### Abstract

We consider the quantum mechanical many-body problem of electrons and fixed nuclei interacting via Coulomb forces, but with a relativistic form for the kinetic energy, namely p^{2}/2m is replaced by (p^{2} c ^{2} + m^{2} c^{4})^{1/2} - mc^{2}. The electrons are allowed to have q spin states (q = 2 in nature). For one electron and one nucleus instability occurs if zα > 2/π, where z is the nuclear charge and α is the fine structure constant. We prove that stability occurs in the many-body case if zα 2/π and α < 1/(47q). For small z, a better bound on α is also given. In the other direction we show that there is a critical α_{c} (no greater than 128/15π) such that if α > α_{c} then instability always occurs for all positive z (not necessarily integral) when the number of nuclei is large enough. Several other results of a technical nature are also given such as localization estimates and bounds for the relativistic kinetic energy.

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 | 485-521 |

Number of pages | 37 |

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. 485-521). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_34