Analytical evaluation of first-order perturbation integrals for inverse-power intermolecular potentials

Some improvements in vibrational energy transfer theory for gaseous systems can be achieved by evaluating first-order, time-dependent perturbation integrals for inverse power (multipolar or Lennard-Jones) intermolecular potentials. Although analytical expressions of the collision trajectories for such potentials are not available in general, by using properties of the Γ-function and phase-stationary integration methods it is possible to find a general analytical expression for the perturbation integrals and for the first-order vibrational energy transfer probability. Taking the appropriate limits in this expression the behaviour previously stated in some different cases by the Landau-Teller, Shin and Sharma-Brau theories is obtained.