Abstract
It was proved by Pekeris (1) that the singly excited states of H - lie exactly at, or slightly above, the ground state of hydrogen. Using a theory of Fano, (2) these fictitious states will have a configuration interaction with the H - continuum. The strength of this configuration interaction is computed for the mixing of a 1 s2p 1 P 0 state with the H - continuum for different values of the fictitious binding energy of the 2 p valence electron. In every case, the effect of the configuration interaction is to induce a rapid change of the phase shift of the continuum wave function by a quantity of π/2 over an energy range of a few times 0.01 eV, at an energy somewhat above the hydrogen ground state. The variation from π/2 to π is much slower. Such a swift change of the phase shift may be identified with the occurrence of a low-lying shape resonance.
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