The primary interaction of low-energy x rays within matter,
viz. photoabsorption and coherent scattering, have been described for
photon energies outside the absorption threshold regions by using atomic
scattering factors, f = f1 + i f2
The atomic photoabsorption cross section, µa
may be readily obtained from the values of f2
using the relation,
where r0 is the classical electron radius, and
λ is the wavelength. The transmission of x rays through a slab of
thickness d is then given by,
T = exp (- n µa d),
where n is the number of atoms per unit volume in the slab.
The index of refraction nr for a material
is calculated by,
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.
Note also that the inelastic Compton scattering cross section
(from ref. 2)
has been included in the transmission calculations of a solid and
of a gas but not in the others.
The Compton cross section is significant for the light elements
(Z < 10) at the higher energies considered here (10 keV to 30 keV).
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.
- B.L. Henke, E.M. Gullikson, and J.C. Davis,
X-ray interactions: photoabsorption, scattering, transmission, and
reflection at E=50-30000 eV, Z=1-92,
Atomic Data and Nuclear Data Tables 54 no.2, 181-342 (July 1993).
- J.H. Hubbell, W.J. Veigele, E.A. Briggs, R.T. Brown, D.T. Cromer,
and R.J. Howerton, Atomic Form Factors, Incoherent Scattering Functions,
and Photon Scattering Cross Sections,
J. Phys. Chem. Ref. Data 4, 471-538 (1975); erratum in 6, 615-616 (1977).
Please direct any comments to Eric
(Last modified: Thursday, July 17, 2003 at 11:41:01 AM)