The Leading Behaviour of The Ground-State Energy of Heavy Ions According to Brown and Ravenhall

TL;DR

This paper proves that relativistic effects do not influence the leading order of the ground-state energy in heavy ions according to the Brown-Ravenhall model, extending previous results to negative ions and systems with electrons proportional to nuclear charge.

Contribution

It establishes the absence of relativistic effects in the leading order of ground-state energy for a broader class of systems within the Brown-Ravenhall framework.

Findings

Relativistic effects are absent in the leading order for negative ions.

The result applies to systems with electron count proportional to nuclear charge.

Extends previous findings from neutral atoms to more general systems.

Abstract

In this article we prove the absence of relativistic effects in leading order for the ground-state energy according to Brown-Ravenhall operator. We obtain this asymptotic result for negative ions and for systems with the number of electrons proportional to the nuclear charge. In the case of neutral atoms the analogous result was obtained earlier by Cassanas and Siedentop [4].