Relativistic electromagnetic charge response: Finite versus infinite systems, exclusive versus inclusive processes

Connections between exclusive and inclusive electron scattering are explored within the framework of the relativistic plane-wave impulse approximation, beginning with an analysis of the model-independent kinematical constraints to be found in the missing-energy--missing-momentum plane. From the interplay between these constraints and the spectral function basic features of the exclusive and inclusive nuclear responses are seen to arise. In particular, the responses of the relativistic Fermi gas and of a specific hybrid model with bound nucleons in the initial state are compared. The latter facilitates extrapolations from light nuclei to very heavy ones where the former model has some validity. As expected, the exclusive responses are significantly different in the two models, whereas the inclusive ones are rather similar. By extending previous work on the relativistic Fermi gas, a reduced response is introduced for the hybrid model such that it fulfills the Coulomb and the higher-power energy-weighted sum rules. Although incorporating specific classes of off-shellness for the struck nucleons, it is found that the reducing factor required is largely model independent and, as such, yields a reduced response that is useful for studies of scaling and of the Coulomb sum rule. In particular, guided by the difference between the energy-weighted sum rules of the two models a new scaling variable appropriate for heavy nuclei is devised. Finally, a version of the relativistic Fermi gas which has zeroth, first, and second energy-weighted moments of the longitudinal response that agree rather well with those of the hybrid model is constructed: this version thus incorporates a priori the binding effects of the struck nucleons while retaining the simplicity of the original Fermi gas and provides the basis for future extensions of the model.