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Kepler Predictor-Corrector Algorithm: Scattering Dynamics with One-Over-R Singular Potentials.

Andreas Markmann1, Frank Graziani2, Victor S Batista1

  • 1Department of Chemistry, Yale University , P.O. Box 208107, New Haven, Connecticut 06520-8107, United States.

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|November 24, 2015
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Summary
This summary is machine-generated.

A new algorithm accurately simulates particle dynamics with 1/r potentials, excelling in electron-proton scattering simulations. This method analytically solves close-encounter collisions, improving accuracy in complex multibody systems.

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Area of Science:

  • Computational Physics
  • Quantum Dynamics
  • Astrophysical Simulations

Background:

  • Simulating particle dynamics with attractive 1/r potentials presents significant computational challenges due to singularities.
  • Existing methods often rely on approximations like pseudopotentials, potentially sacrificing accuracy.

Purpose of the Study:

  • Introduce a novel, accurate, and efficient algorithm for dynamics simulations involving 1/r singular potentials.
  • Validate the algorithm's performance in semiclassical electron-proton scattering simulations.

Main Methods:

  • The algorithm analytically solves the Kepler problem for close-encounter two-body collisions under a true 1/r potential.
  • It incorporates trajectory corrections for multiscattering events using standard numerical integrators (e.g., velocity Verlet, Gear Predictor-Corrector).
  • The approach is applied within the Wigner-transform time-dependent picture for semiclassical dynamics.

Main Results:

  • Demonstrates excellent agreement between the algorithm's predictions and full quantum dynamics calculations for electron-proton scattering.
  • The developed integration method is time-reversal symmetric.
  • The algorithm effectively handles close encounters without resorting to pseudopotentials.

Conclusions:

  • The new algorithm provides an accurate and efficient solution for simulating systems with 1/r potentials.
  • It is applicable to a wide range of multibody dynamics problems, including electron-ion scattering, particle-antiparticle dynamics, and celestial mechanics.