Lattice calculation of muon-pair production with capture in relativistic heavy-ion collisions

We present a schematic study of muon-pair production with capture of the negative muon into the 1s1/2 ground state in relativistic heavy-ion collisions. The muon pairs are generated by a time-dependent, screened electromagnetic field. Our numerical calculations are carried out on a three-dimensional lattice with 20--30 mesh points in each direction, utilizing the B-spline collocation method. Numerical convergence has been demonstrated using a Lorentz-boosted screened Coulomb potential. For the system 197Au+197Au at collider energies of 0.2, 1.0, and 2.0, GeV/nucleon, we obtain probabilities for dimuon production with capture between 1.0x10-3 and 7.0x10-2 at grazing impact parameters. This may indicate that the electromagnetic lepton-pair production is strongly nonperturbative