International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 213
Section 4.2.3.1.2. Variation of X-ray attenuation coefficients with photon energy
D. C. Creaghb
|
When a photon interacts with an atom, a number of different absorption and scattering processes may occur. For an isolated atom at photon energies of less than 100 keV (the limit of most conventional X-ray generators), contributions to the total cross section come from the photo-effect, coherent (Rayleigh) scattering, and incoherent (Compton) scattering. The relation between the photo-effect absorption cross section
and the X-ray anomalous-dispersion corrections will be discussed in Section 4.2.6
.
The magnitudes of these scattering cross sections depend on the type of atom involved in the interactions and on the energy of the photon with which it interacts. In Fig. 4.2.3.1
, the theoretical cross sections for the interaction of photons with a carbon atom are given. Values of
are from calculations by Scofield (1973
), and those for Rayleigh and Compton scattering are from tabulations by Hubbell & Øverbø (1979
) and Hubbell (1969
), respectively. Note the sharp discontinuities that occur in the otherwise smooth curves. These correspond to photon energies that correspond to the energies of the K and
shells of the carbon energies. Notice also that
is the dominant interaction cross section, and that the Rayleigh scattering cross section remains relatively constant for a broad range of photon energies, whilst the Compton scattering peaks at a particular photon energy (∼100 keV). Other interaction mechanisms exist [e.g. Delbrück (Papatzacos & Mort, 1975
; Alvarez, Crawford & Stevenson, 1958
), pair production, nuclear Thompson], but these do not become significant interaction processes for photon energies less than 1 MeV. This section will not address the interaction of photons with atoms for which the photon energy exceeds 100 keV.
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