The general NMR intensity sum rule ∑ kIj0k= ∑ iIij0+2Fz(j0)is proved. The sum on the left is the sum of the intensities of all the transitions to the state j0 (νj0←k), the sum on the right is the sum of the intensities of all the transitions from the state j0 (νi←j0), and the third term is twice the z component of the total spin of this state j0.
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Gioumousis et al. (1962) studied this question.
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