Nuclear magnetic relaxation in spin-1 systems: the response to three-pulse sequences

Abstract

The response of a system of spin-1 nuclei to sequences of three r.f. pulses is calculated using density matrix methods. The system is taken to be in a large but inhomogeneous B ₀ field and subject to both weak secular and time-dependent quadrupole couplings. Two sequences are considered, these being represented as 90° x-τ-ϑ _y -T-Θ _y -t → where, for sequence I, θ _y = Θ _y = 45° _y whilst for sequence II, θ _y = θ _y = 90° _y ; the subscripts x/y refer to axes in the usual rotating reference frame. It is shown that for both sequences, five echoes occur in phase with and following the third pulse, these occurring at times t = τ, (T ± τ) and (2T ± τ). A single echo occurs at the time t = T out of phase with and following the third pulse. The dependence of the amplitudes of these echoes on τ and T and the parameters characterizing the quadrupolar interactions is calculated and experiments are presented which confirm the theoretical predictions. It is shown that observation of certain of the echoes as a function of T allows the determination of individual values of the spectral densities j _Q(0), j _Q(ω₀) and j _Q(2ω₀) of the fluctuating quadrupole coupling.