Double Ionization of Helium by Protons and Electrons at High Velocities

Abstract

Double ionization of helium at high projectile velocities, $v$, is considered in terms of two mechanisms. In the shakeoff mechanism the ratio of double- to single-ionization cross sections, $\frac{{\sigma }^{\mathrm{ii}}}{{\sigma }^i}$, is independent of $v$. In the two-step mechanism it is shown that $\frac{{\sigma }^{\mathrm{ii}}}{{\sigma }^i}\sim {\left(v^2\ln v\right)}^{-1\mathrm{}}$. Combining amplitudes gives a reasonable fit to the observed velocity dependence as well as an explanation of the observed factor-of-2 differences between double ionization of helium by protons and electrons near $v\simeq 10v_{\mathrm{Bohr}}$.