Editorial| Volume 33, ISSUE 7, P455-460, July 01, 2021

# Interactions of Electromagnetic Radiation and Subatomic Particles with Matter – Part 2

Published:March 09, 2021
Understanding the mechanisms by which radiation interacts with tissue is essential for understanding how dose is deposited in patient tissue. This editorial series summarises the predominant interaction processes of photons, electrons and protons with matter, at a level suitable for FRCR candidates preparing for the First FRCR Examination in Physics. Part 1 of this series covered photon interactions [
• Mott J.H.L.
• Daniel J.M.
Interactions of electromagnetic radiation and subatomic particles with matter – Part 1.
]; this second part now considers how charged particles interact with matter.
First-order approximations for the dependence of different interaction processes on energy and atomic material are given as an aid to understanding, but in reality these relationships can be complex and many more interaction processes are also possible.

## Charged Particle Interaction Mechanisms

Interactions of subatomic particles with atoms can be classed as collisional or radiative. Collisions between charged particles and atomic electrons (or more precisely, interactions between their respective electric fields) result in excitation and ionisation, whereas radiative interactions produce Bremsstrahlung radiation. Interactions in which the charged particle loses energy are classed as inelastic. If particles are scattered without significant loss of energy the interactions are classed as elastic. Due to their much smaller mass, electrons are scattered more easily and through larger angles than heavier particles like protons.
The stopping power of a material, S, describes its ability to stop a charged particle. It is defined as the rate at which the particle loses energy (E) with distance (x), in Joules per metre (J m−1). The stopping power of charged particles is proportional to the square of the particle's charge and inversely proportional to the square of the velocity, but is independent of the particle's mass. The mass stopping power S/ρ (in J m2 kg−1) is the linear stopping power divided by the density ρ of the material, and can be measured or calculated for a given material.
$Sρ=−dEρdx$

Whereas stopping power relates to the rate at which energy is lost by the particle, linear energy transfer relates to the rate at which energy is transferred to the medium, which is not necessarily the same. Linear energy transfer is related to collisional interactions that deposit dose close to the interaction site, rather than radiative interactions where the energy is transported away and lost at a distance.

## Electron Interaction Mechanisms

Electrons are charged particles with a charge of –1 e, where e is the elementary charge of 1.602 × 10−19 C. Whether electrons are being used directly as a treatment modality (as in an electron beam generated in a linear accelerator) or whether they are generated during the photon interactions described in Part 1 of this [AQ2]series [
• Mott J.H.L.
• Daniel J.M.
Interactions of electromagnetic radiation and subatomic particles with matter – Part 1.
], the interaction and dose deposition mechanisms in the patient are the same.
The most likely process by which they interact with an atom within a patient depends on the energy of the electron and how close they pass. In soft tissue at typical megavoltage (MV) energies, ionisation and excitation are the predominant mechanisms for energy loss.

### Excitation

An electron passing an atom at a distance may excite an atomic electron to a higher level. The excited electron then returns to its ground state with the emission of a photon, whose energy is the difference between the electron shells involved (Figure 1a). The incident electron continues with reduced energy, having lost the energy transferred to the excited electron (ΔE). For outer shells this may be of the order of a few eV.

### Ionisation

An electron passing close to an atom can interact with an orbiting atomic electron and eject it from the shell, causing ionisation. The incident electron transfers kinetic energy to the ejected electron and carries on in a different direction with reduced energy (Figure 1b). If the ejected secondary electron has enough energy to go on and cause further ionisations at a distance from the original interaction then it is known as a delta ray. The vacancy left behind can be filled by an outer electron with the emission of characteristic X-rays or Auger electrons, as discussed in the section on photoelectric interactions in Part 1 of this [AQ2]series [
• Mott J.H.L.
• Daniel J.M.
Interactions of electromagnetic radiation and subatomic particles with matter – Part 1.
].
Collisions involving ionisation are less likely than those involving excitation, but transfer more energy. Therefore, the overall amount of energy lost by both processes is comparable.

### Bremsstrahlung

If the electron passes close enough to the nucleus for their coulomb fields to interact, the electron's path will be deflected. In most cases a negligible amount of energy is released and the main impact is elastic scattering of the electron. However, in a small percentage of cases, inelastic scattering occurs. As the electron is rapidly decelerated it loses energy, which is then emitted in the form of a photon. This process is known as Bremsstrahlung or ‘breaking radiation’ (Figure 1c). The energy released can be anything up to the kinetic energy of the incident electron. The likelihood of a radiative interaction taking place depends on Z2 and also increases with electron energy.
Table 1 shows the approximate dependencies of the electron interactions on Z, E and the passing distance. For any type of interaction, once the electron has lost almost all of its energy it is finally absorbed by an atom.
Table 1The approximate dependencies of each main interaction mechanism on electron energy (E) and atomic number (Z). The real relationships are much more complex but these first-order approximations are a useful simplification
InteractionInteraction typeDistance of e– from atomZ and E dependenceSummary
ExcitationCollisional>atomic radiusComplex with Z and EIncident electron excites atomic electron to higher state, which then returns to ground state with the emission of a photon.
IonisationCollisional~atomic radiusComplex with Z and EIncident electron ejects orbital electron from shell. Both electrons can go on to deposit dose through further interactions.
BremsstrahlungRadiative<atomic radiusZ2, EIncident electron interacts with field of nucleus; rapid deceleration causes emission of Bremsstrahlung photon.

### Electron Stopping Power

For collisional interactions, the rate of energy loss depends on the electron density of the irradiated material, so mass stopping power is actually greater for lower Z materials. This is explained by low Z materials having more electrons per gram than high Z materials, with those electrons also being less tightly bound. Collisional loss stopping powers decrease with energy to a minimum around 1 MeV then start to gradually increase. Radiative losses increase with both energy and Z2, so X-ray production is more efficient at higher energies and higher atomic numbers (Figure 2).

## Proton Interaction Mechanisms

Protons are positively charged particles. They have the opposite charge to an electron (+1 e) but are much heavier, with a mass around 1836 times higher. There are three main types of proton interaction of interest in radiotherapy: stopping, scattering and nuclear interactions. These all have a different impact on the shape and spread of a proton beam (Table 2). First, multiple collisions with atomic electrons cause the protons to slow down and eventually stop. Slowing down of a charged particle increases the likelihood of further interactions, leading to the familiar Bragg peak at the end of the proton depth dose distribution. Second, protons can be scattered through small angles during interactions with atomic nuclei. This scattering spreads the proton beam, broadening the lateral profile. Finally, direct collisions with the nucleus remove protons from the primary beam and release secondary particles, which go on to deposit dose away from the original proton path, resulting in a low dose ‘halo’ around the main proton beam.
Table 2Summary of proton interactions of interest in radiotherapy
InteractionInteraction typeTargetInfluence on proton beamSummary
StoppingInelasticAtomic electronsLongitudinal shape of depth dose curve including Bragg peakFrequent inelastic Coulomb interactions with electrons cause protons to continuously lose energy. The rate of energy loss increases dramatically towards the end of the range as the proton slows down (proportional to 1/v2)
ScatteringElasticAtomic nucleusSpreading of proton beamProtons passing close to a nucleus are repelled and scattered through small angles. Multiple Coulomb scattering events spread the beam.
Nuclear interactionsInelasticAtomic nucleusRemoval of protons from primary beam, low dose haloIf the proton has enough energy to enter the nucleus it causes an irreversible nuclear reaction. The proton is removed from the primary beam and the nucleus emits nucleons and/or ions.
When protons interact with the Coulomb field of a nucleus, proton Bremsstrahlung is also theoretically possible, in a similar process to that previously described for electrons. However, as the probability of Bremsstrahlung is inversely proportional to the mass of the particle involved, proton Bremsstrahlung is orders of magnitude less likely and therefore of no clinical significance in proton therapy.

### Stopping (Inelastic Coulomb Interactions with Atomic Electrons)

A proton moving through tissue will continuously lose energy through frequent inelastic collisions with atomic electrons. If the proton passes close to an atom it can interact with the Coulomb field of an atomic electron, transferring energy to the electron and causing it to be released (Figure 3a). The proton loses energy and slows down but travels on in almost exactly the same direction due to the large difference in mass between the particles. As the proton slows down the probability of further interactions is increased and the rate of energy loss rises. Energy loss is inversely proportional to the square of the velocity (v), i.e.
$−dEdxα1v2$

For a monoenergetic proton beam, most particles will stop at almost exactly the same depth. The range of a proton is proportional to the square of the kinetic energy. The range (usually taken to be the depth of the distal 80% point) of a typical proton beam varies from about 4 cm for a 70 MeV beam up to around 33 cm for a 230 MeV beam.

### Scattering (Elastic Coulomb Interactions with Nuclei)

In contrast, the nucleus has a larger mass than the proton, and is also positively charged, so a proton passing close to the nucleus will be elastically scattered or deflected from its original path and change direction (Figure 3b). Although individual interactions result in a tiny change in proton direction, the combination of multiple Coulomb scattering events causes the beam to spread and results in the typical Gaussian-shaped lateral profile of proton beams. Higher Z materials will scatter protons more strongly than low Z materials; the angle of spread in soft tissue is usually only a few degrees.

### Nuclear Interactions (Elastic or Inelastic Collisions with Nuclei)

Protons can occasionally collide directly with the nucleus itself. In elastic collisions, the energy and direction of the incident proton will be largely unchanged, but inelastic collisions can also occur. In this case the incident proton enters the nucleus and causes a reaction, in which nuclear fragments, such as secondary protons, neutrons and small nuclear fragments are released, often at large angles from the incident beam (Figure 3c). All of these particles can go on to experience further interactions and deposit dose away from the main beam, causing a ‘low dose halo’ around the proton beam. Nuclear interactions gradually reduce the number of protons in the primary beam as it travels through the patient.

### Bragg Peak

The pronounced peak just before the end of a monoenergetic proton beam depth dose curve is called the Bragg peak (Figure 4). This peak is very distinct for a proton beam as, due to their mass, most protons travel in an almost straight line. Variations in the energy loss of individual protons lead to a small amount of range straggling, resulting in a small distal slope after the maximum. The depth of the peak is determined by the beam energy and the stopping medium. Bragg peaks are not seen in electron beams; due to their much smaller mass, individual electrons change direction many times as they slow down.
The Bragg peak for heavier ions like carbon is even more pronounced. Carbon ions are about 12 times heavier than protons, so are less easily scattered, resulting in a sharper beam with a narrower penumbra. However, there is also a small tail of low dose after the Bragg peak, caused by the fragmentation of the carbon ions in the primary beam into other low energy ions, which can travel a short distance beyond the range of the original carbon particles.
Neutrons are uncharged particles with a similar mass to the proton. They can undergo elastic and inelastic collision with nuclei, the latter of which can result in the emission of further neutrons, protons, alpha particles and other high linear energy transfer nuclear fragments, which can cause high patient doses. Neutron beams have been explored in the past as a treatment modality but with limited success. They are, however, a concern as a by-product of high energy photon interactions when treating with high MV photon beams (above 10 MV). Treatment rooms are designed to provide appropriate shielding against neutrons, and systems of work must be in place to protect engineering staff against induced radioactivity in the linac treatment head.

## Charged Particle Interactions – Single Best Answer Questions

• Question 1. When an electron interacts within a medium
• A.
Excitation is classed as an elastic scattering process
• B.
Ionisation is a less common interaction than excitation but transfers more energy
• C.
Once an electron has lost all of its energy, it combines with a positron and is converted into energy
• D.
Secondary electrons are more likely to produce Bremsstrahlung radiation than the incident electron
• E.
Secondary electrons that deposit all their dose close to the site of interaction are known as delta rays
Answer: B. Note that secondary electrons will be of lower energy than the incident electron so less likely to produce Bremsstrahlung.
• Question 2. Which of the following statements about Bremsstrahlung is correct?
• A.
It is an elastic scattering process
• B.
It is more likely for protons than electrons due to their much higher mass
• C.
Its probability decreases as energy increases
• D.
Its probability increases with the square of the atomic number of the irradiated material
• E.
The maximum energy of radiation emitted depends on the atomic number of the irradiated material
Answer: D. Note that the maximum energy of Bremsstrahlung radiation depends on the energy of the incident electron.
• Question 3. Linear energy transfer
• A.
Describes the rate of energy transferred with time
• B.
Increases towards the end of a proton's path
• C.
Is constant with depth
• D.
Is proportional to the square of the charged particle's velocity
• E.
Is the rate of energy loss per unit distance
Answer: B. Note that linear energy transfer is the rate of energy transferred per unit distance; the rate of energy loss per unit distance is the stopping power.
• Question 4. Proton stopping power
• A.
Decreases as the proton slows down towards the end of its path
• B.
Increases with depth in a medium
• C.
Is calculated using collisional but not radiative losses
• D.
Is independent of the material it travels through
• E.
Is the rate of energy transferred per unit length
• Question 5. Considering the shape of a clinical proton beam
• A.
Nuclear interactions increase the amount of protons in the primary beam
• B.
The Bragg peak is caused by elastic collisions with atomic electrons
• C.
The lateral profile broadens with depth
• D.
The low dose halo is caused by multiple coulomb scattering events
• E.
There is no dose deposited beyond the peak
Answer: C. Note that there is a small distal slope after the peak dose due to range straggling, so some dose is deposited at depths beyond the peak.

## Acknowledgements

The authors would like to thank Matthew Clarke, Head of Proton Therapy Physics at the Christie NHS Proton Beam Therapy Centre, for proofreading the proton section.

## References

• Mott J.H.L.
• Daniel J.M.
Interactions of electromagnetic radiation and subatomic particles with matter – Part 1.
Clin Oncol. 2021; 33 (000–0)
• Berger M.J.
• Coursey J.S.
• Zucker M.A.
• Chang J.
ESTAR, PSTAR, and ASTAR: computer programs for calculating stopping-power and range tables for electrons, protons, and helium ions (version 1.2.3).
National Institute of Standards and Technology, Gaithersburg, MD2005 (Available at:)
http://physics.nist.gov/Star
Date accessed: January 13, 2021