Unfamiliar trajectories for a relativistic particle in a Kepler or Coulomb potential

Relativistic particles in the Kepler and Coulomb potentials may have trajectories that are qualitatively different from the trajectories found in nonrelativistic mechanics. Spiral scattering trajectories were pointed out by C. G. Darwin in 1913 in connection with the relativistic Rutherford scattering of classical charged particles. Relativistic trajectories are of current interest in connection with Cole and Zou's computer simulation of the hydrogen ground state in classical physics.