Many of the doublets in the spectra of alkalies and alkalilike ions are inverted or anomalously narrow. This "tendency to inversion" may be explained by the polarizability of the core, which may be formulated as the repulsion by the excited core configuration states of the levels of the optical doublet. A study is made of the energies and wave functions of these states for the spectra Na I to S VI, on two coupling schemes which allow approximate computations to be made. On the assumption of $\mathrm{LS}$ coupling the separations of the excited core doublets turn out to be of the order of magnitude of the $2p$ x-ray doublet; half the excited core doublets are inverted and half of them normal. The two sets of doublets repel the levels of the optical doublet unequally, and, in the series of spectra considered, the differential repulsion is of the right sign to give an inverting tendency of the same order, though somewhat less, than the observed inversion. The same problem is then treated by another approximation, by assuming the $2p$ x-ray doublet energy large compared to the electrostatic interaction energy of the $3p$ and $3d$ electrons. The results with both models are proportional to the spin orbit interaction energy of the "hole" in the $2p$ shell. The condition that the effects studied should tend to invert and not to broaden the optical doublets, and the further conditions that they should produce an actual inversion are considered. In most cases these questions may be answered from a consideration of the quantum numbers associated with the states capable of perturbing the doublet, and the ratio of optical and x-ray doublet separations. In this way we can understand the observed incidence, both of the tendency toward inversion and of the inversion itself.

• Received 29 June 1933

DOI:https://doi.org/10.1103/PhysRev.44.644