Self-consistent field theory of collisions I. Scattering channels

The conventional Hartree and Hartree-Fock approaches for tr eating many-ele ctron bound systems have been extended recently to positive energy scatteri ng 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 asympt otic boundary conditions are satisfied only approximately, in lowest order, It is important therefore to test the theory for its convergence under con figuration 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 projecti le inside the bound target orbital is manifest through the SCF for the boun d state. Our results show that the theory converges to the correct amplitud es and to the exact boundary conditions as more configurations are added. T he use of the amputated functions and the weak asymptotic condition (WAC) u pon 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-heli um scattering systems where the helium function is calculated simultaneousl y together with the scattering function. The resulting phase shifts and the SCF target functions are compared with those obtained with the pre-determi ned target functions in the conventional approaches.