tokens: analysis the Si q + ions are electrostatically deflected by 45°, then focused and collimated by a three-element einzel lens and a series of three apertures prior to entering the target gas cell. The ions undergo CE collisions with the target gas, lowering their charge states by (considered here) one and two exchanges. Currents for each CE step are measured in a retarding-potential analyzer placed at the end of the CE cell, followed by a deep Faraday beam trap. The target gas-cell pressure is monitored using a calibrated capacitance manometer (CM). Individual charge-state currents are measured through the application of a stepped retarding potential , the value of which depends on the incident charge-state q and ion energy through the relation = , where n is the number of exchanges. Thus, a series of retardations , , , will block the charge states q , q − 1, and q − 2, for a total of two exchanges, the maximum encountered in the present study. As in Machacek et al. ( 2014 ), the cross section σ q , q − n for the exchange of n electrons is given by Here, T is the target gas temperature, k is the Boltzmann constant, P is the gas pressure, L is the effective gas-cell length, and R q,q − n is the particles’ current ratio, given bywhere the currents , , correspond to measured current steps after application of the retarding potentials , , . Additional details on the 28 Si q + mass/charge spectrometry, retarding-potential stepping, measurement of background levels, presence of metastable ion states, tests for gas-cell pressure effects on CE cross sections, and data acquisition, together with sources and the levels of random and systematic errors, are given in Machacek et al. ( 2014 ). The He and H 2 used herein were ultrahigh purity-grade (99.999%) gases, and the 28 Si q + ions were produced by dissociative ionization of silane gas (SiH 4 , UHP-grade 99.999%) in the ECR plasma. 3. Results and Discussion A summary of the sources and magnitudes of the experimental errors is given in Table 1 . Shown in Figures 1 and 2 and listed in Table 2 are results of the present measurements of single and double total cross sections for 28 Si q + ions ( q = 7–10) colliding with He and H 2 at the indicated energies. Also given are the statistical error limits at the 2 σ level of confidence. In Table 2 note that the ratio of single-to-double CE cross sections for 28 Si q + + He is approximately 4.1 ± 1.2 (1 σ ) for all the charge states, with the exception of 28 Si 10+ at 2.25 keV/u, where the double-exchange cross section is small (0.104 × 10 −17 cm 2 ). The single-to-double ratio for 28 Si q + + H 2 shows larger variations, from 0.04 to 49.5. The reason for this is not understood. In order to provide some theoretical insight, calculations of the single-exchange CE cross sections were carried out in the static one-electron model (Mann et al. 1981 ). Here, the captured electrons mainly populate states with principal quantum number n that depend on the charge q of the
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