Near-barrier fusion of heavy nuclei: Coupling of channels

The problem of a quantum-mechanical description of a near-barrier fusion of heavy nuclei that occurs under the conditions of a strong coupling of their relative motion to the rotation of deformed nuclei and to a dynamical deformation of their surfaces is studied. A new efficient method is proposed for numerically solving coupled Schrdinger equations with boundary conditions corresponding to a total absorption of the flux that has overcome a multidimensional Coulomb barrier. The new method involves no limitations on the number of channels that are taken into account and makes it possible to calculate cross sections for the fusion of very heavy nuclei that are used in the synthesis of superheavy elements. A global analysis of the relief of the multidimensional potential surface and of the multichannel wave function in the vicinity of the Coulomb barrier provides a clear interpretation of the dynamics of near-barrier nuclear fusion. A comparison with experimental data and with the results produced by the semiempirical model for taking into account the coupling of channels is performed.