• 6 ≤ A ≤ 19
• Cluster models