The equilibrium state is characterized by a complete lack of coherence (random phase), a slight excess of population in the a state (N/2 + 5), and a deficit in the j state (N/2 - 5). Anything that perturbs this equilibrium (e.g., an RF pulse) will be followed immediately by a process of relaxation back to the equilibrium state that can take as long as seconds to reestablish. Relaxation is extremely important in NMR because it not only determines how long we have to wait to repeat the data acquisition for signal averaging, but it also determines how quickly the FID decays and how narrow our NMR lines will be in the spectrum. Relaxation is also the basis of the nuclear Overhauser effect (NOE), which can be used to measure distances between nuclei: one of the most important pieces of molecular information we can obtain from NMR.

5.5.1 Relaxation After a 90° Pulse

Immediately after a 90° pulse the net magnetization vector is in the x-y plane. This means that the z component of the net magnetization is zero and that there is no difference in population between the upper (j ) and lower (a) energy states. The net magnetization vector will rotate (precess) in the x-y plane at the Larmor frequency, vo. The phase coherence

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