Nonperturbative electromagnetic lepton-pair production in peripheral relativistic heavy-ion collisions

We discuss a nonperturbative treatment of lepton-pair production caused by the strong and sharply pulsed electromagnetic fields generated in peripheral relativistic heavy-ion collisions with an emphasis on the capture process into the atomic {ital K} shell. We calculate, in a field-theoretical framework, impact-parameter-dependent probabilities and cross sections for such processes by solving the time-dependent Dirac equation on a three-dimensional Cartesian lattice using the basis-spline collocation method. We give a full discussion of the stationary states used in computing {ital S}-matrix elements. Use of the axial gauge for the electromagnetic potentials produces an interaction easier to implement on the lattice than the Lorentz gauge. Preliminary calculations are given for muon-pair production with capture into the {ital K} shell in collisions of {sup 197}Au+{sup 197}Au at collider energies per nucleon of 2 and 100 GeV.