Heriot-Watt Mathematics Report Series
HWM98-2, 26 Jan
The Splitting of the $^{3}H_{4}$ Multiplet in Uranium Dioxide
H.U. Rahman
Abstract
A set of empirical calculations for the 'strong' Crystal Field have been
performed, and values of relevant parameters for the U$^{4+}$ ion in
crystals are reported. The 9-fold degeneracy of the free-ion ground
state $^{3}$H$_{4}$ of uranium ion is partially lifted, and is split
into a four-level system of a singlet A$_{1}$, a doublet E, and two
triplets T$_{1} and T$_{2} levels. The experimental data on the
neutron spectroscopy can be fitted to theory by choosing values of the
parameters as B$^{4}_{0} = -893.3$meV, B$^{6}{_0} = 387.7$meV. The
low value of B$^{4}{_0}$ thus obtained suggests that the system can
adequately be treated with the 'weak' Crystal Field approach, and
ground state wavefunction $^{3}$H$_{4}$ can be almost entirely expressed
within a single J = 4 manifold, as is the case for lanthanide systems.
The calculated Lande g value of the ground state T$_{2}$ is 0.8232, and
those for the first three excited levels E, T$_{1}$, A$_{1}$ are 0.8286,
0.8389, 0.8083 respectively.
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