Eur. Phys. J. C 23, 545-550 (2002)
https://doi.org/10.1007/s100520200891

Electron--positron pair production in the external electromagnetic field of colliding relativistic heavy ions

¹ Institute for Theoretical Physics, University of Basel, Klingelbergstrasse 82, 4054 Basel, Switzerland
² Institut für Kernphysik (Theorie), Forschungszentrum Jülich, 52425 Jülich, Germany
³ Institute for Theoretical Physics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland

Received: 30 November 2001
Published online: 22 February 2002

Abstract

The results concerning the e⁺e^- production in peripheral highly relativistic heavy-ion collisions presented in a recent paper by Baltz et al. are rederived in a very straightforward manner. It is shown that the solution of the Dirac equation directly leads to the multiplicity, i.e. to the total number of electron--positron pairs produced by the electromagnetic field of the ions, whereas the calculation of the single pair production probability is much more involved. A critical observation concerns the unsolved problem of seemingly absent Coulomb corrections (Bethe--Maximon corrections) in pair production cross sections. It is shown that neither the inclusion of the vacuum--vacuum amplitude nor the correct interpretation of the solution of the Dirac equation concerning the pair multiplicity is able the explain (from a fundamental point of view) the absence of Coulomb corrections. Therefore the contradiction has to be accounted to the treatment of the high energy limit.