We present a schematic study of muon-pair production with capture of the negative muon into the $1s_{\frac{1}{2}}$ 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 ${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$+${}_{}{}^{197}{}_{}{}^{}\mathrm{Au}$ at collider energies of 0.2, 1.0 and 2.0 GeV/nucleon, we obtain probabilities for dimuon production with capture between 1.0 × ${10}^{-3\mathrm{}}$ and 7.0 × ${10}^{-2\mathrm{}}$ at grazing impact parameters. This may indicate that the electromagnetic lepton-pair production is strongly nonperturbative.

• Received 7 August 1989

DOI:https://doi.org/10.1103/PhysRevA.41.1399