Analytically solvable model of scattering of relativistic charged particles in solids

We propose an analytically solvable model of the differential and total inelastic cross sections, mean free paths, and energy losses of charged projectiles (electrons, positrons, protons, ions, etc) within a unified framework. It is applicable within a broad range of incident energies (from 30-50 eV up to GeV in a case of an electron). Only the optical data are used as an input, without any ad-hoc correction terms, splitting into close and distant collisions, or fitting and adjustable parameters. We demonstrate that the derived expressions are in a very good agreement with other more complex numerical models and experimental data. Application of the derived formulae greatly saves computational time of evaluation of cross sections with respect to the numerical integration required by other models.