Self-Consistent Field Calculation for Three Configurations of Atomic Iron

The Hartree self-consistent field method without exchange is used to calculate atomic wave functions for the 3d⁷4s and 3d⁸ configurations of atomic iron, as well as for the 3d⁶4s² configuration previously studied by Manning and Goldberg. Most sensitive to the change in configuration is the $3d$ electron, whose energy is -0.79, -0.50, and -0.34 ry, respectively, in the 3d⁶4s², 3d⁷4s, and 3d⁸ configurations. The fraction of the charge of a $3d$ electron outside a sphere of radius 2.66a₀ is 0.050, 0.095, and 0.160, respectively, for these configurations. The Racah parameters B, C, and G₂ are evaluated from the wave functions for all three configurations, and are also found for 3d⁶4s² and for 3d⁷4s by a least squares fit of the spectroscopically observed terms. The two sets of values for B and C agree within 15%, but the value of G₂ calculated from the wave functions exceeds the least squares value by almost 50% in 3d⁷4s. Energies of the 3d⁷4s and 3d⁸ configurations relative to 3d⁶4s², calculated from the wave functions, are 0.25 and 0.65 ry, respectively; the corresponding values deduced from the observed spectrum are 0.15 and 0.33 ry.