Two-level model for inner-shell excitation: Effect of translation factors

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Abstract
An analytic model is derived for long-range coupling in inner-shell excitation processes of ion-atom collisions using a two-state wave function with Bates and McCarroll translation factors. The result we derive for the sharing ratio reduces to the Demkov result in the low-velocity limit. At higher velocities, we predict a sharing ratio which drops below the Demkov curve. As the velocity increases, a maximum is reached and the sharing ratio then decreases with further increase in velocity. Numerical calculations using translation factors in a molecular orbital basis have shown such a falloff. The effect has been previously attributed to phasing between interaction regions due to a multistate configuration. We show that the effect is due to the inclusion of translation factors. The modification we derive to the analytic model of Demkov resolves discrepancies with the experimental data which were previously attributed to fluorescence yield problems. In addition, we find that without making adiabatic assumptions in treating the solutions of the equations of motion, we can recover the exact Born result in the high-velocity limit.