Production of $\chi_{c}$ and $\eta_{c}$ production in ultra-peripheral collisions with two-photon processes

We calculate the production of $\chi_{c}$ and $\eta_{c}$ by the semi-coherent and coherent two-photon interaction in ultra-peripheral heavy ion collisions at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies. The differential cross section of transverse momentum distribution and rapidity distribution for $AB\stackrel{\gamma\gamma}{\longrightarrow}AHB$ (H=$\chi_{c}$ and $\eta_{c}$), are estimated by using the equivalent photon approximation in ultra-peripheral nucleus-nucleus collisions. The numerical results demonstrate that the experimental study of $\chi_{c}$ and $\eta_{c}$ in ultra-peripheral nucleus-nucleus collisions is feasible at RHIC and LHC energies.