Bernhard Baumgartner, Jan Philip Solovej, and Jakob Yngvason
Atoms in strong magnetic fields:The high field limit at fixed nuclear charge
(61K, LaTex)
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.