A Statistical Theory of Heavy Atoms: Energy and Excess Charge

TL;DR

This paper provides a simple derivation of bounds on the energy and excess charge in a relativistic atomic model, enhancing understanding of heavy atom behavior in quantum physics.

Contribution

It introduces an elementary derivation of energy bounds and excess charge limits for a relativistic Thomas-Fermi-type model, offering new analytical tools.

Findings

Derived a lower bound on the relativistic Thomas-Fermi-Weizs"acker-Dirac functional.

Established an upper bound on the excess charge of heavy atoms.

Provided insights into the energetic stability of heavy atoms.

Abstract

The purpose of this note is to give an elementary derivation of a lower bound on the relativistic Thomas-Fermi-Weizs\"acker-Dirac functional of Thomas-Fermi type and to apply it to get an upper bound on the excess charge of this model.