The Ground State Energy of Heavy Atoms: Relativistic Lowering of the Leading Energy Correction

TL;DR

This paper proves that the relativistic model for heavy atoms results in a lower Scott correction energy than the non-relativistic model, valid up to the critical coupling constant.

Contribution

It establishes the existence and relativistic lowering of the leading energy correction for heavy atoms within a pseudo-relativistic framework.

Findings

Relativistic correction lowers the Scott energy for heavy atoms.

Proof valid up to the critical coupling constant.

Method based on energy renormalization and comparison to non-relativistic results.

Abstract

We describe atoms by a pseudo-relativistic model that has its origin in the work of Chandrasekhar. We prove that the leading energy correction for heavy atoms, the Scott correction, exists. It turns out to be lower than in the non-relativistic description of atoms. Our proof is valid up to and including the critical coupling constant. It is based on a renormalization of the energy whose zero level we adjust to be the ground-state energy of the corresponding non-relativistic problem. This allows us to roll the proof back -- by relatively simple technical means -- to results for the Schr\"odinger operator.