Exact results on $e^{+}{e}^{-}\to e^{+}{e}^{-}+2\mathrm{}\gamma$ at energies reached at the SLAC Linear Collider and CERN $e^{+}{e}^{-}$ collider LEP

We use the spinor methods of the CALKUL Collaboration, as realized by Xu, Zhang, and Chang, to calculate the differential cross section for $e^{+}{e}^{-}\to e^{+}{e}^{-}+2\mathrm{}\gamma$ for c.m. system energies in the regime of the SLAC Linear Collider (SLC) and CERN $e^{+}{e}^{-}$ collider LEP. An explicit complete formula for the respective cross section is obtained. The leading-logarithmic approximation is used to check the formula. Applications of the formula to high-precision luminosity calculations at the SLAC and/or LEP are discussed.