92-51 Lieb E.H., Solovej J.P., Yngvason J.

Heavy Atoms in the Strong Magnetic Field of a Neutron Star (26K, Plain TeX) May 5, 92

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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 $Z\to\infty$.We show rigorously that there are 5 regions as $Z\to\infty$: $B\ll Z^{4/3}$, $B\approx Z^{4/3}$, $Z^{4/3}\ll B\ll Z^3$, $B\approx Z^3$, $B\gg Z^3$. 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 {\it density matrix} functional theory.

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