Angular momentum coupling schemes for molecular collisions: The stereodirected representation

Frame transformation theory and the classification of rotational spectra of diatomic molecules according to the five Hund cases provide a guide to the quantum-mechanical formulation of alternative coupling schemes for the tre atment of atomic collisions between species carrying spin and electronic an gular momenta. An account of the corresponding diabatic representations of the orthogonal transformations among cases and of extensions needed to deal with molecular encounters is presented. Basic to these developments are th e tools of angular momentum algebra, and in particular the limiting relatio nships known as semiclassical limits. Alternative representations for the q uantum-mechanical scattering matrix are discussed with reference to the des cription of steric effects in molecular collisions. Implications for reacti ve scattering theory, an explicit discretization algorithm (hyperquantizati on), and numerical results are also outlined.