Excitation of Atomic Hydrogen and Helium in the Eikonal Approximation

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.