A mechanism for the effective dissociation of a cc̅ 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/ψ suppressions in minimum bias pA, AB (with light projectile), and Pb + Pb

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... isions at 200 A GeV/c. However the impact parameter (E_T) dependence of the J/ψ 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/ψ suppressions in minimum bias pA, AB, and Pb + Pb collisions and the E_T dependence of the J/ψ suppression factor are better reproduced.