Convergence of bound-electron–positron pair production calculations for relativistic heavy-ion collisions

Large-basis coupled-channel Dirac-equation calculations of bound-electron–positron pair production in relativistic heavy-ion collisions are presented. The relative importance of the enhancement of the coupled-channel calculations over corresponding calculations performed in perturbation theory is shown to decrease with increasing basis size, indicating a systematic reduction of this effect of nonperturbative enhancement with improving convergence of the calculations. The total nonperturbative enhancement of the cross section is shown to be about 7 b for ${\mathrm{Pb}}^{82+}$ on ${\mathrm{Pb}}^{82+}$ at the Brookhaven Relativistic Heavy-Ion Collider, only some 6% over perturbation theory.