A self-consistent field scattering theory and weak asymptotic conditions

A fully self-consistent field (SCF) theory of many-particle collisions atte mpts to treat both the target and scattering orbitals on an equal footing, by simultaneously determining them, all self-consistently. It necessarily r esults in relaxation of the exact asymptotic boundary condition, because th e SCF target orbitals are approximate and depend on the collision energy. T hus the original scattering problem is modified by this weak asymptotic con dition (WAC) in the most fundamental way, and the validity of the theory de pends on multiconfiguration mixing to restore the condition. We show by ext ensive numerical calculations that, as more configurations are mixed, the s olution converges to the correct limit. The theory is then applied to the p ositron-helium and electron-helium scattering systems, where the helium tar get functions are determined self-consistently, as a part of the overall so lution of the collision problem. The result shows that the weak condition i s sufficient in providing physically acceptable target functions. (C) 1999 Published by Elsevier Science B.V.