  We use a simple perturbation theory argument and measurements of charmonium
leptonic widths $\Gamma (\psi_{NS} \rightarrow e^+e^-)$ to estimate the ratio
\mbox{$R_\circ \equiv {\vert \Psi _{\eta_{c1S}}(0) \vert}^2
/{\vert\Psi_{\psi_{1 S}}(0)\vert}^2$} in the general context of non-
relativistic potential models. We obtain $R_\circ = 1.4 \pm 0.1$. We then apply
well known potential model formulas, which include lowest order QCD
corrections, to find $\Gamma (\eta_c \rightarrow \gamma \gamma )/\Gamma
(\psi_{1S} \rightarrow e^+e^-) \approx 2.2\pm 0.2$. The central value for
$\Gamma (\psi_{1S} \rightarrow e^+ e^-)$in the 1992 Particle Data Tables then
leads to a (non relativistic) prediction $\Gamma (\eta_c \rightarrow \gamma
\gamma )\approx 11.8\pm 0.8 $ keV. This prediction is in good agreement with a
recent measurement by the ARGUS collaboration, is consistent with a recent
measurement by the L3 collaboration but is significantly higher than several
earlier measurements and than previous theoretical estimates, which usually
assume $R_\circ =1$. The correction to $R_\circ =1$ is estimated to be smaller
but nonnegligible for the $b\bar b$ system. Using the current central
measurement for $\Gamma (\Upsilon_{1S}\rightarrow e^+e^-)$ we find $\Gamma
(\eta_b\rightarrow \gamma \gamma )\approx 0.58\pm 0.03$ keV. A rough estimate
of relativistic corrections reduces the expected two photon rates to about 8.8
keV and 0.52 keV for the $\eta_c$ and $\eta_b$ mesons respectively. Such
corrections
