Atoms in the Magnetic Field of a Neutron Star

Elliott H. Lieb, Jan Philip Solovej

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


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 ≪Z4/3, B ≈Z4/3, Z4/3 ≪B ≪Z3, B ≈Z3, B ≫Z3. 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 languageEnglish (US)
Pages (from-to)221-237
Number of pages17
JournalMathematics in Science and Engineering
Issue numberC
StatePublished - Jan 1 1993

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Engineering


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