  It is shown that an account for the final-state interaction of real or
virtual nucleon and antinucleon produced in the processes $J/\psi\to
p\bar{p}\gamma$, $\psi(2S)\to p\bar{p}\gamma$, $J/\psi\to p\bar{p}\omega$, and
$J/\psi\to3\left(\pi^{+}\pi^{-}\right)\gamma$ near the threshold of $N\bar{N}$
pair production allows one to obtain self-consistent description of these
processes. Predictions of our model are in good agreement with experimental
data available. The proposed potential model also reproduces the corresponding
partial cross sections of $p\bar{p}$ scattering.
