Relativistic eikonal approximation in high-energy A (e,e ' p) reactions

A fully relativistic model for the description of exclusive ${(e,e}^{\ensuremath{'}}p)$ reactions off nuclear targets at high energies and momentum transfers is outlined. It is based on the eikonal approximation for the ejectile scattering wave function and a relativistic mean-field approximation to the Walecka model. Results for ${}^{12}\mathrm{C}{(e,e}^{\ensuremath{'}}p)$ and ${}^{16}\mathrm{O}{(e,e}^{\ensuremath{'}}p)$ differential cross sections and separated structure functions are presented for four-momenta in the range $0.8l~{Q}^{2}l~20 (\mathrm{GeV}{/c)}^{2}.$ The regions of applicability of the eikonal approximation are studied and observed to be confined to proton knockout in a relatively small cone about the momentum transfer. A simple criterion defining the boundaries of this cone is determined. The ${Q}^{2}$ evolution of the effect of off-shell ambiguities on the different ${(e,e}^{\ensuremath{'}}p)$ structure functions is addressed. At sufficiently high values of ${Q}^{2}$ their impact on the cross sections is illustrated to become practically negligible. It is pointed out that for the whole range of ${Q}^{2}$ values studied here, the bulk of the relativistic effects arising from the coupling between the lower components in the wave functions, is manifesting itself in the longitudinal-transverse interference term.