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. The case of intra-configurational (nlN→nlN) transitions as well as the case of inter-configurational (nlN→nlN-1n'l' with (-)l+(l')=-1) transitions is treated. In both cases, the Wigner-Racah algebra of the chain O(3) contains G allows to extract the polarization dependence from the intensity. The reported results are valid for any strength of the crystalline field. (author) 19 refs