Compton Scattering

In the field of particle physics, Compton scattering is a key principle for understanding the interaction between light and matter, alongside the photoelectric effect at lower energies, pair production at higher energies, and photodisintegration and photofission at very high energies.

Discovered by physicist Arthur H. Compton in 1923, this effect provided critical experimental evidence that light can behave as a particle, specifically that light has a momentum. This earned him the Nobel Prize in Physics in 1927. In the early 1900s, the wave-model of light had been significantly challenged by Planck’s law of black body radiation and Einstein’s interpretation of the photoelectric effect, but the photon theory of light was not widely accepted until Compton’s experiments reinforced that light does indeed have a quantum nature.

What is Compton Scattering?

---

Compton scattering is an interaction between a high-energy photon (typically X-rays or gamma rays) and a free or loosely bound electron. When the photon collides with the electron, it transfers some of its energy to the electron, causing the photon to lose energy and change direction, and the electron to recoil.

The loss in energy of the photon, E_γ, equates to an increase in the photon’s wavelength, λ, called the Compton shift. The magnitude of this shift in wavelength is correlated with the scattering angle, 𝜃, of the photon. This relationship can be written as follows:

Where λ' refers to the photon after scattering, h is planck’s constant, m_e is the rest mass of an electron, and c is the speed of light.

It can also be written in terms of energy:

The limit of this effect is at 180° of scattering, representing the maximum amount of energy that can be imparted onto the electron, beyond which the phenomenon no longer applies. This is responsible for a sudden drop in detections observed at the end range of the Compton continuum, known as the Compton edge.

The low energy limit of Compton scattering is Thomson scattering. When the incident photon energy is significantly lower than the rest mass of the electron, it causes the electron to oscillate and release electromagnetic radiation of the same wavelength.

Compton Scattering Theory

---

Classically, it was believed that continuous light waves would transfer energy to an electron proportional to its intensity. When enough energy is accumulated to accelerate the electron to relativistic speeds, it would be emitted from the atom. However, experimental evidence showed that electrons were emitted only when the frequency of the photon was high enough, regardless of intensity or duration. Max Planck had already shown that the energy of an oscillator in a black body should be quantized into discrete units of E=hf, where f is its frequency. However, Einstein went a step further and suggested that light itself can be considered a stream of quanta, each with energy hf. The photoelectric effect can therefore be understood as individual photons of sufficient frequency being absorbed by electrons bound in an atom at quantized energy levels and subsequently ejecting them.

To understand how photons can scatter off electrons, Compton built upon this work by postulating that photons have a momentum, despite being massless particles. He equated Einstein’s mass-energy relation E=mc² and energy-frequency relation E=hf to give the photon an ‘effective mass’ of hf/c². The momentum of a photon, p, is therefore its effective mass multiplied by the speed of light, hf/c.

The electron is treated as being at rest before collision, and relativistic after collision. By considering conservation of energy (or mass-energy for the electron) and momentum of the photon-electron system, Compton derived the previous relationship between the photon’s scattering angle and its change in wavelength.

The Klein-Nishina formula is the differential cross section of a photon scattering off a free electron. It gives a measure of the likelihood of this event occurring at a given angle.

This formula can also be integrated to give a measure of the total likelihood of a Compton scatter event occurring – though atomic number and material density must also be considered.

When the differential cross section is plotted, you can see the angular distribution of events occurring.

Detecting Compton Scattering

---

Compton scattering events are typically observed in scintillation or semiconductor detectors. They are detected via the following process:

1. As a photon travels through the active material of the detector, it may only partially deposit its energy through scattering with one or more electrons before leaving the detector.
2. The recoiling electron(s) lose energy as they travel through the medium by creating electron-hole pairs (in semiconductors) or ionizing/exciting atoms (in scintillators). This process depends on many factors, such as detector geometry and composition, according to the Blethe formula.
3. The detector has a bias voltage across its electrodes. As the charge carriers drift across the electric potential, the motion of these charge carriers induces a transient current pulse at the electrodes according to the Shockley-Ramo theorem.
4. A pre-amplifier integrates this current within the integration time of the detector, turning it into a voltage pulse.
5. The peak amplitude of the voltage pulse gets sampled by the ADC of a multi-channel analyzer (MCA), which then counts each of these samples into narrow voltage bins (channels).
6. The peak amplitude of a voltage pulse is proportional to the amount of energy deposited in the detector, so a well calibrated MCA provides the distribution of energies detected from all interactions within the detector.

Those detections that occur due to Compton scattering form the observed Compton continuum below the full energy photopeak.

In reality, most of the electrons will be bound to an atom, so the binding energy of the electron must be accounted for. However, it is much more likely for scattering events to occur with weakly-bound electrons, where the binding energy is insignificant compared to the energy of the photon. The photon may also scatter multiple times before leaving the detector, or partially deposit its energy in other ways such as through atomic excitation or the escape of secondary photons from pair-production. Together, the detector’s geometry, material composition, and electronic resolution determine the broadening, slope, and overall shape of the Compton edge in the measured spectrum.

Compton Cameras and Other Applications

---

Compton scattering is an important phenomenon for understanding photon-matter interactions because it is the dominant interaction at high energies of ~30keV – 10MeV. This makes it essential for interpreting spectral features in space telescopes and particle accelerators, as well as for applications in imaging technologies such as Compton cameras.

A Compton camera is a device that resolves the origin of x-rays/gamma rays. They work by scattering gamma or X-ray emissions from a source through a diffuser, which are then measured by multiple detectors. The angle measured by each detector traces out a cone of the ray’s possible path. The intersection of these cones from all detectors must be the source’s origin. Compton cameras typically have much higher spatial resolution and efficiency than collimated cameras and they are able to simultaneously measure gamma rays over a wide energy range. They are particularly good for high energy (MeV) ranges which are too energetic for focusing lenses and too weak for pair-production. The lack of need for collimation also gives them the advantage of being lightweight and able to localize multiple sources with a wide field-of-view without prior knowledge.

These advantages makes compton camaras particularly useful for astrophysics, such as the Imaging Compton Telescope (COMPTEL) and Nuclear Compton Telescope (NTL) which helped mapped the gamma-ray sky and study notable gamma-ray sources such as black holes and supernovae.

Compton cameras have found use in environmental monitoring and security applications, especially for shielded sources, such as cargo monitoring, mapping contamination zones like Fukushima, and finding orphan sources. Various Compton cameras have been used to aid nuclear decommissioning in Sellafield by producing 3D maps of radiation sources in nuclear cells that would be hazardous to handle directly. X-ray backscatter detection is a special case of the Compton camera used in airports for detecting concealed objects and differentiating low atomic number materials like explosives. It is also used in quality assurance for industries such as inspecting pipelines for defects.

Compton Scattering in Medical Imaging

---

Compton scattering actually degrades the results from modern medical imaging techniques such as PET, SPECT and CT, as photons scattering before reaching the detector can cause artifacts, blur and loss of contrast. Typically, this is mitigated with scatter correction algorithms, energy windowing, and hardware design, for example anti-scatter grids and multi-layered detectors running in anti-coincidence (known as Compton suppression).

These medical imaging techniques are also limited in their angular resolution and efficiency due to their need for collimation. Although the results of Compton cameras for medical applications do not currently surpass these technologies, it shows potential to be a more effective diagnostic tool that can lead to better outcomes for patients, making it very much an active area of research .

In the energy range of 1-10 MeV, Compton scattering is the dominant interaction of gamma rays and x-rays with the soft tissues of the body. The recoiling electrons ionize cells along their path, leading to cell damage. In radiation therapy, this effect is utilized to target and destroy tumours. By accurately profiling how high-energy photons interact with tissues and adjusting the depth-dose distribution, these treatments can be optimized to maximise tumour control whilst minimising harm to surrounding healthy tissue.

Learn More

---