Bound-free electron-positron pair production in relativistic heavy-ion collisions

The bound-free electron-positron pair production is considered for relativistic heavy ion collisions. In particular, cross sections are calculated for the pair production with the simultaneous capture of the electron into the 1s ground state of one of the ions and for energies that are relevant for the relativistic heavy ion collider and the large hadron colliders. In the framework of perturbation theory, we applied Monte Carlo integration techniques to compute the lowest-order Feynman diagrams amplitudes by using Darwin wave functions for the bound states of the electrons and Sommerfeld-Maue wave functions for the continuum states of the positrons. Calculations were performed especially for the collision of Au+ Au at 100 GeV/nucleon and Pb+ Pb at 3400 GeV/nucleon.