  The response of a quadrupolar nucleus (nuclear spin with I>1/2) to an
oscillating radio-frequency (RF) pulse/field is delicately dependent on the
ratio of the quadrupolar coupling constant to the amplitude of the pulse in
addition to its duration and oscillating frequency. Consequently, analytic
description of the excitation process in the density operator formalism has
remained less transparent within existing theoretical frameworks. As an
alternative, the utility of the "concept of effective Floquet Hamiltonians" is
explored in the present study to explicate the nuances of the excitation
process in multilevel systems. Employing spin I=3/2 as a case study, a unified
theoretical framework for describing the excitation of multiple-quantum (MQ)
transitions in static isotropic and anisotropic solids is proposed within the
framework of perturbation theory. The challenges resulting from the anisotropic
nature of the quadrupolar interactions are addressed within the effective
Hamiltonian framework. The possible role of the various interaction frames on
the convergence of the perturbation corrections is discussed along with a
proposal for a "hybrid method" for describing the excitation process in
anisotropic solids. Employing suitable model systems, the validity of the
proposed hybrid method is substantiated through a rigorous comparison between
simulations emerging from exact numerical and analytic methods.
