To reduce the discrepancies in the crystal-field analyses of the electronic configurations $4f^N$ of lanthanide ions, it is argued that each component ${\left({C_q}^{\mathrm{}\left(k\right)\mathrm{}}\right)}_i$ of the single-electron tensor $C^{\mathrm{}\left(k\right)\mathrm{}}$ for electron $i$ occurring in the conventional crystal-field Hamiltonian should be augmented to $c_k\left(\overrightarrow{\mathrm{s}}·{\overrightarrow{\mathrm{s}}}_i\right){\left({C_q}^{\mathrm{}\left(k\right)\mathrm{}}\right)}_i$. Parameters $c_k$ of the order of - 0.1 lead to significant improvements in the fit with a wide variety of experimental data.

• Received 3 June 1977

DOI:https://doi.org/10.1103/PhysRevLett.39.242