A formalism using the properties of the irreducible representation of
the scattering tensors has been developed to predict up to the third o
rder the polarization-dependent behavior of the electronic Raman-scatt
ering intensities and the two-photon absorption intensities of transit
ions between Stark levels. The polarization behavior of ions in crysta
ls are tabulated for the 32 crystallographic point groups. The theory
provides a stringent test for the Judd-Ofelt-Axe theory for two-photon
intensities between Stark levels.