The average hamiltonian view of low-energy scattering by a vibrating molecule

The average hamiltonian theory is used to examine the effect of molecular vibration on low-energy scattering. When the relative motion of the colliding molecules is slow on the timescale of molecular vibration, it is appropriate to transform the problem into an oscillating reference frame and to describe the collision in that frame by the average hamiltonian over one period of oscillation. The first-order result is identical to the distorted-wave Born approximation. High-order corrections introduce phase shifts for elastic scattering due to molecular vibration and provide transition amplitudes for inelastic scattering. The extent to which the higher-order corrections modify the distorted waves establishes criteria for the validity of the DWA. These criteria are used to examine recent distorted-wave calculations of V-V energy transfer rate constants.