The plural scattering of 20 kev electrons

Measurements have been made of the angular distribution of electrons, of initial energy 20 kev, transmitted through films of Al, Cu and Au of mass-thicknesses corresponding to between 3 and 20 elastic scattering acts. In form the distributions agree well, over the measured angular range 7 × 10 -3 < θ < 5 × 10 -1 , with that predicted by the Bothe equations for plural scattering as integrated by Lenz. The absolute values of the scattered intensity in Al and Cu agree closely with those calculated by Lenz in the thinner films, but are about 40% higher in the thicker films, for 10 -2 < θ < 10 -1 . Taken together with the measurements of Haefer on carbon, these results support Bothe's plural scattering theory but suggest that certain approximations, made by Lenz in evaluating it, lead to serious underestimation of the intensity scattered into intermediate angles by relatively thick films. In Au the measured intensities are about twice Lenz's values in the main part of the angular range for all thicknesses of films, the most probable explanation being failure of the Born approximation. The mass scattering cross sections S p , derived from the integrated intensity, are generally lower than Lenz's predicted values. The discrepancy is less than that found in the conditions of electron microscopy (θ < 10 -2 and at 50-100 kev), but the variation of S p with Z is found to be stronger, being approximately proportional to Z 4/3 / A for films of small and medium thickness. In thicker films, the dependence on Z is much less marked. The atomic screening factors calculated from our results agree fairly well with those adopted by Lenz; they are closer to the values derived from the magnetic susceptibility than to those obtained by the Hartree self-consistent field method. So far as comparison is possible with the plural scattering theory of Smith and Burge, we find the mass scattering cross section (and the electron microscopical contrast) much lower than their values. The experimental values of their scattering parameter f e (0) are also low, being approximately half the calculated values.