Electromagnetic probes of nuclear structure: Sum rules,yscaling, and final state interactions

We study the response to an electromagnetic probe of a simple system of two scalar particles (‘‘nucleons’’) bound to form a scalar ‘‘deuteron.’’ The use of a covariant separable interaction allows for an elementary solution of the Bethe-Salpeter equation for both the bound state and for the scattering amplitude. Knowledge of the scattering amplitude allows for an exact treatment of the final state interactions within the limitations of the model. We present results for structure functions and sum rules for a large range of momentum transfer. We also present a systematic study of y scaling and discuss the role of the final state interactions in our model. As noted by other authors, we see that y scaling is well satisfied at the quasielastic peak; however, significant deviations from such scaling behavior are seen in our results as one moves away from the quasielastic peak to the region of large, negative y. We also discuss the influence of final state interactions in modifying sum rules which are well satisfied in the plane wave Born approximation at all ${\mathit{Q}}^2$.