Quadrupole perturbation effects upon theHg201magnetic resonance. I. Effects upon free precession of the nuclear spins

The time dependence of free-precession signals from an ensemble of spin-$\frac{3}{2}$ atoms in the presence of a quadrupole perturbation is calculated by examining the time dependence of the density matrix which describes the ensemble. The calculations yield explicit expressions for signals obtained using either a linearly or elliptically polarized off-resonant readout light, applied to a mixture of orientation, alignment, and octupole spin distributions. The results are obtained by expressing the density matrix in terms of spherical basis operators. The theoretical predictions are in good agreement with experimental results which are characterized by "beats" in the decay transients of signals from ${}_{}{}^{201}{}_{}{}^{}\mathrm{Hg}$.