One-Electron Model for Charge Exchange in Ion-Atom Collisions

In attempting to calculate cross sections for charge exchange in other than proton-hydrogen atom collisions, it has been common to simplify the system by assuming that only one active electron is moving in the field of two ions. With this one-electron approximation, the extensive formalism developed to treat proton-hydrogen atom collisions has then been applied. It is shown that the use of some common one-electron orbitals in such a formalism can destroy either the ability to interpret the expansion coefficients as transition amplitudes, or probability conservation. In this work, a one-electron model Hamiltonian and corresponding expansion functions are proposed by which the physical system is more accurately described. With this model it is shown that physically acceptable transition amplitudes can be calculated, probability is conserved, and the principle of microreversibility is satisfied.