Example: electron-atom elastic scattering

In the case of electron-atom scattering total elastic and transport cross sections can be derived in the frame of semi-empirical approach which uses the scattering length (L) and static polarizability of atom (a). In the low energy range when E<Ry/a ( Ry=13.6 eV – Rydberg,  E is electron energy) elastic cross section is expressed in terms of scattering length . Then the electron-atom interaction takes place at large distances from the target. Therefore the main contribution to the cross section comes from the scattering of s wave associated with the incident electron. The phase shift of s wave is proportional to the electron momentum with coefficient equal to L (for small momentum). In high-energy range E<Ry/a all partial waves associated with the incident electron give comparable contribution to the cross section. In this case the electron-atom interaction can be described as charge-dipole interaction with dipole moment induced in the target core by the incident electron. This dipole moment is determined by atomic polarizabilty and electron electric field at the point of target location. Thus scattering cross section in high-energy limit is expressed via parameters a and L.  In the frame of this approach one should conjunct low-energy and high-energy cross sections at some energy E*. The value of E* is chosen so that these two cross sections conjunct smoothly.

Results obtained in the frame of above-described approach with the available experimental data and results of other theoretical treatments are shown in the following figures for electron scattering on alkali atoms.