A Statistical Theory of Heavy Atoms: Asymptotic Behavior of the Energy and Stability of Matter

TL;DR

This paper analyzes the asymptotic behavior of the ground state energy of heavy atoms using a relativistic functional, establishing stability of matter through a new lower bound approach.

Contribution

It provides the asymptotic analysis of atomic energies and demonstrates matter stability for relativistic models, extending prior non-relativistic results.

Findings

Asymptotic behavior of energy for heavy atoms derived

Stability of matter established for relativistic models

New lower bound technique introduced

Abstract

We give the asymptotic behavior of the ground state energy of Engel's and Dreizler's relativistic Thomas-Fermi-Weizs\"acker-Dirac functional for heavy atoms for fixed ratio of the atomic number and the velocity of light. Using a variation of the lower bound, we show stability of matter.