Electromagnetic pair production the ultrarelativistic limit

As we have mentioned above it is possible to evaluate the electromagnetic lepton pair production in the limiting case of infinite Lorentz factors y. One interesting aspect among others is that peripheral heavy-ion collisions at ultrarelativistic energies offer 

In the following we briefly discuss both approaches in more detail. It has been shown that the calculation of the amplitude for lepton scattering in the field of ultrarelativistic colliding nuclei can be performed exactly (Eichmann 2000 Eichmann et al. 2000a). The interaction part of the Dirac Hamiltonian (1.7) for two colliding nuclei, referred to by the subscripts (1) and (2) , at infinite energy y — oo reads 

The resulting amplitude coincides with the single- and double-scattering contributions to the Watson series of multiple scattering (Watson 1953), implying that alternating interactions of the lepton with both ions vanish. 

The direct calculation of the pair-production process is mandatory. It turns out that an exact calculation of the pair-creation process is not possible because diagrams including higher-order interactions of the lepton pair with both ions cannot be entirely evaluated in closed form. One obvious reason for this is the fact that it has not yet been feasible to account for all possible classes of diagram. 

The effect of finite nuclear extension on the total cross-section a may be described in terms of a nonCoulomb correction So to the point-charge cross-section orpo ,t, i.e. 

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