Energy dependence of bound-electron-positron pair production at very-high-energy ion-ion transits.

Abstract

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 \ensuremath{\gamma}\ensuremath{\gtrsim}2\ifmmode\times\else\texttimes\fi{}${10}^{4}$) 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 (\ensuremath{\gamma}) dependence directly. Then, specific gauge transforms remove the \ensuremath{\gamma} dependence for smaller impact parameters, up to negligible terms of higher order in 1/\ensuremath{\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 \ensuremath{\gamma} independent. Putting these results together leads to a simple form for the cross section, A ln\ensuremath{\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 (\ensuremath{\gamma}\ensuremath{\sim}200).