Hartree-Fock theory for pseudorelativistic atoms

TL;DR

This paper investigates the Hartree-Fock model for pseudorelativistic atoms, establishing the existence, regularity, and decay properties of the minimizers with a focus on the pseudorelativistic kinetic energy operator.

Contribution

It provides the first rigorous proof of existence and regularity of Hartree-Fock minimizers for pseudorelativistic atoms, including decay estimates.

Findings

Existence of Hartree-Fock minimizer for pseudorelativistic atoms

Regularity of orbitals away from the nucleus

Exponential decay of orbitals

Abstract

We study the Hartree-Fock model for pseudorelativistic atoms, that is, atoms where the kinetic energy of the electrons is given by the pseudorelativistic operator \sqrt{(pc)^2+(mc^2)^2}-mc^2. We prove the existence of a Hartree-Fock minimizer, and prove regularity away from the nucleus and pointwise exponential decay of the corresponding orbitals.