The dynamical hindrance of fusion after the system of two colliding nuclei overcomes the Coulomb barrier is calculated. Langevin equations, in which the stochastic white noise is added to the conservative and dissipative forces, are solved in the multidimensional space. It is shown that in case of very heavy systems the dynamical trajectories lead from the Coulomb barrier towards the fission valley at locations rather outside the saddle point and then turn downward to scission. Only due to fluctuations a small fraction of trajectories can overcome the saddle point and lead to fusion. Fusion probabilities determined by the ratio of fusion-to-scission fluxes are calculated. In cold fusion reactions induced by different projectiles on 208 Pb and 209 Bi targets, the fusion probability drops down by almost ten orders of magnitude for a range of projectiles from 48 Ca (Zcn = 102) to 86 Kr (Zcn = 118).
Quantum Surface Friction Model for Fusion Reactions around the Coulomb Barrier
