Self-Consistent Solutions for the Scattering State with Two Free Electrons

Wave functions for the scattering states with two free electrons in the field of an ion core are explicitly calculated by the self-consistent, continuum Hartree-Fock (CHF) theory. Typically, such states are associated with the three-body recombination, collisional ionization and photo-double ionization, but have never been directly studied previously. The calculated continuum orbitals are found to be predominantly of the plane-wave forms, as though the system is translation invariant, in the context of many-body HF theory. The symmetry is mildly broken by the presence of the core ion, at about fifteen-percents level, indicating that the orbitals are largely delocalized and the effect of the core potential is an important but minor perturbation. The properties of channel orthogonality and completeness are preserved by the nearly plane wave forms. To test the validity of this finding and the CHF, the continuum orbitals are used to evaluate the amplitudes for the electron impact ionization, and the amputation procedure, that is crucial in the theory, is also critically re-examined.