The slowing down of energetic particles in solids has been studied for the special but important case that the energy loss process is independent of any other interaction characteristic. For a realistic variation of the scattering characteristics with energy this allows one to go over from the continuous energy variable to a discrete variable, being equal to the number of inelastic processes. Then, the energy dissipation can be described in terms of partial intensities of particles having experienced a given number of inelastic collisions and the partial energy distributions associated with them. The important advantage of this so-called partial intensity approach is that it can accurately account for the variation of the scattering characteristics with the energy in a simple way. The key point in this procedure is the distribution of the stochastic process governing multiple collisions in the multispeed case. The exact solution as well as an accurate and efficient analytical approximation is given for the probability for n-fold scattering as a function of the traveled path length. Application of the proposed method to inelastic backscattering of electrons from solids leads to excellent agreement with experimental results and simulation data and constitutes a significant improvement over methods that neglect the energy dependence of the interaction characteristics. The method should prove useful for slowing down problems of different types of particles like electrons, ions, etc., in solids.

DOI:https://doi.org/10.1103/PhysRevB.55.14925