Magnetic Scattering of Neutrons from Rare Earth Ions

The differential cross section for the magnetic scattering of thermal neutrons by paramagnetic rare earth ions is derived theoretically assuming that the ions have Russell Saunders coupling and are in the Hund ground state. Satisfactory agreement with the measured cross sections of ${\mathrm{Er}}_2$ ${\mathrm{O}}_3$ and ${\mathrm{Nd}}_2$ ${\mathrm{O}}_3$ is obtained using hydrogenic radial wave function with $Z-S\approx 23 \mathrm{and} 20$ for ${\mathrm{Er}}^{+++}$ and ${\mathrm{Nd}}^{+++}$, respectively.