Demonstration of moleculelike modes of doubly excited states in hyperspherical coordinates

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Abstract
The moleculelike normal modes formed by a pair of correlated electrons are examined through analysis of their wave functions in a body frame of the atom. The quantum numbers used by Lin for the classification of doubly excited states are reinterpreted from the body-frame viewpoint, and their connections with the rovibrator model of Herrick and Kellman are identified. This analysis also sheds light on the limitations of the rovibrator model of two correlated electrons. Because electrons are light and are not localized like atoms in a molecule, departure from the rovibrator picture grows rapidly as the rovibrational energy rises. Other limitations of the rovibrator model of doubly excited states stem from the following facts: (1) the dominant contribution to the rotational constant comes from the bielectronic repulsion instead of the kinetic energy; (2) the rotational contraction and T doubling result from atomic shell structure. We also include a brief discussion of the correspondence between the molecular stretching modes and the radial correlations of two electrons. The systematics of autoionization widths with respect to the correlation quantum numbers are also considered.