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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 withthe help of the $N\bar{N}$ optical potential. The same calculations are madefor the decays of $\psi(2S)$. We use the potential which has been suggested tofit the cross sections of $N\bar{N}$ scattering together with $N\bar{N}$ andsix pion production in $e^{+}e^{-}$ annihilation close to the $p\bar{p}$threshold. The $p\bar{p}$ invariant mass spectra is in agreement with theavailable experimental data. The anisotropy of the angular distributions, whichappears due to the tensor forces in the $N\bar{N}$ interaction, is predictedclose to the $p\bar{p}$ threshold. This anisotropy is large enough to beinvestigated experimentally. Such measurements would allow one to check theaccuracy of the model of $N\bar{N}$ interaction.

Angular distributions in $J/\psi\to p\bar{p}\pi^{0}(\eta)$ decays