Eighth-order Foldy-Wouthuysen transformation

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 F5/2 and F7/2 states in hydrogenlike ions and compared with the Dirac-Coulomb energy levels.