 9251 Lieb E.H., Solovej J.P., Yngvason J.
 Heavy Atoms in the Strong Magnetic Field of a Neutron Star
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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
ThomasFermi 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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