Line Narrowing by Multiple Pulse Methods

For the heteronuclear two-spin system we found that we could create an average of the two X spin states by decoupling. Clearly such heteronuclear decoupling is inapplicable to the homonuclear two-spin system, but examination of the Hamiltonian of Eq. 7.6 suggests another approach—manipulate the spin system to make the two spin terms equal on the average so that XD = 0. This can be accomplished by use of appropriate pulse sequences. Prior to our discussion of pulse sequences in Chapters 9—11, we are not prepared to treat this rather complex process in detail, but a simple pictorial presentation gives the essential features. 

Consider the sequence of four pulses applied in the rotating frame to the two dipolar-coupled nuclei  

FIGURE 7.7 Pictorial representation of the effect of the WAHUHA pulse cycle. A series of 90° pulses applied as indicated causes M to spend a period 2r along each of the Cartesian axes in the rotating frame. The average orientation of M during the period 6r is thus along the diagonal at 54.7° from the z axis, as shown. 

The sum of these three terms cancels that from the scalar product and makes = 0. As shown in Fig. 7.7, the average orientation of M during the period of 

A rigorous quantum mechanical treatment shows that the process is more complex, particularly when pulse imperfections are taken into account. The basic four-pulse cycle just given (called WAHUHA after its inventors)85 has been supplanted in practice by cycles that use 8-24 pulses (e.g., MREV-8, MREV-16, BLEW-24). The cycle is repeated many times during the period T2, and observation of the magnetization is made after each cycle during one of the t periods. These multiple pulse cycles are difficult to apply but are quite effective in narrowing lines. 

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