Parametric analysis of the energy levels of ${\mathrm{U}}^{4+}$ in $D_{2d}$ and limiting $D_2$ sites in incommensurate Th${\mathrm{Br}}_4$

Below $T_c=95\mathrm{}$ K, ${\mathrm{U}}^{4+}$: Th${\mathrm{Br}}_4$ exists as an incommensurately modulated structure. The ${\mathrm{U}}^{4+}$ ions occupy a range of sites which vary from $D_{2d}$ to a limiting $D_2$ site. The $D_{2d}$ and limiting $D_2$ sites have been identifed spectroscopically. We report a parametric analysis of the ${\mathrm{U}}^{4+}$ energy levels in both sites. For 26 levels in the $D_{2d}$ site the root-mean-square deviation $\sigma =36\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$ and $F^2=42\mathrm{}253\pm 127$, $F^4=40\mathrm{}458\pm 489$, $F^6=25\mathrm{}881\pm 383$, $\zeta =1783\mathrm{}\pm 7$, $\alpha =31\mathrm{}\pm 1$, $\beta =-644\mathrm{}\pm 75$, $\gamma =1200\mathrm{}$, $B_0^2=-1096\mathrm{}\pm 80$, $B_0^4=1316\mathrm{}\pm 146$, $B_4^4=-2230\mathrm{}\pm 85$, $B_0^6=-3170\mathrm{}\pm 379$, and $B_4^6=686\mathrm{}\pm 246$, all in ${\mathrm{cm}}^{-1\mathrm{}}$. For 38 $D_2$ levels $\sigma =39\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and those parameters which occur in both symmetries are only slightly changed. The additional parameters which occur only in $D_2$ symmetry are $B_2^2=-78\mathrm{}\pm 30$,