  The differential decay rates of the processes $J/\psi\to p\bar{p}\pi^{0}$ and
$J/\psi\to p\bar{p}\eta$ close to the $p\bar{p}$ threshold are calculated with
the help of the $N\bar{N}$ optical potential. The same calculations are made
for the decays of $\psi(2S)$. We use the potential which has been suggested to
fit the cross sections of $N\bar{N}$ scattering together with $N\bar{N}$ and
six pion production in $e^{+}e^{-}$ annihilation close to the $p\bar{p}$
threshold. The $p\bar{p}$ invariant mass spectra is in agreement with the
available experimental data. The anisotropy of the angular distributions, which
appears due to the tensor forces in the $N\bar{N}$ interaction, is predicted
close to the $p\bar{p}$ threshold. This anisotropy is large enough to be
investigated experimentally. Such measurements would allow one to check the
accuracy of the model of $N\bar{N}$ interaction.
