Unrestricted Hartree-Fock Method: Electron Densities and Magnetic Form Factors for Spin PolarizedNi++

The effect of relaxing the restrictions associated with the Hartree-Fock method are discussed with particular emphasis on that constraint which requires common radial behavior for wave functions with all quantum numbers except $m_s$ (spin direction) in common. Results of such a "spin polarized" Hartree-Fock self-consistent field calculation are reported for the ${\mathrm{Ni}}^{+2\mathrm{}}$ ion and related to earlier calculations of Wood and Pratt, and Heine. Emphasis is placed on a consideration of the effects on the electron density and on x-ray and magnetic form factors. As is discussed, spin polarization of the $3d$ shell and the core results in an interesting effect on the magnetic form factor for this case. The calculation suggests that one would obtain a magnetic form factor which is measurably expanded (hence, a contracted charge distribution) in comparison with that appropriate for any single $3d$ electron. Also presented are results of calculations of several hyperfine parameters which are in rough agreement with experiment.