  Charmonium production and suppression in In+In and Pb+Pb reactions at SPS
energies is investigated with the HSD transport approach within the 'hadronic
comover model' as well as the 'QGP threshold scenario'. The results of the
transport calculations for J/Psi suppression and the Psi prime to J/Psi ratio
are compared with the recent data of the NA50 and NA60 Collaborations. We find
that the comover absorption model - with a single parameter |M_0|^2 for the
matrix element squared for charmonium-meson dissociation - performs best with
respect to all data sets. The 'threshold scenario' - within different
assumptions for the melting energy densities - yields a reasonable suppression
for J/Psi but fails in reproducing the Psi prime to J/Psi ratio for Pb+Pb at
158 A GeV. Predictions for Au+Au reactions are presented for a bombarding
energy of 25 A GeV in the different scenarios which will allow for a clear
distinction between the models from the experimental side at the future FAIR
facility.
