Abstract The density matrix approach along with fictitious spin-1/2 or tensor operator formalisms were employed to obtain general expressions for <Ix>and thus the signal induced in a coil in the case of physically equivalent non-interacting spin I = 1 and 3/2 nuclei in a single crystal with a three-pulse composite pulse. The corresponding powder averages were then obtained and the dependence of the signal on the i-th pulse flip angle (θi) and phase (ϕi) studied. A numerical procedure established the optimum "π/2" composite pulse for polycrystalline samples as (90)0 -(70)45 -(20)25 , where the quantity in parentheses denotes the flip angle and the subscript the phase. A two-pulse composite pulse of the form (126)0 -(300)80 was also inferred, but the three-pulse composite pulse is superior. These composite pulses are shown to have general validity for other spin I values.
Narrowband and passband composite pulses for variable rotations
