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A series of experiments has shown that both elastic scattering and charge-exchange scattering of a directed ion beam by residual gas are dominant factors causing contamination in electromagnetic mass separators. These phenomena are treated numerically for various double-direction focusing machines. The method is based on geometrical considerations and on an appropriate and reliable interaction potential between the ions and the residual gas molecules. Significant expressions for the fractional contaminations as caused by these scattering phenomena are derived. The values depend on such factors as the residual gas molecule concentration, the fractional mass difference, the collector hole area, the magnet radius, a configuration factor, and some constants which appear in the expressions for the differential cross sections. By performing the various integrations in a different sequence, general expressions for the transmission from source to collector are obtained.

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