The possible existence of a bound state in the charmonium-neutron-${}^{10}\mathrm{Be}$ system is investigated within a three-cluster model in which the system is treated as $c\overline{c}+n+{}^{10}\mathrm{Be}$. The three-body problem is solved using a hyperspherical-harmonics expansion within the coupled Faddeev-equation framework. The neutron-${}^{10}\mathrm{Be}$ interaction is described by an $l$-dependent Woods-Saxon potential that provides a satisfactory description of the low-energy properties of ${}^{11}\mathrm{Be}$. The effective ${}^{10}\mathrm{Be}\text{−}c\overline{c}$ interactions are constructed by folding the $S$-wave charmonium-nucleon potentials obtained from the HAL QCD Collaboration at nearly physical pion mass with the ${}^{10}\mathrm{Be}$ matter density. Bound three-body states are obtained for all three spin-dependent charmonium-nucleon interactions considered. The central three-body binding energies are 3.297(493) MeV for $J/\psi N\left({}^{4}S_{3/2}\right)$, 4.650(632) MeV for $J/\psi N\left({}^{2}S_{1/2}\right)$, and 2.009(325) MeV for ${\eta }_{c}N\left({}^{2}S_{1/2}\right)$, with corresponding nuclear matter rms radii of 2.542(24), 2.474(17), and 2.680(42) fm, respectively. These results demonstrate that the attractive charmonium-nucleon interactions obtained from lattice QCD can generate bound $c\overline{c}+n+{}^{10}\mathrm{Be}$ configurations within the present three-body framework, while the predicted binding energies retain a substantial sensitivity to the spin dependence of the underlying interaction.

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• Few-body systems
• Hypernuclei & mesic nuclei
• Lattice QCD
• Charm quark