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On the basis of perturbative QCD and the relativistic quark model wecalculate relativistic and bound state corrections in the production processesof a pair of S-wave and P-wave charmonium states. Relativistic factors in theproduction amplitude connected with the relative motion of heavy quarks and thetransformation law of the bound state wave function to the reference frame ofthe moving S- and P-wave mesons are taken into account. For the gluon and quarkpropagators entering the production vertex function we use a truncatedexpansion in the ratio of the relative quark momenta to the center-of-massenergy $\sqrt{s}$ up to the second order. The exact relativistic treatment ofthe wave functions makes all such second order terms convergent, thus allowingthe reliable calculation of their contributions to the production crosssection. Relativistic corrections to the quark bound state wave functions inthe rest frame are considered by means of the Breit-like potential. It turnsout that the examined effects change essentially the nonrelativistic results ofthe cross section for the reaction $e^++e^-\to J/\Psi(\eta_c)+\chi_{cJ}(h_c)$at the center-of-mass energy $\sqrt{s}=10.6$ GeV.

Relativistic effects in the double S- and P-wave charmonium production in e^+e^- annihilation