@article{3f699a5cba624c848f0522dd7aeb14f0,

title = "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(θ) and the differential scattering cross section d σ(θ) dΩ were computed at 15 degree intervals 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(θ) and dσ dΩ(θ) 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% smaller.",

author = "Lin, {Shin R.} and Noah Sherman and Percus, {Jerome K.}",

note = "Funding Information: One of the methods in current use for measuring the transverse polarization of electron beams with energies below 500 keV is Mott scattering 1, 2). This method assumes the applicability of the Mort theory 3) for the single scattering of electrons by heavy atoms, in which the effect of screening by atomic electrons, among other phenomena, is ignored. In this paper we report the results of numerical calculations which attempt to include the screening effect. The Mott calculations predict that the electrons scattered out of a polarized beam by heavy point nuclei will be distributed with an azimuthal asymmetry about the axis of the incident beam. This asymmetry depends on the transverse polarization of the incident beam, its energy, the scattering angle and the charge of the nucleus. If the asymmetry factor S(0) is known at experimentally accessible angles (which constitute the central fraction of the range of angles reported in this paper), the polarization t Now at Physics Department, Yale University, New Haven, Connecticut. tt This work was supported in part by the Office of Naval Research, the National Science Foundation and the U. S. Atomic Energy Commission, Contract AT(30-1) 1480 and is based in part on thesis submitted by one oftbe authors (S.R.L.) in partial fulfillment of the requirements for the Ph.D. degree in Physics at the University of Michigan. 492",

year = "1963",

doi = "10.1016/0029-5582(63)90824-1",

language = "English (US)",

volume = "45",

pages = "492--504",

journal = "Nuclear Physics",

issn = "0029-5582",

publisher = "North-Holland Publ Co",

number = "C",

}