Simple models for the energy loss

The coupled-channel calculations are used as benchmark results to check simple models of the impact parameter dependence of the electronic energy loss. A detailed description of such models (convolution approximation) may be found elsewhere [25,26]. Here we present only a short outline of the method. The electronic energy loss involves a sum over all final target states for each impact parameter. Usually this demands a computational effort that precludes its direct calculation in 

In recent works [25] we have proposed a simple formula for Q(Jy) (called PC A) that virtually reproduces SCA results for all impact parameters for bare and also for screened projectiles. 

the even orders of an Zp expansion, as included in the unitary convolution approximation (UCA), dominate the non-perturbative efifects. The present UCA results are plotted as a solid curve. This curve lies close to the average of the AO results for particles and antiparticles. Hence, although the present UCA does not include sign-of-charge efifects it perfectly describes the majority of the energy transfer processes (dominated by ionization) of fast heavy particles at small impact parameters. 

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