Crystalline field and spin polarization effects on electron densities and magnetic form factors

The combined effects of spin (or exchange) polarization and an external crystalline field on charge densities, x-ray and magnetic form factors, and hyperfine parameters are investigated following the analytic Hartree-Fock self-consistent field approach. The crystalline field was represented by a crude cubic field arising from an octahedral array of point charges surrounding the central ionin this case Ni+2. In the strong field approximation the atomic 3d electrons are "split" by the crystalline field and the spinpolarization effect, resulting in a description of these electrons by a set of three distinct orbitals (each having different radial distributions and called t2g, t2g and eg). The ion's spin density leads to a Fermi contact hyperfine term in better agreement with experiment than the value reported in an earlier spin polarized calculation for the free Ni+2 ion and a magnetic form factor whose Fourier transform resembles none of the individual 3d charge distributions.