NIST Electron Elastic-Scattering Cross-Section Database, SRD 64

Theoretical description of electron transport in solids is important in radiation physics, electron lithography, electron-probe microanalysis, analytical electron microscopy, and surface analysis by Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). In these and other applications, the trajectories of electrons in a solid are generally modified by single and multiple elastic-scattering events. An evaluation of the effects of elastic scattering on the process of interest requires knowledge of the cross sections for electron elastic scattering by the constituent atoms of the particular solid. Although calculated and measured electron elastic-scattering cross sections are available in the literature for selected elements and a limited number of electron energies, this information is incomplete and insufficient for general use.

NIST released Version 1.0 of the Elastic-Electron-Scattering Cross-Section Database (SRD 64) in 1996. This version provided differential and total elastic-scattering cross sections for elements with atomic numbers from 1 to 96 and for electron energies between 50 eV and 9999 eV in steps of 1 eV. These cross sections were calculated using the Thomas-Fermi-Dirac potential to describe the interaction between an electron and an atom, and using both relativistic and non-relativistic models. This version was designed for analyses of the transport of signal electrons in AES and XPS although it could, of course, be used for other applications.

Version 2.0 of the database was released in 2000. In this version, the upper electron-energy limit was extended to 20 keV, and phase shifts and transport cross sections were also provided. The elastic-scattering cross sections, phase shifts, and transport cross sections, however, were obtained only with a relativistic model because this was believed to be more reliable than the non-relativistic model.

Version 3.0 of the database was released in 2002, and contained two major changes. First, the differential elastic-scattering cross sections, total elastic-scattering cross sections, phase shifts, and transport cross sections were calculated from a relativistic Dirac partial-wave analysis in which the potentials were obtained from Dirac-Hartree-Fock electron densities computed self-consistently for free atoms. This potential is believed to be more reliable than the Thomas-Fermi-Dirac potential used previously [1]. Differences in elastic-scattering cross sections and transport cross sections resulting from this change of potential are described in a review article [1].

In addition, it is possible in Version 3.0 to create and/or print files illustrating variation of differential elastic-scattering cross sections versus scattering angle for one or more elements or for one or more energies. Some of the database screens were redesigned as a result of the increase in the upper electron-energy limit to 300 keV.

Version 3.1 of the database, issued in August, 2003, contains two corrections to Version 3.0. First, a numerical mistake was found in the calculation of differential cross sections for a small number of elements and energies (e.g., F at 300 eV). Second, the routine used for interpolations between differential cross sections at certain scattering angles was found to be inadequate in the vicinity of deep minima in the differential cross sections (e.g., Cu at 319 eV). The libraries of cross-section data and the software have been revised to correct these problems.

Version 3.2 of the database was issued in December, 2010. The installation program for Version 3.2 was changed so that it would operate on newer versions of the Windows operating system. There were no changes or additions to the data in the database although a new About box was added to the main menu. This box shows two references, a 2004 critical review [1] and a 2005 review [2], that discuss evaluations of the compiled data, methods of determination, and uncertainty.

Version 3.2 of the Electron Elastic-Scattering Cross-Section Database has the following capabilities:

  • Graphical display of differential elastic-scattering cross sections in different coordinate systems
  • Graphical display of the dependence of transport cross sections on electron energy
  • Display of numerical values of differential elastic-scattering cross sections, total elastic-scattering cross sections, and transport cross sections
  • Creation of files containing differential elastic-scattering cross sections for specified elements, energies and coordinates
  • Creation of files containing plots of differential elastic-scattering cross sections versus scattering angle for one or more elements or for one or more electron energies
  • Creation of files containing phase shifts for specified elements and for energies up to 20 000 eV
  • Creation of files containing transport cross sections for specified elements and energies
  • Creation of random number generators providing the polar scattering angles to be used in Monte Carlo simulations of electron transport in solids; and
  • Runs of the random number generators

Version 4.0 of the database was released in June, 2016. The database has been redesigned to operate in a user’s browser rather than as an installed database on a personal computer with the Windows operating system. All screens have been redesigned. The database now provides differential elastic-scattering cross section and transport cross sections, as in previous versions. Graphical displays of these cross sections are available as before, and data files can be downloaded in JSON and CSV formats. Phase Shifts are now not provided.

The differential elastic-scattering cross sections (DCSs) were calculated using the relativistic Dirac partial-wave method, as described by Walker [3]. The scattering potential was obtained from the self-consistent Dirac-Hartree-Fock electron density for free atoms [4] with the local exchange potential of Furness and McCarthy [5]. The numerical calculations were performed with the algorithm described by Salvat and Mayol [6]. Transport cross sections were calculated from the DCSs as described by Jablonski et al. [1]. Further details of the calculations are available in the Users' Guide for the database [7] which also contains guidance on the database functions.

Cross sections are expressed in units of the square of the Bohr radius, a0, which is 0.52917721 x 10-10 m.


  • [1] A. Jablonski, F. Salvat, and C. J. Powell, J. Phys. Chem. Ref. Data 33, 409 (2004).
  • [2] F. Salvat, A. Jablonski, and C. J. Powell, Comput. Phys. Commun. 165, 1571 (2005).
  • [3] D. W. Walker, Advances in Physics 20, 257 (1971).
  • [4] J. P. Desclaux, Computer Physics Communications 9, 31 (1975); erratum ibid 13, 71 (1977).
  • [5] J. B. Furness and I. E. McCarthy, J. Phys. B: At. Mol. Phys. 6, 2280 (1973).
  • [6] F. Salvat and R. Mayol, Computer Physics Communications 74, 358 (1993).
  • [7] A. Jablonski, F. Salvat, and C. J. Powell, NIST Electron Elastic-Scattering Database Users' Guide, September, 2016;