The paper "Optical Absorption Intensities of Rare-Earth Ions" by B. R. Judd, published in 1962, explores the theoretical framework for calculating the oscillator strengths of electric dipole transitions in rare-earth ions. The author assumes that the transitions occur between states of the ground configuration 4f^N, where the nucleus is not at a center of inversion. The oscillator strength P for a transition between two states is given by a sum over matrix elements involving tensor operators U(λ) of rank λ (λ = 2, 4, 6). The paper discusses the simplification of the matrix elements through the use of closure procedures and the consideration of vibrational modes in the complex comprising the rare-earth ion and its surroundings. The parameters T_λ are chosen to fit experimental data on aqueous solutions of NdCl_3 and ErCl_3, with the results showing good agreement for Nd³⁺ but discrepancies for Er³⁺. The author also examines the influence of the anion on the oscillator strengths and proposes a model for the immediate surroundings of a rare-earth ion in solution, suggesting that the presence of a center of inversion in the first hydration layer could explain some of the observed discrepancies.The paper "Optical Absorption Intensities of Rare-Earth Ions" by B. R. Judd, published in 1962, explores the theoretical framework for calculating the oscillator strengths of electric dipole transitions in rare-earth ions. The author assumes that the transitions occur between states of the ground configuration 4f^N, where the nucleus is not at a center of inversion. The oscillator strength P for a transition between two states is given by a sum over matrix elements involving tensor operators U(λ) of rank λ (λ = 2, 4, 6). The paper discusses the simplification of the matrix elements through the use of closure procedures and the consideration of vibrational modes in the complex comprising the rare-earth ion and its surroundings. The parameters T_λ are chosen to fit experimental data on aqueous solutions of NdCl_3 and ErCl_3, with the results showing good agreement for Nd³⁺ but discrepancies for Er³⁺. The author also examines the influence of the anion on the oscillator strengths and proposes a model for the immediate surroundings of a rare-earth ion in solution, suggesting that the presence of a center of inversion in the first hydration layer could explain some of the observed discrepancies.