The spectrum of Tm III in CaF 2

Abstract

The crystal field of CaF$_2$ is evaluated on a point-charge model, and from comparison with the crystal field constants derived from the optical spectrum (Kiss 1962) of Tm III in CaF$_2$, empirical values of $\langle r^4\rangle$ = 4.3 a.u., $\langle r^6\rangle$ = 36 a.u. are found. These are considerably larger than the estimates of Freeman & Watson (1962). The crystal field data reveal a small discrepancy with the paramagnetic resonance data of Hayes & Twidell (1961), which can be resolved by the introduction of an orbital k-factor which is slightly less than unity (1 - k = 0.009 $\pm$ 0.001). Comparison with the spectrum of Tm I measured by atomic beams (Ritter 1962) shows that the magnetic hyperfine constant for a free Tm III ion is (2.2 $\pm$ 0.5)% greater, while the spin-orbit coupling is 1.2% greater, assuming a core polarization correction of the same magnitude as that measured for Eu III in CaF$_2$. Similar effects are shown to occur for Ho III in CaF$_2$. The results suggest that the values of $\langle r^{-3}\rangle$ and the spin-orbit coupling parameter $\zeta$ are only about 1 to 2% greater for the free divalent 4f ions than for the atoms.