Photon Interactions on the Microscopic Scale

1. Rayleigh Scattering (Coherent Scattering)

In Rayleigh scattering (also known as 'coherent scattering'), a photon interacts with the entire complement of tightly bound atomic orbital electrons in an absorber atom. This interaction is elastic, meaning the photon does not lose significant energy (\(h\nu\)), but is scattered at a relatively small angle \( \theta \). This event is considered to be 'coherent' because the photon retains its energy after scattering.

Fig. 1.9(b): Diagram of Rayleigh Scattering (Elastic Scattering Process).

2. Energy Transfer and Absorption

In Rayleigh scattering, no energy transfer occurs from the photon to charged particles in the absorber material. As a result, it does not contribute to the energy transfer attenuation coefficient or energy absorption coefficient. However, it does play a role in the total attenuation coefficient \( \mu/\rho \) through the elastic scattering process. Rayleigh scattering is important in photon attenuation, especially at low photon energies.

While Rayleigh scattering does not directly impact radiation dosimetry, it is still a significant process in the context of photon attenuation, contributing a small percentage to the total attenuation in tissues or tissue-equivalent materials. The relative importance of Rayleigh scattering is usually only a few percent of the total \( \mu/\rho \), but it should not be neglected entirely in detailed calculations.

3. Mathematical Formulation

The Rayleigh atomic attenuation coefficient \( a_{\sigma_R} \) is proportional to the square of the atomic number \( Z \) and inversely proportional to the square of the photon energy \( h\nu \):

\[ a_{\sigma_R} \propto \frac{Z^2}{(h\nu)^2} \]

The Rayleigh mass attenuation coefficient \( \sigma_R/\rho \) has a similar dependence, proportional to \( Z \) and inversely proportional to the square of the photon energy:

\[ \frac{\sigma_R}{\rho} \propto \frac{Z}{(h\nu)^2} \]

This relationship shows that Rayleigh scattering is more significant for materials with a higher atomic number (\( Z \)) and lower photon energies (\( h\nu \)).

4. Importance of Rayleigh Scattering

Key Point: Rayleigh scattering is of little importance in radiation dosimetry because it does not transfer energy to charged particles. However, it does affect photon attenuation in materials, especially at lower photon energies.

Rayleigh scattering is crucial in understanding photon interactions with matter, particularly for soft tissue and low-Z materials. While it contributes only a small percentage to the total photon attenuation, it plays an important role in the overall interaction of photons with matter.

5. Example Calculation

Example: Calculate the Rayleigh mass attenuation coefficient for a material with \( Z = 20 \) at photon energy \( h\nu = 100 \, \text{keV} \). Using the formula:

\[ \frac{\sigma_R}{\rho} \propto \frac{Z}{(h\nu)^2} \]

Substitute the values:

\[ \frac{\sigma_R}{\rho} \propto \frac{20}{(100)^2} = \frac{20}{10000} = 0.002 \]

This demonstrates how the mass attenuation coefficient decreases with increasing photon energy.