We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of $J/psi$ and $psi^{prime}$ are alleviated spontaneously. This work also intends to provide an inspection and suggestion for the possible $cbar{c}$ among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as $M(2^1D_2)= 4164.9$ MeV and $M(3^3P_2)= 4352.4$ MeV, which strongly favor the $J^{PC}=2^{-+}, 2^{++}$ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.
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