  We derive Next-to-Eikonal (NEik) corrections to the background quark
propagator, which stem from (i) considering a finite longitudinal width target
instead of an infinitely thin shockwave and (ii) including the interaction of
the quark with the transverse components of the background field. These two
different corrections to the eikonal approximation combine together and
provides a gauge covariant expression for the quark propagator at NEik
accuracy. We then apply our results to quark (or antiquark) scattering on a
nucleus at NEik accuracy, considering both unpolarized cross section and
helicity asymmetry.
