“…Unlike the situation for double photoionization, for direct multiple ionization of outer-shell electrons by charged-particle impact the most common approach is to use an independent-electron model (IEM) where the projectile interacts with each target electron independently. In the independent-electron model, the single-and multipleionization cross sections scale as (Ze/v) 2n , where Z and v are the projectile charge and velocity, e is the electron charge, and n is the number of ionized electrons (see [1,2] and references therein). However, two aspects of the independent-electron model that are inconsistent with experimental data are that * Corresponding author: dubois@mst.edu (a) it predicts the relative amount of double ionization, i.e., R 2 = σ 2 /σ 1 , which corresponds to n = 2 and 1 in the scaling relationships, to steadily decrease and ultimately become negligible for very large v and (b) the double-to singleionization ratios should be the same for positive and negative values of Z, i.e., for electron and proton impact, positron and electron impact, and antiproton and proton impact.…”