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The differential cross section dsigma/dt of elastic photoproduction of J/Psi at different gamma p center of mass energies W are used to determine the properties of the exchanged trajectory in the reaction gamma p --> J/Psi p. In the region |t| < 1 GeV^2, the resulting trajectory is alpha(t) = (1.153 \pm 0.027) + (-0.001 \pm 0.072)t. The vanishing value of the slope of the trajectory is an experimental evidence for no shrinkage and thus for the perturbative nature of the exchange.

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