Relativistic magnetic form factors of tripositive rare-earth ions

Magnetic form factors have been obtained from Dirac-Fock calculations for all the rare-earth tripositive ions. In addition to using relativistic $4f$ wave functions, the coupling of the neutron magnetic moment to the current density has been treated consistently using a relativistic formulation for the scattering amplitude. For each rare-earth ion we evaluated the odd magnetic multipoles, of order less or equal to seven, which are needed for the evaluation of the magnetic scattering amplitude in most cases of experimental interest. We find that in all cases the magnetic form factor decreases faster with increasing scattering angle than predicted by nonrelativistic calculations. This is because (i) the relativistic $4f$-electron wave functions are more expanded in space as a result of the relativistic core contraction than the Hartree-Fock wave functions and (ii) the net effect of the spin orbit and mass correction term on the scattering of neutrons, implicitly included in our relativistic formulation of the scattering amplitude, is such that the neutron senses a current density more expanded in space than predicted by nonrelativistic calculations.