Scott correction for large atoms and molecules in a self-generated magnetic field

Abstract

We consider a large neutral molecule with total nuclear charge $Z$ in non-relativistic quantum mechanics with a self-generated classical electromagnetic field. To ensure stability, we assume that $Z\al^2\le κ_0$ for a sufficiently small ${\kappa }_0$, where $\al$ denotes the fine structure constant. We show that, in the simultaneous limit $Z\to \infty$, $\al\to 0$ such that $κ=Z\al^2$ is fixed, the ground state energy of the system is given by a two term expansion $c_1{Z}^{7/3}+c_2(\kappa )Z^2+o(Z^2)$. The leading term is given by the non-magnetic Thomas-Fermi theory. Our result shows that the magnetic field affects only the second (so-called Scott) term in the expansion.

References in corpus (1)

• The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction

Cited by in corpus (4)

• Relativistic Scott correction in self-generated magnetic fields
• The Scott conjecture for large Coulomb systems: a review
• The Ground State Energy of Heavy Atoms: the Leading Correction
• The reduced Hartree-Fock model with self-generated magnetic fields