  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 $c\bar{c}$ 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.
