### Abstract

The ground state energy of an atom of nuclear charge Ze and in a magnetic field B is evaluated exactly in the asymptotic regime Z → ∞. We present the results of a rigorous analysis that reveals the existence of 5 regions as Z → ∞: B ≪Z^{4/3}, B ≈Z^{4/3}, Z^{4/3} ≪B ≪Z^{3}, B ≈Z^{3}, B ≫Z^{3}. Different regions have different physics and different asymptotic theories. Regions 1, 2, 3, 5 are described exactly by a simple density functional theory, but only in regions 1, 2, 3 is it of the semiclassical Thomas-Fermi form. Region 4 cannot be described exactly by any simple density functional theory; surprisingly, it can be described by a simple density matrix functional theory.

Original language | English (US) |
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Pages (from-to) | 221-237 |

Number of pages | 17 |

Journal | Mathematics in Science and Engineering |

Volume | 192 |

Issue number | C |

DOIs | |

State | Published - Jan 1 1993 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Engineering(all)

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## Cite this

*Mathematics in Science and Engineering*,

*192*(C), 221-237. https://doi.org/10.1016/S0076-5392(08)62384-X