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Low-Energy X-ray Interaction Coefficients:
Photoabsorption, Scattering, and Reflection
E = 30-30,000 eV, Z = 1-92
B. L. Henke, E. M. Gullikson, and J. C. Davis
Center for X-Ray Optics, 2-400
Lawrence Berkeley Laboratory
Berkeley, California 94720
These files were used to generate the tables published in reference [1].
The files contain three columns of data: Energy(eV), f_1, f_2,
where f_1 and f_2 are the atomic (forward) scattering factors.
There are 500+ points on a uniform logarithmic mesh with points
added 0.1 eV above and below "sharp" absorption edges.
(Note: below 29 eV f_1 is set equal to -9999.)
The tabulated values of f_1 contain a relativistic, energy independent,
correction given by, Z* = Z - (Z/82.5)^(2.37).
The atomic photoabsorption cross section, mu_a, may be readily obtained
from the values of f_2 using the relation,
mu_a = 2*r_0*lambda*f_2
where r_0 is the classical electron radius, and lambda is the wavelength.
The index of refraction for a material with N atoms per unit volume
is calculated by,
n = 1 - N*r_0*(lambda)^2*(f_1+if_2)/(2*pi).
These (semi-empirical) atomic scattering factors are based upon
photoabsorption measurements of elements in their elemental state.
The basic assumption is that condensed matter may be modeled as a
collection of non-interacting atoms. This assumption is in general
a good one for energies sufficiently far from absorption thresholds.
In the threshold regions, the specific chemical state is important
and direct experimental measurements must be made.
These tables are based on a compilation of the available experimental
measurements and theoretical calculations. For many elements there is
little or no published data and in such cases it was necessary to
rely on theoretical calculations and interpolations across Z.
In order to improve the accuracy in the future considerably more
experimental measurements are needed.
Please send any comments to EMGullikson@lbl.gov.
Note that the following elements have been updated since the publication
of Ref. [1] in July 1993. Check
http://henke.lbl.gov/optical_constants/update.html
for more recent updates.
======== ========== =================
Element Updated Energy Range (eV)
======== ========== =================
Pt Aug 2023 0.1-800
Cr Aug 2023 0.4-813
Nb Aug 2023 10-1000
Y Aug 2023 50-1300
Er Aug 2023 3-1580
Mg Jan 2011 10-1300
Zr Apr 2010 20-1000
La Jun 2007 14-440
Gd Jun 2007 12-450
Sc Apr 2006 50-1300
Ti Aug 2004 20-150
Ru Aug 2004 40-1300
W Aug 2004 35-250
Mo Aug 2004 25-60
Be Aug 2004 40-250
Mo Nov 1997 10-930
Fe Oct 1995 600-800
Si Jun 1995 30-500
Au Jul 1994 2000-6500
Mg,Al,Si Jan 1994 30-200
Li Nov 1994 2000-30000
======== ========== =================
[1] B. L. Henke, E. M. Gullikson, and J. C. Davis,
Atomic Data and Nuclear Data Tables Vol. 54 No. 2 (July 1993).
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