  A mechanism for the effective dissociation of a $c\bar{c}$ pair in the colour
electric field of strings is introduced into a hadron and string cascade model,
i.e. JPCIAE, which is based on the LUND model, simulating ultra-relativistic
nucleus - nucleus collisions. This new mechanism together with the known
mechanism of nuclear absorption (both baryons and mesons) could reproduce
fairly the data of the normal and anomalous $J/\psi$ suppressions in minimum
bias pA, AB (with light projectile), and Pb + Pb collisions at 200 A GeV/c.
However the impact parameter (E_T) dependence of the $J/\psi$ suppression
factor, both, in S + U and Pb + Pb reactions at 200 A GeV/c and 158 A GeV/c,
respectively, is not well reproduced. We also tested the additional mechanism
of the energy degradation of leading particles, with which both, the normal and
anomalous $J/\psi$ suppressions in minimum bias pA, AB, and Pb + Pb collisions
and the E_T dependence of the $J/\psi$ suppression factor are better
reproduced.
