Unelastische Streuung in der dynamischen Theorie der Elektronenbeugung

A general solution to the fundamental equations of inelastic scattering of fast electrons in crystals is obtained by using a Green function constructed of Bloch waves. Inelastic interband transitions are shown to vanish if they are of a direct type, but not when implying simultaneous Bragg reflexion. These selection rules hold for any type of electron-crystal interaction. The resulting imaginary absorption potentials for the different intraband and interband transitions can be calculated separately. They are reduced to a simple form in the two-beam case. The expression measuring the anomalous absorption contains the Yoshioka potential C ₀ ⁱ g and an additional term which gives a small contribution in the case of crystal electron excitation and no contribution in the case of phonon excitation. Numerical calculations for the scattering of 100 keV electrons in Al, Cu, Ge, Si and MgO are made and compared with experimental data. An analytic expression forYoshioka's C ₀ ⁱ g due to plasmon excitation is derived which vanishes in the random phase approximation.