Screening and antiscreening by projectile electrons in high-velocity atomic collisions

The scattering amplitude for a projectile of nuclear charge $Z_1$ carrying $N$ electrons colliding with an atomic target with charge $Z_2$, evaluated in the first Born approximation using hydrogenic wave functions, is compared with recent experimental results. In the present approximation where the minimum momentum transfer $t_{min}$ is considered to be approximately independent of the final state of the projectile, the differential cross sections separate into a product of one term that depends only on the target times the square $Z_1^2\mathrm{}\left(t\right)\mathrm{}$ of an effective projectile charge. Here an analytic expression for $Z_1^2\mathrm{}\left(t\right)\mathrm{}$ is given for 2, 1, and 0 electrons. Some total ionization cross-section ratios are also given.