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

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

1999-11-19

arxiv.org/abs/math-ph/9911025v1

Physics

Mathematical Physics

Scientific paper

10.1007/s002200000239

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 {\em bosons} with delta interactions in {\em 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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