We have searched for the two-photon production of the ${\eta }_c$, ${\chi }_0$, and ${\chi }_2$ charmonium states at the SLAC $e^{+}{e}^{-}$ collider PEP in the channels $\gamma \gamma \to K^{\pm }{K}_S^0{\pi }^{\mp }$, $\gamma \gamma \to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$, $\gamma \gamma \to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$, and $\gamma \gamma \to K^{+}{K}^{-}{K}^{+}{K}^{-}$. We identify four ${\eta }_c$ candidates in the $K^{+}{K}^{-}{K}^{+}{K}^{-}$ channel on a negligible background; the one $\phi \phi$ event among them implies a 95%-confidence-level (C.L.) lower limit for ${\Gamma }_{\gamma \gamma }\left({\eta }_c\right)$ of 1.7 keV. In the other channels we find no evidence for any of the three states. We establish 95%-C.L. upper limits ${\Gamma }_{\gamma \gamma }\left({\eta }_c\right)<\mathrm{}15.5\mathrm{}$ keV, ${\Gamma }_{\gamma \gamma }\left({\chi }_0\right)<\mathrm{}17.0\mathrm{}$ keV, and ${\Gamma }_{\gamma \gamma }\left({\chi }_2\right)<\mathrm{}4.2\mathrm{}$ keV. From all channels combined, we obtain the value ${\Gamma }_{\gamma \gamma }\left({\eta }_c\right)={6.4}_{-3.4\mathrm{}}^{+5.0\mathrm{}}$ keV.

• Received 30 November 1987

DOI:https://doi.org/10.1103/PhysRevLett.60.2355