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NRQED approach to the fine and hyperfine structure corrections of orderm$\alpha$ 6 and m$\alpha$ 6 (m/M)-Application to the hydrogen atom The NRQEDapproach is applied to the calculation of relativistic corrections to the fineand hyperfine structure of hydrogenlike atoms at orders m$\alpha$ 6 andm$\alpha$ 6 (m/M). Results are found to be in agreement with those of therelativistic theory. This confirms that the derived NRQED effective potentialsare correct, and may be used for studying more complex atoms or molecules.Furthermore, we verify the equivalence between different forms of the NRQEDLagrangian used in the literature.

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