How the choice of model dielectric function affects the calculated observables

It is investigated how the model used to describe a dielectric function (i.e. a Mermin, Drude, Drude-Lindhard, Levine-Louie with relaxation time dielectric function) affects the interpretation of a REELS experiment, the calculation of the electron inelastic mean free path as well proton stopping and straggling. Three dielectric functions are constructed that are based on different models describing a metal, but have identical loss functions in the optical limit. A loss function with the same shape, but half the amplitude, is used to derive four different model dielectric functions for an insulator. From these dielectric functions we calculate the differential inverse mean free path, the mean free path itself, as well as the stopping force and straggling for protons. The similarity of the underlying physics between proton stopping, straggling and the electron inelastic mean free path is stressed by describing all three in terms of the differential inverse inelastic mean free path. To further highlight the reason why observed quantities depend on the model dielectric function used we study partial differential inverse inelastic mean free paths, i.e. those obtained by integrating over only a limited range of momentum transfers. In this way it becomes quite transparent why the observable quantities depend on the choice of model dielectric function.