The coupled-channel calculation of the particle emission rates for deformed nuclei

We propose a model, theoretical and mathematical formalism and computational methods necessary for low energy resonant scattering analysis of deformed nuclei and show how the model works for α-decay. We will review some of the recent advances in both structure and dynamics of superheavy elements (SHE) focusing on the issues currently of interest along with possible direct applications to resonant particle spectroscopy technique in next experimental studies of clustering and decaying phenomena. Emission rates and 'fine structure' intensity patterns are calculated and compared to experiment and previous estimations. Extensions and applications of the model to new phenomena like subbarrier fusion, quasifission, formation of nuclear molecules, decay of dinuclear system are also discussed. Some predictions are made for the α half-lives of possible new deformed superheavy elements. The procedure may be useful for designing the resonant particle spectroscopy technique in next experimental studies of clustering and decaying phenomena involving the radioactive states (usually produced by a nuclear reaction or by decay from other nuclei). The solution of coupled equations is obtained by a direct numerical integration using step-by-step methods. However, in the case of large number of channels the solution remains a very difficult and time-consuming operation, and therefore it is of major interest to find the most efficient methods of integration. Some variants of the Gordon method are found to be most efficient for these problems. (authors)