Density matrix calculation of spin 5/2 pure nuclear quadrupole resonance echoes

Using the interaction representation, the pure nuclear quadrupole resonance transient pulsed response of a system of spin is comprehensively worked out, only for η = 0. The method consists on writing all interest operators as a linear combination of generators of the Lie algebra of the SU (6) group. Also an exact solution of the eigenvalues and transition frequencies is presented. The final result presents a general expression of the signal, following an echo sequence, as a function of the second pulse phase and duration. The result also involves the contribution of the second moments due to dipolar, quadrupolar couplings.