  The upcoming Facility for Rare Isotope Beams (FRIB) at the National
Superconducting Cyclotron Laboratory (NSCL) at Michigan State University has
reemphasized the importance of accurate modeling of low energy nucleus-nucleus
scattering. Such calculations have been simplified by using the eikonal
approximation. As a high energy approximation, however, its accuracy suffers
for the medium energy beams that are of current experimental interest. A
prescription developed by Wallace \cite{Wallace:1971zz,Wallace:1973iu} that
obtains the scattering propagator as an expansion around the eikonal propagator
(Glauber approach) has the potential to extend the range of validity of the
approximation to lower energies. Here we examine the properties of this
expansion, and calculate the first-, second-, and third-order corrections for
the scattering of a spinless particle off of a ${}^{40}$Ca nucleus, and for
nuclear breakup reactions involving ${}^{11}$Be. We find that, including these
corrections extends the lower bound of the range of validity of the down to
energies of 40 MeV. At that energy the corrections provide as much as a 15\%
correction to certain processes.
