Singly Differential Cross-Sections for Producing Secondary Electrons from Hydrogen Gas by keV to MeV Proton Collisions

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Abstract
An analytical equation is presented which yields singly differential cross-sections for electron ejection by proton collisions. The expression is a combination of a modification of the classical binary encounter approximation for small electron energies and an exponential equation for high energies which was derived from a promotion model. The equation is consistent with the Bethe theory of inelastic scattering. The equation is fitted to experimental energy distributions of electrons over the range of proton energies from 5 keV to 1.5 MeV. Related quantities such as the average electron energy and stopping cross-section are easily calculated from the model.