Classification and supermultiplet structure of doubly excited states

Based upon the analysis of electron correlations in hyperspherical coordinates for two-electron atoms for arbitrary L, S and π states, a classification scheme for all doubly excited states is presented. A new set of correlation quantum numbers K, T and A, is introduced. Here (K, T) describes wave functions in hyperspherical coordinates, it is shown that states with identical (K, T)^A have isomorphic correlations. This isomorphism is shown to be the origin of the supermultiplet structure of doubly excited states.