Summary of the Vector Model

The vector model is a way of visualizing the NMR phenomenon that includes some of the requirements of quantum mechanics while retaining a simple visual model. We will jump back and forth between a classical spinning top model and a quantum energy diagram with populations (filled and open circles) whenever it is convenient. The vector model explains many simple NMR experiments, but to understand more complex phenomena one must use the product operator (Chapter 7) or density matrix (Chapter 10) formalism. We will see how these more abstract and mathematical models grow naturally from a solid understanding of the vector model. 

Consider a large population of identical spins—for example the protons in a liquid sample of 12CHCl3—in a strong, uniform magnetic field B0 oriented along the positive z axis. 

Each XH nucleus precesses about the z axis, with its spin axis tracing a conical path always at a 45° (or 135°) angle to the +z axis, at a rate equal to the Larmorfrequency 

The radio frequency pulse is a very short (tens of microseconds), and a very high power (tens or hundreds of watts) pulse of radio frequency power applied to the probe coil at or very near the Larmor frequency. It has a rectangular envelope the power turns on and instantly reaches full power, then at the end of its duration it goes instantly to zero. The pulse creates an oscillating magnetic field, which can be represented by a vector (the Z i vector ) that rotates in the x-y plane at the frequency of the pulse. The length of the B vector is equal to the amplitude of the radio frequency pulse. 

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