  The $p\bar{p}$ invariant mass spectra of the processes $J/\psi\to
p\bar{p}\omega$, $J/\psi\to p\bar{p}\rho$, and $J/\psi\to p\bar{p}\gamma$ close
to the $p\bar{p}$ threshold are calculated by means of the $N\bar{N}$ optical
potential. The potential model for $N\bar{N}$ interaction in the $^{1}S_{0}$
state is proposed. The parameters of the model are obtained by fitting the
cross section of $N\bar{N}$ scattering together with the $p\bar{p}$ invariant
mass spectra of the $J/\psi$ decays. Good agreement with the available
experimental data is achieved. Using our potential and the Green's function
approach we also describe the peak in the $\eta'\pi^{+}\pi^{-}$ invariant mass
spectrum in the decay $J/\psi\to\gamma\eta'\pi^{+}\pi^{-}$ in the energy region
near the $N\bar{N}$ threshold.
