A Relationship Between Photoionization and Electron Impact Ionization and Its Application to Al and Au

A simple relation between electron-atom inner shell ionization and the photoionization process is derived. This relation is applied to the calculation of inner shell inverse mean free paths for aluminum and gold needed in soft x-ray photoemission calculations. Good agreement is found between our results and available generalized oscillator strength calculations, as well as with experimental data. The difference between the present derivation and that using a Gaunt factor is also discussed. Comparison with empirical formulas of Lotz and Gryzinski indicates our results are about a factor of two smaller than that from the latter two methods.