Numerical Design of Composite Pulses for Polycrystalline Samples in Pulsed NQR Spectroscopy

The density matrix approach along with fictitious spin-1/2 or tensor operator formalisms were employed to obtain general expressions for 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 (θ ) and phase (ϕ ) studied. A numerical procedure established the optimum "π/2" composite pulse for polycrystalline samples as (90) -(70) -(20) , where the quantity in parentheses denotes the flip angle and the subscript the phase. A two-pulse composite pulse of the form (126) -(300) 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.