Interaction of Photons with Matter

High-energy photons interact with matter by three main mechanisms, depending on the energy of the electromagnetic radiation. These are (i) the photoelectric effect, (ii) the Compton effect, and (iii) pair production. In addition, there are other mechanisms such as coherent (Rayleigh) scattering, an interaction between a photon and a whole atom which predominates at energies less than 50 keV; triplet production and photonuclear reactions, where high energy gamma rays induce decay in the nucleus, and which require energies of greater than ~10 MeV. We will focus on the three main mechanisms which dominate in the energies of interest in imaging in nuclear medicine.

Photoelectric Effect

The photoelectric effect occupies a special place in the development of the theory of radiation. During the course of experiments which demonstrated that light acted as a wave, Hertz and his student Hallwachs showed that the effect of an electric spark being induced in a circuit due to changes in a nearby circuit could be enhanced if light was shone upon the gap between the two coil ends. They went on to show that a negatively charged sheet of zinc could eject negative charges if light was shone upon the plate. Philipp Lenard demonstrated in 1899 that the light caused the metal to emit electrons. This phenomenon was called the photoelectric effect. These experiments showed that the electric current induced by the ejected electrons was directly proportional to the intensity of the light. The interesting aspect of this phenomenon was that there appeared to be a light intensity threshold below which no current was produced. This was difficult to explain based on a continuous wave theory of light. It was these observations that led Einstein to propose the quantized theory of the electromagnetic radiation in 1905, for which he received the Nobel Prize.

The photoelectric effect is an interaction of photons with orbital electrons in an atom. This is shown in Fig. 2.9. The photon transfers all of its energy to the electron. Some of the energy is used to overcome the

Photon Shell Theory
Figure 2.9. The photoelectric effect involves all of the energy from a photon being transferred to an inner shell electron, causing ionization of the atom.

binding energy of the electron, and the remaining energy is transferred to the electron in the form of kinetic energy. The photoelectric effect usually occurs with an inner shell electron. As the electron is ejected from the atom (causing ionisation of the atom) a more loosely bound outer orbital electron drops down to occupy the vacancy. In doing so it will emit radiation itself due to the differences in the binding energy for the different electron levels. This is a characteristic X ray. The ejected electron is known as a photoelectron. Alternately, instead of emitting an X ray, the atom may emit a second electron to remove the energy and this electron is known as an Auger electron. This leaves the atom doubly charged. Characteristic X rays and Auger electrons are used to identify materials using spectro-scopic methods based on the properties of the emitted particles.

The photoelectric effect dominates in human tissue at energies less than approximately 100 keV. It is of particular significance for X-ray imaging, and for imaging with low-energy radionuclides. It has little impact at the energy of annihilation radiation (511 keV), but with the development of combined PET/CT systems, where the CT system is used for attenuation correction of the PET data, knowledge of the physics of interaction via the photoelectric effect is extremely important when adjusting the attenuation factors from the X-ray CT to the values appropriate for 511 keV radiation.

Compton Scattering

Compton scattering is the interaction between a photon and a loosely bound orbital electron. The electron is so loosely connected to the atom that it can be considered to be essentially free. This effect dominates in human tissue at energies above approximately 100 keV and less than ~2 MeV. The binding potential of the electron to the atom is extremely small compared with the energy of the photon, such that it can be considered to be negligible in the calculation. After the interaction, the photon undergoes a change in direction and the electron is ejected from the atom. The energy loss by the photon is divided between the small binding energy of the energy level and the kinetic energy imparted to the Compton recoil electron. The energy transferred does not depend on the properties of the material or its electron density (Fig. 2.10).

The energy of the photon after the Compton scattering can be calculated from the Compton equation:

Atomic Level Tomography
Figure 2.10. In Compton scattering, part of the energy of the incoming photon is transferred to an atomic electron. This electron is known as the recoil electron. The photon is deflected through an angle proportional to the amount of energy lost.

e.g., What is the energy of an annihilation photon after a single scatter through 60°?

Fy- 511 keV

=511keV 511

From consideration of the Compton equation it can be seen that the maximum energy loss occurs when the scattering angle is 180° (cos (180°) = -1), i.e., the photon is back-scattered. A 180° back-scattered annihilation photon will have an energy of 170 keV.

Compton scattering is not equally probable at all energies or scattering angles. The probability of scattering is given by the Klein-Nishina equation [1]:

where da/dQ is the differential scattering cross-section, Z is the atomic number of the scattering material, r0 is the classical electron radius, and a = EY/m0c2. For positron annihilation radiation (where a = 1) in tissue,

CD c UJ

Figure 2.11. The angular probability distribution (differential scattering cross-section, broken line) and resultant energy (solid line) for Compton-scattered annihilation photons are shown.

CD c UJ

Figure 2.11. The angular probability distribution (differential scattering cross-section, broken line) and resultant energy (solid line) for Compton-scattered annihilation photons are shown.

Compton Scattering Angular Distribution

Scattering Angle 6C (degrees)

Scattering Angle 6C (degrees)

this equation can be reduced for first-order scattered events to give the relative probability of scatter as:

da dQ

Figure 2.11 shows the form that this function takes in the range 0-180°. A number of Monte Carlo computer simulation studies of the interaction of annihilation radiation with tissue-equivalent material in PET have shown that the vast majority (>80%) of scattered events that are detected have only undergone a single scattering interaction.

Pair production: The final main mechanism for photons to interact with matter is by pair production. When photons with energy greater than 1.022 MeV (twice the energy equivalent to the rest mass of an electron) pass in the vicinity of a nucleus it is possible that they will spontaneously convert to two electrons with opposed signs to conserve charge. This direct electron pair production in the Coulomb field of a nucleus is the dominant interaction mechanism at high energies (Fig. 2.12). Above the threshold of 1.022 MeV, the probability of pair production increases as energy increases. At 10 MeV, this probability is about 60%. Any energy left over after the production of the electron-positron pair is shared between the particles as kinetic energy, with the positron having slightly higher kinetic energy than the electron as the interaction of the particles with the nucleus causes an acceleration of the positron and a deceleration of the electron.

Pair production was first observed by Anderson using cloud chambers in the upper atmosphere, where high-energy cosmic radiation produced tracks of diverging ionisation left by the electron-positron pair.

The process of pair production demonstrates a number of conservation laws. Energy is conserved in the process as any residual energy from the photon left over after the electron pair is produced (given by Ey - 2m0 c2) is carried away by the particles as kinetic energy; charge is conserved as the incoming photon

Figure 2.12. The pair production process is illustrated. As a photon passes in the vicinity of a nucleus spontaneous formation of positive and negatively charged electrons can occur. The threshold energy required for this is equal to the sum of the rest masses for the two particles (1.022 MeV).

Figure 2.12. The pair production process is illustrated. As a photon passes in the vicinity of a nucleus spontaneous formation of positive and negatively charged electrons can occur. The threshold energy required for this is equal to the sum of the rest masses for the two particles (1.022 MeV).

has zero charge and the outgoing positive and negative electrons have equal and opposite charge; and momentum is conserved as the relatively massive nucleus absorbs momentum without appreciably changing its energy balance.

Electron-positron pair production offered the first experimental evidence of Dirac's postulated "antimatter", i.e., that for every particle in the universe there exists a "mirror image" version of it. Other particles can produce matter/antimatter pairs, such as protons, but, as the mass of the electron is much less than a proton, a photon of lower energy is required for electron-positron pair production, thus making the process more probable. The particles produced will behave like any other free electron and positron, causing ionisation of other atoms, and the positron will annihilate with an orbital electron, producing annihilation radiation as a result.

At energies above four rest-mass equivalents of the electron, pair production can take place in the vicinity of an electron. In this case it is referred to as "triplet production" as there is a third member of the interaction, the recoiling electron.

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  • Balbo
    Why high energy compton effect for free electrons while photoelectric effect for inner shells?
    3 years ago
  • zahra
    Why photon interacts inner orbit in photoelectric effect?
    2 years ago
  • Tove
    What are the three mechanisms through which photons interact with matter?
    11 months ago

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