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

Abstract

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.