A general numerical analysis of time-domain NQR experiments

We introduce a general numerical approach for solving the Liouville equation of an isolated quadrupolar nuclide that can be used to analyze the unitary dynamics of time-domain NQR experiments. A numerical treatment is necessitated by the dimensionality of the Liouville space, which precludes analytical, closed form solutions for I > 3/2. Accurate simulations of experimental nutation curves, forbidden transition intensities, powder and single crystal spectra, and off-resonance irradiation dynamics can be computed with this method. We also examine the validity of perturbative approximations where the signal intensity of a transition is proportional to the transition moment between the eigenstates of the system, thus providing a simple basis for determining selection rules. Our method allows us to calculate spectra for all values of the asymmetry parameter, η, and sample orientations relative to the coil axis. We conclude by demonstrating the methodology for calculating the response of the quadrupole system to amplitude- and frequency-modulated pulses.