### Abstract

The Dirac equation for hydrogenic atoms has a well known instability when z±>1. A similar instability occurs for the "relativistic Schrödinger equation" with p22m replaced by (p2c2+m2c4)12-mc2 at z±=2. These instabilities concern only the product z±, but when the many-electron-many-nucleus problem is examined (in the relativistic Schrödinger theory) we find that a bound on ± alone (independent of z) is then required for stability. If ±<194 we find that stability occurs all the way up to the critical value z±=2, whereas if ±>12815 then the system is unstable for all values of z. Some implications of these findings are also discussed.

Original language | English (US) |
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Pages (from-to) | 1695-1697 |

Number of pages | 3 |

Journal | Physical Review Letters |

Volume | 61 |

Issue number | 15 |

DOIs | |

State | Published - Jan 1 1988 |

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

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## Cite this

Lieb, E., & Yau, H. T. (1988). Many-body stability implies a bound on the fine-structure constant.

*Physical Review Letters*,*61*(15), 1695-1697. https://doi.org/10.1103/PhysRevLett.61.1695