Eikonal expansion as the high-energy limit of the Born series

The Glauber version of the eikonal expansion in potential theory is shown to be the unique result of calculating the high-energy, fixed-momentum-transfer limit of the Born series. Correction terms are systematically calculated and agree with the form proposed by Wallace. These results are used to understand the fact that the Glauber eikonal is an accurate approximation to the exact scattering amplitude at all energies.