Asymptotics of the ground state energy in the relativistic settings and with self-generated magnetic field

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 establishes the accuracy of Thomas-Fermi density approximation.

Contribution

It introduces sharp asymptotics for relativistic ground state energies with self-generated magnetic fields, including correction terms and density approximation validation.

Findings

Derivation of relativistic Scott correction term

Validation of Thomas-Fermi density approximation

Estimation of ionization energy and charge limits

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, with the self-generated magnetic field, 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.