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 $ABAHB$ (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.