Corrections to the Dirac equation, relativistic to the order v²c², due to the motion of the nucleus, for the case of an electron in the field of a heavy particle of mass M, are derived with the aid of the Breit two-body relativistic interaction, to the order m/M, m being the mass of the electron. A calculation of the value of the correction for a $1s$ electron gives a result in agreement with that obtained from the Schr\"odinger treatment to the order m/M.
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Irving S. Lowen (1937) studied this question.
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