The paper by B.R. Judd (1962) investigates the optical absorption intensities of rare-earth ions, focusing on the oscillator strength $ P $ of transitions between states of the $ 4f^N $ configuration. Judd derives an expression for $ P $, which depends on tensor operators $ T_\lambda $, and shows that these parameters can be used to fit experimental data for aqueous solutions of $ NdCl_3 $ and $ ErCl_3 $. The calculations assume that the first hydration layer of the rare-earth ion does not possess a center of symmetry, leading to parameters $ T_\lambda $ that are smaller than those observed for $ Nd^{3+} $ and $ Er^{3+} $ by factors of 2 and 8, respectively. Judd also discusses the role of vibrational modes in the complex of a rare-earth ion and its surroundings, which contribute to $ P $ in a similar form. The paper compares theoretical results with experimental data, showing that the model provides a good fit for the oscillator strengths of the absorption lines. The results suggest that the observed intensities are influenced by the environment of the rare-earth ion, and that the assumption of a center of inversion in the first hydration layer may be incorrect. The paper also discusses the symmetry of the environment of a rare-earth ion in solution, noting that the point symmetry is likely low, and that the immediate surroundings may consist of water molecules arranged in a specific configuration. The paper concludes that the observed values of $ T_\lambda $ are consistent with the hypothesis that a center of inversion exists in the first hydration layer of the rare-earth ion.The paper by B.R. Judd (1962) investigates the optical absorption intensities of rare-earth ions, focusing on the oscillator strength $ P $ of transitions between states of the $ 4f^N $ configuration. Judd derives an expression for $ P $, which depends on tensor operators $ T_\lambda $, and shows that these parameters can be used to fit experimental data for aqueous solutions of $ NdCl_3 $ and $ ErCl_3 $. The calculations assume that the first hydration layer of the rare-earth ion does not possess a center of symmetry, leading to parameters $ T_\lambda $ that are smaller than those observed for $ Nd^{3+} $ and $ Er^{3+} $ by factors of 2 and 8, respectively. Judd also discusses the role of vibrational modes in the complex of a rare-earth ion and its surroundings, which contribute to $ P $ in a similar form. The paper compares theoretical results with experimental data, showing that the model provides a good fit for the oscillator strengths of the absorption lines. The results suggest that the observed intensities are influenced by the environment of the rare-earth ion, and that the assumption of a center of inversion in the first hydration layer may be incorrect. The paper also discusses the symmetry of the environment of a rare-earth ion in solution, noting that the point symmetry is likely low, and that the immediate surroundings may consist of water molecules arranged in a specific configuration. The paper concludes that the observed values of $ T_\lambda $ are consistent with the hypothesis that a center of inversion exists in the first hydration layer of the rare-earth ion.