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A realistic microscopically-based quantum approach to the competition betweenfusion and quasi-fission in a heavy fusing system is applied to severalreactions leading to $^{256}$No. Fusion and quasi-fission are described interms of a diffusion process of nuclear shapes through a dynamical collectivepotential energy landscape which is initially diabatic and gradually becomesadiabatic. The microscopic ingredients of the theory are obtained with arealistic two-center shell model based on Woods-Saxon potentials. The resultsindicate that (i) the diabatic effects play a very important role in the onsetof fusion hindrance for heavy systems, and (ii) very asymmetric reactionsinduced by closed shell nuclei seem to be the best suited to synthesize theheaviest compound nuclei.Comment: 6 pages, 5 figures, To be published in the AIP Proceedings of  FUSION06, International Conference on Reaction Mechanisms and Nuclear  Structure at the Coulomb barrier, March 19-23, 2006, San Servolo (Venice),  Ital

Dynamical Collective Potential Energy Landscape: Its Impact on the Competition Between Fusion and Quasi-fission in a Heavy Fusing System