Longitudinal spin order

Longitudinal spin order Extended Solomon equations... 

The remaining two are the longitudinal spin order, which results when the macroscopic z magnetization of one nucleus (e.g., H) is opposite depending on the microscopic z magnetization (a or P) state of the other nucleus (e.g., 13C), and the identity (1) operator, which simply represents the vast majority of spins that cancel each other out and play no role in NMR experiments. Longitudinal spin order can be viewed as an intermediate state in coherence transfer 2 US- 21-S- 2I-S.r = 2SX z. Like z magnetization, it is not affected... 

The final two product operators are the longitudinal spin order operator (2IZSZ) and the identity operator (1) ... 

Figure 4. Intensity patterns in an AX2 spin system (left, resonances of A right, of X2) resulting from different longitudinal spin order. Spin 1 is that of the A nucleus. Circles at line positions mean that the respective transition is unobservable owing to cancellation (e.g., 2I2zI3z would be observable in an AMX spin system). For further explanation, see the text.

The difference compared to equation B 1.13.2 or equation B 1.13.3 is the occurrence of the expectation value of the operator (the two-spin order), characterized by its own decay rate pjg and coupled to the one-spin longitudinal operators by the tenus 8j aud 5. We shall come back to the physical origin of these tenus below. 

So far, we have not considered the so-called longitudinal two-spin order, represented by the product operator9 2J ff, a quantity related to the polarization of nuclei A and B. This spin state can be created in different ways. The easiest way is probably to let the system evolve under the sole Jab coupling so as to obtain an antiphase doublet, for instance the B antiphase doublet represented by 2//Vf (corresponding to the two proton-carbon-13 satellites in an antiphase configuration). 

The complete microscopic details of how longitudinal (spin-lattice, r,) and transverse (spin-spin, T2) relaxation occur is beyond the scope of this book. But a little further discussion might be profitable in order to provide us with at least a qualitative understanding of the subject. 

S, second-order contamination L, possible longitudinal spin modulation. (From Cowley and Bates 1988.)... 

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