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Abstract
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 $4{f}^{3}$. The positions of the free-ion levels of Nd IV $4{f}^{3}$ and Er IV $4{f}^{11}$ 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.
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