Pairing model for doubly excited atoms

A model is investigated for doubly excited states, in which two electrons move on the surface of a spherical shell with restricted angular momentum to account for a hydrogenlike shell structure. Hybridized two-electron wave functions are constructed for the short-range part of the intrashell interaction potential using a modified version of hybridization theory originally developed by Pauling for molecules. The highest energy level obtained by this approach is identified as being invariant under SO(4) rotations on the restricted-shell basis, and is thus seen to be compatible with the SO(4) structure and rotation-vibration levels in a recent "supermultiplet" theory of doubly excited states. The highest energy level in each shell has ${}_{}{}^1{}_{}{}^{}S$ symmetry, and is interpreted as a "perfect pairing" level which maximizes the electron density at values of the interelectronic angle ${\theta }_{12}=0\mathrm{}°$, and hence is an exact eigenstate of a $\delta$-function interaction between the two electrons. Formulas are described for the explicit ${\theta }_{12}$ dependence of related ${}_{}{}^1{}_{}{}^{}S$ states for SO(4), and these give rise to approximate decoupling of the radial Schrödinger equation for two electrons in the same shell.