We present a semi-empirical scaling law for non-resonant ion-atom single charge exchange cross sections for collisions with velocities from 10 to 10 cm s 7 9 1and ions with positive charge q 8 < . Non-resonant cross sections tend to have a velocity peak at collision velocities v 1 au  with exponential decay around this peak. We construct a scaling formula for the location of this peak then choose a functional form for the cross section curve and scale it. The velocity at which the cross section peaks, v m , is proportional to the energy defect of the collision, E D , which we predict with the decay approximation. The value of the cross section maximum is proportional to the charge state q, inversely proportional to the target ionization energy I T , and inversely proportional to v m . For the shape of the cross section curve, we use a function that decays exponentially asymptotically at high and low velocities. We scale this function with parameters v I Z Z , , , and m T T P , where the Z T,P are the target and projectile atomic numbers. For the more than 100 cross section curves that we use to find the scaling rules, the scaling law predicts cross sections within a little over a factor of 2 on average.

We present an extension of the classical overbarrier model [F. Sattin, Phys. Rev. A 62, 042711 (2000)] to include the effect of electron back-capture. Back-capture is the process by which an electron that has already been captured by the projectile ion is recaptured by the target atom. Back-capture reduces the electron capture cross section at low impact velocities when the projectile ionization energy is less than that of the target. This creates a cross section peak. We alter the location of this peak to correspond to that predicted by an adiabatic criterion by using a free parameter of the model. These extensions bring the overbarrier model more in line with experimental data, especially at low impact velocity.

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