WAHUHA sequence

It is known that for the WAHUHA sequence all purely dipolar terms in the Magnus expansion of the effective Hamiltonian F vanish for a two-spin system in the S-pulse limit (Bowman, 1969). The lines in a WAHUHA m.p. spectrum (S-pulse limit) of a two-spin system should, therefore, be infinitely narrow, irrespective of the pulse spacing t. A two-spin system is, hence, obviously too small for out purpose. Likewise, two-spin systems are too small to meaningfully test any line-narrowing... 

To gain some insight into the theory of multi-pulse NMR, the WAHUHA sequence (t, -Fx, t, —y, T, T, -Fy, t, —x, t) is applied in the rotating coordinate frame to a pair of spins coupled by the dipole-dipole interaction [Sch9]. The pulses are considered to be infinitely short. Their flip angle is 90°, and they are applied in -Fx, —y, -Fy, and —x directions of the rotating coordinate frame. The density matrix p to- -6x) after completion of a WAHUHA cycle is obtained from the density matrix p(ta) before application of the cycle by transformation with the evolution operator U(i) of the cycle. 

Another way in which digital data manipulation cannot be matched by analog methods easily is in sampling. It is straightforward to pick off the tops of CPMG echoes, for example, (see section I.C.2.) or the magnetization to be monitored during a WAHUHA sequence (section IV. E. 4.). 

Multiple pulse sequences average the dipolar Hamiltonian, but also affect other Hamiltonians to an extent which depends on the particular sequence. For example, the WAHUHA sequence scales chemical shift anisotropies by a factor of l/VS. 

Multiple pulse sequences can also be used to provide effective broad-band decoupling. The original pulse sequence of this kind was the WAHUHA sequence of Waugh and co-workers which was designed to minimize broadening arising from homonuclear dipolar coupling in solid-state spectra. 

The homonuclear dipolar H- H interactions can be removed by modulating the spin states rather than the spatial factors [19]. This multipulse sequence reduces the line widths in rigid solids from 10 to 10 Hz. The multiple-pulse sequence used is the WAHUHA sequence (after the initials of the originators) and is... 

Unfortunately, the WAHUHA sequence does not completely eliminate dipole-dipole interactions because the applied pulses have finite widths [20,21]. To minimize these effects, more complex sequences have been developed. 

Figure 15.13. Rotating-frame diagrams for the Lee-Goldberg and WAHUHA pulse sequences.

To consider the efficiency of dipolar decoupling in more detail, a WAHUHA pulse sequence is taken as an example [Hael]. One pulse cycle (cf. Table 3.3.1) leads to the time evolution operator (cf. eqn (3.3.22))... 

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