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.

In a crossed beam atomic energy transfer experiment, relative cross sections are measured between initial and final magnetic substates of atomic orbitals in a three vector correlation experiment. A pulsed laser beam prepares Ca(4s5p 1P1) in a single magnetic sublevel ‖j1mi〉 with respect to the laser polarization vector. Subsequent collision with He at a well-defined relative velocity yields Ca(4s5p 3P2). The near-resonant Ca(4s5p 3P2) is probed by a second polarized pulsed laser, revealing its magnetic sublevel ‖j2mf〉 distribution with respect to the probe laser polarization vector. The experiment is analyzed in the collision frame where the direction of the initial relative velocity vector serves as the quantization axis. In this frame, the initial and final Ca states are characterized by substates ‖j1m1〉 and ‖j2m2〉, respectively. Fourteen collision frame cross sections are needed to describe the energy transfer completely. Eight of these cross sections are real and positive (conventional type—describing population transfer) and six are complex (coherence type—containing phase information). By symmetry, only 15 unique parameters for the real and imaginary parts of the cross sections are required, nine of which are obtained here using linear polarizations and collinear laser beams. Possible cases for circularly polarized light are also tabulated; measurement of these cases would provide several more parameters. For initial parallel preparation of the 1P1 p orbital with respect to the relative velocity (m1=0), the final 3P2 state is highly aligned in the m2=±1 and m2=±2 sublevels. Initial preparation of the p orbital perpendicular to the relative velocity vector (m1=±1) produces an aligned 3P2 state with greater population in the m2=0 and m2=±1 sublevels compared to the m2=±2 sublevels. Using the coherence information and symmetry, orientation cross sections are obtained into the m2=±1 sublevels (i.e., m preserving 1→1 and m-changing 1→−1) and are nearly identical. Preparation of the Ca p orbital perpendicular to the initial relative velocity enhances the state-specific collisional transfer of 1P1→3P2 by a factor of 2.2±0.2 over initial parallel preparation.