The time dependence of different interaction Hamiltonians of nuclear spins as encountered in NMR experiments where the external field is applied at the "magic angle" in the rotating frame is treated with the average Hamiltonian theory. First- and second-order correction terms of the average Hamiltonian are obtained for symmetric and antisymmetric cycles. New types of pulsed "magic-angle" experiments are treated in detail and experiments are performed to show their capability to resolve chemical shifts in solids. It is shown that such magic-angle methods, employed with applied fields of high duty factor, in principle offer advantages in the high-resolution NMR of solids over resonant multiple-pulse schemes. The problem of observing the nuclear-precession signal during applications of the strong fields is solved by "nesting" an observing cycle of low duty factor into the continuous or quasicontinuous irradiation sequence.

• Received 1 September 1971

DOI:https://doi.org/10.1103/PhysRevB.5.3459