Convolution approximation for the energy loss, ionization probability and straggling of fast ions

In this work we describe an extension of the convolution approximation for the ionization probability and energy-loss straggling as a function of the impact parameter for swift ions. Analytical formulas for these quantities are derived and compared to full first-order Born calculations. The physical inputs of the model are the electron density and oscillators strengths of the target as well as the screening function of the projectile (in the case of dressed ions). A very good agreement is obtained for all impact parameters. In addition, we propose a general schema to add contributions from distant and close collisions. In this way physical processes arising from large and small impact parameters can be easily included into a single expression valid for all impact parameters. This model is then used to investigate the projectile-charge q dependence of ionization, stopping and straggling cross-sections.