Quantum mechanical potentials and inactive electron effects in charge exchange collisions

Scattering angle differential cross sections for the He⁺ + He single electron capture process are studied using plane wave Born approximation models for projectile energies between 180 keV and 1.89 MeV. Within this simplistic framework, we study the effects of the frozen core approximation by performing a full 5-Body calculation that explicitly includes all particles in the collision and comparing it with a single bound state model that neglects the bound electron in the projectile and a double bound state model that neglects the inactive electron in the target atom. Results are compared with experiment and we show that inclusion of the inactive electron in the perturbation potential is more important than inclusion in the wave functions. We also introduce a semi-quantum mechanical (SQM) perturbation potential that treats the atomic electrons as a quantum mechanical electron cloud rather than point particles. The SQM perturbation removes the deep, unphysical minimum that exists in cross sections calculated with Born-type models, but also has the effect of greatly reducing the magnitude of the small scattering angle cross sections.