Semi-empirical scaling for ion–atom single charge exchange cross sections in the intermediate velocity regime. (11th May 2017) - Friedman, B; DuCharme, G
Abstract: We present a semi-empirical scaling law for non-resonant ion–atom single charge exchange cross sections for collisions with velocities from 10 7 t o 10 9 cm s − 1 and ions with positive charge q < 8 . Non-resonant cross sections tend to have a velocity peak at collision velocities v ≲ 1 a u 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, Δ E, 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 m, I T, Z T, and Z 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.