Asymptotics of the ground state energy in the relativistic settings

TL;DR

This paper derives precise asymptotic formulas for the ground state energy of heavy atoms and molecules in relativistic regimes, including correction terms, and shows the Thomas-Fermi density approximates the true ground state density.

Contribution

It provides the first sharp asymptotics for relativistic ground state energies and establishes the validity of Thomas-Fermi density approximation in this setting.

Findings

Derivation of relativistic Scott correction term

Identification of Dirac, Schwinger, and relativistic correction terms

Proof that Thomas-Fermi density approximates the actual ground state density

Abstract

The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger and relativistic correction terms. Also we will prove that Thomas-Fermi density approximates the actual density of the ground state, which opens the way to estimate the excessive negative and positive charges and the ionization energy.