Photon Scattering from a Relativistic Bound Particle.

A detailed study is presented of the structure and the properties of the amplitude describing the scattering of real and virtual photons from a bound, relativistic, quantal system. The discussion is restricted to a model problem which is chosen in such a way as to make feasible an analytic solution and, at the same time, illustrate many of the features that are expected to appear in the analysis and the interpretation of more realistic situations. The motivation for the work is provided by the availability, actual or anticipated, of experiments studying elastic and inelastic scattering of photons from hadronic targets and the need to test, justify and illustrate theoretical conjectures concerning the behaviour of the appropriate amplitudes. Among the topics studied in this work we mention the derivation of low-energy theorems including recoil and terms which depend quadratically in the photon energy, the identification of the electric polarizability and the magnetic susceptibility of the system, which, in the relativistic case, exhibit some rather unconventional features, the high-frequency limit, gauge transformations, dispersion relations, a detailed discussion of various energy-weighted sum rules together with a comparison with the familiar results in the non-relativistic limit and a complete treatment of the effect of retardation. The potentials responsible for the binding include both Lorentz-scalar and Lorentz-vector components. It is expected and is explicitly verified in the calculation that in the Lorentz-scalar case, bound states with energy between zero and {-}m where m is the mass of the particle, appear even if the potential strength is relatively weak. The Compton amplitude, in this case, exhibits resonances corresponding to the virtual formation of bound particle-antiparticle pairs in the intermediate state. A number of additional topics, indirectly related to the main work, are also discussed. They include a study of the relativistic response function of the system under the influence of external fields, a relativistic treatment of the Landau levels for a particle confined on a plane and a study of the total absorption cross section of longitudinal virtual photons which in the non-relativistic limit is known to be restricted by a sum rule.