The Ground State Energy of Heavy Atoms: Leading and Subleading Asymptotics

TL;DR

This paper investigates the asymptotic behavior of ground state energies in large neutral atoms within the no-pair formalism, demonstrating that these energies align with Furry energy estimates up to subleading terms.

Contribution

It extends Séré's results to a broad class of projections, showing no-pair energies match Furry energies at leading and subleading orders for large atomic numbers.

Findings

No-pair ground state energies do not exceed Furry energies at leading order.

The results hold for a wide class of projections, including non-physical ones.

Extension of Séré's results to the no-pair formalism.

Abstract

We study atomic ground state energies for neutral atoms as the nuclear charge $Z$ is large in the no-pair formalism. We show that for a large class of projections defining the underlying Dirac sea -- covering not only the physical reasonable cases but also ``weird'' ones -- the corresponding no-pair ground state energy does not exceed the one of the Furry energy up to subleading order. An essential tool is the use and extension of S\'er\'e's results on atomic Dirac-Hartree-Fock theory.