The Critical Voltage Effect in Transmission Electron Microscopy: VI. Renormalized Perturbation Theory for the Treatment of Absorption

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Abstract
For a study of the critical voltage effect (CVE) with absorption, treating the latter as a perturbation, one has to apply degenerate perturbation theory to a non‐Hermitean perturbation. It is pointed out that the perturbation expansion may then become divergent under certain illumination conditions. A renormalization technique is developped to remove the divergence. The following conclusions result: In all centrosymmetric crystals where the CVE occurs, and in certain noncentrosymmetric ones, the dynamical matrix with absorption becomes degenerate at a voltage close to the usual CV and for two small misorientations which are symmetrical with respect to the exact Bragg orientation for the second order reflection. At the degeneracy the diagonalizing matrix is singular. Nevertheless the renormalized perturbation theory yields for the latter a simple and very accurate approximative expression which is valid even at the singularity.