Eighth-Order Foldy-Wouthuysen Transformation

TL;DR

This paper performs an eighth-order Foldy-Wouthuysen transformation to accurately compute higher-order binding corrections in bound systems, providing detailed matrix element evaluations for hydrogenlike ions.

Contribution

It extends the Foldy-Wouthuysen transformation to eighth order in momentum, enabling more precise calculations of relativistic effects in atomic systems.

Findings

Matrix elements for F_5/2 and F_7/2 states calculated

Comparison with Dirac-Coulomb energy levels shows improved accuracy

Provides a foundation for higher-order relativistic corrections

Abstract

The calculation of higher-order binding corrections to bound systems is a fundamental problem of theoretical physics. For any nonrelativistic expansion, one needs the Foldy-Wouthuysen Transformation which disentangles the particle and the antiparticle degrees of freedom. This transformation is carried out here to eighth order in the momenta, or, to eighth order in the momentum operators, which is equivalent to the eighth order of the fine-structure constant. Matrix elements of the eighth-order terms are evaluated for F_5/2 and F_7/2 states in hydrogenlike ions and compared with the Dirac-Coulomb energy levels.