Compton and double Compton scattering processes at colliding   electron-photon beams
  Radiative corrections (RC) to the Compton scattering cross section are calculated in the leading and next-to leading logarithmic approximation to the case of colliding high energy photon-electron beams.   RC to the double Compton scattering cross section in the same experimental set-up are calculated in the leading logarithmic approximation.   We consider the case when no pairs are created in the final state. We show that the differential cross section can be written in the form of the Drell-Yan process cross-section.   Numerical values of the $K$-factor and the leading order distribution on the scattered electron energy fraction and scattering angle are presented. 
A.N. Ilyichev, E.A. Kuraev, V. Bytev, Yu. P. Peresun'ko