CLASSICAL DYNAMICS OF S-WAVE HELIUM

s-wave helium is a model of a two-electron atom in which both electrons are restricted to spherical states. The classical dynamics of this model exhibits considerable resemblance to the collinear approximation of real helium, which has been studied in detail by Ezra et al. [J. Phys. B 24 (1991) L413] and Wintgen et al. [Chaos 2 (1992) 19]. Both systems are fully chaotic, the periodic orbits are all unstable, proliferate exponentially and can be labelled by the same simple binary code. In s-wave helium, non-periodic trajectories can unambiguously be assigned an ionisation time or a scattering time delay, and they can be classified using this binary code. Ionisation times impose a fractal structure on phase space and the initial conditions of the non-ionising trajectories form a Cantor set. The density of bound trajectories decreases exponentially with increasing number of encounters of the two electrons, but follows a power law as a function of the ionisation time. The mean lifetime of the bound atom against autoionisation is infinite.