Origin of the persistent ~30 cm^-1 discrepancy for Tb3+ in LaF3

Determine the cause of the approximately 30 cm^-1 systematic discrepancy that appears from the fiftieth state onward in the calculated energy spectrum of Tb3+ in lanthanum trifluoride (LaF3) when reproducing the reference energies reported by Carnall et al. using the corrected spectroscopic tables and including the spin–spin term in the parametric semi-empirical Hamiltonian, in order to reconcile the remaining mismatch specific to terbium.

Background

The paper revisits and corrects historical calculations of lanthanide spectra in LaF3, addressing known and newly identified errors in spectroscopic tables and clarifying the treatment of magnetic interactions. After correcting errors and analyzing the inclusion/exclusion of spin–spin interactions, the authors reproduce most ions’ spectra to within a few cm^-1 when compared to Carnall et al.

However, for Tb3+ a consistent ~30 cm^-1 discrepancy emerges beginning around the fiftieth energy level, and this deviation persists despite the corrections applied elsewhere. Identifying the specific source of this terbium-only deviation would resolve an outstanding inconsistency in the widely used reference datasets and models.