A semi-empirical formula for calculation of absolute cross sections for ionization and excitation of atoms by electrons

A simple analytical expression for the absolute ionization and (optically allowed) excitation cross sections, as a function of the electron energy, is “derived”. In this expression there are two parameters. The first one is proportional to the optical oscillator strength and the second one is dependent on the shape of the differential cross section (generalized oscillator strength), for scattering of energetic electrons as a function of their (small) momentum loss. The analytical expression is exact for large energies of the impinging electron. For small energies of this electron, the expression gives good agreement with experiment. Ionization cross sections are calculated for H, He, Ne, Ar, Kr, Xe, H2, N2 and O2. Excitation cross sections are calculated for H and He