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 and parity-forbidden n-photon transitions. 
M. Daoud and M. Kibler