Nonlinear Effects in Spectra of the Iron Group

As known for the last ten years, calculations made with the linear theory agree poorly with the experimental results for the 3d⁶ configuration of Fe III, compared with the agreement obtained for the 3d⁵4s configuration of that spectrum. It is shown that effects of 3s3d⁶4s on 3s²3d⁵4s satisfy the necessary conditions for linear behavior, consistent with the close agreement obtained in the latter configuration of Fe III. Corresponding effects of 3s3d⁷ on 3s²3d⁶ are not linear. When they are included in the calculation, close agreement is obtained in the 3d⁶ configuration as well; the mean error is reduced from ±{}364 cm^-1 to ±{}66 cm^-1. An additional parameter, γ, is introduced to define this nonlinear effect. The value of γ obtained from the experimental data by use of least squares is confirmed reasonably well by the value calculated from Watson's self-consistent field results. The parameters of the linear theory are changed considerably when this non-linear effect is accounted for.