Effects of Coulomb Anomalies on Heavy Particle and Ion-Impact Collisions

One of the main conditions of the standard scattering theory is that the asymptotically active potentials, both in the incoming and outgoing channels, must decay to zero faster than a Coulomb potential. Obviously, this essential "asymptotic condition" is not met in most of the scattering processes in Atomic and Molecular Physics.  

From a pioneering work by John D. Dollard (1964), two ways of reconstructing the scattering theory to include long-range potentials were developed, using alternative forms of asymptotic free states.  It was even rigorously demonstrated that both generalizations were equivalent and can be deduced from each other.

These latest studies were developed for the simplest case of two unstructured particles interacting via a Coulombian potential. On the other hand, their respective generalizations for the multichannel case, although internally coherent and physically plausible, lack a rigorous demonstration, to the point that their validity could be questioned.

In recent years, mainly due to the possibility of making measurements of fully differential cross sections for different collision processes, serious differences between experimental data and theoretical calculations began to be noticed, being in most cases difficult to discern the origins of such discrepancies.

Some of the causes of these differences include, for example, an incorrect treatment of the branch cut at the on-shell limit of the (unavoidable) intermediate off-shell states, an inadequate definition (or even elimination) of the secondary term in the Gell-Mann and Goldberger amplitude, or an overuse of Wick's argument.

In this communication we will show how to discern and even correct these errors by critically reviewing the conceptual foundations and standard assumptions of the most common theoretical approaches.