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 γ≳2×${10}^4$) 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 (γ) dependence directly. Then, specific gauge transforms remove the γ dependence for smaller impact parameters, up to negligible terms of higher order in 1/γ. 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 γ independent. Putting these results together leads to a simple form for the cross section, A lnγ+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 (γ∼200).