Symmetry Adaptation and Two-Photon Spectroscopy of Ions in Molecular or Solid-State Finite Symmetry

Finite symmetry adaptation techniques are applied to the determination of the intensity strength of two-photon transitions for ions with one partly-filled shell nl in crystalline environments of symmetry G. We treat the case of intra- configurational transitions as well as the case of inter-configurational transitions. In both cases, the Wigner-Racah algebra of the chain O(3) > G allows to extract the polarization dependence from the intensity. The reported results are valid for any strength of the crystalline field.