Elastic scattering of relativistic electrons by screened atomic nuclei

Abstract

The effect of screening by atomic electrons on the scattering of relativistic electrons by heavy atoms has been computed numerically using different screening models. Exponential and Hartree potentials were used to simulate the screening. The asymmetry factor S(0) and the differential scattering cross section d~(0)/d.Q were computed at 15 degree intervaTs from 15°to 165 °. We report here the results for (a) 121 keV electrons scattered by gold, Z = 79, using two exponential potentials of different range, (b) 79 keV (v/c = 0.5) electrons scattered by mercury, Z = 80, using exponential and Hartree fields, (c) 46 keV (v/c ~ 0.4) electrons scattered by mercury as in (b). The asymmetry factor S(0) and d~/d.Q(0) were computed using a partial wave expansion in which the phase shifts were obtained both by numerical integration of a suitably transformed Dirac radial equation and also computed in WKB approximation. The results are compared with corresponding calculations for the Coulomb field. In general the differences are no more than a few percent, but below 30 ° the screened field cross-sections are as much as 50~o smaller.

Measurement of the absolute cross section for the elementary process of atomic field bremsstrahlung

“…It was calculated by the partial wave method (the necessary calculations are described e.g. by Lin [8,9]) using a screened atomic potential [10].…”

Precision electron polarimetry

“…The analyzing power depends on the scattering angle and reaches about 50% in the backward direction, closer to 180 • at higher energies. The uncertainty of the Sherman function is a few percent at low energy due to electron cloud screening [10] or at the percent level above 1 MeV due to finite nuclear size penetration [11]. Plural and multiple scattering on thicker targets dilute the measured asymmetry.…”

Determination of the IMFP from electron elastic backscattering probability

“…19 The phase shifts can be derived from the solution of the Dirac equation. As shown by Lin et al 20 and Bunyan and Schonfelder, 16 the Dirac equation for an electron interacting with the atomic potential V r can be transformed to the first-order differential equation…”