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

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