A new multiple (mass ratio) scale analysis of atom-diatom collisions

Atom-diatom collisions are investigated within the framework of a general mass weighted mixed coordinate system. It is found that physically distinct parts of the Hamiltonian are controlled by functions that depend on the mass weighted mixing coefficients of the new coordinates. In principle, the mixing coefficients can be derived variationally from a stationary functional for the T matrix. The mixed coordinate system developed in this paper can also be used to investigate a quantum mechanical decoupling approximation by parametrizing the mixing coefficients of the new coordinates in terms of the approximation's decoupling parameter. The goal of this paper is to examine the case when the mixing coefficients are expressed in terms of the ES decoupling parameter for vibrational transitions. A brief discussion is also given to the application of this technique to the investigation of the ES method for rotational transitions and vibrational transitions. This approach offers a practical avenue for improving ES results for collision systems having very small mass ratios. It is found in an example that when the collision system strongly satisfies the mass scaling criterion, the method gives uniformly accurate results for all energies and all transitions. When the collision system weakly satisfies the criterion, the method improves only the energy sudden results for multiple quantum transitions at energies which are close to the threshold limit.