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It is shown that, to order alpha 2 , S -2 = Sigma j mod (o mod z mod j) mod 2 /E j - E o =4.499752 for the dipole sum over Dirac states of the hydrogen atom. This compares with the value 9 / 2 for the sum over Schrodinger states.
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Bartlett et al. (1969) studied this question.
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