Complete experiment in e∓N-elastic scattering, in presence of two-photon exchange

Using a general parametrization of the spin structure of the matrix element for elastic eN-scattering, in terms of three independent complex amplitudes, we found the expressions for all polarization observables, in electron-proton elastic scattering. This allows to suggest possible methods to measure the nucleon electromagnetic form factors, in presence of two-photon exchange. We show that the measurements of the differential cross section for electron and positron nucleon elastic scattering, in the same kinematical conditions, allows to extract the nucleon electromagnetic form factors. The same is correct for the polarization method, with the measurement of the P-x,P-z components of the final nucleon polarization (for the scattering of longitudinally polarized electrons and positrons). An alternative way, in absence of positron beam, is to measure a definite set of T-odd polarization observables, which includes three different experiments or only T-even observables, with five independent experiments. In both cases, the ratio G(E) (Q(2))/G(M)(Q(2)) is related to quantities of the order of alpha and requires different polarization experiments with very high accuracy. (C) 2004 Elsevier B.V. All rights reserved.