KAHIBARO
12.4. Gamma Interactions
Table of Contents
Photoelectric effect
In Geant4 the photoelectric effect describes the complete absorption of a gamma photon by an atom, with the energy transferred to a bound electron. The electron is then ejected from the atom as a so‑called photoelectron. This process is modeled by electromagnetic physics classes that are activated through the physics list, so you usually do not have to implement it yourself, but you do need to know what it does to interpret your simulation results.
The basic kinematics are simple. A gamma of energy $E_\gamma$ interacts with an atomic electron of binding energy $E_b$. The electron is ejected with kinetic energy
$$
E_{e^{-}} = E_\gamma - E_b.
$$
The photon disappears in a single step, so its track is terminated at the interaction point. In Geant4 this appears as an energy deposition at the interaction location, plus the creation of a new secondary track for the ejected electron.
The probability for the photoelectric effect strongly depends on the gamma energy and on the atomic number $Z$ of the material. For low and moderate gamma energies, the cross section increases very rapidly with $Z$ and decreases with increasing energy. Qualitatively, at a given energy the process is much more likely in lead than in silicon or water. At higher energies it becomes less important compared to Compton scattering and pair production. In a simulation of low‑energy gammas in high‑$Z$ materials, such as detector shielding or gamma spectroscopy crystals, the photoelectric effect is often the dominant interaction.
When the bound electron is removed, the atom is left in an excited or ionized state. The vacancy is filled by electrons from higher shells. This de‑excitation can produce characteristic X‑rays or Auger electrons, which Geant4 can also generate as secondary particles if appropriate models are enabled in the physics list. Whether you see these low‑energy secondaries depends on your chosen electromagnetic physics and production cuts.
In geometry terms, a photoelectric interaction deposits most or all of the photon energy very locally. In an ideal gamma spectrometer this produces a full energy peak in the energy spectrum, because the entire gamma energy is absorbed within the detector. In Geant4, this appears as a large energy deposition in one or a few nearby steps, usually all within the same sensitive volume if your detector is thick enough.
In a photoelectric interaction the gamma is fully absorbed in one step, the photon track is terminated, and a single energetic photoelectron is created with $E_{e^{-}} = E_\gamma - E_b$, often leading to a full energy peak in high‑$Z$ detectors.
For absolute beginners using reference physics lists, it is enough to remember that the photoelectric effect is responsible for strong local energy deposition at low gamma energies, especially in materials with large atomic number.
Compton scattering
Compton scattering in Geant4 describes the elastic scattering of a gamma photon on an (effectively) free or weakly bound electron. The photon loses part of its energy and changes direction, and an electron is ejected with the transferred energy. Since the photon survives the interaction with reduced energy, it can scatter multiple times, producing a complex track through the detector and surrounding materials.
Physically, Compton scattering is dominant for intermediate gamma energies in many materials, particularly in tissues, water, and low‑ to medium‑$Z$ detector materials. The probability depends on the energy and, more weakly than the photoelectric effect, on atomic number. In many medical physics and radiation protection problems, Compton scattering is the main interaction mechanism for diagnostic and therapeutic photon energies.
The energy and angle of the scattered photon follow the Compton formula. If an incident photon with energy $E_\gamma$ is scattered by an angle $\theta$ with respect to its initial direction, the scattered photon energy $E_\gamma'$ is
$$
E_\gamma' = \frac{E_\gamma}{1 + \frac{E_\gamma}{m_e c^2}(1 - \cos\theta)} ,
$$
where $m_e c^2 \approx 511\ \text{keV}$ is the electron rest energy. The ejected electron receives the difference, $E_{e^{-}} = E_\gamma - E_\gamma'$. In Geant4, each Compton interaction creates two secondaries: the scattered photon and a recoil electron.
From the detector point of view, Compton scattering tends to distribute the gamma energy over a larger volume than the photoelectric effect. A gamma can undergo several Compton scatters, each depositing part of its energy via the electron, and then may eventually escape the detector. In an energy spectrum, such partial energy deposition produces the so‑called Compton continuum, and a Compton edge at the maximum energy transfer to the electron.
In a Geant4 simulation, the scattered photon track is updated with new energy and direction, and continues to propagate until it is absorbed, converted, or leaves the geometry. The electron track is also followed, depositing energy along its path via ionization and other processes. If you record energy deposition in a sensitive detector, Compton scattering will often appear as multiple separated deposits within or across volumes, rather than a single localized point.
In Compton scattering the photon survives with reduced energy, following
$$
E_\gamma' = \frac{E_\gamma}{1 + \frac{E_\gamma}{m_e c^2}(1 - \cos\theta)},
$$
and the transferred energy $E_\gamma - E_\gamma'$ goes to the recoil electron, which produces distributed energy deposition along its track.
For beginners choosing a physics list, it is enough to understand that Compton scattering is what lets gammas penetrate deeply and spread their energy over a wide region, which is crucial in medical dose calculations and shielding studies.
Pair production
Pair production in Geant4 is the conversion of a gamma photon into an electron positron pair in the electric field of a nucleus or, less frequently, an electron. This process requires the gamma to have energy above the threshold of twice the electron rest energy,
$$
E_\gamma \ge 2 m_e c^2 \approx 1.022\ \text{MeV}.
$$
Below this threshold pair production cannot occur, so Geant4 will not invoke this process for low‑energy photons.
In a typical pair production event, the gamma disappears completely and two new charged particles are created: one electron and one positron. The total kinetic energy of the pair equals the gamma energy minus the rest mass energy of both particles,
$$
T_{e^{-}} + T_{e^{+}} = E_\gamma - 2 m_e c^2.
$$
Momentum conservation in the nuclear field determines their directions. Geant4 generates these two secondaries at the interaction point, and the original photon track is terminated.
The cross section for pair production increases rapidly with photon energy above the threshold and grows with atomic number. At sufficiently high gamma energies, especially in high‑$Z$ materials such as lead, pair production becomes the dominant interaction mechanism, exceeding both the photoelectric effect and Compton scattering. In electromagnetic calorimeters and high‑energy detector simulations, pair production drives the development of electromagnetic showers.
Once created, the electron and positron propagate independently. Both lose energy via ionization and bremsstrahlung. The positron, after slowing down, eventually annihilates with an electron in the material, typically producing two 511 keV annihilation gammas emitted nearly back to back. These secondary gammas are then transported and can themselves undergo photoelectric absorption, Compton scattering, or further pair production if their energy is sufficiently high.
In the detector response, pair production leads to more complex patterns of energy deposition than a single photoelectric event. Energy is carried by multiple particles and can be distributed over a larger volume. In high‑energy detectors designed to measure the total energy of incoming gammas, this cascade of pair production and subsequent processes is the basis of electromagnetic shower formation and calorimetry.
Pair production converts a gamma with $E_\gamma \ge 1.022\ \text{MeV}$ into an $e^{-}e^{+}$ pair, with total kinetic energy
$$
T_{e^{-}} + T_{e^{+}} = E_\gamma - 2 m_e c^2,
$$
and the original photon is fully absorbed. The positron later annihilates, producing additional 511 keV gammas.
When you select a physics list that includes standard electromagnetic physics, Geant4 will automatically handle pair production above threshold. For absolute beginners it is sufficient to recognize that, at high gamma energies, pair production is responsible for creating additional charged particles and annihilation gammas, which strongly affects how energy is deposited in thick and dense detectors.
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