Neutron magnetic form factors and X-ray atomic scattering factors for rare-earth ions

The theory of neutron scattering by paramagnetic rare-earth ions has been given by Trammell and more recently by Odiot and Saint-James. Unlike the case for the iron-series transition metals, for which the orbital angular momentum of the 3d electrons is almost completely quenched, the magnetic scattering of neutrons from the rare earths (except for gadolinium and europium) arises from both the spin and orbital contributions to the magnetization. Using recently determined Hartree-Fock wave functions for some of the trivalent rare-earth ions we have determined the functions (j_n) and (g_n) (for n = 0, 2, 4, and 6) which are necessary for the theoretical evaluation of the spin and orbital contributions, respectively, to the magnetic form factor. A comparison of these theoretical results with the experiments of Koehler and Wollan for Nd³⁺ and Er³⁺ and of Koehler, Wollan, and Wilkinson for Ho³⁺ is presented. Large differences are found between TrammelFs theory and experiment and some possible reasons for this are discussed. X-ray atomic scattering factors for these ions are also given and found to agree very closely with the results of the ThomasFermi-Dirac statistical method.