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The semiclassical helium atom.

D. Wintgen1, K. Richter, G. Tanner

  • 1Fakultat fur Physik der Universitat, Hermann-Herder-Str. 3, 7800 Freiburg, Germany.

Chaos (Woodbury, N.Y.)
|January 1, 1992
PubMed
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This study details a semiclassical approach for two-electron atoms, revealing mixed regular and chaotic electron motion. It quantifies stability islands and chaotic states, comparing results with new quantum calculations.

Area of Science:

  • Atomic Physics
  • Quantum Mechanics
  • Classical Dynamics

Background:

  • Semiclassical methods offer insights into complex atomic systems.
  • Two-electron atoms, like helium, exhibit intricate dynamics.

Purpose of the Study:

  • To advance the semiclassical description of two-electron atoms.
  • To analyze the mixed phase space structure of the helium atom.
  • To compare semiclassical results with ab initio quantum calculations.

Main Methods:

  • Treating regular and chaotic electron motion separately.
  • Quantizing stability islands using torus quantization.
  • Employing periodic-orbit cycle expansion for hyperbolic motion.
  • Performing highly accurate ab initio quantum calculations.

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Main Results:

  • Demonstrated mixed regular and chaotic dynamics in the helium atom's classical description.
  • Successfully quantized stability islands and accounted for chaotic states.
  • Presented new, highly accurate ab initio quantum calculations for comparison.

Conclusions:

  • The semiclassical approach provides a robust framework for understanding two-electron atomic systems.
  • Separate treatments for regular and chaotic motion are essential.
  • New quantum calculations validate the semiclassical findings and offer deeper insights into doubly excited states.