3-VECTOR CORRELATION THEORY FOR ORIENTATION ALIGNMENT STUDIES IN ATOMIC AND MOLECULAR-COLLISIONS

The laboratory integral cross section under crossed-beam conditions is examined for collisions between a structured and an unstructured species, where the orientation (or alignment) of the initial and final states is determined with respect to arbitrarily configured laboratory axes. Three parameters are necessary to characterize the mutual orientation of the relevant axes in this case and these parameters then also characterize the cross section. The laboratory cross section is expanded in terms of a more fundamental (angle-independent) set of cross sections as determined in the so-called collision frame, where projections of the structured species are taken with respect to the direction of the initial relative velocity vector. Drawing upon a number of symmetry relations, we count the numbers of fundamental cross sections for arbitrary initial and final angular momenta. Then we consider the explicit dependence on angular parameters which can be anticipated for the laboratory cross section. Finally, we raise a number of experimental considerations in attempting to determine the fundamental cross sections. These considerations are "fleshed out" by applying our cross-section analysis to a recent three-vector correlation experiment involving collisions between Ca and He.