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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
C.T. Chantler,1 K. Olsen,2
R.A. Dragoset,2 J. Chang,2 A.R. Kishore,2
S.A. Kotochigova,2 and D.S. Zucker2
1Present address: School of Physics, University of Melbourne,
Parkville, Victoria, 3010 Australia
2NIST, Physics Laboratory, Office of Electronic Commerce in
Scientific and Engineering Data
© 1995, 1996, 2001 copyright by the U.S. Secretary of Commerce on
behalf of the United States of America. All rights reserved. -
NIST reserves the right to charge for these data in the future.
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Example of how to reference this online database:
Chantler, C.T., Olsen, K., Dragoset, R.A., Chang, J.,
Kishore, A.R., Kotochigova, S.A., and Zucker, D.S. (2005),
X-Ray Form Factor, Attenuation and Scattering Tables (version 2.1).
[Online] Available: http://physics.nist.gov/ffast
[2009, January 18]. National Institute of Standards and
Technology, Gaithersburg, MD. Originally published as Chantler, C.T.,
J. Phys. Chem. Ref. Data 29(4), 597-1048 (2000); and
Chantler, C.T., J. Phys. Chem. Ref. Data 24, 71-643
(1995). |
Tables for form factors and anomalous dispersion are of wide general use in the
UV, x-ray and -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 ( PE) 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.
Publications |
Theoretical Form Factor, Attenuation and Scattering Tabulation for
Z=1-92 from E=1-10 eV to E=0.4-1.0 MeV
J. Phys. Chem. Ref. Data 1995 |
Detailed Tabulation of Atomic Form Factors, Photoelectric Absorption and
Scattering Cross Section, and Mass Attenuation Coefficients in the Vicinity of
Absorption Edges in the Soft X-Ray (Z = 30-36,
Z = 60-89, E = 0.1 keV-10 keV), Addressing
Convergence Issues of Earlier Work
J. Phys. Chem. Ref. Data 2000 |
This work was supported in part by the National Institute of Standards and
Technology, Standard Reference Data
Program and by NIST's Systems
Integration for Manufacturing Applications (SIMA) Program.
NIST Standard Reference Database 66
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Online: April 1997 - Last Update: August 2005
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