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What if we start on +x? The pulses have no effect, but each t delay rotates 180° in the x-j plane from +x to —x and vice versa:

t t t t t x ^ x ^ x ^ x ^ x ^ x ^ x ^ x ^ x ^ x ^ x ^ x

As there is a odd number (5) of t delays, we end up on the opposite axis. If we start on —x, we end up on +x:

t t t t t x ^ x ^ x ^ x ^ x ^ x ^ x ^ x ^ x ^ x ^ x ^ x

So for that exact offset (1/2t in hertz) we have a true 180° pulse on the y' axis:

The same is true for the opposite side of the spectral window (—1/2t) as a 180° rotation gives the same result whether it is cw or ccw. If we put this 6-pulse sequence at the center of our PFGSE, it will reverse the sense of the coherence helix for the resonance 1/2t away from the center, and it will maintain the sense of the coherence helix for the on-resonance water peak and for peaks 1/t away from the center. The resonance 1/2t away will be "unwound" under the influence of the second gradient, whereas the on-resonance (water) peak will be wound twice as tightly, leading to zero net magnetization when summed over the whole sample (Fig. 8.21).

What happens between these two extremes? With so many pulses and delays it becomes impossible to draw simple diagrams, and we need to do some calculations. Pulse rotations are simple sine and cosine calculations and they can be simulated on a simple spreadsheet. Figure 8.22 shows the simulated "extinction profile" of the Watergate sequence using the 3-9-19 strategy. For the simulation, the delay t is set to 217.4 |xs, which gives a maximum signal (180° rotation during t) at an offset of ±2300 Hz (3.833 ppm on a 600-MHz

Watergate

Watergate

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