Multiple scattering and eikonal pole approximation

The eikonal pole approximation to the multiple scattering Watson series is introduced and explored. For noncommuting potentials this approximation naturally defines the ordering of the $z$ coordinates of the scatterers and for commuting potentials leads to the Glauber multiple scattering series. It is shown that the cancellations in the Watson expansion which produce the usual form of Glauber theory are between the infinite series of reflection terms and the off-pole contribution of nonreflective ones. This generalizes the earlier result on cancellations for a two-particle target to targets of arbitrary size.