Design of composite pulses for nuclear quadrupole resonance spectroscopy

Abstract

Composite pulses that compensate the inhomogeneities of electric field gradient (efg) and radio frequency (rf) field strength for nuclear quadrupole resonance (NQR) spectroscopy are presented. The theoretical procedure for constructing these composite pulses employs the Magnus expansion technique in a manner similar to NMR average Hamiltonian theory. Composite pulse sequences, for which the zeroth-order term in the Magnus expansion vanishes, have been obtained using the fictitious spin- 1 2 operator formalism for spin I = 1 case. Some typical NMR composite pulses have also been examined in the NQR context. The efficiency of these pulses for broadband excitation in NQR of single crystals is analyzed by simulation of the appropriate responses. We propose the sequence (90) 0–(300) 90 as a composite π/2 pulse for compensating efg inhomogeneity and (90) 0–(θ) 90–(90) 0 as a composite inversion π pulse which, for a large range of θ, compensates both efg and rf field inhomogeneities in pure NQR of single crystals containing physically equivalent spin I = 1 nuclei. The results obtained are independent of the asymmetry parameter of the electric field gradient in the absence of a Zeeman field.