International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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

4.2.3.1.2. Variation of X-ray attenuation coefficients with photon energy

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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. [\sigma=\sigma_{\rm pe}+\sigma_R+\sigma_C. \eqno (4.2.3.6)]The relation between the photo-effect absorption cross section [\sigma_{\rm pe}] and the X-ray anomalous-dispersion corrections will be discussed in Section 4.2.6[link].

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[link] , the theoretical cross sections for the interaction of photons with a carbon atom are given. Values of [\sigma_{\rm pe}] are from calculations by Scofield (1973[link]), and those for Rayleigh and Compton scattering are from tabulations by Hubbell & Øverbø (1979[link]) and Hubbell (1969[link]), 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 [L_{\rm I}] [L_{\rm II}] [L_{\rm III}] shells of the carbon energies. Notice also that [\sigma_{\rm pe}] 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[link]; Alvarez, Crawford & Stevenson, 1958[link]), 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.

[Figure 4.2.3.1]

Figure 4.2.3.1| top | pdf |

Theoretical cross sections for photon interactions with carbon showing the contributions of photoelectric, elastic (Rayleigh), inelastic (Compton), and pair-production cross sections to the total cross sections. Also shown are the experimental data (open circles). From Gerstenberg & Hubbell (1982[link]).

References

First citation Alvarez, L. W., Crawford, F. S. & Stevenson, M. L. (1958). Elastic scattering of 1.6 MeV gamma rays from H, Li, C and Al nuclei. Phys. Rev. 112, 1267–1273.Google Scholar
First citation Gerstenberg, H. & Hubbell, J. H. (1982). Comparison of experimental with theoretical photon attenuation cross sections between 10 eV and 100 GeV. Nuclear data for science and technology, edited by K. H. Bockhoff, pp. 1007–1009. Amsterdam: North-Holland.Google Scholar
First citation Hubbell, J. H. (1969). Phonon cross sections, attenuation coefficients, and energy absorption coefficients from 10 keV to 100 GeV. Report NRDS-NBS29. National Institute of Standards and Technology, Gaithersburg, MD, USA.Google Scholar
First citation Hubbell, J. H. & Øverbø, I. (1979). Relativistic atomic form factors and photon coherent scattering cross sections. J. Phys. Chem. Ref. Data, 8, 69–105.Google Scholar
First citation Papatzacos, P. & Mort, K. (1975). Delbrück scattering calculations. Phys. Rev. D, 12, 206–221.Google Scholar
First citation Scofield, J. H. (1973). Theoretical photoionization cross sections from 1 to 1500 keV. Report UCRL-51326. Lawrence Livermore National Laboratory, Livermore, CA, USA.Google Scholar








































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