Definition: A scattering process with no loss of kinetic energy of the incident electron is called elastic.
In our case, the electrons are elastically scattered at the nucleus of the atoms. The kinetic energy of the electron is almost conserved due to the high mass of an atom compared with an electron. The cross sections of elastic scattering of nuclei in solids can be approximated to be the same as for free atoms.
The Rutherford formula based on classical physics is simple but it is a poor approximation for heavy elements, particularly in the low-energy region. The differential form of the cross section is
and can be found in [SD92]. Z is the atomic number,
e the elementary charge, E the energy of the electron and
the polar scattering angle.
The partial wave appoache of Mott [MM65] yields better results, but with considerably higher computational effort. The calculation program applied in SESAME is based on Yates [Yat71]. Mathematically, the cross section is described as follows:
with
using
K is the wave vector of the electron having the energy E,
is the phase shift of the l-th partial wave and
are the Legendre polynomes.
In SESAME the elastic scattering is calculated exclusivly by means of
the Mott cross sections.