We address the problem of observed charmonium decays which should be forbidden in perturbative QCD. We examine the model in which these decays proceed through a gluonic component of the $J/Psi$ and the $eta_c$, arising from a mixing of $(cbar c)$ and glueball states. We give some bounds on the values of the mixing angles and propose the study of the $p bar{p} to phi phi$ reaction, at $sqrt{s} simeq 3$ GeV, as an independent test of the model.
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