Premium
Non‐Condon Approximations and the Static Approach in the Theory of Non‐Radiative Multiphonon Transitions
Author(s) -
Gutsche E.
Publication year - 1982
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.2221090217
Subject(s) - adiabatic process , anharmonicity , operator (biology) , degenerate energy levels , perturbation theory (quantum mechanics) , physics , diagonal , adiabatic theorem , quantum mechanics , phonon , radiative transfer , perturbation (astronomy) , matrix element , mathematics , chemistry , transcription factor , gene , biochemistry , geometry , repressor , particle physics
The off‐diagonal matrix element of the non‐adiabaticity operator, on which usually the theory of non‐radiative multiphonon transitions is based, is recast into a form much more convenient for the calculation of the transition probability W in non‐Condon approximation. This is demonstrated first for a two‐level system coupled to a single vibrational mode and then extended to the more general case of a complete set of non‐degenerate electronic states coupled linearly to N normal modes. The strong anharmonicity of the adiabatic potentials due to the mixture of states caused by the electron–phonon interaction operator is stressed, which limits the applicability of the theory to situations where only transitions well below “level crossing” are important, and, consequently, imposes serious restrictions on the parameters of the system and the temperature. Keeping to these restraints and to two electronic levels, the transformed matrix element of the non‐adiabaticity operator is identical with that of the perturbation operator used in the static coupling scheme of Haug and Pässler, which turns out in this way to be equivalent to a closed‐form of non‐Condon approximation based on a well defined set of adiabatic wave functions. Explicit expressions for W are also given, and some aspects of the theory in general are discussed.