The dependence of the anomalous $J/\psi$ suppression on the number of participant nucleons

The observation of an anomalous J/$\psi$ suppression in Pb-Pb collisions by the NA50 collaboration can be considered as the most striking indication for the deconfinement of quarks and gluons at SPS energies. In this letter, we determine the J/$\psi$ suppression pattern as a function of the forward hadronic energy $E_{ZDC}$ measured in a Zero Degree Calorimeter (ZDC). The direct connection between $E_{ZDC}$ and the geometry of the collision allows us to calculate, within a Glauber approach, the precise relation between the number of participant nucleons $N_{part}$ and $E_{ZDC}$. Then, we check if the experimental data can be better explained by a sudden or a smooth onset of the anomalous J/$\psi$ suppression as a function of the number of participants.