The flow of spin populations

A surprising amount of insight concerning nuclear spin relaxation can be obtained simply by treating the various available spin states as analogous to chemical states linked by kinetics. Although the spin transition probabilities such as W+ remain to be determined either by experiment or by quantum mechanical theory, as do kinetic rate constants, nevertheless the flow of spins obeys essentially the same kinetic laws as does any other equilibrating system. 

Equation (4.2) may also be used to study the approach to thermal equilibrium. Thermal non-equilibrium can arise either from deliberate perturbation of the spins, as described later, or simply as the sample is placed into the main magnetic field at the outset of the experiment. In general, for any spin. 

Alternatively, one may say that the population difference (n2 — ni), which determines the strength of the NMR signal, reverts to its Boltzmann value 

A further possibility for obtaining a non-Boltzmann equilibrium arises when the spins receive fairly strong irradiation at their resonance frequency. This adds a further transition probability to both W+ and above. In the extreme case where 1T, it follows that nj = W2. As nuclear 

One of these, however, is not independent of the other three. The four equations can describe a wide variety of relaxation behaviour, not all of which is exponential. Here we consider only one case, where S, typically the proton spin, is saturated via continuous irradiation. Other possibilities are treated elsewhere [2]. 

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