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We present the derivation of the effective higher-order Hamiltonian, which gives an mα⁶ contribution to the energy levels of an arbitrary light atom. The derivation is based on the Foldy-Wouthuysen transformation of the one-particle Dirac Hamiltonian followed by perturbative expansion of the many-particle Green function. The obtained results can be used for the high precision calculation of relativistic effects in atomic systems.
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Krzysztof Pachucki (2005) studied this question.
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