Perturbation Theory in Transmission Electron Diffraction II. The Perturbing Matrix is Constant but not Hermitian

Abstract

Instead of using the usual Schrödinger equation, perturbation theory is directly applied to the system of Howie and Whelan. According to the nature of the perturbing dynamical matrix generally three different types of perturbation are distinguished. The perturbing matrix may be a) constant and Hermitian b) constant but not Hermitian c) not constant but depth dependent. The first case has been discussed previously, now case b) is considered. In full matrix notation both generate and degenerate perturbation theory is presented. Special attention is given to the usual treatment of absorption effects. General recurrence relations are presented for the calculation of the corrections on eigenvalues and eigenvectors. The influence of these corrections on the amplitudes and the intensities of the constituent beams is discussed.