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Consistent theory of electron scattering with atoms in electron microscopes

The potential function consisting of the power and exponential forms as a function of a screened atomic radius is proposed, by which the electron scattering amplitude is a complex quantity and involves the effects of energy dependence. An empirical relation is used for the exponent, and the cross sections of elastically and inelastically scattered electrons with atoms thus obtained are shown to be in good agreement with previous exact numerical calculations. The energy losses are in good agreement with experiments over the energy range 10-1000 keV. A small fitting factor is required in the range 1-10 keV.