Radiative corrections to the scattering of electrons and positrons by electrons

The e6 corrections to the Moller formula for the scattering of electrons by electrons and the Bhabha formula for the scattering of positrons by electrons, arising from the interaction of the particles with virtual photons, are formulated using the Feynman-Dyson techniques. After removing ultra-violet divergences by mass and charge renormalization the cross-section still suffers from a logarithmic infra-red divergence. This is cancelled by adding on the cross-section for the production of a single real photon of low energy during the collision. The result is evaluated assuming that the maximum bremsstrahlung energy radiated is small compared with the rest energy of the electron, as viewed from the laboratory frame. Non-relativistic and extreme relativistic approximations to the formulae are presented, together with the results of exact calculations for a laboratory energy of 20mc2.

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