Arbitrary Pulse Width in the Four-Pulse NMR Experiment

The classical four-pulse experiment as invented by W A U G H , H U B E R , and H Ä B E R L E N 2 has been proven to be very effective in reducing the dipolar broadening in the nmr spectra of solids and unravelling weaker interactions such as magnetic shielding anisotropics, /-coupling etc. 3. There is a considerable amount of other types of line narrowing experiments which are capable of reducing dipolar broadening, but they will not be dealt with here 4. In the classical four-pulse experiment the rf pulses were considered as <5 pulses, i. e. pulse width tp = 0. By applying a cycle of rf pulses to the spins, the interaction Hamiltonian beoomes modulated, i. e. time dependent. If this modulated interaction Hamiltonian is now averaged over a cycle, it can be made to vanish for certain types of interaction (f. e. dipolar and quadrupolar) and on the other hand retained, but scaled by a scalingf actor 5 (e. g. magnetic shielding 5 < 1 , /-coupling S = 1), for others2. Thus far it has been assumed, that the rf pulses in the four-pulse experiment had to be d pulses in order to achieve line narrowing and only small deviations from zero pulse width could be compensated for by making the total rotation angle > 90° 2. It will be demonstrated, however, in Sect. 2 that coherent averaging takes place also during rf irradiation. This can be utilized, as shown in Sect. 3, to operate the four-pulse experiment with any finite pulse width up to an upper limit, given by the timing of the four-pulse sequence. The total rotation angle ßx of the rf pulses has to be increased gradually with increasing pulse width up to the limit of ßn = 116°