A Large Population of Identical Spins Net Magnetization

Before the pulse no phase coherence (random phase) 

Now that the concept of coherence has been introduced, let us make our model of the ensemble of spins a little more accurate. Instead of lining up the spins in a row, we move their magnetic vectors to the same origin, with the South pole of each vector placed at the same point in space (Fig. 5.3(a)). Furthermore, we need to consider both quantum states, the up cone (a or lower energy state) and the down cone (/3 or higher energy state). 

How big is this population difference at equilibrium The Boltzmann distribution defines the populations of the two states precisely, and it turns out that the equilibrium population difference APeq is proportional to the energy difference between the two states (a and ft) 

So the net magnetization at equilibrium is proportional to the number of identical spins in the sample (i.e., the concentration of molecules), the square of the nuclear magnet strength, and the strength of the NMR magnet, and inversely proportional to the absolute temperature. For example, M0 for H is 16 times larger than M0 for 13C because yn/yc = 4. This net magnetization vector is the material that we mold, transform and measure in all NMR experiments. 

Now consider the effect of a 180° pulse on the ensemble of spins represented in Fig. 5.3. The RF pulse is actually a rotation, and we will see in Chapter 6 that this rotation is exactly analogous to the precession of magnetic vectors around the B0 field. The pulse itself can be viewed as a magnetic field (the Bi field) oriented in the x-y plane, perpendicular to the B0 field, and for the short period when it is turned on it exerts a torque on the individual nuclear magnets that makes them precess counterclockwise around the B field. This is shown in Fig. 5.4. Each magnetic vector is rotated by 180°, so the entire structure of two cones is turned upside down, with the upper cone and all its magnetic vectors turned down to become the lower cone, and the lower cone turned up to become the upper cone. This 

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