The Orbit of a Radiating Charged Particle
University of Rochester, U.S.A.
We all know that a classical charged particle orbiting a nucleus will lose energy and angular momentum and plunge to the center. What is the shape of this orbit? Surprisingly, the answer was not known until I found it a year ago. The reason is that the correct equation of motion of a radiating charged particle was not agreed upon for over a century. Dirac derived one a while ago which is wrong because it predicts an instability: the particle gains energy rather than loses energy. The correct answer was given in the book by Landau and Lifshitz, but the proof by Herbert Sphn was only about a decade ago. He solved it for constant electric and magnetic fields. I solved it for the Coulomb field. The orbit is an elliptic spiral. The solution is in terms of Painleve transcendents of type II.