Elastic γ-proton scattering at low and intermediate energies

Abstract

A new dispersive analysis of the elastic γ-proton scattering at photon laboratory energies lower than 450 MeV, based on the use of Bardeen-Tung invariant amplitudes free of both kinematical singularities and zeros, is presented. The requirements of relativistic (and gauge) invariance are then incorporated from the beginning, no ad hoc subtractions being necessary any longer to satisfy the existing low-energy theorems. The adopted dispersion representation makes use as much as possible of fixed momentum transfer ( t) dispersion relations, the subtraction functions (when unavoidable) being expressed as dispersion relations in t. The absorptive parts in various channels are evaluated within the two-particle unitarity approximation by means of recent tables of pion photoproduction multipoles and a simple model which accounts for the ππ I = J = 0 interaction. The comparison between the experimental data and the numerical values obtained for the unpolarized differential cross section (in the form of energy and angular distributions) shows that the output of our approach is somewhat better than that of the previous theoretical calculations, although the problem of discrepancies around the photoproduction threshold and at the N ∗ resonance (at 90°) is still there. As we confined ourselves to natural assumptions, approximations, and procedures and did not attempt to improve the agreement with experiment by suitable fits or parametrizations, the conclusion emerges that the proposed formalism represents a more than adequate tool for further investigations of the proton Compton effect. The question of proton's generalized electromagnetic polarizabilities is also discussed in connection with the influence of the exchanges in the annihilation channel on the process considered.