Sum Rules for Multi-Photon Spectroscopy of Ions in Finite Symmetry
  Models describing one- and two-photon transitions for ions in crystalline environments are unified and extended to the case of parity-allowed and parity- forbidden p-photon transitions. The number of independent parameters for characterizing the polarization dependence is shown to depend on an ensemble of properties and rules which combine symmetry considerations and physical models. 
M. Kibler and M. Daoud