Series representation of differential elastic scattering cross section for electrons: Applications in theoretical models of electron transport in condensed matter
Quantitative applications of surface sensitive electron spectroscopies require availability of reliable theoretical models describing electron transport in the surface region of solids. An important effect to be accounted for in these models is the phenomenon of elastic scattering of signal electrons on atoms constituting a studied solid. A convenient representation of the elastic scattering cross sections (DCS) for a given interaction is the expansion into the series of Legendre polynomials. Knowledge of the expansion coefficient provides a useful tool for the software developers when a large number of the DCSs is needed in the course of calculations. The enclosed computer program AL_CREATE makes possible to calculate the expansion coefficients from three different algorithms. Much attention is devoted to evaluate the accuracy of the DCSs. High accuracy of the DCS is reported when the expansion coefficients are calculated from the relativistic phase shifts. The database of these coefficients for all elements and for the energy range from 50 eV to 20 keV is accompanying the program AL_CREATE. Taking advantage of smooth variation of expansion coefficients with energy, this database makes possible a convenient and accurate determination of the expansion coefficients for any analytical conditions. It is shown that a number of different parameters needed for quantification of electron spectroscopies can be expressed by a relatively simple formalism based on known expansion coefficients. An attention is drawn to a possibility of creating a universal sampler of the elastic scattering angles that requires only the input of the complete series of expansion coefficients. This would greatly facilitate development of programs designed for Monte Carlo simulations of electron transport. A proposition of such a generator is implemented in the program SAMPLER which is also enclosed to the present report. The program AL_CREATE has an option of testing the performance of this generator. It is shown that the frequency histogram reproduces the DCS even when a sharp and narrow features are observed.