  We study the J/Psi production from nuclei near the kinematic threshold within
the collision model, based on the nuclear spectral function, for incoherent
primary proton-nucleon charmonium creation processes. The model takes into
account the initial proton and final J/Psi absorption, target nucleon binding
and Fermi motion, the formation length of J/Psi mesons as well as the effect of
their nuclear mean-field potential on these processes. We calculate the A
dependences of the absolute and relative (transparency ratio) charmonium yields
as well as its excitation function within the different scenarios for the
J/PsiN absorption cross section, for the J/Psi formation length and for J/Psi
in-medium modification. We demonstrate that the former observables, on the one
hand, are not practically affected by the charmonium formation length effects
and, on the other hand, they are appreciably sensitive to the genuine J/PsiN
absorption cross section at beam energies of interest, which means that these
observables can be useful to help determine the above cross section from the
comparison of the results of our calculations with the future data from the CBM
experiment at FAIR-the upcoming accelerator facility at GSI-Darmstadt, Germany.
We also show that the excitation function for J/Psi subthreshold production in
pA reactions reveals some sensitivity to adopted its in-medium modification
scenarios. Therefore, such observable may be an important tool to get valuable
information on the charmonium in-medium properties.

Nuclear Theory;High Energy Physics - Phenomenology;Nuclear Experiment