Self-Similarity in Classical Atom-Diatom Scattering and its Applications

The classical scattering of He + I_2 collisions system exhibits chaotic behavior in the initial angle-final action plot. The plot shows a complicated structure region called "the chattering region" which corresponds to complex scattering. The chattering region consists of an infinite number of spattered points and an infinite number of smooth curves called icicles. The pattern of the icicles implies the existence of the asymptotic self-similarity and fractal behavior of the structure. Each of the icicles corresponds to a specific characteristic vibration of the system. The simple formula to describe the specific characteristic vibration associated with any icicle is described. The asymptotic self-similarity evidences the existence of the asymptotic scaling laws, the renormalization treatment and the cantor set behavior of the structure observed. The self-similarity of the structure and Miller's semiclassical S-matrix theory are used in the calculation of the semiclassical transition probabilities. The scaling laws of the transition probabilities is developed. It is also found that the structure of the icicles in the chattering region can be used to partition phase space into volumes associated with different types of complexes in the He + I_2 collisions.