Covalent Effects in Rare-Earth Crystal-Field Splittings

Covalent contributions to the optical splitting of rare-earth ions are discussed. ${\mathrm{Tm}}^{2+}$ in Ca${\mathrm{F}}_2$, the system studied by Bleaney, Axe, and Burns, and others, was chosen because it is an outstanding example of the breakdown of the traditional electrostatic theory when applied to rare-earth ions in cubic environments. Upon separating out overlap from covalent contributions, overlap effects are found to dominate. The role of the closed $5p$ shell in covalent mixing is shown to be as important as, or more important than, that due to the $4f$ shell alone.