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The two-electron Schrödinger equation is analyzed in hyperspherical coordinates, with the electrons described throughout as a pair. In contrast to the current adiabatic hyperspherical method, which reverts at large distances to a description in terms of individual electrons, the pair aspect is preserved also asymptotically. Whereas the adiabatic potential wells converge to single-ionization limits, we develop potential wells converging to the double-ionization limit of the system, and doubly excited states are then viewed as eigenstates of the pair in these wells. At the simplest level, we get series converging to the double-ionization limit which are described analytically by the pair-Rydberg formula, with an effective charge that increases logarithmically with the principal quantum number. © 1992 The American Physical Society.

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Physical Review A

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