Approximate wave functions for two electrons in the continuum of a Coulomb charge

Abstract

The outgoing scattering state describing two electrons in the continuum of a Coulomb charge is investigated. Boundary, simple, and double conditions are used to construct ab initio wave functions. Simple conditions describe the limits when the Coulomb charges are switched off, and double conditions take into account the cases when two out of three particles are close and have low relative velocity. A base to expand the double continuum---here called the $\ensuremath{\Lambda}$ base---is introduced. All the components of the three-body wave function in this base have the appropriate Coulomb conditions and are versatile enough to build up simple as well as double conditions.