Compton interaction cross sections

Interactions of photons (including both X-rays and y-radiation) with matter may be classified according to (a) the kind of target, such as electrons, atoms or nuclei, with which the photons interact, and (b) the type of event, such as absorption, scattering or pair production, that takes place. Possible interactions are summarized in Table 1, where r is the total photoelectric absorption cross-section per atom, (Tr and (Tc are the Rayleigh and Compton collision cross-sections, respectively, and K is the cross-section for pair production. The sum of all these cross-sections, normalized to a per atom basis, is the probability cTjot that the incident photon will have an interaction of some kind while passing through a very thin absorber that contains one atom per unit of area normal to the path of the... 

Figure 17.14 Summary of the relative importance of the three mechanisms by which photons interact with matter. The curves indicate the locations in the atomic number-photon energy plane at which the cross section for Compton scattering is equal to that for photoelectric absorption, left side, or is equal to that for pair production, right side.

This conclusion appears to be in conflict with the relative magnitudes of the coherent and Compton interaction coefficients, illustrated for an organic explosive such as trinitrotoluene (TNT) in Fig. 3. It is apparent that the cross-section for Compton scatter dominates over the energy range above 10 keV. 

The Compton effect is essentially an elastic collision between a photon and an electron during this interaction, the photon gives a fraction of its energy to the electrons, and its frequency v is therefore decreased. The cross section for this effect decreases with increasing energy, but the decrease is less rapid than for the photoelectric effect. 

Some other useful information has been compiled in the balance of this appendix. Two sets of curves entitled "Mass Absorption Coefficients" are included, both of which are taken from ORNL 421. Figures A7.A and B, comprising Supplement 1 to this report, give the macroscopic total cross-section divided by density. Figures A7.C and D, which form Supplement 2, present the macroscopic absorption cross section divided by density. In the latter case, an averaged probability for energy absorption in Compton interaction has been added to the photoelectric and pair cross-sections. 

The relative values of absorption and transmission of adjacent elemental ray paths in an x-ray beam provide the contrast in a projected image. The associated interaction of the x-rays with the material body can be defined in terms of collision cross sections that describe the probability of particular events occurring along the ray path. Here, the principal effects, for x-ray energies below 1 MeV, are identified in Sec. 26.2 as the photoelectron event and the Compton scattering event. These effects are combined to define a linear attenuation coefficient pj(x) that describes the variation of photon intensity along the ray path x according to the exponential relation = o... 

When photons penetrate a substance, they can interact with the nuclei or with the shell electrons. O Table 8.7 shows a classification of the interactions of photons (X-ray and 7 radiation) in matter. The dependence of the cross section cr of the interaction on the atomic number Z of the medium is also shown. Note that the Compton effect is inelastic for the atom but it is treated theoretically as elastic scattering on free electrons as the binding energy of the atomic electron is much smaller than that of the scattered electron. 

Total cross section (in units of 1 barn = 10 m ) of photon interaction in carbon and lead as a function of photon energy and the contributions of the following processes photoelectric effect, Rayleigh and Compton scattering, pair production in the field of the nucleus (nuclear p.p.) and of the shell electrons (electron p.p.). Note the resonances ( edges" as they are called) in photoelectric effect. The total cross section curve is flat for another two orders of magnitude in energy beyond the plot... 

---