Gaussian Weighted Trajectory Method IV: No Rainbow Effect in Practice

The Gaussian weighted trajectory method (GWTM) is a practical implementation of classical S matrix theory (CSMT) in the random phase approximation, CSMT being the first and simplest semi-classical approach of molecular collisions, developped in the early seventies. Though very close in spirit to the purely classical description, GWTM accounts to some extent for the quantization of the different degrees-of-freedom involved in the processes. While CSMT may give diverging final state distributions, in relation to the rainbow effect of elastic scattering theory, GWTM has never led to such a mathematical catastrophe. The goal of the present note is to explain this finding.