Contributions to the study of photons electric scattering on the nucleon at low and intermediate energies

The goals of this work are: a) to examine and turn to account in the study of γ-proton elastic scattering the possibility of using a dispersion representation assumed for the amplitude set Asub(i), free of singularities and kinematic zeroes. This is achieved through a direct calculation of the effective unpolarized differential section of the Compton effect on the proton, at various scattering angles in an energy range of 0 <= ω <= 450 MeV and by comparing the results with existent experiments and other theoretical results. b) to calculate the generalized electromagnetic polarizabilities α, β by means of a sum rule which evolves directly from the dispersion representation previously admitted for the relevant invariant amplitude as well as by means of a sum rule derived from a dispersion relation for the same amplitude, unsubtracted, at a scattering angle of 180 deg. The advantage of this second sum rule is that, both in the direct channel and in the annihilation one, the absorptive parts are calculated at a physical scattering angle. Both sum rules confirm as a theoretical result the order α > β which agrees with current experimental data. c) to establish a law regarding low ω5 order energies for the helicity amplitudes and for the unpolarized differential effective section of the process γ + p → γ' + p'. We believe this law to be necessary on one hand for a more accurate determination of the α, β variables out of existent experiments and, on the other hand, for the opportunity to define within the Compton effect on the nucleon new structure constants of the nucleon such as the quadrupolar electromagnetic polarizabilities. By fitting the formula of the unpolarized differential effective section in order ω5 to the experimental data we obtained modified values of α, β, but still in accordance with the order α > β. d) to establish an inequality based upon the analyticity properties of the Compton invariant amplitudes between expressions that include measurable physical variables, static properties of the nucleon and integrals on the effective differential section for the process γ + p → γ' + p'. (author)