Kinematics of the CS method for the treatment of molecular collisions

The problem of the quantum treatment of nonreactive collisions of two simple molecules or of an atom and a molecule is considered mathematically. Kinematical structure theorems analogous to the Wigner-Eckart theorem for scalar operators are derived for the transition operator (T-operator) of a two-molecule system, where, in addition to the usual conservation laws, certain additional conservation laws are presumed satisfied in a collision. The additional conservation laws were examined in order to develop a testable approximation scheme (CS method) for the specification of the kinematics of a system of two rigid diatomic molecules. The rand p-helicity basis states for a two-rigid rotor system are defined and unitary transformations established between these and conventional bases. It is found that only questionable criteria exist for testing the on-the-energy-shell matrix of a T(energy) operator for the presence of properties of two of the additional conservation laws.