L2discretization and complex coordinates in the calculation of bound-free amplitudes in the presence of long-range forces

The formalism of Møller wave operators is shown to provide a stable basis for computation of bound-free transition amplitudes for both short- and long-range potentials without the direct calculation of scattering wave functions. This method, which relies on the techniques of expansion in finite $L^2$ bases and rotation of the coordinates into the complex plane, is applied to both an exponential potential and one that behaves asymptotically as $-\frac{1}{r^4}$. It is demonstrated that one obtains not only accurate magnitudes of the matrix elements, but accurate phases (i.e., the scattering phase shift) as well. Some relevant theoretical results with regard to the application of wave operators are also presented. Although couched in terms of potential scattering, the procedures are readily extendible to multichannel problems.