### Abstract

As an approximation to a relativistic one-electron molecule, we study the operator H=(-Δ+m^{2})^{1/2}-e^{2} Z _{j}|x-R_{j}|^{-1} with Z_{j}0, e ^{-2}=137.04. H is bounded below if and only if e^{2} Z _{j}>2/π, all j. Assuming this condition, the system is unstable when e^{2}ΣZ_{j}>2/π in the sense that E _{0}=inf spec (H) → - ∞ as the R_{j} → 0, all j. We prove that the nuclear Coulomb repulsion more than restores stability; namely E_{0}+0.069e^{2} Z_{i}Z_{j}|R _{i}-R_{j}|^{-1}0. We also show that E_{0} is an increasing function of the internuclear distances |R_{i}-R _{j}|.

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 | 471-484 |

Number of pages | 14 |

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

Daubechies, I., & Lieb, E. (2005). One-electron relativistic molecules with coulomb interaction. In

*The Stability of Matter: From Atoms to Stars: Fourth Edition*(pp. 471-484). Springer Berlin Heidelberg. https://doi.org/10.1007/3-540-27056-6_33