Nuclear Pascal triangle

Multiplicity rules for first-order spectra systems) When coupled, n nuclei of an element X with nuclear spin quantum number = i produce a splitting of the 4 signal into n.+ I lines the relative intensities of the individual lines of a first-order multiplet are given by the coefficients of the Pascal triangle (Fig. 1.5). 

Something of scientific interest (among numerous other applications, Pascal s triangle is used to predict nuclear magnetic resonance [NMR] multiplet splitting patterns) has been created from the repeated application of a simple rule. 

Figures 1.9a and b demonstrate the effect of proton broadband decoupling in the 13C NMR spectrum of a mixture of ethanol and hexadeuterioethanol. The CH3 and CH2 signals of ethanol appear as intense singlets upon proton broadband decoupling while the CD3 and CD2 resonances of the deuteriated compound still display their septet and quintet fine structure deuterium nuclei are not affected by lH decoupling because their Larmor frequencies are far removed from those of protons further, the nuclear spin quantum number of deuterium is ID = 1 in keeping with the general multiplicity rule (2 nxh+ 1, Section 1.4), triplets, quintets and septets are observed for CD, CD2 and CD3 groups, respectively. The relative intensities in these multiplets do not follow Pascal s triangle (1 1 1 triplet for CD 1 3 4 3 1 quintet for CD2 1 3 6 7 6 3 1 septet for CD3).

Since Pascal s triangle has proven successful in determining atomic magic numbers, the question arises as to whether it can also help to identify nuclear magic numbers - can it provide a geometrical image and an analytical formula just as for atoms ... 

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