Bound on the maximum negative ionization of atoms and molecules

Elliott H. Lieb

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Scopus citations


It is proved that Nc, the number of negative particles that can be bound to an atom of nuclear Charge z, satisfies Nc < 2z+1. For a molecule of K atoms, Nc < 2Z+K where Z is the total nuclear charge. As an example, for hydrogen Nc=2, and thus H- is not stable, which is a result not proved before. The bound particles can be a mixture of different species, e.g., electrons and π mesons; statistics plays no role. The theorem is proved in the static-nucleus approximation, but if the nuclei are dynamical, a related, weaker result is obtained. The kinetic energy operator for the particles can be either [p-eA (x)/c]2/2m (nonrelativistic with magnetic field) or [pc-eA(x)]2+m2 c41/2-mc2 (relativistic with magnetic field). This result is not only stronger than that obtained before, but the proof (at least in the atomic case) is simple enough to be given in an elementary quantum-mechanics course.

Original languageEnglish (US)
Title of host publicationThe Stability of Matter
Subtitle of host publicationFrom Atoms to Stars: Fourth Edition
PublisherSpringer Berlin Heidelberg
Number of pages11
ISBN (Print)3540420835, 9783540222125
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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