Symmetry Relation for Radiating Particles in Attractive Versus Repulsive Coulomb Fields

It is demonstrated that the radiative properties of charged particles moving in an attractive Coulomb field are related by a remarkable symmetry property to those for a repulsive Coulomb field. This symmetry relation is discussed from the classical as well as the quantal point of view. The classical results allow a rather unusual interpretation in which the two branches of the hyperbola (attractive and repulsive fields) are united into a single closed integration contour. This interpretation is shown to agree with the classical limit of the complete result.