Supermultiplet classification of higher intrashell doubly excited states ofH−and He

Abstract

We compute new estimates of energy levels of doubly excited states with two electrons in the same shell, for all principal quantum numbers $N\le 5$ and angular momentum values $0\le L\le 2N-2$ in ${\mathrm{H}}^{-}$ and He. We investigate the structure of these intrashell spectra using a recent "supermultiplet" approach which orginates in the O(4) shell structure of one-electron atoms. We provide new interpretations of the electron correlation underlying the O(4) states and supermultiplets of two-electron atoms; this accounts qualitatively for approximate separability of rotationlike and vibrationlike progressions of levels found in the computed spectra. Certain diamond-shaped patterns of supermultiplet energies are found to contain near degeneracies of levels with $\Delta L=\pm 2$; this accounts in part for level clustering we find in the unresolved spectra. Our investigation of scaling of the apparent rotational and vibrational parts of the energy with higher $N$ shows consistency with a simple model of the atom which has electrons on the surface of a spherical shell, with radius $R\simeq N^2$. We investigate the model group theoretically, and find two different O(4) groups which describe angular electron correlation in limiting cases of large or small shell radius for each principal quantum number $N$. A third O(4) group is related to intrashell radiative transitions.