Strong Coupling in Optically Allowed Atomic Transitions produced by Electron Impact

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Abstract
Optically allowed transitions have long-range interaction potentials, behaving asymptotically as s1/r2 where s1 is proportional to the dipole matrix element. In calculating cross sections many angular momentum states l must therefore be considered. When the coupling is strong the usual Born approximation leads to violations of conservation conditions which are serious for the smaller values of l. Three variants of the first Born approximation are considered: I is the Born approximation for the total scattering amplitude, II the Born approximation for the reactance matrix and III (suggested by Percival) the Born approximation for the proper phase of the scattering matrix. Approximations II and III satisfy conservation conditions and make some allowance for processes such as a → a' → a, a → a' → a" and of a → a" competing with a → a'. Considering the case of exact resonance, and replacing the potentials by their asymptotic forms, one obtains equations for which exact analytic solutions may be obtained. The exact solutions are compared with those obtained using approximations I, II and III.

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