# Fundamental Radiation Physics: Photon and Electron Interactions

## Overview

Therapeutic radiation functions by transferring energy from photon and electron beams to biological tissue. A thorough understanding of the mechanisms by which these particles interact with matter is crucial for predicting how radiation dose is deposited, how deeply beams penetrate tissue, and how different beam energies behave clinically. Within the therapeutic energy range, three primary photon interaction processes dominate: the photoelectric effect, Compton scattering, and pair production.

## Photon Interactions with Matter

### Photoelectric Effect

The photoelectric effect occurs when an incident photon is completely absorbed by a bound inner-shell electron of an atom. This absorption results in the ejection of the electron with kinetic energy equal to the photon’s original energy minus the binding energy of the electron shell. The probability of this interaction is highly dependent on the atomic number (Z) of the material, scaling approximately with Z cubed, and inversely proportional to the cube of the photon energy (E). Consequently, the photoelectric effect is most dominant at low photon energies, typically below 100 keV in soft tissue. As the atom de-excites following electron ejection, it emits characteristic x-rays and Auger electrons. This effect underlies the contrast seen in diagnostic imaging, such as the differentiation between bone and soft tissue. Clinically, it explains why there is an increased radiation dose near high-Z materials like dental fillings or hip prostheses, due to enhanced photoelectric absorption.

### Compton Scattering

Compton scattering involves a photon interacting with a loosely bound outer-shell electron, ejecting it and producing a scattered photon with reduced energy. This interaction is the most significant in the megavoltage therapeutic energy range, which spans roughly 1 to 20 MeV. Unlike the photoelectric effect, the probability of Compton scattering is nearly independent of atomic number and depends primarily on electron density—the number of electrons per gram of material. This means that in the megavoltage range, soft tissue, fat, and bone absorb dose roughly in proportion to their physical density. The scattered photon continues with diminished energy and a changed direction, contributing to exit dose, scatter radiation, and some degradation of imaging quality. The Klein-Nishina formula mathematically describes the differential cross-section of Compton scattering as a function of the scattering angle.

### Pair Production

Pair production takes place when a photon with energy exceeding 1.022 MeV interacts within the nuclear Coulomb field of an atom. The photon disappears, and an electron-positron pair is created. Any photon energy above the 1.022 MeV threshold is shared as kinetic energy between the electron and positron. The positron eventually annihilates with an electron, producing two photons each with 0.511 MeV energy. The probability of pair production increases with the square of the atomic number (Z²) and with photon energy above the threshold. This interaction becomes increasingly significant at photon energies above 10 MeV and is clinically relevant for high-energy photon beams, such as those in the 18 to 25 MV range.

### Relative Importance by Energy and Z

The dominance of these photon interactions depends on both photon energy and the atomic number of the material. At low energies and high Z, the photoelectric effect predominates. In the intermediate energy range of 1 to 10 MeV and for low-to-medium Z materials like tissue, Compton scattering is the primary interaction. At high energies and high Z, pair production becomes significant. For example, at 6 MV photon beams, which have a mean energy around 2 MeV, Compton scattering accounts for nearly all photon interactions in tissue.

| Interaction | Dominant Energy Range | Z-Dependence | Clinical Relevance |
|---|---|---|---|
| Photoelectric Effect | < 100 keV (soft tissue) | ~Z³ | Diagnostic imaging contrast; dose enhancement near high-Z implants |
| Compton Scattering | 1–10 MeV | Independent of Z (depends on electron density) | Dominant in therapeutic MV beams; skin-sparing buildup effect |
| Pair Production | > 10 MeV (threshold 1.022 MeV) | ~Z² | Relevant for 18–25 MV beams; annihilation photon production |

## Electron Interactions with Matter

### Coulomb Interactions

Electrons interact with matter primarily through Coulomb forces, affecting both atomic electrons and the nuclear field. When electrons interact with atomic electrons, they cause ionization and excitation, leading to energy loss known as collisional or ionizational stopping power. This mechanism dominates at therapeutic electron energies in tissue. Electrons also lose energy through radiative processes, specifically bremsstrahlung, which occurs when electrons decelerate in the nuclear Coulomb field. Radiative stopping power increases with both the electron energy and the atomic number of the medium.

### Restricted vs. Unrestricted Stopping Power

Stopping power can be characterized as either unrestricted or restricted. The unrestricted mass stopping power (S/ρ) represents the total energy loss per unit path length of the electron. In contrast, the restricted stopping power (L-δ/ρ) accounts only for the energy deposited locally, excluding energy carried away by delta rays (secondary electrons) above a certain cutoff energy. This distinction is important for understanding the difference between total energy loss and actual dose deposition within tissue.

### Electron Range and Depth-Dose Characteristics

Unlike photons, electrons have a finite range in tissue. The practical range (Rp) in centimeters can be approximated by dividing the electron energy in MeV by two when considering water or tissue. The therapeutic range, often defined as R80 or R90 (the depth at which dose falls to 80% or 90% of maximum), is shorter than the practical range. Beyond this therapeutic range, the dose falls off rapidly, making electrons particularly suitable for treating superficial targets. Electron beams also deliver a relatively high surface dose, typically between 75% and 95% depending on energy, which contrasts with the lower surface dose of photon beams.

### Bremsstrahlung Production

Bremsstrahlung, or braking radiation, is produced when electrons decelerate in the Coulomb field of atomic nuclei. This process generates x-rays and is the fundamental mechanism by which linear accelerators produce therapeutic photon beams. The yield of bremsstrahlung increases with the atomic number of the target material; tungsten is commonly used due to its high Z and efficiency. At therapeutic electron energies, bremsstrahlung contamination results in a low-dose tail beyond the electron range, which must be considered in treatment planning.

## Beam Quality Specification

### Photon Beams

Photon beams are specified by their nominal accelerating potential, such as 6 MV or 15 MV, but the beam itself is polyenergetic, containing a spectrum of photon energies. Beam quality is often characterized by the tissue-phantom ratio at 20 cm to 10 cm depth (TPR20,10), as recommended by the AAPM TG-51 protocol. Percentage depth dose (PDD) curves show that the depth of maximum dose (dmax) increases with beam energy, while the surface dose decreases correspondingly.

### Electron Beams

Electron beams are specified by their nominal energy at the surface, for example, 6 MeV or 12 MeV. The beam quality index for electrons is R50, the depth at which the dose falls to 50% of its maximum, also per TG-51 guidelines. The electron energy at a given depth (E(d)) can be approximated by the equation E(d) = E(0) × (1 - d/Rp), where E(0) is the initial energy and Rp is the practical range.

## Mass Attenuation and Energy Absorption Coefficients

The mass attenuation coefficient (μ/ρ) quantifies the probability of photon interaction per unit mass thickness of a material. The mass energy absorption coefficient (μ_en/ρ) represents the fraction of photon energy that is actually absorbed locally within the material. This distinction is important for dose calculations because not all energy from photon interactions is deposited locally; some energy is carried away by scattered photons.

## Charged Particle Equilibrium (CPE)

Charged particle equilibrium occurs when the energy carried into a volume by charged particles equals the energy carried out. This condition is necessary to relate kerma (kinetic energy released per unit mass) to the absorbed dose. CPE is established at depths beyond dmax for broad photon beams. At depths less than dmax, there is a buildup region where the dose is less than kerma, representing a transient state before equilibrium is reached. Understanding CPE is essential for accurate dosimetry and the application of cavity theory.

<image>A diagram showing the three major photon interaction mechanisms (photoelectric effect, Compton scattering, and pair production) side by side. Each panel shows an incident photon approaching an atom, with labeled arrows showing incoming photon energy, ejected electrons, scattered photons, and (for pair production) the electron-positron pair and annihilation photons. Energy thresholds and Z-dependence equations are annotated below each panel.</image>

<image>A graph showing the relative dominance of photoelectric effect, Compton scattering, and pair production as a function of photon energy (x-axis, 0.01 to 100 MeV, log scale) and atomic number Z (y-axis, 0 to 120). Two curves divide the plot into three regions, with tissue (Z~7.4) and bone (Z~13) marked as horizontal reference lines, and therapeutic energy range (1-25 MeV) highlighted.</image>

<image>A comparison of central axis percentage depth-dose curves for photon beams of different energies (6 MV, 10 MV, 18 MV) and electron beams of different energies (6 MeV, 12 MeV, 20 MeV) in water. The x-axis shows depth in cm, the y-axis shows percentage depth dose. Key features labeled include dmax, buildup region, Rp, R90, and the bremsstrahlung tail for electron beams.</image>

## Key Clinical Pearls

In the megavoltage energy range commonly used clinically (6 to 18 MV), Compton scattering dominates photon interactions in tissue, which makes dose deposition largely independent of tissue composition. This contrasts with diagnostic kilovoltage beams where tissue composition plays a larger role. The skin-sparing effect observed with megavoltage photon beams arises from the buildup region created by forward-scattered Compton electrons; however, this advantage can be lost when bolus material is applied or when the beam enters tangentially. Electron beams are particularly well suited for treating superficial targets due to their finite range in tissue, and the practical rule that the electron energy in MeV divided by two approximates the range in centimeters is invaluable for quick clinical estimations. High-Z materials such as metal implants or dental work cause dose perturbations differently depending on beam energy: at kilovoltage energies, photoelectric enhancement is significant, whereas at megavoltage energies, the effect is minimal though backscatter remains relevant. When selecting beam energy for treatment, higher energy beams provide deeper penetration but also increase neutron contamination (notably above approximately 10 MV), exit dose, and penumbra width, all of which must be balanced against clinical goals.

## References
- Khan FM, Gibbons JP. *Khan's The Physics of Radiation Therapy*, 6th edition. Chapters 5-7.
- Attix FH. *Introduction to Radiological Physics and Radiation Dosimetry*. Wiley, 1986.
- Johns HE, Cunningham JR. *The Physics of Radiology*, 4th edition. Charles C Thomas, 1983.
- AAPM TG-51: Almond PR et al. "AAPM's TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams." *Med Phys*. 1999;26(9):1847-1870.