Search

We study the formal structure of the influence of channel coupling on near- and sub-barrier fusion. The reduction to a one-channel description is studied, with emphasis on the channel-coupling effects being manifest primarily as an energy dependence (the “threshold anomaly”) of the real nuclear potential. The relation to the barrier penetration model is examined critically. The results of large-scale coupled-channel calculations are used as “data” to illustrate the discussion. Particular emphasis is placed on the importance of reproducing correctly the partial-wave (or “spin”) distributions. The simple barrier penetration model is found to be adequate to exhibit the strong enhancements due to channel couplings when the threshold anomaly is taken into account, although there may be important corrections due to the long-ranged peripheral absorption, especially from Coulomb excitation.

We consider the amplitudes for reactions between any two clusters with a total number of N particles. Assuming simple analytic structure for partial wave amplitudes one may write down ND −1 equations embodying those properties. Those equations describe a channel coupling which preserves two-cluster unitarity. Three-cluster unitarity is treated approximately while fragmentation into more than three clusters is neglected altogether. Driving terms of, in general, longest range are constructed from one-cluster exchange amplitudes with dressed vertex functions. In some cases it may be necessary to include repetitions of the same (triangular graphs) when these exchanges turn out to have ranges comparable to one-cluster exchanges. Amplitudes for the latter can be given for the most general spin configuration, thus doing away completely with the geometry of channel coupling. The dynamics then resides in the vertex functions and we discuss methods to derive those functions from nuclear models or from scattering data. It is further shown that the antisymmetrization problem can be solved whatever the reaction will be. We conclude with a summary of the program, a listing of the obtainable information, and finally attempt a comparison with other dispersion approaches and existing reaction theories.

If open channels are strongly coupled by direct reactions, the traditional Hauser-Feshbach method of calculating fluctuation cross sections is invalid, because of non-statistical correlations which the direct channel-coupling induces between resonance partial widths in different channels. The fluctuation cross sections can still be computed from the optical S-matrix elements, however, and the formulas necessary for doing so are obtained here with the aid of an “optical background” representation of the full S-matrix. The resulting compound-elastic cross section is increased over the Hauser-Feshbach expression by a factor of 2(Γ ⪢ D) or 3(Γ ⪡ D) in the large-N limit, and compound-reaction cross sections are increased by roughly a factor of (N + 1) N , where N is the number of directly-coupled open channels.