5.2 Interaction of gamma rays with matter

Gamma rays interact with matter through three main processes: photoelectric effect, Compton scattering, and pair production. These interactions depend on the photon energy and the material's atomic number, affecting how gamma rays are absorbed or scattered.

Understanding gamma ray interactions is crucial for radiation protection and medical imaging. The attenuation coefficient and half-value layer help quantify how materials shield against gamma radiation, with high-Z materials like lead being more effective at stopping these powerful photons.

Photoelectric Effect and Compton Scattering

Photoelectric Effect

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• Occurs when a photon interacts with a bound electron in an atom, ejecting the electron from the atom
• Photon must have energy greater than the binding energy of the electron
• Ejected electron has kinetic energy equal to the difference between the photon energy and the binding energy
• Probability of photoelectric effect is highest for low energy photons and high atomic number (Z) materials
• Cross-section for photoelectric effect is proportional to $Z^4$ and inversely proportional to $E^3$, where E is the photon energy

Compton Scattering

• Elastic scattering of a photon by a free or loosely bound electron
• Photon transfers part of its energy to the electron, which is ejected from the atom
• Scattered photon has lower energy and longer wavelength than the incident photon
• Probability of Compton scattering is highest for photon energies around 1 MeV and low Z materials
• Cross-section for Compton scattering is proportional to the electron density of the material and decreases with increasing photon energy

Energy and Z-Dependence

• Photoelectric effect dominates at low photon energies (below ~100 keV) and high Z materials (lead, tungsten)
• Compton scattering dominates at intermediate photon energies (~100 keV to ~10 MeV) and low to medium Z materials (water, tissue, aluminum)
• Relative importance of photoelectric effect and Compton scattering depends on the photon energy and the atomic number of the material
• Cross-sections for both processes decrease with increasing photon energy, but at different rates

Pair Production

Pair Production Process

• Occurs when a photon with energy greater than 1.022 MeV interacts with the electric field of a nucleus
• Photon disappears and creates an electron-positron pair
• Excess energy above 1.022 MeV is shared between the electron and positron as kinetic energy
• Positron eventually annihilates with an electron, producing two 511 keV photons
• Pair production is the dominant interaction for high energy photons (above ~10 MeV) in high Z materials

Energy and Z-Dependence

• Threshold energy for pair production is 1.022 MeV, twice the rest mass energy of an electron
• Probability of pair production increases rapidly with photon energy above the threshold
• Cross-section for pair production is proportional to $Z^2$ and increases with photon energy
• Pair production is more likely to occur in materials with high atomic number (lead, tungsten) due to the stronger electric fields of the nuclei

Attenuation of Gamma Rays

Attenuation Coefficient

• Describes the reduction in intensity of a gamma ray beam as it passes through matter
• Sum of the contributions from photoelectric effect, Compton scattering, and pair production
• Depends on the photon energy and the material properties (density, atomic number)
• Expressed in units of inverse length (cm$^{-1}$) or area per unit mass (cm$^2$/g)
• Higher attenuation coefficients indicate stronger interaction and more rapid reduction in beam intensity

Half-Value Layer (HVL)

• Thickness of a material required to reduce the intensity of a gamma ray beam by half
• Inversely related to the attenuation coefficient: $HVL = \ln(2) / \mu$, where $\mu$ is the attenuation coefficient
• Smaller HVL values indicate stronger attenuation and more effective shielding materials
• HVL depends on the photon energy and the material properties (density, atomic number)
• Commonly used to characterize the penetrating power of gamma rays and the effectiveness of shielding materials

Energy and Z-Dependence of Attenuation

• Attenuation coefficient decreases with increasing photon energy, as the interaction cross-sections for photoelectric effect, Compton scattering, and pair production decrease
• Attenuation coefficient increases with increasing atomic number (Z) of the material, due to the higher probability of photoelectric effect and pair production in high Z materials
• For a given material, the relative contributions of photoelectric effect, Compton scattering, and pair production to the total attenuation coefficient vary with photon energy
• Low energy photons are more strongly attenuated than high energy photons, requiring thicker shielding materials for effective protection