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Perturbation approximations for scattering amplitudes in ion-atom collisions.

Approximate amplitudes for excitation and electron capture in ion-atom collisions frequently employ plane waves of relative motion, even though it is known that higher-order terms in the formal expansion are frequently divergent when the fragments in the final state interact through long-range Coulomb interactions. The Coulomb-Born expansion is free of such divergences, but the higher-order terms are more difficult to evaluate than the corresponding terms with plane waves. We show how to use plane waves of relative motion without encountering divergent terms in higher order even with Coulomb potentials present. The procedures apply to several common expansions, but encounter conceptual difficulties when applied to multiple-scattering expansions.