Abstract
This lecture introduces a simplified single-pole approximation (SSPA) for calculating the inelastic mean free path (IMFP) of electrons in surface electron spectroscopy. The SSPA is a further simplification of Penn’s single-pole approximation (SPA), in which the dispersion relation is expressed in a quadratic form with a single adjustable parameter. By optimizing this parameter, the accuracy of the IMFP can be improved while maintaining computational simplicity. IMFPs calculated using the SSPA were evaluated for 41 elemental solids and compared with results from the full Penn algorithm (FPA) and the original SPA. The SSPA demonstrated good agreement with the FPA across the 300 eV to 10 keV energy range. In particular, the optimized SSPA, employing a dispersion coefficient of 0.4167, yielded relative deviations within 3% of the FPA results, confirming its practical utility. This lecture also provides a detailed explanation of the Mathematica implementation of the SSPA-based IMFP calculation, including procedures for dispersion parameter optimization. These descriptions aim to ensure reproducibility and facilitate further applications in surface electron spectroscopy.
https://ror.org/026v1ze26 
