Method of Effective Potentials: Scattering of Positrons and Electrons by Light Atoms

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Abstract
The theory of effective potentials is developed in a way which lends itself to variational formulations. The positron-helium and electron-helium systems are chosen to illustrate the method. The effective potential is defined in terms of the resolvent operator for a system which has been modified by removal of the open-channel states. Rigorous maximum and minimum principles are derived which should be useful in the computation of the effective potential and which are valid, for sufficiently low energies, even when the target bound-state wave function is not known exactly. A numerical application of this method to positron-hydrogen scattering has been made and results are reported. The effective-potential approach to the scattering problem leads naturally to a model for resonance calculations. This model is reviewed here and formulated variationally. An Appendix is devoted to further elaboration of this approach to resonance calculations in the context of potential scattering, with the aid of Jost-function theory.