Effect of crystalline fields on magnetic-form factors

The effects of crystalline fields on magnetic-form factors are discussed on the basis of recent Hartree-Fock calculations of Watson augmented by an analysis of experimental optical absorption data. It is shown that the crystalline field has two effects on the free ion 3d wave functions and hence on their form factors as well: (1) a differentiation or "splitting" of the two types of cubic 3d functions by an expansion of the t_2g (or e_g) orbital and a contraction of the e_g (or t _2g) orbital resulting in two different radial charge densities and (2) a net expansion of the charge distribution from the free ion value. The magnetic-form factor due to this "splitting" effect when calculated according to the methods of Weiss and Freeman shows measurable deviations from the free atom results. A form factor for Mn⁺² based on optical absorption data shows a large expansion of the 3d charge density, in agreement with the measurements of Hastings, Elliott, and Corliss.