Multiple-vacancy production in the independent-Fermi-particle model

Measurements of $K$ x-ray (or Auger) satellite intensities produced by ion impact have yielded $K^u{L}^v$ multiple-vacancy distributions which in most cases are nearly binomial. This implies that, statistically, the holes are nearly independent, which is surprising in view of the known influence of correlations on other collision processes. We give a detailed derivation of general expressions for ion-induced multiple-vacancy distributions in the independent-Fermi-particle collision model, based on the Hartree-Fock description of the target, which contains Pauli correlations. Our coupled-channels calculations employing these expressions have shown that the electron exchange terms tend to mutually cancel because of "random" phases, but need not cancel when a single channel, such as a resonant electron capture, is dominant.