Measuring sigma(e+ e- --> hadrons) with Tagged Photons at Electron Positron Colliders

A Monte Carlo generator has been constructed to simulate the reaction e+ e- --> gamma + 2 pions and gamma + 4 pions, where the photon is assumed to be observed in the detector. Predictions are presented for cms energies of 1GeV, 3GeV and 10GeV, corresponding to the energies of DAPHNE, BEBC and of B-meson factories. The event rates are sufficiently high to allow for a precise measurement of R(Q^2) in the region of Q between approximately 1GeV and 2.5GeV. Estimates for the kinematic breaking of isospin relations between different channels as a consequence of the mass difference between charged and neutral pions are given.