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

TL;DR

This paper investigates the asymptotic behavior of atomic ground state energies in extremely strong magnetic fields, revealing that the leading term scales with the square of the logarithm of the field strength and relates to a one-dimensional bosonic system.

Contribution

It extends previous results by characterizing the high magnetic field limit for atoms with fixed nuclear charge and electron number, connecting it to a one-dimensional bosonic model.

Findings

Leading term of energy scales as $( ext{ln} B)^2 e(Z,N)$

Shows the asymptotics extend known results for N=1 and large N,Z

Connects atomic energy asymptotics to a 1D bosonic system

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.