### Abstract

The ground state energy of an atom in the presence of an external magnetic filed B (with the electron spin-field interaction included) can be arbitrarity negative when B is arbitrarily large. We inquire whether stability can be restored by adding the self energy of the field, ∫B^{2}. For a hydrogenic like atom we prove that there is a critical nuclear charge, z_{c}, such that the atom is stable for z<z_{c} and unstable for z>z_{c}.

Original language | English (US) |
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Pages (from-to) | 251-270 |

Number of pages | 20 |

Journal | Communications in Mathematical Physics |

Volume | 104 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 1986 |

### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Fröhlich, J., Lieb, E. H., & Loss, M. (1986). Stability of coulomb systems with magnetic fields - I. The one-electron atom.

*Communications in Mathematical Physics*,*104*(2), 251-270. https://doi.org/10.1007/BF01211593