Semi-empirical scaling for ion–atom single charge exchange cross sections in the intermediate velocity regime

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We present a semi-empirical scaling law for non-resonant ion–atom single charge exchange cross sections for collisions with velocities from and ions with positive charge . Non-resonant cross sections tend to have a velocity peak at collision velocities 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, vm, is proportional to the energy defect of the collision, , 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 IT, and inversely proportional to vm. 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 , where the 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.