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The general structure of the cross section of γN scattering with polarized photon and/or nucleon in initial and/or final state is systematically described and exposed through invariant amplitudes. A low-energy expansion of the cross section up to and including the order O(ω 4 ) is given which involves ten structure parameters of the nucleon (dipole, quadrupole, dispersion, and spin polarizabilities). Their physical meaning is discussed in detail.Using fixed-t dispersion relations, predictions for these parameters are obtained and compared with results of chiral perturbation theory. It is emphasized that Compton scattering experiments at large angles can fix the most uncertain of these structure parameters. Predictions for the cross section and double-polarization asymmetries are given and the convergence of the expansion is investigated. The feasibility of the experimental determination of some of the structure parameters is discussed.

The Compton scattering cross section on the proton has been measured at laboratory angles of 90 • and 135 • using tagged photons in the energy range 70-100 MeV and simultaneously using untagged photons in the range 100-148 MeV. With the aid of dispersion relations, these cross sections were used to extract the electric and magnetic polarizabilities,ᾱ andβ respectively, of the proton. We find α +β = (15.0 ± 2.9 ± 1.1 ± 0.4) × 10 −4 fm 3 ,in agreement with a model-independent dispersion sum rule, and α −β = (10.8 ± 1.1 ± 1.4 ± 1.0) × 10 −4 fm 3 ,

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