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Descriptions of inelastic processes for the slowing down of electrons in condensed matter are presented for the energy range between a few eV and a few keV. Attempts at quantitative theories of stopping are summarized, with an emphasis on obtaining useful cross section expressions for Monte Carlo simulations and analytic transport theories. Inelastic scattering with both electrons (conduction and core) and density fluctuations (phonons) are included. The main emphasis in the theories for the former is in the dielectric (self-energy) formulation for the conduction band and in using generalized oscillator strengths or semiclassical excitation functions for the core. Recent applications to specific systems are discussed.

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