Abstract
An accurate and efficient algorithm for dynamics simulations of particles with attractive 1/r singular potentials is introduced. The method is applied to semiclassical dynamics simulations of electron-proton scattering processes in the Wigner-transform time-dependent picture, showing excellent agreement with full quantum dynamics calculations. Rather than avoiding the singularity problem by using a pseudopotential, the algorithm predicts the outcome of close-encounter two-body collisions for the true 1/r potential by solving the Kepler problem analytically and corrects the trajectory for multiscattering with other particles in the system by using standard numerical techniques (e.g., velocity Verlet, or Gear Predictor corrector algorithms). The resulting integration is time-reversal symmetric and can be applied to the general multibody dynamics problem featuring close encounters as occur in electron-ion scattering events, in particle-antiparticle dynamics, as well as in classical simulations of charged interstellar gas dynamics and gravitational celestial mechanics.
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