New quantum numbers in collision theory. III. Symmetries of the scattering geometry

Scattering geometries are represented by tensorial parameters classified according to symmetry under permutations P and Q: P changes a base set of wave functions into its Hermitian conjugate and Q interchanges the directions of incidence and scattering. These parameters interlink initial and final states of projectile and target, a linkage mediated by the angular momentum ${\mathrm{j}}_t$ transferred in the collision. Collision cross sections and expectation values of the observables are constructed as sums of geometrical parameters with different symmetries, weighted by dynamical parameters.