Scaling relations for inelastic collision data obtained from the initial value representation (IVR)

In this paper we have developed scaling relations for inelastic collision data based upon the IVR, an approximation which is accurate in both the sudden and adiabatic limits. We have used this to obtain connections between S-matrix elements at either the same kinetic energy or the same total energy. The constant kinetic energy scaling has the same overall form as the earlier energy corrected sudden (ECS) theory, but with different adiabaticity factors. In a practical application these factors may be obtained from a knowledge of the scattering potential or else from model collision lifetime functions, examples of which are presented in this work. The IVR scaling theory reduces the importance of multiquanta transitions relative to the ECS result, and it also provides an adiabatic correction to the phases of the S-matrix elements. Numerical calculations for a collinear oscillator problem are given as a test of the total energy scaling relations.