Electron scattering cross sections with relativistic correction in the first Born approximation for Thomas-Fermi and Hartree potentials

Abstract

In this paper we calculate the electron scattering cross sections which include the effect due to relativity in the first Born apptoximation for Thomas-Fermi and Hartree potentials The Thomas-Fermi potential and the Hartree potentials are approximated by analytica fits. The results of Table I show that the electron scattering cross sections without relativistic correction agree quite well with the numerical results of the exact Thomas-Fermi potential. In Table II we have a comparison of electron scattering cross sections for approximate Thomas-Fermi and approximate Hartree potentials with the exact numerical data calculated from Hartree fields for argon. Table II shows that the analytical fits for Hartree fields do not differ essentially from the fits for Thomas-Fermi potential. In Table III we have collected 19 fits of Hartree potentials for neutral atoms. We derive an analytical approximate formula for the electron scattering total cross section which includes relativistic correction. In Table IV we have several numerical data for the electron scattering total cross section without the relativistic correction for argon for the Thomas-Fermi and Hartree potential.