  The production of the charmonium states in proton-antiproton experiments is
considered at the energy rates near threshold in NLO. Such a consideration
allows one to obtain non zero distributions over the transverse momentum of the
final charmonium and gives a natural explanation to the existence of
$\chi_{c1}$-meson in final state, that is observed experimentally and cannot be
produced in leading order processes. The crucial role of scale parameter choice
in $\alpha_s (Q^2)$ and partonic distributions $f(x,Q^2)$ shown, and the
correct choice offered.
