Empirical forms for the electron/atom elastic scattering cross sections from 0.1 to 30 keV

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Abstract
Empirical forms have been found for the total and differential elastic scattering cross sections for electron/atom scattering. The cross sections are valid over the range 0.1–30 keV and across the periodic table. The empirical forms of the cross sections are derived from trends in tabulated Mott scattering cross sections. The form of the total cross section is similar to a previously published cross section and is based on the screened Rutherford cross section. The fit to the differential Mott cross sections is decomposed into two parts, one part being of the same mathematical form as the screened Rutherford cross section σR, and the second part being an isotropic distribution σI. These two mathematical forms were chosen because they give a straightforward generation of random scattering angles. The screened Rutherford part of the differential scattering cross section is first fitted to the half‐angle of the Mott cross sections. This fit of the differential screened Rutherford is in turn reduced to a fit of the screening parameter alone over energy and atomic number. The screened Rutherford part of the cross section is highly peaked in the forward scattering direction and needs to be balanced by the isotropic distribution. The ratio of the total cross sections (σR/σI) between the screened Rutherford part of the differential scattering cross section and the isotropic part of the distribution is then fitted to give the same ratio of forward to backscattered currents as the tabulated Mott differential cross sections. Using this dual form of the scattering cross section for the differential cross section, and the previously (independently) fitted total cross section, the backscattering coefficients for normal incidence are calculated. The two equations describing the differential cross section, one for the Rutherford screening parameter and one for the ratio σR/σI, are simplified to remove redundant parameters, and then fitted to the backscattering coefficients calculated directly from the tabulated Mott cross sections. A straightforward expression for the differential cross section was found to give backscattering results covering all the major trends with energy and atomic number compared to the backscattering coefficients calculated using tabulated Mott cross sections.