Time delay for bimolecular collisions: Utility of the spectral theorem in the classical limit

The recently proven multichannel spectral theorem for time delay is explored with the goal of providing a useful expression for ’’lifetimes’’ of bimolecular collisions. The theorem is reduced to an approximate relationship between the classical time delay and the classical excess density of states. Numerical studies on collinear atom–diatom systems confirm the accuracy of the classical relationship and a simple geometric interpretation of the excess density of states for these systems is provided. Results on the sensitivity of collisional time delays to variations in potential surface well depths and system masses are presented. the time delays being simply obtained from the excess density of states.