Controlling coherence using the internal structure of hard π pulses

The tiny difference between hard pi pulses and their delta-function approximation can be exploited to control coherence. Variants on the magic echo that work despite a large spread in resonance offsets are demonstrated using the zeroth- and first-order average Hamiltonian terms, for C-13 NMR in C-60. The Si-29 NMR linewidth of silicon has been reduced by a factor of about 70 000 using this approach, which also has potential applications in magnetic resonance microscopy and imaging of solids.