Tables for form factors and anomalous dispersion are widely used 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 synthesized by Henke et al.
More recent developments in both areas have led to new and revised
tables. These works have employed numerous simplifications compared
to detailed relativistic S-matrix calculations; the latter do not
lend themselves to 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 important
limitations with regard to extrapolation to energies outside tabulated ranges.
In the present study, 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).
The method used herein is primarily theoretical and considers
intermediate assumptions which limit the precision and
applicability of previous theoretical tabulations. Particular
concern involves the application of the dispersion relation to
derive Re(f) from photoelectric absorption cross-sections.
The revised formulation presented here explicitly avoids most of
the limitations of previous works. Revised formulae can lead to
significant qualitative and quantitative improvement, particularly
above 30-60 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
revised theoretical tables are in better agreement with experiment
than are those based on experimental syntheses.