Symmetry Adaptation Techniques in N-photon Absorption Spectroscopy Symmetry Adaptation Techniques in N-photon Absorption Spectroscopy

We present some recent progress achieved in the application of symmetry adaptation techniques to n-photon absorption spectroscopy of rare earth ions in finite symmetry. More specifically, this work is concerned with the determination of the intensity of n-photon transitions between Stark levels (rather than J levels) of an ion in an environment with a given symmetry. The role of symmetry is taken into account through the use of initial and final state vectors characterized by irreducible representations of the (double) group for the ion site symmetry. Two distinct situations are considered, viz., the case of parity-allowed n-photon transitions (as e.g. intra-configurational transitions between Stark levels of the 4f N configuration for n even) and the case of parity-forbidden n-photon transitions (as e.g. inter-configurational transitions from Stark levels of the 4f N configuration to Stark levels of the 4f N−1 5d configuration for n even).