1. Overview of Photon Interactions
When a photon interacts with matter, it can undergo different interactions depending on its energy \(h\nu\) and the atomic number \(Z\) of the absorber. The three primary photon interaction effects are:
- Photoelectric Effect: Predominates at low photon energies.
- Compton Scattering: Predominates at intermediate photon energies.
- Pair Production: Predominates at high photon energies above 1.022 MeV.
The relative predominance of each effect varies based on the photon energy \(h\nu\) and the atomic number \(Z\) of the material involved.
2. Regions of Predominance: Photoelectric, Compton, and Pair Production
Figure 1.10 below shows a diagram of the regions of predominance for each of the photon interaction effects with respect to photon energy (\(h\nu\)) and the atomic number (\(Z\)) of the absorber. The diagram clearly delineates the following:
- The photoelectric effect predominates at low photon energies (below a few hundred keV), particularly for high atomic number materials (large \(Z\)).
- The Compton scattering dominates at intermediate photon energies (a few hundred keV to several MeV), and is less dependent on the atomic number.
- The pair production effect becomes important at photon energies above 1.022 MeV, with a higher dominance for materials with higher atomic numbers \(Z\).
3. How Photon Energy and Atomic Number Influence Interaction Type
The interaction type that predominates in a given material depends significantly on both the photon energy and the atomic number of the absorber:
- At low photon energies (e.g., 100 keV), the photoelectric effect is dominant in high atomic number materials like lead (Z = 82), and the Compton effect is more prominent in low atomic number materials like soft tissue (Zeff ≈ 7.5).
- At high photon energies (e.g., 10 MeV), pair production dominates in high-Z materials like lead, whereas Compton scattering continues to be dominant in low-Z materials like tissue.
Therefore, understanding these interactions is crucial for applications in radiation shielding, medical imaging, and radiation therapy, where different photon energies are used for diagnosis and treatment.
4. Mathematical Formulation of Interaction Effects
The relative attenuation coefficients for these interactions depend on photon energy and atomic number:
Photoelectric Effect: The attenuation coefficient \( \tau \) is proportional to \( Z^3 / h\nu^3 \) at low photon energies.
\[ \tau \propto \frac{Z^3}{h\nu^3} \]Compton Scattering: The Compton attenuation coefficient \( \sigma_C \) is proportional to \( Z \) and is relatively independent of photon energy.
\[ \sigma_C \propto Z \]Pair Production: The pair production attenuation coefficient \( \kappa \) is proportional to \( Z^2 \) and becomes significant at high photon energies (> 1.022 MeV).
\[ \kappa \propto Z^2 \]Example: Photon Interactions in Lead vs Soft Tissue
Consider a photon with energy of 100 keV. It will interact with a lead absorber (Z = 82) predominantly through the photoelectric effect, while with soft tissue (Zeff ≈ 7.5), the interaction will predominantly be via Compton scattering. In contrast, a photon with 10 MeV energy will interact with lead predominantly via pair production, while soft tissue will still experience Compton scattering as the dominant effect.