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{\bf Coulomb Corrections in the Lepton-Pair Production in Ultrarelativistic Nuclear Collisions}\\[0.2cm]
Mehmet Cem G\"{u}\c{c}l\"{u}\\
\.{I}stanbul Technical University, Physics Department, Maslak- \.{I}stanbul, TURKEY\\[0.2cm]
Melek Y\i lmaz \c{S}eng\"{u}l\\
Kadir Has University, Faculty of Arts and Science, Cibali- \.{I}stanbul, TURKEY\\
\.{I}stanbul Technical University, Physics Department, Maslak- \.{I}stanbul, TURKEY\\

The strong electromagnetic field of heavy ions can produce different kind of two-photon reactions at relativistic heavy ion colliders. Recently the  STAR collaboration has presented \cite{adams} results on electron-positron pair productions on ultra-relativistic peripheral collisions. The authors compare the experimental data with QED and equivalent photon approximation (EPA).

We have calculated the electron-positron pair production cross section by using second-order Feynman diagrams. We have employed Monte Carlo methods and solved it exactly. We have generalized this calculation for all energies and charges of the heavy ions. This gives us a semi-analytic cross section and impact parameter dependence of cross-section expressions. Monte Carlo calculation gives an equation for the impact parameter dependence cross section valid for all impact parameters. In these impact parameter regions, the electromagnetic field is very high and a detailed study of this region is important for nonperturbative effects.

We then compare our results with Born methods that include Coulomb corrections. The method loses applicability at impact parameters less than the Compton wavelength of the electron, which is the region of greatest interest for the study of nonperturbative effects. We present our results and argue that the Coulomb correction terms are not exact and these terms need to be improved.

On the other hand, the authors of Ref. \cite{lee} made a small-momentum approximation  and obtained an analytic expression. Although most of the integration comes from the small-momentum range, the lowest order in transverse momentum is not adequate to obtain accurate Coulomb corrections and higher orders should be also included. This was first noticed by Baltz \cite{baltz}, and in this work we were also convinced that the small-momentum approximation  alone is not adequate to obtain correct Coulomb corrections.

Recent publications about peripheral relativistic heavy ion collisions \cite{bertulani,baur,hencken} show that the impact parameter dependence cross sections of lepton-pair production are very important and detailed knowledge of impact parameter dependence cross sections particularly for small impact parameters can help to understand many physical events in STAR experiments.

\begin{thebibliography}{00}
\bibitem{adams}
J. Adams at al. Phys. Rev. C 70 (3) , 031902 (2004).

\bibitem{lee}
R. N. Lee and A. I. Milstein, Phys. Rev. A 64, 032106 (2001).

\bibitem{baltz}
A. J. Baltz, Phys. Rev. C 68, 034906 (2003).

\bibitem{bertulani}
C. A. Bertulani, S. R. Klein, J. Nystrand, Annual Review of Nuclear and Particle Science 55: 271-310 (2005).

\bibitem{baur}
G. Baur, K. Hencken, A. Aste, D. Trautmann, and S. R. Klein, Nucl. Phys. A 729, 787 (2003).

\bibitem{hencken}
K. Hencken, G. Baur, and D. Trautmann, Phys. Rev. C 69, 054902 (2004).
\end{thebibliography}
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