Three-body Coulomb-problem

III. Coulomb Three-Body Problem The 2D Case with Zero Angular Momentum... 

In the next two sections, we shall apply the McGehee s method to our Coulomb three-body problem. 

III. COULOMB THREE-BODY PROBLEM THE 2D CASE WITH ZERO ANGULAR MOMENTUM... 

CLASSICAL COULOMB THREE-BODY PROBLEM Hydrogen negative ion... 

In this chapter, we presented the geometry of the orbits near triple collisions in the Coulomb three-body problem for the collinear eZe configuration and the 2D case with zero angular momentum. 

The Arnold model with ft = 0 corresponds to scattering processes. In the planar Coulomb three-body problem, the asymptotic limit where one of the three bodies goes to infinity corresponds to the Arnold model with 0 = 0 [35]. For three-body clusters interacting with van der Waals potential, the Arnold model with 0 = 0 also arises when one of the three bodies goes to infinity [37]. 

The contributions of Komatsuzaki and Berry, and of Uzer s group, discuss these manifolds, and they present their calculations using Lie perturbation theory methods. The contribution of Wiesenfeld discusses these manifolds in reaction processes involving angular momenta, and the contribution by Joyeux et al. shows applications of the perturbation theory method to reactions involving Fermi resonance. The contribution of Sano discusses invariant manifolds in the Coulomb three-body problem. 

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