Determination of product population and alignment using laser-induced fluorescence

For collision systems having axial symmetry, the anisotropy of the laser-induced fluorescence is given explicitly in terms of the zeroth, second, and fourth rank moments of the angular momentum distribution, which, respectively, are proportional to the population, the quadrupole alignment, and hexadecapole alignment of the product internal state under study. Expressions are presented for determining these three quantities from the dependence of the fluorescence intensity on the polarizations of the absorbed and detected photons. Results are presented for an arbitrary excitation-detection geometry which is then specialized to the commonly occurring cases where the direction of fluorescence detection is at right angles to the axis of cylindrical symmetry and the direction of the incoming light beam is either along the axis of cylindrical symmetry or at right angles to it and to the fluorescence detection direction. The approach of these expressions to the high-J limit is considered. The effect of nuclear spin on the fluorescence intensity is analyzed and the extent of depolarization is shown to be unimportant for large J. The use of angular momentum recoupling algebra permits the geometrical and dynamical aspects of this problem to be completely disentangled.