Spin Kinetics Derivation of the Rate Equation for Cross-Relaxation

NMR pulse sequence without getting tied up in the details of pulse phases and a mountain of sine and cosine terms only the essential elements of the sample net magnetization will be described at each point. Finally, the formal Hamiltonian description of solution-state NMR will be described and applied to explain two related phenomena strong coupling ( leaning of multiplets) and TOCSY mixing (the isotropic mixing sequence). 

1 SPIN KINETICS DERIVATION OF THE RATE EQUATION FOR CROSS-RELAXATION 

Because z magnetization is the result of population differences between spin states, we can equate z magnetization with population difference (actually it is proportional, but for simplicity the proportionality constant is omitted)  

Note that in each case we subtract the population of the higher energy (less populated at equilibrium) state from the population of the lower energy (more populated at equilibrium) state. We can also define the amount of disequilibrium as the difference between the actual z magnetization and the equilibrium z magnetization. 

Note that AMza and Aboth tend toward zero (AP = 28) as the nuclei relax. 

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