Single differential electron impact ionization cross sections in the binary-encounter-Bethe approximation for the low binding energy regime

An analytical expression based on the binary-encounter-Bethe model for energy differential cross sections in the low binding energy regime is presented. Both the binary-encounter-Bethe model and its modified counterpart are extended to shells with very low binding energy by removing the constraints in the interference term of the Mott cross section, originally introduced by Kim et al. The influence of the ionic factor is also studied for such targets. All the binary-encounter-Bethe based models presented here are checked against experimental results of low binding energy targets, such as the total ionization cross sections of alkali metals. The energy differential cross sections for H and He, at several incident energies, are also compared to available experimental and theoretical values.