The charmonium-nucleon interaction is studied by the time-dependent HAL QCD method. We use a larger lattice volume and the relativistic heavy quark action for charm quark to obtain less systematic errors than those in our previous study. As a result, the sizable J/$psi$N hyperfine splitting is observed, indicating that the spin-spin interaction is important to understand this system quantitatively. No J/$psi$N or $eta_c$N bound state is observed below the thresholds as in the previous results.
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