Corrections to the Glauber Scattering Amplitude

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Abstract
Extensions of the eikonal approximation differ most significantly in the means by which velocity symmetry is introduced in the scattering amplitude. One can either employ a manifestly symmetric representation at the outset, or follow Glauber's lead in choosing the incoming momentum direction for the plane wave; if the latter course is followed, then restoration of symmetry by a coordinate rotation is an essential step, and should not be thought of as an auxiliary approximation. Moreover, physical considerations that go beyond the mathematically prescribed order of calculation underlie the success of this approximation, and offer clues to the most effective means for generating corrections.