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

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 Séré's results on atomic Dirac-Hartree-Fock theory.

arXiv comment26 pages, 1 figures

References in corpus (7)

• On the eigenvalues of operators with gaps. Application to Dirac operators
• Equivalence of Sobolev norms involving generalized Hardy operators
• The Scott correction in Dirac-Fock theory
• Lower bounds on the moduli of three-dimensional Coulomb-Dirac operators via fractional Laplacians with applications
• The Ground State Energy of Heavy Atoms: the Leading Correction
• The Scott conjecture for large Coulomb systems: a review
• A new definition of the Dirac-Fock ground state