EMPIRICAL FORMS FOR THE ELECTRON-ATOM ELASTIC-SCATTERING CROSS-SECTIONS FROM 0.1 TO 30 KEV

Empirical forms have been found for the total and differential clastic scattering cross sections for electron/atom scattering. The cross sec tions are valid over the range 0.1-30 keV and across the periodic tabl e. The empirical forms of the cross sections are derived from trends i n tabulated Mott scattering cross sections. The form of the total cros s section is similar to a previously published cross section and is ba sed on the screened Rutherford cross section. The fit to the different ial Mott cross sections is decomposed into two parts, one part being o f the same mathematical form as the screened Rutherford cross section sigma(R), and the second part being an isotropic distribution sigma(I) . These two mathematical forms were chosen because they give a straigh tforward generation of random scattering angles. The screened Rutherfo rd part of the differential scattering cross section is first fitted t o the half-angle of the Mott cross sections. This fit of the different ial screened Rutherford is in turn reduced to a fit of the screening p arameter alone over energy and atomic number. The screened Rutherford part of the cross section is highly peaked in the forward scattering d irection and needs to be balanced by the isotropic distribution. The r atio of the total cross sections (sigma(R)/sigma(I)) between the scree ned Rutherford part of the differential scattering cross section and t he isotropic part of the distribution is then fitted to give the same ratio of forward to backscattered currents as the tabulated Mott diffe rential cross sections. Using this dual form of the scattering cross s ection for the differential cross section, and the previously (indepen dently) fitted total cross section, the backscattering coefficients fo r normal incidence are calculated. The two equations describing the di fferential cross section, one for the Rutherford screening parameter a nd one for the ratio sigma(R)/sigma(I), are simplified to remove redun dant parameters, and then fitted to the backscattering coefficients ca lculated directly from the tabulated Mott cross sections. A straightfo rward expression for the differential cross section was found to give backscattering results covering all the major trends with energy and a tomic number compared to the backscattering coefficients calculated us ing tabulated Mott cross sections.