Validity of Eikonal - Type Approximations for Potential Scattering

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Abstract
It is shown that for a wide class of potentials the slightly modified form of the Glauber eikonal approximation, recently proposed by Abarbanel and Itzykson, is essentially equivalent to the simplified form of the Saxon-Schiff formula obtained by Sugar and Blankenbecler. Insight into the relationship among several high-energy approximations is thereby gained. It is then suggested that the above modified Glauber approximation may possess a rather large angular range of validity and may be as reliable as several of the recently proposed "improved" high-energy approximations. This is also numerically illustrated.