The behavior of photons in matter is completely different from that of charged particles. In particular, the photon’s lack of an electric charge makes impossible the many inelastic collision with atomic electrons so characteristic of charged particles. For this kind of radiation the most important mechanism of interaction are:
a) Photoelectric
effect
b) Compton
and Rayleigh scattering
c) Pair
production
As consequence of such kind of interactions a photon that interacts with the target is completely removed from the incident beam, in other words a beam of photons that cross a medium is not degraded in energy but only attenuated in intensity. Moreover, due to the smallest cross section of all this kind of reactions,x‑ray or γ-ray are many times more penetrating than charged particles. The attenuation of the incident beam is exponential with the thickness of the absorbing medium and can be expressed by the following relation:
I(x)= I0 exp (-xμl)
where μl is the linear attenuation coefficient, I0 is the incident beam intensity and x the thickness. The linear attenuation coefficient is related to the cumulative cross section by the relation:
μl =ηA σtot
where ηA is the number of atoms per unit of mass and σtot is the total cross section. The total or cumulative cross section σtot is the sum of all the cross sections of the interactions mentioned above. A plot of this quantity is shown in Figure 1.6 where the different components have been highlighted.
Photoelectric absorption
In photoelectric absorption, a photon disappears being absorbed by an atomic electron. The process results in ionization by subsequent ejection of the electron from the atom. The energy of the liberated electron is the difference between the photon energy and the energy needed to extract the electron from the atom i.e. the binding energy of the electron.
The recoil momentum is absorbed by the nucleus to which the ejected electron was bound. If the resulting photoelectron has sufficiently enough of kinetic energy, it may be a source of a secondary ionization occurring along its trajectory, and in the case of the semiconductor material, it may create further e-h pairs. If the electron does not leave the detector the deposited energy corresponds to the energy possessed by the incident photon.
This feature of the photoelectric effect allows calibrating the gain of the detector chained with its readout system if the energy required to create a single e-h pair is known. The range R of the electron having the kinetic energy E is of the order of some micrometers, as given by the follow equation:
R[um] = 40.8 10^(-3) x ( E[keV] )^1.5
Thus the cloud of generated charge is confined close to the photon absorption point. The clear image may be smeared by escape photons, which can leave the detector volume leading to less amount of energy deposited. These photons are actually the fluorescence photons emitted by de-exciting atoms. Photons of fluorescence radiation are emitted by atoms after the ejection of a deep shell (K, L) electron.
The incident photon creates a vacancy in the shell, thus leaving an atom in an excited state. Then, the vacancy can be filled by an outer orbital electron, giving rise to the emission of the characteristic X-rays photons of the fluorescence radiation.
The missing energy, which is conveyed by the escape photons leads to, so called escape peaks in the measured energy spectrum. Photon interaction coefficient for photoelectric absorption depends strongly on the atomic number of the absorbing material. The relevant cross section increases roughly as Z^3. For silicon, the photoelectric effect is a dominant process for photon energies below 100 keV.
Figure 1 Cross sections of photons in Carbon (a) and Lead (b) in barns/atom; 1barn=10-24 cm2.
Compton and Rayleigh scattering
The Compton scattering, instead of photoelectric effect, involves the free electrons. In matter of course, the electrons are bound to an atom; however, if the photon energy is high with respect to the binding energy, this latter energy can be ignored and the electrons can be treated as essentially free. When Compton scattering occurs, the electron is scattered away in conjunction with a new photon that have a lower energy than the incoming one.
In Rayleigh scattering the photon interact with the whole atom and the only effect of this interaction is a deflection of the incoming photon; it does not participate to the absorption and for most purposes can be neglected.
Pair production
At very high energy another effect starts to be relevant: the pair production. In this process the photon interacts with an electron or a nucleus producing a positron-electron pair. In order to produce the pair the photon must have at least an energy of 1.022 MeV. In Figure 1, with knuc and ke, are shown the two components of the pair production cross section, respectively for the interaction with nuclei or electrons. Another possible interaction, but usually negligible compared to the previous ones is the Photonuclear reaction, in this case the photon interact directly with the nucleus.
The related cross section is shown in Figure 1 in dotted line (σg.d.r.). The above cross section in barns/atom (1barn = 10-24 cm2, approximately the section of an uranium nucleus) expresses the probability of an interaction. A more suitable quantity, often used to characterize the absorption of a photon shower, is the mass attenuation coefficient. The mass attenuation coefficient is defined as:
μm=ηA σtot/ρ
where ρ is the density of the material. Figure 2 shows the mass attenuation coefficient of the silicon with the indication of its different components.
Figure 2 Mass attenuation coefficient of the silicon and its components.
References
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Yung-Su Tsai, Pair production and bremsstrahlung of charged leptons, Reviews of Modern Physics, vol. 46, no. 815, 1974
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M.Bronshtein, B.S. Fraiman, “Determination of the Path Lengths of Slow Secondary Electrons”, Sov. Phys. Solid State, Vol.3, (1961), pp.1188-1197.
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R. Wunstorf, Systematische Untersuchungen zur Strahlenresistenz von Silizium-Detektoren fur die Verwendung in Hochenergiephysik-Experimenten, PhD Thesis, Universitat Hamburg, Germany (1992)
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S. Meroli "Interaction of radiation with matter: from the theory to the measurements"
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