  In relativistic heavy-ion collisions, the strong Lorentz-contracted
electromagnetic fields are capable of producing copious numbers of lepton pairs
through the two-photon mechanism. Monte Carlo techniques have been developed
that allow the exact calculation of production by this mechanism when a
semi-classical approximation is made to the motion of the two ions. Here, we
develop a hybrid Monte Carlo technique that enables us to calculate the impact
parameter dependence of the two-photon mechanism for lepton-pair production,
and by using this result, we obtain the probability distribution for
multiple-pair production as a function of impact parameter. Computations are
performed for S$+$Au and Pb$+$Pb systems at 200 A GeV and 160 A GeV,
respectively. We also compare our results with the equivalent photon
approximation and elucidate the differences.
