7.2 Photon interactions with matter

Photons interact with matter in fascinating ways, shaping how radiation behaves around us. From the photoelectric effect to pair production, these processes determine how energy is transferred and absorbed in materials.

Understanding photon interactions is key to grasping radiation's impact on our world. We'll explore how different materials and energies affect these interactions, and how we can use this knowledge for protection and practical applications.

Photon Interactions

Photoelectric Effect and Compton Scattering

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• Photoelectric effect occurs when a photon transfers all its energy to an atomic electron
  • Electron is ejected from the atom with kinetic energy equal to photon energy minus binding energy
  • Predominant at low photon energies (below 100 keV for most materials)
  • Cross-section varies approximately as $Z^4/E^3$, where Z is atomic number and E is photon energy
• Compton scattering involves partial energy transfer from photon to electron
  • Scattered photon continues with reduced energy and changed direction
  • Dominant process for intermediate photon energies (0.1 to 10 MeV for most materials)
  • Energy of scattered photon given by $E' = \frac{E}{1 + \frac{E}{m_ec^2}(1-\cos\theta)}$, where θ is scattering angle
• Both processes contribute to ionization and energy deposition in matter

Pair Production and Cross-section

• Pair production creates an electron-positron pair from a high-energy photon
  • Requires photon energy of at least 1.022 MeV (twice the electron rest mass)
  • Occurs in the electric field of an atomic nucleus
  • Dominant process for high photon energies (above 10 MeV for most materials)
  • Cross-section increases with atomic number and photon energy
• Cross-section represents probability of photon interaction per atom
  • Total cross-section is sum of individual process cross-sections
  • Measured in units of area (barns, $1 \text{ barn} = 10^{-24} \text{ cm}^2$)
  • Varies with photon energy and atomic number of absorber
  • Used to calculate attenuation coefficients and interaction probabilities

Attenuation Properties

Attenuation Coefficient and Mean Free Path

• Attenuation coefficient quantifies photon beam intensity reduction in matter
  • Linear attenuation coefficient (μ) measured in cm^-1
  • Mass attenuation coefficient (μ/ρ) in cm^2/g, independent of material density
  • Beam intensity follows exponential decay: $I = I_0 e^{-\mu x}$
• Mean free path represents average distance traveled by photon before interaction
  • Calculated as inverse of linear attenuation coefficient: $\lambda = 1/\mu$
  • Varies with photon energy and material composition
  • Longer mean free path indicates greater penetration depth

Half-value Layer and Energy Absorption

• Half-value layer (HVL) thickness of material that reduces beam intensity by half
  • Related to attenuation coefficient: $HVL = \ln(2)/\mu$
  • Used in radiation shielding calculations and quality assurance
  • Multiple HVLs can be used to achieve desired attenuation (tenth-value layer)
• Energy absorption describes transfer of photon energy to matter
  • Energy absorption coefficient (μen) accounts for energy carried away by scattered photons
  • Fraction of photon energy absorbed depends on interaction process and material
  • Important for dosimetry and radiation protection calculations
  • Energy absorption build-up factor corrects for multiple scattering events