Two-Photon Laser Spectroscopy of Transition Ions in Crystals: Inter-   Configurational Transitions
  Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The equivalence between third-order mechanisms and second- plus first-order mechanisms is clearly established. A compact formula is derived for the intensity of a two-photon transition between two levels with well-defined symmetries. A set of (selection) rules which controls the number of intensity parameters for inter-configurational transitions is given. The formalism is illustrated with the case of an ion with 4f configuration in tetragonal symmetry. 
M. Daoud and M. Kibler