Geometrical interpretation of doubly excited states

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Abstract
The theory of doubly excited atomic states is analysed with particular focus on the physical nature of level structure previously identified by group theoretical methods. An explicit factorisation in terms of external rotational and independent intrinsic parts provides a direct identification of the quantum numbers K and T commonly used to characterise correlation patterns of doubly excited states. Two important intrinsic symmetry operators are also identified. One of these differentiates between the two components of T doublets while the other directly determines the radial correlation quantum number introduced by Lin (1984) on phenomenological grounds. Intrinsic states appear in general as simple linear combinations of two-electron product Stark states. The rotor pertaining to the important case where K is maximum is found to be a pure product Stark state. Finally, the authors clarify an open question concerning the angular momentum distribution of Rydberg states of hydrogen excited by electron impact at energies near the ionisation threshold.