The classical dynamics of two-electron atoms near the triple collision

Details The classical dynamics of two-electron atoms near the triple collision The classical dynamics of two-electron atoms near the triple collision

2004-12-14

arxiv.org/abs/nlin/0412037v1

Nonlinear Sciences

Chaotic Dynamics

21 pages, 17 figures

Scientific paper

10.1103/PhysRevE.71.056208

The classical dynamics of two electrons in the Coulomb potential of an attractive nucleus is chaotic in large parts of the high-dimensional phase space. Quantum spectra of two-electron atoms, however, exhibit structures which clearly hint at the existence of approximate symmetries in this system. In a recent paper,(Phys. Rev. Lett. 93, 054302 (2004)), we presented a study of the dynamics near the triple collision as a first step towards uncovering the hidden regularity in the classical dynamics of two electron atoms. The non-regularisable triple collision singularity is a main source of chaos in three body Coulomb problems. Here, we will give a more detailed account of our findings based on a study of the global structure of the stable and unstable manifolds of the triple collision.

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