Abstract
Some of the key approximations involved in the application of the eikonal method to atomic physics are analyzed, and the method is related to the close-coupling approach. The importance of an accurate treatment of kinematics is stressed, and a Monte Carlo integration technique is used to facilitate the application of eikonal equations without simplifying kinematical assumptions. Results are presented on the excitation of the $2^{1}P$ state of helium by electron impact, on the excitation of the $2p$ state of atomic hydrogen by electron impact, and on the excitation of the $2s$ state of hydrogen by electron and positron (or proton) impact. Detailed comparison with experiment is made wherever possible.
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