We demonstrate that the array of techniques employing complex basis functions, which have been broadly applied in the calculation of resonance positions and lifetimes, can also be used, with appropriate modification, in the practical computation of photoionization cross sections and nonresonant scattering amplitudes. We illustrate a procedure with which controlled complex distortions over a localized region of the energy spectrum can be realized in a finite basis-set calculation. This technique is used to directly obtain scattering amplitudes for potentials which are not exponentially bounded at large distances, in contrast to complex scaling techniques which have been shown to be divergent in such cases. Four numerical examples are presented to exhibit the utility of the local complex distortion approach in calculations of photoionization cross sections and scattering amplitudes. We also discuss this approach in the context of variational principles for continuum amplitudes and in the context of applications to many-electron systems.

• Received 23 July 1984

DOI:https://doi.org/10.1103/PhysRevA.31.624