KAHIBARO
12.3. Gamma Physics
Table of Contents
Photoelectric effect
In GATE, all microscopic gamma physics is provided by Geant4. When you configure a physics list that includes electromagnetic processes for photons, Geant4 models how gamma rays interact with materials at each step. One of the three main interaction channels for diagnostic and therapy-relevant photons is the photoelectric effect.
In the photoelectric effect, an incident gamma photon is completely absorbed by an atomic electron, usually in a low-lying shell such as K or L. The photon disappears and its energy is transferred to the bound electron, which is then ejected from the atom. The kinetic energy of the emitted photoelectron is approximately
$$
E_{\text{e}} = E_{\gamma} - E_{\text{bind}},
$$
where $E_{\gamma}$ is the incident photon energy and $E_{\text{bind}}$ is the binding energy of the electron shell.
In the photoelectric effect the photon is fully absorbed in a single interaction, so there is no scattered photon. This makes photoelectric interactions especially important for imaging photopeaks and for dose at low photon energies.
In medical physics simulations, the relative importance of the photoelectric effect depends strongly on photon energy and atomic number of the material. At typical SPECT energies such as 140 keV from Tc 99m, and in high Z materials such as lead or tungsten, photoelectric absorption is dominant and drives collimator and shielding behavior. In soft tissue or water at the same energy, photoelectric interactions still occur but are less dominant than in lead.
In a PET detector crystal such as LYSO, photoelectric interactions around 511 keV are responsible for a large fraction of full energy deposition events that form the 511 keV photopeak in the energy spectrum. If your physics list disables low energy electromagnetic processes or uses inappropriate models, the fraction of photoelectric interactions in the crystal can change, which will affect peak shape, detector efficiency, and ultimately image quality.
GATE uses Geant4 models to describe the probability of a photoelectric interaction and how the secondary electron is produced and transported. Different predefined Geant4 electromagnetic physics options include or exclude detailed atomic relaxation, which governs characteristic X ray emission and Auger electrons after the atom is ionized. In materials such as bone or detector crystals, these additional secondaries can produce local, finely distributed energy deposition. For applications such as microdosimetry or detailed detector studies, you should choose physics configurations that keep these processes active.
In practice, you do not configure a single process called “photoelectric effect” from GATE, but you select an electromagnetic physics list that contains it. Once included, every gamma step in each volume will be tested against the probability of a photoelectric interaction in that material. The resulting photoelectrons are then followed and will deposit their energy locally over very short ranges compared to the photon mean free path, which is important for accurate dose calculations at low energies and near high Z boundaries.
Compton scattering
Compton scattering is the dominant interaction mechanism for medium energy photons in soft tissue and water for a broad range of medical applications. In Compton scattering, a gamma photon collides with a quasi free electron, transfers part of its energy and momentum to the electron, and continues with reduced energy and a changed direction.
Energy and angle of the scattered photon are linked by the Compton formula:
$$
E_{\gamma}' = \frac{E_{\gamma}}{1 + \frac{E_{\gamma}}{m_e c^2}(1 - \cos\theta)},
$$
where $E_{\gamma}$ is the initial photon energy, $E_{\gamma}'$ the scattered photon energy, $\theta$ the scattering angle, and $m_e c^2 \approx 511\ \text{keV}$ is the electron rest mass energy.
In Compton scattering the photon is not destroyed. It continues with lower energy and altered direction, and a recoil electron carries the remaining energy. Repeated Compton scatters can occur before the photon is finally absorbed or leaves the geometry.
In imaging simulations, Compton scattering is often the main source of image degrading events. In PET, photons that undergo Compton scattering before detection can still be counted as coincidences, but their apparent line of response is wrong, producing scattered coincidences. In SPECT and CT, photons scattered in the patient or surrounding structures may still reach the detector and contribute to background, lower contrast, and cupping artifacts.
In dose simulations for external beam therapy and diagnostic radiology, Compton scattering spreads photon energy deposition over larger volumes, and the resulting Compton electrons create dose locally along their tracks. Correct modeling of Compton scattering is therefore critical for accurate dose distributions, build up regions, and out of field dose.
Within GATE, the detailed description of Compton scattering, including accurate cross sections and angular distributions, is provided by the chosen Geant4 electromagnetic models. Some options use more detailed low energy data to match measured cross sections in different materials. For example, in soft tissue, water, and lung, Compton is the main interaction process for megavoltage photons, while photoelectric is negligible. In higher Z materials such as bone or contrast agents, the relative ratio between Compton and photoelectric interactions changes, especially at lower energies.
The balance between Compton and photoelectric processes strongly affects simulated energy spectra. For a gamma camera, the observed spectrum around the photopeak includes a Compton continuum produced when photons deposit only part of their energy in the crystal then escape, and a peak region corresponding to full energy deposition, often involving both Compton and photoelectric interactions inside the crystal. In PET detectors, energy windows are chosen to include most of the photopeak and to reject as many pure Compton events as possible. If Compton scattering physics is disabled or configured incorrectly, these spectra will be unrealistic and any analysis based on them, such as scatter fraction or energy window optimization, will be unreliable.
Pair production
Pair production is a higher energy interaction mechanism in which a gamma photon disappears near the electric field of a nucleus or, less frequently, an electron, and materializes as an electron positron pair. Conservation of energy and momentum require that the photon energy be greater than twice the electron rest mass energy:
$$
E_{\gamma} \ge 2 m_e c^2 \approx 1.022\ \text{MeV}.
$$
Pair production can only occur if $E_{\gamma} \ge 1.022\ \text{MeV}$. The excess energy above 1.022 MeV appears as kinetic energy shared between the electron and the positron.
The threshold means that pair production is not possible for common SPECT radionuclide photons such as 140 keV Tc 99m or 171 and 245 keV In 111, and is also not directly relevant for the 511 keV photons in PET. However, for higher energy gamma emitters, for annihilation photons that have been upscattered in extreme cases, and especially for megavoltage photons used in external beam radiotherapy, pair production becomes an important or even dominant interaction process.
In a pair production event, the energy balance can be written as
$$
E_{\gamma} = 2 m_e c^2 + K_e + K_p,
$$
where $K_e$ and $K_p$ are the kinetic energies of the electron and positron. Both particles are then transported by Geant4 according to the electron and positron physics in your selected physics list. The electron deposits energy continuously along its track through ionization and bremsstrahlung. The positron loses energy similarly, then eventually annihilates, producing typically two 511 keV photons that can themselves undergo photoelectric absorption, Compton scattering, or further transport out of the geometry.
In radiotherapy simulations with megavoltage beams, pair production in high Z materials such as treatment head components or shielding structures contributes significantly to dose distributions and out of field radiation. In detector simulations that involve high energy photons, for example in beam monitors or portal imaging devices, pair production inside the detector material creates electron positron pairs that deposit energy and produce characteristic detector signals. If pair production and the resulting positron transport are disabled or poorly modeled, the simulated dose at depth and the shape of high energy spectra will not match experimental results.
In GATE you typically do not enable a standalone “pair production” toggle, but instead select an electromagnetic physics list suitable for your energy range. For simulations with photon energies that extend above 1 MeV, you must ensure that the chosen list includes proper gamma conversion, which is Geant4 terminology for pair production, in the relevant materials. For purely diagnostic imaging at lower energies, pair production has negligible effect and is often irrelevant, but as soon as you study linac beams, high energy gamma sources, or shielding for such beams, an appropriate configuration for pair production becomes essential for physically accurate results.
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