Computation of Multiplet Intensity Ratios

For higher spin nuclei, one can construct a splitting diagram. For example, for two spin-1 nuclei  

This procedure quickly gets out of hand, however, and a more compact notation is preferable. Thus if we think of each of the three lines resulting from coupling to the first spin-1 nucleus split into a 1 1 1 triplet, we have  

This procedure can be extended to three spin-1 nuclei by thinking of each line of a 1 1 1 triplet split into a 1 2 3 2 1 quintet  

For really complicated situations, this method can be used as the basis for a computer algorithm. 

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