X-Ray Form Factor, Attenuation, and Scattering Tables
Detailed Tabulation of Atomic Form Factors, Photoelectric Absorption and Scattering Cross Section, and Mass Attenuation Coefficients for Z = 1-92 from E = 1-10 eV to E = 0.4-1.0 MeV
Tables for form factors and anomalous dispersion are of wide general use in the UV, x-ray and γ-ray communities, and have existed for a considerable period of time. Much of the recent theoretical basis for these was contributed by Cromer, Mann and Liberman while much of the experimental data was synthesised by Henke et al. More recent developments in both areas have led to new and revised tables. The generality of these works has entailed numerous simplifications compared to detailed relativistic S-matrix calculations; however, the latter do not appear to give convenient tabular application for the range of Z and energy of general interest. Conversely, the former tables appear to have large regions of limited validity throughout the range of Z and energies, and in particular have limitations with regard to extrapolation to energies outside tabulated ranges.
Herein, the primary interactions of x-rays with isolated atoms from Z = 1 (hydrogen) to Z = 92 (uranium) are described and computed within a self-consistent Dirac-Hartree-Fock framework. This has general application across the range of energy from 1-10 eV to 400-1000 keV, with limitations (described below) as the low- and high-energy extremes are approached. Tabulations are provided for the f1 and f2 components of the form factors, together with the photoelectric attenuation coefficient for the atom, µ, and the value for the K-shell, µK, as functions of energy and wavelength. Also provided are estimated correction factors as described in the text, conversion factors, and a simple estimate for the sum of the scattering contributions (from an isolated atom).
Revised formulae can lead to significant qualitative and quantitative improvement, particularly above 30 keV to 60 keV energies, near absorption edges, and at 0.03 keV to 3 keV energies. Recent experimental syntheses are often complementary to this approach. Examples are given where the predictions underlying revised theoretical tables are in qualitative agreement with experiment, as opposed to results in experimental syntheses.
Reliable knowledge of the complex x-ray form factor (Re(f) and f″) and the photoelectric attenuation coefficient (σPE) is required for crystallography, medical diagnosis, radiation safety and XAFS studies. Discrepancies between currently used theoretical approaches of 200 % exist for numerous elements from 1 keV to 3 keV x-ray energies. The key discrepancies are due to the smoothing of edge structure, the use of non-relativistic wavefunctions, and the lack of appropriate convergence of wavefunctions. This tabulation addresses these key discrepancies and derives new theoretical results of substantially higher accuracy in near-edge soft x-ray regions [0.1 keV to 10 keV]. The high-energy limitations of the current approach are also illustrated.
The associated figures and tabulation demonstrate the current comparison with alternate theory and with available experimental data. In general experimental data are not sufficiently accurate to establish the errors and inadequacies of theory at this level. However, the best experimental data and the observed experimental structure as a function of energy are strong indicators of the validity of the current approach. New developments in experimental measurement hold great promise in making critical comparisons with theory in the near future.