We report on a search by Fermilab experiment E835 for the eta'(c) (2 S-1(0)
) charmonium resonance in the process (p) over barp --> eta'(c)--> gamma ga
mma. No signal was observed and, based on 34 pb(-1) integrated luminosity,
we determine the following upper limits (90% confidence level) to the produ
ct of the branching ratios for a resonance mass in the region 3575-3660 MeV
/c(2): Br(eta'(c)-->(p) over barp) x Br(eta'(c)--> gamma gamma)< 12.0x10(-8
) for <Gamma>= 5 MeV; <5.9x 10(-8) for <Gamma> =10 MeV; <4.8x 10(-8) for <G
amma> = 15 MeV. Combiing the present data with those of the predecessor exp
eriment, E760, the upper limits become 8.0x10(-8), 5.0x10(-8), and 4.5x10(-
8), respectively. In the restricted region 3589-3599 MeV/c(2), where a cand
idate was reported by the Crystal Ball experiment, we obtain the following
limits from the combined E760-E835 experiments: Br(eta'(c)-->(p) over barp)
x Br(eta'(c)--> gamma gamma)<5.6x10(-8) for <Gamma>=5 MeV; <3.7x10(-8) for
<Gamma> = 8 MeV. A comparison of these with other experimental results is
presented.