Decoupling surface analysis of classical irregular scattering and clarification of its icicle structure

Abstract

Irregular scattering in molecular inelastic collision is analyzed classical mechanically by a novel method called ‘‘decoupling surface analysis.’’ Effective Hamiltonian of this analysis provides a phase space view of collision processes analogous to the Poincaré section of coupled-oscillator systems. In this phase space view irregular scattering occurs in a stochastic layer formed around separatrix connected to resonance structure of the effective Hamiltonian. This circumstance is parallel to that in the coupled-oscillator systems, in which stochastic motion is known to be connected to nonlinear resonance. The resonance structure in collision indicates trapping of classical trajectories in a certain dynamical well. The decoupling surface analysis suggests that the dynamical well is formed by a dip of stability exponents of trajectories as a function of time. By using a prototypical model exhibiting irregular scattering, a formal theoretical treatment is developed to analyze the structure of the fractal, termed icicle structure, observed in the plot of final vibrational action against the initial vibrational phase angle.