Using the Dirac equation, we consider the contributions to atomic levels of terms quadratic in A. A may be, for example, the nuclear magnetic dipole field. We show that a consistent quantum mechanical treatment cancels all terms arising from [Aᵢ, Aⱼ]≠0. This resolves a disagreement between hyperfine structure corrections calculated nonrelativistically and relativistically.
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Morton M. Sternheim (1962) studied this question.
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