The inelastic mean free path (IMFP) is a quasi-universal curve which describes how far a beam of electrons will travel through a material before scattering inelastically. I have been searching for derivations of a functional form but have not been successful; however, this is not my main question.
I am curious: is there an intuitive explanation as to why at low energy the mean free path is inversely proportional to the electron energy and why it is linear at high energy? I imagine it is because different scattering processes dominate in the two regimes, but I would like a definitive answer. Is there a way to intuitively picture the minimum (e.g. the minimum occurs when scattering from process x balances with that of process y)?