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The Critical Voltage Effect in Transmission Electron Microscopy : VI. Renormalized Perturbation Theory for the Treatment of Absorption
Author(s) -
David M.,
Gevers R.,
Serneels R.
Publication year - 1976
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220740139
Subject(s) - degenerate energy levels , renormalization , perturbation (astronomy) , singular perturbation , physics , singularity , degeneracy (biology) , perturbation theory (quantum mechanics) , mathematical physics , quantum electrodynamics , quantum mechanics , condensed matter physics , mathematical analysis , mathematics , bioinformatics , biology
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.