Convergence of a lattice calculation for bound-free muon-pair production in peripheral relativistic heavy-ion collisions

We have developed a nonperturbative treatment of bound-free lepton-pair production caused by the strong and sharply pulsed electromagnetic fields generated by heavy ions in peripheral, relativistic collisions based on the solution of the time-dependent Dirac equation using lattice techniques. In this paper, we discuss refinements and extensions of our numerical methods for this problem and demonstrate convergent calculations, with respect to the parameters of the lattice, for bound-free muon-pair production in collisions near grazing incidence of 238U92++238U92+ and beam kinetic energies of 30 GeV per nucleon in the fixed-target frame. copyright 1996 The American Physical Society