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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1999-46
December 1999

Atoms in strong magnetic fields: The high field limit at fixed nuclear charge


Jan Philip Solovej

Bernhard Baumgartner, Jakob Yngvason


Let E(B,Z,N) denote the ground state energy of an atom with N electrons and nuclear charge Z in a homogeneous magnetic field B. We study the asymptotics of E(B,Z,N) as B\to \infty with N and Z fixed but arbitrary. It is shown that the leading term has the form (\ln B)^2 e(Z,N), where e(Z,N) is the ground state energy of a system of N bosons with delta interactions in one dimension. This extends and refines previously known results for N=1 on the one hand, and N,Z\to\infty with B/Z^3\to\infty on the other hand.

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This paper has now been published in Commun. Math. Phys. 212, 713-724 (2000)