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Inelastic photoproduction of J/ψ particles at high energies is one of the processes to determine the gluon distribution in the nucleon. We have calculated the QCD radiative corrections to the color-singlet model of this reaction. They are large at moderate photon energies, but decrease with increasing energies. The cross section and the J/ψ energy spectrum are compared with the available fixed-target photoproduction data and predictions are given for the HERA energy range. * Supported in part by Deutsche Forschungsgemeinschaft DFG † Present address: Deutsches Elektronen-Synchrotron DESY,

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