Theorie vibronischer Spektren in Ionenkristallen

The electronic bands of some foreign ions in a crystal exhibit one or a few intermixed sequences of equidistant lines (vibronic spectra.) Examples are the divalent rare-earth ions in alkali-halide and alkaline-earth-halide crystals. It is shown that such sequences of lines are only possible if a) the disturbed lattice dynamics gives rise to localized or quasi-localized modes and b) the electronic functions of the defect ion (properly symmetrized in the static crystal field) do not overlap the nearest lattice ions. To calculate the single lines of a vibronic band a refined method of moments is developed. Its parameters (oscillator displacement and frequency change) follow from the dynamics of the disturbed lattice. The lattice vibrations are calculated by means of modern scattering theory. To describe the scattering resonance the advantageous concept of metastable (quasi-localized) vibrations is introduced. Then the projection of the cartesian coupling functions of first and second order onto the disturbed lattice eigenvectors can be determined. Their matrix elements <n|U _x |n> and <n|U _xx |n> define the change of the equilibrium positions and frequencies during the transition. Further on general symmetry-selection rules are derived for the electron-lattice coupling. Finally the important case of a pure electrostatic coupling is discussed in more detail. It is evident that the study of vibronic spectra gives important information about the dynamics of the disturbed lattice and the electron-lattice coupling. Especially they constitute a method to investigate localized and quasi-localized modes, even if their dipole moment is too small for direct optical excitation, or if their frequency lies in the absorbing region of the crystal.