Improved algorithm for calculating transport cross sections of electrons with energies from50eVto30keV

Abstract

We report an analytical expression for transport cross sections (TCSs) calculated from the Dirac-Hartree-Fock potential for 92 elements (H to U) and electron energies between $50\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and $30\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. This expression is the product of an approximate TCS formula and a correction function. Parameters in the correction function were obtained from separate fits for each element to computed TCSs for energies between 50 and $300\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and between $300\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and $30\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. Over the entire energy range, the mean deviation between TCSs from the expression and the calculated TCSs for any element was typically between 0.01% and 0.5%, and the maximum deviation was between 0.1% and 3%; both deviations generally increased with atomic number. The TCS expression will facilitate evaluation of parameters needed for quantitative Auger-electron spectroscopy and x-ray photoelectron spectroscopy that have been derived from the solution of the kinetic Boltzmann equation within the transport approximation.