Classification of Doubly Excited States of Two-Electron Atoms

Abstract

Based upon the analysis of electron correlations in hyperspherical coordinates, a classification scheme for all doubly excited states of two-electron atoms is presented. A new set of correlation quantum numbers, $K$, $T$, and $A$, is introduced, where ($K$, $T$) describes angular correlations and $A$ describes radial correlations. It is shown that states with different $L$, $S$, and $\ensuremath{\pi}$ but identical ${(K,T)}^{A}$ have isomorphic correlations. Such isomorphism is shown to result in the general supermultiplet structure of doubly excited states.