The J/\Psi(1S) and \Psi'(2S) production near threshold in antiproton-nucleus reactions is calculated on the basis of the Glauber model. The model takes into account the antiproton (pre)absorption, proton Fermi motion, and charmonium formation length. We confirm earlier prediction that the charmonium production in $\bar pA$ collisions at $p_{lab}=3-10$ GeV/c is not influenced by formation length effects and is very well suited to determine the genuine charmonium-nucleon dissociation cross sections. The comparison is performed with the J/\Psi photoproduction at high energies, where formation length effects play a very important role. However, we demonstrate that the detailed structure of the proton and neutron density profiles has to be taken into account, if one wants to extract information on the J/\Psi N dissociation cross section from J/\Psi transparency ratios. These studies are relevant for the upcoming PANDA experiment at FAIR.
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