Neutron magnetic form factors of uranium ions

The radial $〈j_i〉$ integrals, which contribute to the neutron magnetic form factors, of several uranium ions (${\mathrm{U}}^{3+}$, ${\mathrm{U}}^{4+}$, ${\mathrm{U}}^{5+}$) are determined from fully relativistic Dirac-Fock wave functions. The expectation values of the $r^n$ operators, $〈r^n〉$, with $n=-3,2,4,\mathrm{and}6$ are given for the uranium ions. The possibility of determining the ionization state by magnetic scattering experiments is discussed. The radial $〈j_i〉$ integrals are used to analyze the experimental form factor of US determined by Wedgwood. Satisfactory agreement is found by choosing a $5f^2 {\Gamma }_1$ crystal-field ground state with a large internal exchange field inducing ferromagnetism. Contributions to the magnetic scattering from $6d$ electrons are found to be negligible for values of $\frac{sin\theta }{\lambda }>0.2\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$.