Executive Summary

Elastic scattering has a direct influence on the spatial distribution of energy deposited by electrons and positrons. Because of elastic scattering, the trajectories of these particles are tortuous and, consequently, they penetrate distances substantially shorter than their path lengths. Thus, although energy transfers in elastic collisions are negligible, elastic-scattering properties of the medium have a strong effect on the spatial distribution of dose from electrons and positrons. Knowledge of differential cross-sections for elastic scattering of these particles is needed for modeling the energy deposition from any form of ionizing radiation, because of the production of energetic electrons, and occasionally positrons, in the interactions of the primary radiation. Specific applications that require accurate information on elastic scattering extend from radiation dosimetry, radiation therapy, radiation processing, radiation sensors, and radiation protection to atmospheric studies, plasma physics, and material analysis (through electronprobe microanalysis, analytical electron microscopy, Auger-electron spectroscopy, and x-ray photoelectron spectroscopy). The present Report contains a review of theoretical methods and experimental techniques for studying elastic scattering of electrons and positrons by single atoms, positive ions, and molecules, as well as in condensed materials. The emphasis of the theoretical sections is in the scattering by neutral atoms and in the range of intermediate and high energies, from a few keV upwards. At these energies, the target atom behaves nearly as a frozen distribution of electric charge, and the process can be described as scattering of the projectile by the electrostatic field of the atom (the so-called static-field approximation). In the case of electron scattering, exchange effects can be accounted for by means of an approximate local potential. More elaborate optical-model potentials, which account for the effects of atomic charge polarizability and inelastic absorption, are also described. Calculations with semi-empirical opticalmodel potentials provide results consistent with experimental information for lower energies, down to about 100 eV, and are used to evaluate the limitations of the static-field approximation. The non-relativistic (Schrödinger) and relativistic (Dirac) theories of scattering by a central potential are described, together with calculational methods and approximations relevant to elastic scattering of electrons and positrons by neutral atoms and positive ions. Information is also provided on various atomic-charge distribution models, approximate exchange potentials, and optical-model potentials that have been used in elastic-scattering calculations. The theoretical differential cross-sections for atoms presented in the Report were calculated by using the Dirac partial-wave expansion method, which consistently accounts for spin and relativistic effects. Accurate and robust numerical methods for the solution of the radial Dirac equations and for the summation of the partial-wave series are described. These methods were implemented in the computer code system ELSEPA (Salvat et al., 2005), which calculates scattering amplitudes, differential cross sections, spin-polarization functions, and total cross sections for elastic scattering by neutral atoms from the static-field approximation and optical-model potentials. At high energies (higher than about 20Z keV, where Z is the atomic number), where the partial-wave series converge too slowly, the atomic differential cross-section is calculated as the product of the partial-wave crosssection for scattering by the bare nucleus and a pre-calculated screening function. This type of numerical calculation is feasible for energies up to about 500 MeV. For higher energies, the differential cross-section of the bare nucleus is obtained from the first Born approximation. The program ELSEPA can also calculate elastic scattering by molecules (within the independent-atom approximation) and by positive ions for electrons and positrons with kinetic energies up to about 1 MeV. Experimental techniques for measuring elasticscattering differential cross-sections and related quantities are surveyed. Available experimental cross-section data for atoms, and for water molecules, are compared with calculated theoretical Journal of the ICRU Vol 7 No 1 (2007) Report 77 doi:10.1093/jicru/ndm005 Oxford University Press