Magnetic Parameters for the Configurationf3

The energy-level schemes of several atomic configurations $f^3$ are analyzed in terms of effective operators. These include all possible Hermitian two-electron scalar operators and six three-body spin-independent scalar operators. This collection of operators allows for spin-spin and spin-other-orbit interactions as well as for the most important effects of configuration interaction. Several alterations and extensions are suggested for the terms of Pr III $4f^3$. The positions of the free-ion levels of Nd IV $4f^3$ and Er IV $4f^{11}$ are inferred from the crystal spectra of ${\mathrm{Nd}}^{3+}$ in La${\mathrm{Cl}}_3$, and analyses with restricted sets of operators are carried out.