### Abstract

It is proved that N_{c}, the number of negative particles that can be bound to an atom of nuclear Charge z, satisfies N_{c} < 2z+1. For a molecule of K atoms, N_{c} < 2Z+K where Z is the total nuclear charge. As an example, for hydrogen N_{c}=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}+m^{2} c^{41/2}-mc^{2} (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 language | English (US) |
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Title of host publication | The Stability of Matter |

Subtitle of host publication | From Atoms to Stars: Fourth Edition |

Publisher | Springer Berlin Heidelberg |

Pages | 91-101 |

Number of pages | 11 |

ISBN (Print) | 3540420835, 9783540222125 |

DOIs | |

State | Published - Jan 1 2005 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

*The Stability of Matter: From Atoms to Stars: Fourth Edition*(pp. 91-101). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_8