A self-consistent field scattering theory and weak asymptotic conditions

A fully self-consistent field (SCF) theory of many-particle collisions attempts to treat both the target and scattering arbitals on an equal footing, by simultaneously determining them, all self-consistently. It necessarily results in relaxation of the exact asymptotic boundary condition, because the SCF target orbitals are approximate and depend on the collision energy. Thus the original scattering problem is modified by this weak asymptotic condition (WAC) in the most fundamental was and the validity of the theory depends on multiconfiguration mixing to restore the condition. We show by extensive numerical calculations that, as more configurations are mixed, the solution converges to the correct limit. The theory is then applied to the positron-helium and electron-helium scattering systems, where the helium target functions are determined self consistently, as a part of the overall solution of the collision problem. The result shows that the weak condition is sufficient in providing physically acceptable target functions.