Chaotic scattering in collinear Ze-e- three-body Coulomb systems

We study the collinear chaotic scattering between an electron and a one-electron ion (e.g., He⁺) with negative total energy. The global dynamics of the unbounded motion in phase space can be illustrated by introducing two submanifolds of critical injecting and critical escaping. We find a type of bifurcation of chaotic scattering resulted from the tangency between these two submanifolds, which explains the emergence or disappearance of an extra zeroth-order chaotic band in the scattering functions as the nuclear charge Z is changed.