Calculation of Cross Sections for Electron Ionization of Atoms Using Classical Mechanics

In order to determine the range of validity of Gryzinski's classical theory for inelastic electron-atom scattering, we evaluate exactly the classical cross section for the electron ionization of atomic hydrogen. At large electron-impact energies the exact classical cross section disagrees with the experimental cross section. This is due to the inability of the classical theory to describe an electron-atom collision if the energy of the incident electron is large. For low-impact energies the classical description of a collision becomes valid. The electron energy at which the classical theory becomes applicable is in good agreement with the energy predicted by the uncertainty principle.