We present predictions for the exclusive and dissociative production of vector mesons off protons in an electron-ion collider. The computation is based on the energy-dependent hot spot model that has successfully described the available photoproduction data. We find that the model also describes correctly all available electroproduction data. In addition, we find that the cross section for dissociative production as a function of the center-of-mass energy of the photon-proton system has a maximum, whose position depends on the virtuality of the photon and the mass of the vector meson. We use these maxima to define a geometrical saturation scale and find that it grows linearly with energy as a function of the scale of the process. This phenomenon can be studied at the proposed electron-ion colliders, JLEIC, eRHIC and LHeC.
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