Electron–positron pair production in ultrarelativistic heavy ion collisions

Abstract

In recent years, a large number of papers have appeared that dealt with e + e - pair production in heavy ion collisions at high energies. To a large extent these studies were motivated by the existence of relativistic heavy ion accelerators all over the world. There pair production can be studied in so called “ultra-peripheral collisions”, where the ions do not come close enough to interact strongly with each other. Various different methods have been used and it is the purpose of this review to present a unified picture of the present status of the field. The lowest order Born result has been known for more than seven decades. The interest and focus is now on higher order effects for values of Z α ≲ 1 , where Z is the charge number of the ion. A similar problem appears for the Bethe–Heitler process, the production of e + e - pairs in photon–nucleus collisions. It was solved essentially some five decades ago by Bethe and Maximon. The result of Bethe and Maximon can also be recovered by summing over a class of Feynman diagrams to infinite order. These results can be used for a study of Coulomb corrections in nucleus–nucleus collisions. Indeed, the major part of these corrections have a structure closely related to the Bethe–Maximon solution. There are additional terms which give a small contribution to the total cross section at high energies. Their importance can be enhanced by concentrating on small impact parameters. An interesting exact solution of the one-particle Dirac equation in the high-energy limit was found independently by several authors. This led to some discussion about the interpretation of these results within quantum electrodynamics (QED) and the correct regularization necessary to get the correct result. The dust of previous debates has settled and, indeed, a consistent picture has emerged. Another interesting higher order effect is multiple pair production, which we also discuss. We compare experimental results obtained recently at relativistic heavy ion collider (RHIC) for free and bound-free pair production with theoretical results. We also make some more remarks on the physics of strong electric fields of longer duration. A new field is opened up by ultra-intense laser pulses. We argue that due to the short interaction time in ultraperipheral heavy ion collisions pair production can be well understood in the frame of QED perturbation theory.