  The energy dependence of the cross sections of $p\bar p$, $n\bar n$, and
meson production in $e^+e^-$ annihilation in the vicinity of the $p\bar p$ and
$n\bar n$ thresholds is studied. The proton-neutron mass difference and the
$p\bar p$ Coulomb interaction are taken into account. The values of the cross
sections are very sensitive to the parameters of the optical potential. It is
shown that the commonly accepted factorization approach for the account of the
Coulomb interaction does not work well enough in the vicinity of the threshold
due to the finite size of the optical potential well.
