Helicity asymmetry for proton emission from polarized electrons in the eikonal regime

Abstract

The nuclear response to longitudinally polarized electrons, detected in coincidence with out-of-plane high-energy protons, is discussed in a simple model where the ejectile wave function is approximated as a plane wave with a complex wave vector. This choice is equivalent to solving the problem of final-state interactions (FSI) in homogeneous nuclear matter, as the residual nucleus can be described to a first approximation when dealing with very fast emitted protons. The main advantage of the present method is that in the framework of the distorted-wave impulse approximation at the one-photon exchange level it allows for an analytical derivation of all the components of the nuclear response, including the so-called fifth structure function ${f}_{01}^{\ensuremath{'}}$, which is very sensitive to FSI. The imaginary part of the complex wave vector produces purely geometrical FSI effects and, consequently, breaks the symmetry of the cross section with respect to the incoming electron helicity. Inspection of every single contribution in the analytical formulas, here considered up to the fourth order in the nonrelativistic reduction in powers of the inverse nucleon mass, allows for a detailed study of the role of each elementary reaction mechanism. In particular, cancellations among the leading contributions determine the very small absolute size of ${f}_{01}^{\ensuremath{'}}$ and produce a nontrivial asymptotic scaling of the related helicity asymmetry for large values of the momentum transfer.