A more rigorous treatment of inelastic scattering processes and the
electron energy loss is the summation of individual theoretical
stopping powers. The simplest possibility is to distinguish between
innershell excitation and valence electron excitation. The total
energy loss due to valence electron excitation is calculated
by:
where the stopping power for valence electron excitation is estimated by the difference of the Bethe stopping power and the stopping power for inner-shell electron ionization:
The formula of the Bethe stopping power is formula A.4 and
formula A.5 for small electron energies ().
The inner shell stopping power was published by Gryzinski:
The angular deflections caused by inelastic scattering events are
related to the energy loss according to a classical
approach [Sch86] (momentum and energy conservation):
A rigorous summation of all stopping power during an inelastic scattering process has been proposed by Ritchie [RGNB69]. A modified approach is by Shimizu and includes:
Further information can be found in the review paper of Shimizu [SD92].