Adiabatic pair creation in heavy-ion and laser fields

The planned generation of lasers and heavy-ion colliders renews the hope to see electron-positron pair creation in strong classical fields. This old prediction is usually referred to as spontaneous pair creation. We observe that both heavy-ion collisions and pair creation in strong laser fields, are instances of the theory of adiabatic pair creation. We shall present the theory, thereby correcting earlier results. We give the momentum distribution of created pairs in overcritical fields. We discuss carefully the proposed experimental verifications and conclude that pure laser-based experiments are highly questionable. We propose a new experiment, joining laser fields and heavy ions, which may be feasible with present-day technology and which may indeed verify the theoretical prediction of adiabatic pair creation. Our presentation relies on recent rigorous works in mathematical physics. (authors)