Ion-atom inelastic scattering cross sections and energy loss in the plane-wave Born approximation

Abstract

A procedure discussed by Bates for calculating ion-atom excitation and ionization cross sections and energy loss in the plane-wave Born approximation has been programmed. The procedure involves integration over the product of elastic scattering factors or generalized oscillator strengths for excitation or ionization from both projectile and target. The calculations are done in the center-of-mass system where the distinction between projectile and target is lost. Thus the cross sections and energy loss in the laboratory frames of both target and projectile emerge from a center-of-mass calculation symmetrical in nuclear and net charges. The traditional simple modeling of energy loss, using scaled proton stopping power (SP) and an effective projectile charge, is unsymmetrical, and therefore dubious as a guide for extrapolating to ion-ion energy loss. Because the energy loss includes processes that cannot be uniquely allocated to one ion or the other, e.g., mutual ionization, one does not expect, in general, a simple SP picture to suffice. However, it is found at intermediate and high center-of-mass energies that the energy loss is dominated by elastic scattering of one ion and ionization of the other. From this observation, and the requirement that hydrogenic ion results be recovered in the appropriate limit, a simple extension of the Bethe formula is obtained. Explicit subshell and total ionization cross sections are presented for Li ions interacting with neutral Zn and Au, and the calculated energy loss is compared with experiment. It is found that the simple extension of the Bethe formula is in surprisingly good agreement with the explicit calculations, suggesting that an improved extension of the Bethe formula may exist.