Two-photon absorption in gadolinium ions

Abstract

Recent observations of two-photon absorption within the configuration 4f⁷ of Gd³⁺ in LaF₃ have indicated an anomalously high line strength for the transition ⁸S_7/2 to ⁶P_7/2 compared with ⁸S_7/2 to ⁶P_5/2 and ⁸S_7/2 to ⁶P_3/2. It is shown that the standard expression for the two-photon intensity is unusually small for all three transitions and that a higher-order correction, involving matrix elements of the spin-orbit interaction within the intermediate configuration 4f⁶5d, predominates. The principal term is scalar, implying (in the absence of J mixing by the crystal field) isotropic contributions to the various components of the Delta J=0 transition. The line strengths that have been observed can be accounted for reasonably well without having to invoke variations in the radial integral (4f mod r mod 5d) or inadequacies in the closure approximation. Expressions for the transition matrix elements are given for the general configuration l^N.