Convergence of the Born and Coulomb-Born approximations for the electron-impact excitation of positive ions.

Abstract

The convergence of the Born and Coulomb-Born approximations for the electron-impact excitation cross sections of positive ions was examined both formally and by sample calculations on several lithiumlike ions. It was found that the convergence of the two approximations with increasing energy is not necessarily monotonic and may not occur until many tens of threshold units. An analytic expansion of the Coulomb partial waves, in terms of spherical Bessel functions, indicates that partial-wave collision strengths in the two approximations do not necessarily converge in the limit of high angular momentum, although agreement at high incident energies occurs for all partial cross sections. Criteria for the use of the Born approximation for highly ionized atoms are discussed.