Coulomb problem for classical spinning particle

Abstract

We consider a motion of a weakly relativistic charged particle with an arbitrary spin in central potential $e/r$ in terms of classical mechanics. We show that the spin-orbital interaction causes the precession of the plane of orbit around the vector of total angular momentum. The angular velocity of precession depends on the distance of the particle from the center. The effective potential for in-plane motion is central, with the corrections to Coulomb terms coming from spin-orbital interaction. The possible orbits of a quantum particle are determined by the Bohr-Sommerfeld quantization rule. We give examples of orbits corresponding to small quantum numbers, which were obtained by numerical integration of equations of motion. The energies of stationary states are determined by spin-orbital interaction.

18 pages, 2 figures

References in corpus (9)

• Muon g-2: Review of Theory and Experiment
• Spinning test particles in the $\gamma$ spacetime
• Recent progress on the description of relativistic spin: vector model of spinning particle and rotating body with gravimagnetic moment in General Relativity
• Twisted electron in a strong laser wave
• Relativistic corrections to the algebra of position variables and spin-orbital interaction
• Spinning particle orbits around a black hole in an expanding background
• World sheets of spinning particles
• Fundamental Relativistic Rotator. Hessian singularity and the issue of the minimal interaction with electromagnetic field
• Motion of Spinning Particles around Black Holes