Matrix methods for single and multiple inelastic scattering in electron diffraction

A matrix formulation for inelastic scattering of high-energy electrons in crystals is presented. It is shown how, under a suitable approximation for the matrix elements of inelastic scattering, a compact expression for the intensity of single inelastic scattering is derived. With the same approximation also the multiple inelastic scattering intensity can be written in this form if an effective thickness-dependent scattering factor is used. It is further demonstrated that, for single inelastic scattering, numerical calculations based on the new expression are faster by several orders of magnitude than previously existing expressions, especially in many-beam situations.