Spin dynamics in the pulsed spin locking of nuclear quadrupole resonance

We theoretically examine the perturbative effects of a series of radio-frequency (rf) pulses, electric field gradient inhomogeneity, and dipole-dipole coupling on the spin dynamics of spin-1 nuclei dominated by the quadrupole interaction. The dipole-dipole coupling is between neighboring spin-1 nuclei with identical nuclear quadrupole resonance frequencies, but the principal axes frames of the electric field gradient at each nucleus are not aligned. Such a comprehensive treatment is necessary to determine the optimal sequence of rf pulses which maximizes the echoes in the detection of the substance of interest, for example, an explosive or other contraband material. We confirm our theoretical model using the nitrogen in powder samples of p-chloroaniline and sodium nitrite.