Oleg Zabluda's blog
Tuesday, January 17, 2017
 
"""
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The hydrogen anion is a negative ion of hydrogen, H−. The hydrogen anion is an important constituent of the atmosphere of stars, such as the Sun. [...] The ion has two electrons bound by the electromagnetic force to a nucleus containing one proton. [...] Its existence was first proven theoretically by Hans Bethe in 1929. H− is unusual because, in its free form, it has no bound excited states, as was finally proven in 1977 (Hill 1977).
"""
https://en.wikipedia.org/wiki/Hydrogen_anion

Proof that the H- Ion Has Only One Bound State (1976) Robert Nyden Hill,
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It is rigorously demonstrated that the nonrelativistic H ion has only one bound state in the fixed (infinite-mass) nucleus approximation with Coulomb interactions only. The H- ion, made up of a, proton and two electrons, has long been known to have one bound state. ' Additional bound states have never been found, but their nonexistence has so far not been proved. The present note provides the proof in the fixed (infinite-mass) nucleus approximation with Coulomb interactions only. The importance of the present result stems from the qualitative difference between the bound-state spectrum of negative ions (of which H- is the simplest example) and the bound-state spectrum of positive ions and neutrals. Negative ions have only a finite number of bound states, for which correlation effects are decisive (H, for example, is believed to have no bound states in Hartree-Pock approximation). Positive ions and neutrals, on the other hand, have an infinite number of bound states.
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http://journals.aps.org.sci-hub.bz/prl/abstract/10.1103/PhysRevLett.38.643
http://journals.aps.org.sci-hub.bz/prl/abstract/10.1103/PhysRevLett.38.643

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