Scattering Compton

The Compton scattering absorption cross-section, often given the symbol a, is related to the atomic number of the material and the energy of the gamma-ray  

An energy function of 1 /E has been suggested as appropriate. Using an analogous relationship to that of Equation (2.3), we can calculate a Compton scattering coefficient, If we also take into account the fact that over a large part of the Periodic Table the ratio A/Z is reasonably constant with a value near to 2 we can show that  

Sq and S are the unit vectors of the incident and scattered beams, 29 being the scattering angle, m the mass of the electron and V the electron s recoil velocity once it is stmck by the photon. If the vibration frequencies of the incident photon and the scattered photon are denoted by v and v , respectively, the energy conservation principle leads to the relation  

Calculation of the difference in wavelength between the incident wave and the scattered wave 

By using the two principles just applied, we will be able to calculate this difference 8X, since we have  

Therefore, the variation in wavelength is independent of the initial wavelength and increases with 6. 

In the case of a free electron, nothing prevents it from moving, since it is subjected to no outside force. Hence, the predominant effect is Compton scattering. However, it can be shown that the intensity of this scattering effect is accurately described by Thomson s relation. When considering a set of free electrons, the different waves scattered by these electrons have different wavelengths and therefore do not lead to interference effects. What we observe is merely the sum of the scattered intensities. 

In the case of a photon of light the velocity cannot change, so it is the frequency which changes so as to conserve both the energy and the momentum. Such behaviour cannot be explained by a wave picture of light. It is clear that the photon of an X-ray must be a kind of particle of dimensions of the same order as the electron. 

Assuming the collision is elastic, conservation of energy gives us 

Combining these equations (see Problems) and utilizing the relativistically correct expressions for the energy and momentum of the electron 

67 (degrees) Emitted Photon Energy (hv ) Electron Kinetic Energy 

Note that the shift in 7-ray energy is independent of the incident energy. The expressions for the energies of the scattered photon and electron are given in Table 17.2. 

It is clear that the minimum energy of the scattered 7 ray occurs when 0 = 180° (cos 0 = — 1). In this case, we have 

---

Matscheko and Ribberfors, A Compton scattering spectrometer for determining X-ray photon energy spectra. Phys. Med. Biol., 1987. 32(5) p. 577-594. 

Williams B (ed) 1977 Compton Scattering (New York MoGraw-Flill)... 

Fig. 6. Schematic illustration of the relationships of the original y-ray and the scattered radiations for Compton scattering where E is the energy of the incident photon, E is the energy of the recoiling electron, and E is the energy of the scattered photon.

In addition to Compton scattering, y-rays having energies above 1022 keV interact with matter by a process called pair production, in which the photon is converted into a positron and an electron. The y-ray energy in excess of the 1022 keV needed to create the pair is shared between the two new particles as kinetic energy. Each j3 -particle is then slowed down and annihilated by an electron producing two 511-keV photons. 

Thus, the contribution of coherent and non-coherent (Compton) scattering in attenuation of primary radiation and fluorescence increase in comparison with the solid samples. 

Detection limits for various elements by TXRF on Si wafers are shown in Fig. 4.13. Synchrotron radiation (SR) enables bright and horizontally polarized X-ray excitation of narrow collimation that reduces the Compton scatter of silicon. Recent developments in the field of SR-TXRF and extreme ultra violet (EUV) lithography nurture our hope for improved sensitivity down to the range of less than 10 atoms cm ... 

For 7-ray energies below 1 MeV (the range of interest) there are two principal modes of interaction with matter — Compton scattering and photoelectron absorption. Compton scattering is the elastic scattering of the 7 photon by an orbital electron in which part of the incident 7-energy is imparted to the recoiling electron. 

Hie number of Compton scatters occurring in a given volume depends on the number of electrons present and is relatively independent of incident 7-energy. For the lower atomic number elements (excluding hydrogen), the number of electrons present is directly proportional to atomic wt. Thus Compton scattering on a per unit volume basis is a function of density and is independent of chem compn. The density of soils is widely variable and the density of expls falls within the normal range of soil... 

Compton scattering is the principal mechanism for organic polymers (R) when high energy interacts with them. 

The Compton scattering cannot be neglected, but it is independent of molecular structure. Then, fitting experimental data to formulas from gas phase theory, the concentration of excited molecules can be determined. Another problem is that the undulator X-ray spectrum is not strictly monochromatic, but has a slightly asymmetric lineshape extending toward lower energies. This problem may be handled in different ways, for example, by approximating its spectral distribution by its first spectral moment [12]. 

It is important to note that expression (23) can be applied to the crystalline phase intensities only if we include, in the first integral, its own smooth diffuse background and not just the intensity belonging to the crystalline peaks. In fact, a pure crystalline sample also has a smooth background due to the incoherent inelastic scattering (i.e. Compton scattering), the TDS, disorder scattering and, very often, unresolved tails of overlapped peaks. 

Expression (25) describes the smooth background belonging to a crystalline phase due to the incoherent (or Compton) scattering and the TDS or disorder scattering. The last contribution in (25) is very approximate because it is known that the TDS has a very complicated shape with very large peaks centered in the same position as the Bragg ones [56]. 

We are interested in the transmission of y-quanta through the absorber as a function of the Doppler velocity. The radiation is attenuated by resonant absorption, in as much as emission and absorption lines are overlapping, but also by mass absorption due to photo effect and Compton scattering. Therefore, the number Tt E2)AE of recoilless y-quanta with energies EXo E + AE traversing the absorber is given by... 

Scattered radiation. In a transmission experiment, the Mossbauer sample emits a substantial amount of scattered radiation, originating from XRF and Compton scattering, but also y-radiation emitted by the Mossbauer nuclei upon de-excitation of the excited state after resonant absorption. Since scattering occurs in 4ti solid angle, the y-detector should not be positioned too close to the absorber so as not to collect too much of this unwanted scattered radiation. The corresponding pulses may not only uimecessarily overload the detector and increase the counting dead time, but they may also affect the y-discrimination in the SCA and increase the nonresonant background noise. 

The thickness of a Mossbauer sample affects not only the strength of the Mossbauer signal but also the intensity of the radiation arriving at the detector because the y-rays are inherently attenuated by the sample because of nonresonant mass absorption caused by the photo effect and Compton scattering as mentioned earlier. The counting rate C in the detector decreases exponentially with the density of the absorber,... 

Fig. 3.25 Left signal-to-noise ratio (SNR) of the Mbssbauer spectra of a basalt taken with MIMOS II (full SI-PIN detector system black data-points) and MIMOS IIA (1/4 of full SDD system red data-points) respectively. Right XRF spectra of low Z elements measured with MIMOS IIA (SDDs) at —20°C. The Compton scattered 14.4 keV line (at 13.8 keV) and the resonant 14.4 keV Mossbauer line are well separated...

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

---