We investigate the quasi-fission reactions in the basis on the Stochastic Mean-Filed (SMF) approach that provides a microscopic and quantal description of the multi-nucleon exchange mechanism. In deep-inelastic heavy-ion collisions, colliding ions stick and move together for a long time. During this contact time many nucleons exchange between projectile and target nuclei, and the composite system then separate in two main primary fragments without forming a compound nucleus. Quasi-fission is a non-compound nuclear process in deep-inelastic heavy-ion collisions and the multi-nucleon exchange mechanism in the quasi-fission reactions is important. We calculate the quantal transport coefficients for heavy-ion collisions at bombarding energies below their fusion barriers and determine the primary fragment mass distributions. Quantal calculations are compared with the experimental data.
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