Generalized Hartree and Hartree - Fock approaches for atomic collisions

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Abstract
The conventional Hartree and Hartree - Fock approaches for treating many-electron bound systems are extended to positive-energy scattering problems, in which both the bound and continuum orbitals are determined by the requirement of self-consistency. This new formulation is made possible by: (i) the use of square-integrable functions associated with the scattering wavefunction and (ii) relaxation of the asymptotic boundary conditions. Unlike in the existing approaches for scattering of atoms and molecules, the theory treats both the bound target states and the scattering orbitals on an equal footing, and improves them systematically via configuration interaction. This feature is appropriate for scattering by targets with more than one electron, where the precise target functions are not known. As a first test case, the theory is illustrated by applying it to the simple positron - hydrogen scattering. It is shown that the self-consistent mean field for the target electron behaves asymptotically as an attractive Coulomb potential of twice the strength of the proton; this is caused by the positron penetrating the electron orbital during the collision. Generally, the phase shift is much larger than that obtained in the static and all-s approximations. Potential applications of this generalization are discussed, including a weighted projection for coupled equations.