Abstract
A treatment to evaluate numerically both the direct and exchange amplitudes within the exact framework of the eikonal approximation is considered. The eikonal or unrestricted Glauber-scattering amplitude is decomposed into two partial amplitudes. One of them is reduced to either a closed form for the direct amplitude or to a single-integral expression for the exchange amplitude and is found to approach the Born amplitude at high energy. The other amplitude is expressed in a double-integral form in which the numerical convergence is clearly recognised. By evaluating the direct and exchange amplitudes the results for electron-hydrogen elastic scattering are obtained without the difficulty related to numerical convergence.
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