Self-consistent field theory of collisions I. Scattering channels

Abstract

The conventional Hartree and Hartree-Fock approaches for treating many-electron bound systems have been extended recently to positive energy scattering problems, in which both the bound and continuum orbitals are determined by the requirement of full self-consistency. Serious consequences of such a theory are that the target orbitals become energy dependent and the asymptotic boundary conditions are satisfied only approximately, in lowest order. It is important therefore to test the theory for its convergence under configuration mixing. This self-consistent field (SCF) theory for scattering has been tested here for scattering from hydrogenic target as a model where the target function is determined dynamically. Penetration of the projectile inside the bound target orbital is manifest through the SCF for the bound state. Our results show that the theory converges to the correct amplitudes and to the exact boundary conditions as more configurations are added. The use of the amputated functions and the weak asymptotic condition (WAC) upon which the SCF theory is based, is justified as the WAC converges to the correct limit. It is then applied to the positron-helium and electron-helium scattering systems where the helium function is calculated simultaneously together with the scattering function. The resulting phase shifts and the SCF target functions are compared with those obtained with the pre-determined target functions in the conventional approaches.PACS. 34.10.+x General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.) -31.10.+z Theory of electronic structure, electronic transitions, and chemical binding -24.10.-i Nuclear-reaction models and methods

Self-Consistent Field Theory of Ionization Collisions

“…It is termed a generalized Hartree-Fock theory (GHF). The theory was tested for its validity and applicability [18] [19] as it was successfully applied to the positron-hydrogen and electron-hydrogen scattering systems, and further extended to the positron-helium and electron-helium scattering systems, where the exact target functions are not known. In fact both the scattering and target functions are simultaneously determined self-consistently by the theory.…”