Revised high energy behavior of the Deutsch-Märk (DM) formula for the calculation of electron impact ionization cross sections of atoms

Abstract We modified the Deutsch-Mark (DM) formula for the calculation of single atomic ionization cross sections by replacing the previously used Gryzinsky-type energy dependence by a “scaled” ln( E )/ E energy dependence. This modified energy dependence yields, in the limit of high impact energies, the well-established Born–Bethe ln( E )/ E energy dependence, while reproducing, at lower impact energies, the DM cross section function. The revised DM formula, whose energy dependence has been determined from a fitting procedure using reliable, measured ionization cross sections for the atoms H, He, C, Ne, Mg, Al, and Ag, was subsequently used to calculate as an example ionization cross sections for the atoms O, F, P, Ar, Ge, Kr, and Xe and excellent to very good agreement was found between the calculated and the measured cross sections for these atoms over a wide range of impact energies.

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