The Foldy-Wouthuysen Hamiltonian of a light atomic system that has an 𝑚𝛼 8 contribution to energy levels is calculated. The case of a Dirac-Coulomb field is discussed. The results can be used for relativistic and radiative corrections to energy levels in the low-energy part. A divergent operator 𝛿 2 (𝑟) emerges. This is probably due to the nature of the point-like charge source. The effective method of radiation calculation may be re-checked.
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