Distorted-wave theory of multistep processes

The theory of multistep processes based upon the distorted-wave Born approximation as a leading term is investigated. Iterative procedures in which the many-body Green's operator for the complete system is replaced by a non-Hermitian or optical Green's operator are shown to have some unappealing features. Alternative procedures using a nonlinear form of the distorted transition matrix equation, corresponding to a dispersion-theory approach, are discussed and appear to provide a more consistent iterative procedure. A generalized optical theorem is derived and used to sum the multistep amplitudes which conserve energy. The summed result shows that the normal distorted-wave matrix element should be replaced by a modified leading term unless the absorption in initial and final states is weak. Difficulties with the theory involving multistep amplitudes off the energy shell and a new calculable form for two-step processes are suggested.