An independent-electron model for charge-state distributions and beam-foil populations

The foundations for an independent-electron model for charge-state distributions of heavy elements having passed through solids, as well as for beam-foil populations, are presented and discussed. It is proposed that the fraction $P_i$ of particles with charge $\mathrm{ie}$, $e$ being the charge of the proton, is given by the simple expression $P_i=\left[\frac{n!}{i!(n-i)!}\right]{\alpha }^{n-i}{(1-\alpha )}^i$, where $n$ is the number of electrons possible outside a closed core, and $\alpha$ is a parameter accounting for outer electrons. Modification of this expression in case the core becomes ionized is discussed. The model and its implications are compared to experimental data, and good agreement is generally found.