Crystal-field calculations for energy levels ofU4+in ZrSiO4

A crystal-field calculation has been made for the energy levels of an ion with an $f^2$ configuration in a $D_{2d}$ crystal field, appropriate to ${\mathrm{U}}^{4+}$ in zircon, ZrSi${\mathrm{O}}_4$. A previous analysis is found to be incorrect. The present analysis, using ten parameters, gives an energy-level fit which has a standard deviation of 112 ${\mathrm{cm}}^{-1\mathrm{}}$ relative to 30 observed levels. This fit is comparable to those obtained by other workers for ${\mathrm{U}}^{4+}$ in octahedral and tetrahedral symmetries. Zeeman experiments and magnetic-circular-dichroism measurements have yielded g values for a number of the $\sigma$-polarized absorption lines. The values of the parameters for the best fit are (in units of ${\mathrm{cm}}^{-1\mathrm{}}$): $F_2=196.7\mathrm{}$, $F_4=37.0\mathrm{}$, $F_6=4.25\mathrm{}$, $\zeta =1740\mathrm{}$, $\alpha =22.8\mathrm{}$, $A_2^0〈{\mathcal{r}}^2〉=-1000\mathrm{}$, $A_4^0〈{\mathcal{r}}^4〉=250\mathrm{}$, $A_4^4〈{\mathcal{r}}^4〉=5360\mathrm{}$, $A_6^0〈{\mathcal{r}}^6〉=-362\mathrm{}$, and $A_6^4〈{\mathcal{r}}^6〉=-300\mathrm{}$.