Elastic scattering is defined as scattering in which the incident particle or radiation does not give up any of its energy to the scatterer. Electrons are elastically scattered in atoms by both the nucleus and the atomic electrons which screen the nuclear charge. When considering only nuclear scattering the first Born approximation quantum mechanical cross section and the classical Rutherford cross section are identical. The effects of the atomic electrons can be taken into account by a simple screening term or by more exact treatments based on Hartree-Fock or Dirac-Fack wave functions. The partial wave expansion can be used to go beyond the first Born approximation but it is only really appropriate for isolated atoms. All elastic scattering cross sections at energies of interest in electron microscopy are strongly forward peaked. Mott cross sections calculated by solving the radial Dirac equation incorporate more than just the relativistic changes in mass and wave vector and so can-not be compared directly to Rutherford cross sections.
"Elastic Scattering of Electrons by Atoms,"
Scanning Electron Microscopy: Vol. 1982
, Article 4.
Available at: https://digitalcommons.usu.edu/electron/vol1982/iss1/4