On the Determination of the Unperturbed Energy Levels and the Interaction Matrix Elements Leading to a Complex Vibronic Analogue of the Fermi Resonance

摘要

A noniterative solution to the problem of determination of the unperturbed energy levels a_(i) and interaction matrix elements b_(i) describing a complex vibronic analogue of the Fermi resonance (the number of interacting states n > 2) is found. It is assumed that a_(i) and b_(i) can be determined on the basis of experimental data known for the resonance region, namely, the transition energies e_(k) and intensities I_(k). The source of the intensity of observed transitions is assumed to be only one perturbed transition (the S_(0) -> S_(2) transition of the 0-0 type or its vibronic sideband). The algorithm uses algebraic methods based on finding eigenvectors of real matrices of a particular form, whose elements are constructed from combinations of e_(k) and I_(k).