Inclusive and exclusive cross sections for multiple ionization by fast, highly charged ions in the independent-electron approximation.

Abstract

Cross sections for the ionization of n of N electrons with equal single-electron ionization probability P are considered. When both N and the projectile charge q are large, the cross sections for single and double ionization are both found to be approximately linear in q at 1 MeV/amu. The ratio of double-to-single-ionization cross sections is independent of q. Moreover, first-order perturbation theory for the single-electron ionization probability P, which varies as ${q}^{2}$, is found to be applicable due to the damping of contributions with large P caused by factors of (1-P${)}^{N\mathrm{\ensuremath{-}}n}$. For large P there are differences between the inclusive probability P and the probability NP commonly used for a target with N electrons. Both of these probabilities differ significantly from the exclusive probability NP(1-P${)}^{N\mathrm{\ensuremath{-}}1}$ for the ionization of only one electron. For large N and large q, the exclusive ionization probabilities for removing exactly n of the N electrons tend to be concentrated in somewhat separate ranges of impact parameters b, defining impact-parameter ``windows.'' The windows which we obtain using the quantum-mechanical semiclassical-Coulomb-approximation (SCA) probabilities are similar to those using classical Monte Carlo calculations. Model calculations, based on analytic fits to the SCA probabilities, are used to obtain approximate analytic expressions for single- and double-ionization cross sections and for the impact-parameter windows. Results of this simple model are in reasonable agreement with measured cross sections for single and multiple ionization of neon atoms by projectiles of charge q varying from 1 to 13 at a velocity corresponding to 1 MeV/amu.