Coupled Equations and the Minimum Principle for Collisions of an Atom and a Diatomic Molecule, Including Rearrangements

The collision of an atom with a diatomic molecule is treated by a coupled-channel expansion augmented by a finite number of square-integrable basis functions. The method is, in principle, capable of essentially exact results if the total energy is less than that necessary for the existence of three free atoms and should be practical for light systems at low energies. The coupled equations which must be solved to apply the minimum principle are obtained and the direct and exchange interaction matrices are given in reduced form. The case that two, or all three, of the atoms are identical simplifies the equations, and the cross-section formulas are given for arbitrary spin of the indentical nuclei.