The Ground State Energy of Heavy Atoms According to Brown and Ravenhall: Absence of Relativistic Effects in Leading Order

TL;DR

This paper demonstrates that the leading order ground state energy of heavy atoms aligns with non-relativistic predictions, despite using a relativistic Hamiltonian derived from quantum electrodynamics.

Contribution

It proves that relativistic effects do not influence the leading order energy of heavy atoms, using the Brown and Ravenhall Hamiltonian.

Findings

Ground state energy matches non-relativistic Thomas-Fermi energy at leading order

Relativistic effects are absent in the leading order energy calculation

Brown and Ravenhall Hamiltonian accurately captures energy levels up to order α²Ry

Abstract

It is shown that the ground state energy of heavy atoms is, to leading order, given by the non-relativistic Thomas-Fermi energy. The proof is based on the relativistic Hamiltonian of Brown and Ravenhall which is derived from quantum electrodynamics yielding energy levels correctly up to order $\alpha^2$Ry.