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The convergence of the eigenchannel (EK) and R-matrix (RM) theories - depending on their free parameters - is numerically investigated by comparing with a simple, analytically solvable model. The comparison shows that the results of the EK-theory are in general closer to the exact solution than those of the RM-theory. Especially in regions of sharp resonances the dependence of the expansion of the wave functions on the interaction radius ac and on the boundary condition Bc is very strong in the RM-theory and one needs very many levels to achieve good results.
A scattering theory for reactions with three-particle channels above the two-particle threshold is developed. The S-matrix-technique is used for the calculation of the extended S-matrix. Correlated two-particle wave functions in the exit channels are employed to describe the exact two-particle continuum. For the usual shell model only a few partial waves dominate. The cross section depends on the energy-distribution between the two outgoing nucleons. Numerical results are presented for the model (d, 2n)-reaction exciting 0+ -states in O16 without Coulomb-effects. The treatment is restricted to three (2p2h)-states with the particles in the (sd)-shell and holes in the p-shell.