The Effect of Off-Resonance Pulses on Net Magnetization

To understand selective (shaped) pulses and the spin lock, we need to look in detail at the effect of pulses on spins as a function of their resonant frequency, v0, that is to say the position of a resonance within the spectral window. 

In the acquisition of a simple ID spectrum, our goal is to excite all of the spins of a certain type (e.g., H) in the sample, regardless of chemical shift, at the same time. This requires a radio frequency pulse of very high power and short duration. The frequency of the pulse is adjusted to correspond to the resonance frequency at the center of the spectral window, so that it will be close to the resonance frequency of all of the spins in the sample. 

For a spin whose chemical shift is exactly at the center of the spectral window, we call the pulse an on-resonance pulse because the pulse (or carrier ) frequency is exactly equal to the resonant frequency (precession frequency or Larmor frequency vG) of the spin. During the pulse, we can use the vector model to show the B field (the pulse) as stationary in the rotating frame of reference, because the x and y axes are rotating about the z axis at exactly the frequency of the pulse. The position of the B field in the x -y plane depends on the phase of the pulse, which is just the place in the sine function (0-360°) where the radio frequency oscillation starts at the beginning of the pulse. This can be controlled by the spectrometer and is written into the pulse sequence by the user  

Thus for an on-resonance pulse, the B0 field does not exist in the rotating frame and the effective field experienced by the spins is just the B field. The magnitude of the effective 

SHAPED PULSES, PULSED FIELD GRADIENTS, AND SPIN LOCKS 

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