Possible Existence of Charmonium-Nucleus Bound States

Possible existence of $(c\bar{c})-$nucleus bound states are examined. We adopt Gaussian potentials for the $\eta_{c}-N$ and $J/\psi-N$ interactions. The relations between the scattering lengths $a$ of $(c\bar{c})-N$ interactions and the binding energies of $\eta_{c}-NN$, $J/\psi-NN$ and $J/\psi-^{4}$He are given. The results show that scattering lengths $a \le -0.95$ fm are needed to make $\eta_{c}-NN$ and $J/\psi-NN$ bound states, while for $a \le -0.24$ fm there may exist a $J/\psi-^{4}$He bound state.