1.3 - Photon Interactions

Photons are quanta of electromagnetic energy that exhibit both wave-like and particle-like properties. A photon can be considered to have a wavelength and frequency (like a wave), as well as momentum and energy (like a particle). Despite carrying electromagnetic energy, a photon has no 'charge' and has a much lower chance of interacting with matter than charged particles such as electrons and protons.
There are six ways in which photons may interact with matter:

• Coherent Scattering
• Photoelectric Effect
• Incoherent Scattering, also known as Compton Scattering or Compton Effect
• Pair Production
• Triplet Production
• Photodisintegration

These may cause the photon to attenuate (lose some of its energy and/or disappear). Photon interactions are very important when considering how a photon beam interacts with a patient.

## Coherent Scattering - σcoh

Coherent (or Rayleigh) scattering occurs at low photon energies. A photon may interact with an orbital electron and is then deflected (or scattered) at a small angle. There is no change in energy of the photon and no other effects occur.
Coherent scattering is more probably as atomic number increases and as photon energy decreases. This makes it of some concern in diagnostic x-ray, where it can cause loss of contrast and blurring. For radiotherapy it has minimal impact on attenuation.

## Photoelectric Effect - τ

The photoelectric effect occurs when a photon interacts with an orbital electron whose binding energy is close to that of the photon energy. In this scenario, the photon disappears and all of its energy is given to the orbital electron, which is then ejected from the atom with kinetic energy equivalent to the photon energy minus the binding energy.
The space left by the departing electron is filled by another orbital electron, with emission of charateristic x-rays or Auger electrons (when a characteristic x-ray causes ejection of another orbital electron within the same atom). In soft tissues, these characteristic x-rays have a low energy (about 500 eV) and are absorbed locally.
The probability of the photoelectric effect occuring is:

• Inversely propotional to the cube of the photon energy (ie: $\frac{1}{E^3}$ )
• Proportional the cube of the atomic number ie: $Z^3$

Therefore, as photon energy increases, the likelihood of the photoelectric effect decreases rapidly.
As the atomic number of a material increases, the likelihood of the photoelectric effect increases rapidly.
The photoelectric effect ceases to become likely at energies over 100-200 keV in water, but remains an important factor for attenuation in lead at energies up to 1 MeV.

### Absorption Edges

An important concept is that when the photon energy is very closely aligned with the binding energy of a particular electron shell, the likelihood of photoelectric interactions jumps. This is an absorption edge, and reflects the ability of photons above that energy to interact more frequently.

## Incoherent Scattering (Compton Effect) - σinc

Incoherent scattering is the most important interaction in radiotherapy. It occurs when a photon has a much greater amount of energy than the binding energy of the electron, effectively considering the electron as 'free'. In this interaction, the photon interacts with the 'free' electron, giving up some of its energy and undergoing scattering. The electron receives the energy and is set in motion in a different direction.
Photons may be scattered in any direction, whereas electrons are only scattered in a forward direction (maximum 90o from the original path of the photon). The energy given to the electron is dependant on the photon energy (low energies tend to give up minimal energy to the electron) and the angle of impact.

• Direct impact scatters the photon at 180 degrees and gives a large amount of energy to the electron which continuous in the photons original path.
• Glancing hits cause no photon scattering and give a small amount of energy to the electron, which moves at 90 degrees away from the photon direction.

Importantly, incoherent scattering is not directly related to atomic number but rather the concentration of electrons in tissue. As atomic number rises, the density of electrons falls slowly, so incoherent scattering becomes slightly less likely in high Z materials. Incoherent scattering also decreases with energy, but nowhere near as rapidly as the photoelectric effect. This makes it more relevant as photon energies rise above the K-shell binding energies of orbital electrons.

## Pair Production - κ

Pair production occurs when a photon passes very close to the nucleus of an atom. If the energy of the photon is high enough, the photon may disappear and 'create' an electron and a positron. The new particles move away with the remaining energy of the photon converted to kinetic energy.
The positron will typically annihalate once it loses its kinetic energy, giving rise to annihalation quanta (two photons with energy of 0.511 keV).

### Situations in which pair production is possible

Pair production only occurs when photon energy is high enough and when there is an object of sufficient mass to take on the momentum gained by the new particles.

• Photon energy must be at least 1.022 MeV to generate a positron/electron pair. This is because 1.022 MeV is required to create the mass of the electron and the positron (through $E=mc^2$.
• Pair production only occurs in close proximity to the nucleus. This is so momentum of the electron and positron is conserved.
• It is possible for pair production to occur in proximity to an electron. This is called triplet production, below.

### Relation of pair production with atomic number and photon energy

Pair production does not occur with photon energy under 1.022 MeV. Once this threshold is reached, it becomes more likely as photon energy increases.
Pair production is related to the atomic number of a material through Z2.

## Triplet Production - κtr

Triplet production is a special case of pair production which occurs in the vicinity of an orbital electron. The photon disappears and the energy is used to create an electron and positron. The orbital electron also receives energy and is freed from the atom. The threshold for this to occur is a photon of 2.044 MeV.

## Photodisintegration - π

Photodisintegration is an uncommon event that occurs when a photon is absorbed by the nucleus of an atom. The photon is destroyed and a nucleon (either a proton or a neutron) is released. The threshold for this effect is over 10 MeV for most nuclei (with the exception of beryllium and deuterium, where it is 2 MeV). Even at high energies, photodisintegration is an uncommon event and does not attenuate a substantial portion of a photon beam. It is more important for radiation protection concerns - if neutrons are released they are highly penetrating and can convert atoms into unstable isotopes. The release of a nucleon from the atom in question also usually results in a radioactive daughter product. The production of neutrons in high energy linear accelerators means that bunkers must be regularly ventilated to prevent buildup of radioactive gasses.