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Chaotic dynamics in classical s-wave helium.

Z Q Bai1, Y Gu

  • 1Department of Astronomy and Applied Physics, Center of Nonlinear Science, University of Science and Technology of China, Hefei, Anhui 230026, China.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study reveals that below a critical energy threshold, s-wave helium exhibits chaotic scattering. This chaotic behavior, characterized by resonant scattering, is linked to the fundamental domain and the principal two-electron critical collision orbit.

Area of Science:

  • Atomic and Molecular Physics
  • Quantum Dynamics
  • Chaos Theory

Background:

  • Investigating the classical dynamics of s-wave helium with negative energy (E<0) is crucial for understanding atomic interactions.
  • Previous studies lacked a clear classification of scattering orbits and the underlying mechanisms of chaotic behavior in such systems.

Purpose of the Study:

  • To investigate the classical dynamics of s-wave helium for E<0 using a geometric method.
  • To classify scattering orbits and explain the onset of chaotic scattering below a specific energy threshold.

Main Methods:

  • Employed a geometric method to analyze the classical dynamics of s-wave helium.
  • Defined a fundamental domain (r1>r2) to eliminate ambiguity in electron orbits after two-electron critical collisions (TECC).

Related Experiment Videos

  • Constructed a global Smale horseshoe on the surface of section for Z=2 to demonstrate chaotic motion.

    • Main Results:

    • Scattering orbits were classified into undelayed and delayed (resonant) types.
    • A global Smale horseshoe confirmed that bounded motion is purely chaotic for Z=2, explaining resonant scattering below the energy threshold.
    • The probability of resonant scattering increases linearly with energy difference immediately below the threshold, and orbit sequences are dictated by the principal TECC orbit.

    Conclusions:

    • The study elucidates the chaotic nature of s-wave helium dynamics below a critical energy threshold, characterized by resonant scattering.
    • Compared to collinear helium, s-wave helium exhibits less chaotic behavior but a more complex threshold response.
    • The geometric method provides a framework for understanding and classifying complex scattering phenomena in few-body atomic systems.