Near-barrier fusion of heavy nuclei. Coupling of the channels

The problem of quantum description of near-barrier fusion of heavy nuclei taking place under strong coupling of relative motion with rotation of deformed nuclei and with dynamic deformations of their surfaces is studied. A new effective method is proposed for numerical solution of a set of coupled Schroedinger equations with boundary conditions corresponding to a full absorption of the flux penetrated through the multi-dimensional coulomb barrier. The method has no limitation on the number of coupled channels and allows one to calculate fusion cross sections of very heavy nuclei used for synthesis of super-heavy elements. A combined analysis of the multi-dimensional potential energy surface relief and the multi-channel wave function in the vicinity of the Coulomb barrier gives a clear interpretation of near-barrier fusion dynamics. Comparison with experimental data and with semi-empirical model calculations is performed. The computing codes are allocated at the web-server http://nrv.jinr.ru/nrv/ with free access. (author)