Calculations of the Spectra of SrF2:Gd3+in a Tetragonal Crystal Field

A theoretical calculation by means of parameter fitting to the experimentally observed crystal-field splittings of Sr${\mathrm{F}}_2$: ${\mathrm{Gd}}^{3+}$ for a tetragonal symmetry site is presented. The calculation uses free-ion wave functions which include spin-orbit, spin-other-orbit, spin-spin, and configuration interactions as basis vectors. The Stark splittings are calculated to all orders of the crystal field within the space defined by the first 15 free-ion states as basis. The tetragonal crystal-field coefficients were found to be $B_0^2=205.9\mathrm{}$, $B_0^4=-1715.2\mathrm{}$, $B_4^4=-1224.5\mathrm{}$, $B_0^6=1874.6\mathrm{}$, and $B_4^{ 6}=-499.5\mathrm{}$ in ${\mathrm{cm}}^{-1\mathrm{}}$ with a mean error of 7.0 ${\mathrm{cm}}^{-1\mathrm{}}$ for 37 experimentally observed levels.