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 $3d^6$ configuration of Fe III, compared with the agreement obtained for the $3d^{5}4s$ configuration of that spectrum. It is shown that effects of $3s3d^{6}4s$ on $3s^{2}3d^{5}4s$ satisfy the necessary conditions for linear behavior, consistent with the close agreement obtained in the latter configuration of Fe III. Corresponding effects of $3s3d^7$ on $3s^{2}3d^6$ are not linear. When they are included in the calculation, close agreement is obtained in the $3d^6$ configuration as well; the mean error is reduced from ±364 ${\mathrm{cm}}^{-1\mathrm{}}$ to ±66 ${\mathrm{cm}}^{-1\mathrm{}}$. An additional parameter, $\gamma$, is introduced to define this nonlinear effect. The value of $\gamma$ 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.