Ground state energy of large atoms in a self-generated magnetic field

TL;DR

This paper proves that for large atoms with self-generated magnetic fields, the ground state energy is accurately described by non-magnetic Thomas-Fermi theory in the limit of large atomic number and small fine structure constant, under certain conditions.

Contribution

It establishes the leading order behavior of the ground state energy of large atoms with self-generated magnetic fields, connecting quantum mechanical models to Thomas-Fermi theory.

Findings

Ground state energy matches non-magnetic Thomas-Fermi theory in the specified limit.

Validates the approximation under the condition Zα^2 ≤ κ.

Provides rigorous proof for the asymptotic behavior of large atoms with magnetic fields.

Abstract

We consider a large atom with nuclear charge $Z$ described by non-relativistic quantum mechanics with classical or quantized electromagnetic field. We prove that the absolute ground state energy, allowing for minimizing over all possible self-generated electromagnetic fields, is given by the non-magnetic Thomas-Fermi theory to leading order in the simultaneous $Z\to \infty$, $\al\to 0$ limit if $Z\al^2\leq \kappa$ for some universal $\kappa$, where $\al$ is the fine structure constant.