Classification of Doubly Excited States of Two-Electron Atoms

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 π but identical (K,T)A have isomorphic correlations. Such isomorphism is shown to result in the general supermultiplet structure of doubly excited states.