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 (RHIC) and the Large Hadron Colliders (LHC). 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 P b + P b at 3400 GeV/nucleon.

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We calculate the cross sections of electromagnetic productions of muon-and tauon-pair productions from the ultra-relativistic heavy ion collisions. Since the Compton wavelengths of muon and tauon are comparable to the radius of the colliding ions, nuclear form factors play important roles for calculating the cross sections. Recent measurement (Abrahamyan et al., Phys Rev Lett 108:112502, 2012) indicates that the neutrons are differently distributed from the protons; therefore this affects the cross section of the heavylepton pair production. In order to see the effects of the neutron distributions in the nucleus, we used analytical expression of the Fourier transforms of the Wood-Saxon distribution. Cross section calculations show that the Wood-Saxon distribution function is more sensitive to the parameter R compared to the parameter a.

In this paper, the effects of different nucleus form factors to the cross-sections of electromagnetically produced heavy lepton pairs such as muons and tauons from the ultrarelativistic heavy ion collisions have been calculated. Nucleus form factors play important roles in the calculation of the cross-sections, because the Compton wavelengths of muon and tauon are comparable to the radius of the colliding ions. Some realistic form factors in these calculations have been used and compared the results among them. It has been shown that nucleus form factors reduce the cross-section calculations for muon and tauon pair production very strongly especially at RHIC energies.

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