Periodic Orbits and Binary Collisions in the Classical Coulomb Three-Body Problem

In the helium case of the classical Coulomb three-body problem in two dimensions with zero angular momentum, we develop a procedure to find periodic orbits applying two symbolic dynamics for one-dimensional and planar problems. A sequence of periodic orbits are predicted and are actually found numerically. The results obtained here will be a cornerstone for finding the remaining periodic orbits, which needed for semiclassical applications such as periodic orbit quantization.