Scanning of the e+e- to pi+pi- cross--section below 1 GeV by radiative events with untagged photon

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We discuss an inclusive approach to the measurement of the e+e- --> pi+ pi- cross--section by the radiative return method without photon tagging. The essential part of this approach is the choice of rules for event selection which provide rejection of events with 3 (or more) pions and decrease the final--state radiation background. The radiative corrections to the initial--state radiation process are computed for DAPhNE conditions, using the quasi--real electron approximation for both, the cross--section and the underlying kinematics. The two cases of restricted and unrestricted pion phase space are considered. Some numerical calculations illustrate our analytical results.