Classical dynamics of collinear e−Ze− Coulomb three-body systems

Abstract

We study the classical dynamics of the collinear e−Ze− Coulomb three-body systems by geometrical methods. By making use of the reduced phase space through scaling symmetry, we show that the behavior of the E ≠ 0 orbits near triple collision resembles that of the zero energy motion, in which all the normal scattering orbits can be represented by two symbolic sequences in an appropriately defined code system. Based on this result, the completeness of the symbolic dynamics in the case of E < 0 is proved. Furthermore, the partition of surface of section (SOS) by the stable manifold of triple collision gives a natural order to the symbolic sequences which is similar to that in the one-dimensional unimodal map. The stretching and folding of the incident ensemble in the tilling of SOS provides the dynamical origin of the chaotic scattering, and the fractal patterns exhibited in the scattering functions are explained straightforwardly. We also show that the bounded motion in this system is conjugated to the motion of a two-dimensional Baker's transformation.