Neutron-diffraction study of UO2: Paramagnetic state

The magnetic form factor of the induced moment in U${\mathrm{O}}_2$ has been measured in the paramagnetic state at $T=64\mathrm{}$ K with polarized neutrons in an applied field of 50 kOe. The theoretical form factor is derived with the tensor-operator method and the $〈j_i〉$ integrals for ${\mathrm{U}}^{4+}$ derived from relativistic Dirac-Fock wave functions. Three models for the electronic state are considered: (i) the free-ion ${\mathrm{U}}^{4+}$ ground state, (ii) the ${}_{}{}^3{}_{}{}^{}H_4^{}{}_{}{}^{}$ ${\Gamma }_5$ crystal-field ground state, and (iii) the Rahman and Runciman mixed-$J$ ${\Gamma }_5$ ground state. The calculation of the magnetic scattering in the presence of intermediate coupling and $J$ mixing is discussed. Whereas the experimental data are unable to distinguish between the small angular differences predicted for the three models, the radial dependence of the magnetic scattering is found to be in good agreement with theory and confirms the validity of the Dirac-Fock $〈j_i〉$ integrals.