CONVOLUTION APPROXIMATION options

In order to access this option you should select the EXPERT OPTIONS sheet (close to the upper left corner of the main program window).

The PCA option is designed mainly for specific theoretical investigations, whereas the UCA option should be used for comparison with experimental data.

Choose PCA, to select the perturbative convolution approximation. For intermediate to high projectile velocities, the corresponding results are very close to results from exact calculations within 1st order perturbation theory.* Different forms or names for the 1st order perturbation theory are the Bethe theory (the well-known simple Bethe formula, is valid only at asymptotically high velocities and somewhat less accurate than the PCA model), 1st Born approximation, plane-wave Born approximation (PWBA), and the so-called semi-classical approximation (SCA). Note that only the latter yields directly impact-parameter dependencies (SCA results are similar to the PCA results).

Choose UCA, to select the unitary convolution approximation. The UCA model is appropriate for fast light ions and even for fast heavy ions. Although some approximations are involved in the UCA, the corresponding results seem to be more accurate for heavy ions than exact classical-trajectory Monte Carlo results for S_e as well as for Q(b). So far, only complex and time-consuming quantum calculations (AO coupled-channel model and CDW-EIS model) seem to provide more accurate Q(b) results for fast heavy ions on an ab initio basis, in comparison with the current code. For these fast ions the accuracy of the current S_e results is comparable with some fits to experimental data, as used, e.g., in the Ziegler-Biersack-Littmark code TRIM or SRIM.

For intermediate to high projectile velocities, the corresponding integrated results S_e are very close to results from the Bloch theory, which accounts for the motion of electron wavepackets at high energy transfers.*

* for comparisons, see the original references