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Classical dynamics of two-electron atoms at zero energy
Min-Ho Lee1, Nark Nyul Choi, Gregor Tanner
1School of Natural Science, Kumoh National Institute of Technology, Kumi, Kyungbook 730-701, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
This study details the classical dynamics of two electrons near a nucleus, revealing distinct stable and chaotic regions within their phase space. Findings offer insights into atomic systems and symbolic dynamics for collinear and noncollinear electron interactions.
Area of Science:
- Atomic Physics
- Quantum Mechanics
- Classical Dynamics
Background:
- Understanding the behavior of multi-electron systems is crucial in atomic physics.
- The Coulomb potential governs the interactions between charged particles in an atom.
- Previous studies have explored symbolic dynamics in collinear two-electron atoms.
Purpose of the Study:
- To provide a comprehensive description of the classical dynamics of two electrons in a Coulomb potential.
- To analyze the phase space structure and identify symmetries in this system.
- To explore the extension of symbolic dynamics to noncollinear configurations.
Main Methods:
- Analysis of classical dynamics for two electrons with E=0 and L=0.
- Division of the four-dimensional phase space using stable and unstable manifolds.
- Identification of an approximate symmetry via a Poincaré surface of section.
- Characterization of dividing surfaces between collinear spaces (stable Zee and chaotic eZe).
Main Results:
- The phase space is partitioned by the Wannier ridge's stable and unstable manifolds.
- An approximate symmetry was identified using a specific Poincaré surface of section.
- Distinct regions, the stable Zee space and the chaotic eZe space, were identified.
- The study provides a framework for understanding the transition from collinear to noncollinear dynamics.
Conclusions:
- The classical dynamics of two electrons in a Coulomb potential exhibit complex phase space structures.
- Symbolic dynamics, initially observed in collinear systems, shows potential for extension to more complex configurations.
- This work contributes to a deeper understanding of electron correlation and atomic system dynamics.
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