Utilization of Canonical Transformations for the Vibronic Self-Energies of Coupled Impurity Centers

The self-energies of a system of two electronically coupled impurity centers, one of which inter-acts with the vibrations of the surrounding crystal (Fano system), are derived by use of non-linear canonical transformations. The regions of applicability of this method are discussed and the results compared with those derived by Green’s function techniques in an earlier paper of one of the authors (N. N. K.). The self-energies calculated up to second order have a very simple form and exhibit the correct behaviour also in regions where the results of the Green’s function method are no longer valid.