Cross section Compton

The relativistic derivation of the relationship between the Compton cross section and the Compton profile leads to a further correction factor [7]. Finally a background subtraction and a normalization of the valence profiles to the number of valence... 

Significance in Practical Problems. Close to the source, the Compton scattering of the primary gamma rays is the main process. In cobalt, for instance, the total Compton cross section is 0.054 cm.2/gram and the photoelectric cross section is 0.00028 cm.2/gram at 1.25 Mev. This... 

The probability that Compton scattering will occur is called the Compton coefficient or the Compton cross section. It is a complicated function of the photon energy, but it may be written in the form... 

Figure 4.19 Dependence of the Compton cross section on (a) photon energy and (b) atomic number of the material.

Only the valence Compton profiles are needed for the reconstruction of the momentum density and the occupation number density. So one has to subtract an appropriate core Compton profile. Furthermore the contribution of the multiple scattered photons to the measured spectra has to be taken into account (for example by a Monte Carlo simulation [6]). Additionally one has to take heed of the fact that the efficiency of the spectrometer is energy dependent, so the data must be corrected for energy dependent effects which are the absorption in the sample and in the air along the beam path, the vertical acceptance of the spectrometer and the reflectivity of the analyzing crystal. The relativistic derivation of the relationship between the Compton cross section and the Compton profile leads to a further correction factor [7j. Finally a background subtraction and a normalization of the valence profiles to the number of valence... 

In a typical Compton scattering experiment with unpolarized radiation, the cross section is expressed as... 

For lOOkeV photons, the photoelectric cross section is proportional to where Zis the atomic number of the atom. For 3 MeV photons, the photoelectric cross section is proportional to The Compton photon cross... 

An example of the features of the spectrum of secondary electrons emitted in H° impact on water molecules from the work of Bolorizadeh and Rudd [67] is shown in Fig. 16. Compared to the simple spectrum of electrons emitted by proton impact shown as the solid line in Fig. 16 the spectrum from H° impact has an additional peak centered at an electron energy of approximately 82 eV. This broad peak is from the superposition of the spectrum of electrons stripped (elastically scattered) from the projectile on the spectrum of electrons ejected from the target. Because the stripped projectile electrons originate as bound electrons in the rest frame of the moving projectile, their laboratory energy is given approximately hy W = meE jM and the width of the peak is determined by the Compton profile of electrons in the projectile frame, but also transformed to the laboratory frame-of-reference. The results shown in Fig. 16 clearly illustrate that the cross-sections for... 

The Compton scattering cross section per electron of the stopping material is independent of Z, and thus the cross section per atom goes as Z. For energies about 0.5 MeV, it varies roughly as 1 /Er... 

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 Klein-Nishina96 formulas give the total cross section for Compton scattering as... 

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. 

The attenuation coefficient for a beam of gamma rays is related to the number of gamma rays removed from the beam, either by absorption or scattering. For the Compton effect, the absorption cross section is determined by the energy absorbed by the electron, which is the total collision energy minus the average scattered photon... 

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