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The E760 Collaboration performed an experiment in the Antiproton Accumulator at Fermilab to study the two photon decay of the ${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$(1 $^{1}$${\mathit{S}}_{0}$) charmonium state formed in p\ifmmode\bar\else\textasciimacron\fi{}p annihilations. This resulted in a new measurement of the mass ${\mathit{M}}_{\mathrm{\ensuremath{\eta}}\mathit{c}}$=2988.${3}_{\mathrm{\ensuremath{-}}3.1}^{+3.3}$ MeV/${\mathit{c}}^{2}$ and of the product B(${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$\ensuremath{\rightarrow}p\ifmmode\bar\else\textasciimacron\fi{}p)\ifmmode\times\else\texttimes\fi{}\ensuremath{\Gamma}(${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}$\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}) =(8.${1}_{\mathrm{\ensuremath{-}}2.0}^{+2.9}$) eV. We performed a search for the process p\ifmmode\bar\else\textasciimacron\fi{}p\ensuremath{\rightarrow}${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}^{\ensuremath{'}}$(2 $^{1}$${\mathit{S}}_{0}$)\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma} over a limited range of center-of-mass energies. Since no signal was observed, we derived upper limits on the product of branching ratios B(${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}^{\ensuremath{'}}$\ensuremath{\rightarrow}p\ifmmode\bar\else\textasciimacron\fi{}p)\ifmmode\times\else\texttimes\fi{}B(${\mathrm{\ensuremath{\eta}}}_{\mathit{c}}^{\ensuremath{'}}$\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}) in the center-of-mass energy range 3584\ensuremath{\le} \ensuremath{\surd}s \ensuremath{\le}3624 MeV. We observed no signal for the nonresonant process p\ifmmode\bar\else\textasciimacron\fi{}+p\ensuremath{\rightarrow}\ensuremath{\gamma}+\ensuremath{\gamma} and obtain upper limits.