Radial and angular correlations of two excited electrons. III. Comparison of configuration-interaction wave functions with adiabatic channel functions in hyperspherical coordinates

Abstract

Wave functions for doubly excited states of helium $^{1,3}S^{e}$ states calculated in the configuration-interaction (CI) method are examined in hyperspherical coordinates. It is shown that these wave functions are essentially identical to the wave functions calculated in the adiabatic approximation except in regions where the charge density is vanishingly small. This comparison establishes the connection between the classification of doubly excited states based upon the adiabatic approximation in hyperspherical coordinates and the classification of Herrick and Sinanoglu\ifmmode \check{}\else \v{}\fi{} which is based upon the approximate CI wave functions. It is also shown that states calculated from the CI method which have similar quantum defects have the same correlation patterns except in regions where the charge density is small. This establishes the approximate channel classification of doubly excited states as implied in the adiabatic approximation in hyperspherical coordinates.