Nonrelativistic QED approach to the fine- and hyperfine-structure corrections of order m α6 and m α6(m /M ) : Application to the hydrogen atom

The nonrelativistic QED (NRQED) approach is applied to the calculation of relativistic corrections to the fine and hyperfine structure of hydrogenlike atoms at orders m α⁶ and m α⁶(m /M ) . Results are found to be in agreement with those of the relativistic theory. This confirms that the derived NRQED effective potentials are correct, providing a reliable basis for studies in more complex atoms or molecules. Furthermore, we verify the equivalence between different forms of the NRQED Lagrangian used in the literature. It is found that the gauge-invariant form derived according to the initial formulation of NRQED by Caswell and Lepage [Phys. Lett. B 167, 437 (1986), 10.1016/0370-2693(86)91297-9] yields a different set of effective potentials, which are simpler for numerical computations.