Comparison of Electron Elastic-Scattering Cross Sections Calculated from Two Commonly Used Atomic Potentials

Abstract

We have analyzed differential cross sections (DCSs) for the elastic scattering of electrons by neutral atoms that have been derived from two commonly used atomic potentials: the Thomas–Fermi–Dirac (TFD) potential and the Dirac–Hartree–Fock (DHF) potential. DCSs from the latter potential are believed to be more accurate. We compared DCSs for six atoms (H, Al, Ni, Ag, Au, and Cm) at four energies (100, 500, 1000, and 10 000 eV) from two databases issued by the National Institute of Standards and Technology in which DCSs had been obtained from the TFD and DHF potentials. While the DCSs from the two potentials had similar shapes and magnitudes, there can be pronounced deviations (up to 70%) for small scattering angles for Al, Ag, Au, and Cm. In addition, there were differences of up to 400% at scattering angles for which there were deep minima in the DCSs; at other angles, the differences were typically less than 20%. The DCS differences decreased with increasing electron energy. DCSs calculated from the two potentials were compared with measured DCSs for six atoms (He, Ne, Ar, Kr, Xe, and Hg) at energies between 50 eV and 3 keV. For Ar, the atom for which experimental data are available over the largest energy range there is good agreement between the measured DCSs and those calculated from the TFD and DHF potentials at 2 and 3 keV, but the experimental DCSs agree better with the DCSs from the DHF potential at lower energies. A similar trend is found for the other atoms. At energies less than about 1 keV, there are increasing differences between the measured DCSs and the DCSs calculated from the DHF potential. These differences were attributed to the neglect of absorption and polarizability effects in the calculations. We compare transport cross sections for H, Al, Ni, Ag, Au, and Cm obtained from the DCSs for each potential. For energies between 200 eV and 1 keV, the largest differences are about 20% (for H, Au, and Cm); at higher energies, the differences are smaller. We also examine the extent to which three quantities derived from DCSs vary depending on whether the DCSs were obtained from the TFD or DHF potential. First, we compare calculated and measured elastic-backscattered intensities for thin films of Au on a Ni substrate with different measurement conditions, but it is not clear whether DCSs from the TFD or DHF potential should be preferred. Second, we compare electron inelastic mean free paths (IMFPs) derived from relative and absolute measurements by elastic-peak electron spectroscopy and from analyses with DCSs obtained from the TFD and DHF potentials. In four examples, for a variety of materials and measurement conditions, we find differences between the IMFPs from the TFD and DHF potentials ranging from 1.3% to 17.1%. Third, we compare mean escape depths for two photoelectron lines and two Auger-electron lines in solid Au obtained using DCSs from the TFD and DHF potentials. The relative differences between these mean escape depths vary from 4.3% at 70 eV to0.5% at 2016 eV at normal electron emission, and become smaller with increasing emission angle. Although measured DCSs for atoms can differ from DCSs calculated from the DHF potential by up to a factor of 2, we find that the atomic DCSs are empirically useful for simulations of electron transport in solids for electron energies above about 300 eV. The atomic DCSs can also be useful for energies down to at least 200 eV if relative measurements are made.