ENERGY-DEPENDENCE OF BOUND-ELECTRON POSITRON PAIR PRODUCTION AT VERY-HIGH-ENERGY ION-ION TRANSITS

The problem of calculating the cross section for bound-electron-positron pair creation in very-high-energy heavy-ion colliders (100 GeV/u or higher, an effective gamma greater-than-or-similar-to 2 x 10(4)) is addressed. The multipole decomposition of the basic time-varying interaction is explicitly written in terms of simple and compact forms that display the energy (gamma) dependence directly. Then, specific gauge transforms remove the gamma-dependence for smaller impact parameters, up to negligible terms of higher order in 1/gamma. For larger impact parameters b, the interaction is shown to weaken as 1/b, where the known perturbative results apply. Only at small impact parameters are strong-coupling calculations necessary, but the gauge choices show that the contributions from these regions are gamma-independent. Putting these results together leads to a simple form for the cross section, A ln-gamma + B, where A and B are energy independent and A is known from the perturbative calculations. This form and its weak dependence on energy makes extrapolation from lower-energy results reliable and indicates the usefulness of a possible experiment at comparatively low energies (gamma approximately 200).