  The two-center Dirac equation for an electron in the external electromagnetic
field of two colliding heavy ions in the limit in which the ions are moving at
the speed of light is exactly solved and nonperturbative amplitudes for free
electron-positron pair production are obtained. We find the condition for the
applicability of this solution for large but finite collision energy, and use
it to explain recent experimental results. The observed scaling of positron
yields as the square of the projectile and target charges is a result of an
exact cancellation of a nonperturbative charge dependence and holds as well for
large coupling. Other observables would be sensitive to nonperturbative phases.
