Uniform semiclassical IVR treatment of the S-matrix

An initial value representation (IVR) expression was obtained to develop a semiclassical treatment of the S-matrix for collinear collisions. These methods used integrals over initial conditions for the classical trajectories and were based on asymptotic analysis. The collision of an atom with a harmonic diatom was considered and then the final expression was generalized to arbitrary collinear collisions. The relation between the expression and the existing semiclassical methods was discussed and the developed method was found to be accurate having high computational efficiency requiring small number of classical trajectories.