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

Min-Ho Lee·Gregor Tanner·Nark Nyul Choi
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Abstract

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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Min-Ho Lee, Gregor Tanner, Nark Nyul Choi. 2004-12-14. The classical dynamics of two-electron atoms near the triple collision. https://doi.org/10.1103/physreve.71.056208

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