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

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.