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 $3d^{7}4s$ and $3d^8$ configurations of atomic iron, as well as for the $3d^{6}4s^2$ 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 $3d^{6}4s^2$, $3d^{7}4s$, and $3d^8$ configurations. The fraction of the charge of a $3d$ electron outside a sphere of radius $2.66a_0$ is 0.050, 0.095, and 0.160, respectively, for these configurations. The Racah parameters $B$, $C$, and $G_2$ are evaluated from the wave functions for all three configurations, and are also found for $3d^{6}4s^2$ and for $3d^{7}4s$ 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 $G_2$ calculated from the wave functions exceeds the least squares value by almost 50% in $3d^{7}4s$. Energies of the $3d^{7}4s$ and $3d^8$ configurations relative to $3d^{6}4s^2$, 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.