By use of the universal scattering cross section derived by Lindhard et al., the velocity of an ion in a scattering medium is calculated as a function of time. The effect of both electronic and atomic collisions is included. In addition, the average scattering angle (in the lab system) resulting from multiple atomic collisions is derived. It is shown that in most cases the attenuation of the Doppler shift as a result of the changed direction of the scattered nucleus is more important than the effect of slowing down due to atomic collisions. In fact, at low velocities and for heavy scatterers the change in the direction of motion is the dominating factor. The results are given in a form amenable to numerical analysis. In the limiting cases of (i) very short lifetimes and (ii) predominantly electronic scattering, the average Doppler shifts are given in an analytical form.
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