A SIMPLE CORRECTION FOR THE BORN APPROXIMATION FOR ELECTRON-IMPACT EXCITATION OF HYDROGENIC IONS

We develop an analytic procedure for obtaining the electron impact excitation cross sections for hydrogenic ions. A simple modification of the Born approximation, in order to include Coulomb focusing of the continuum wave functions, produces the correct energy dependence of the cross section near excitation threshold. We use this procedure to compute the 1 s --> 2s and 1 s --> 2p excitation cross sections for hydrogenic ions (Z --> infinity), and compare these modified-Born cross sections with numerical Colomb-Born calculations. The modified-Born cross sections agree well with the Coulomb-Born cross sections and thus provide a reliable generalized analytic expression for electron impact excitation of hydrogenic ions. By treating effective charges, the results in this work can be extended to nonhydrogenic target systems.