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 F_5/2 and F_7/2 states in hydrogenlike ions and compared with the Dirac-Coulomb energy levels.

9 pages; RevTeX; discussion in Appendix A enhanced; accepted for publication by Physical Review A

References in corpus (6)

• The NRQED lagrangian at order 1/M^4
• General treatment of quantum and classical spinning particles in external fields
• NRQED approach to the fine and hyperfine structure corrections of order $m{\alpha }^6$ and $m{\alpha }^6(m/M)$ -- Application to the hydrogen atom
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• Quantum Electrodynamic Corrections to Cyclotron States in a Penning Trap

Cited by in corpus (1)

• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian