Physical Processes Important for Radiation Detection

Electrons move in a zigzag manner within matter and they give off most of their energy at the end of their path. Therefore, it is at the end of their path where the most electron-induced ionisation per unit length appears. It is fundamentally important to know that the mean free path of a positron in matter is in the order of 1 mm, consequently the theoretical resolution limit of PET is 1 mm because the decay of the positron decaying isotope is isotropic to positron emission.
Regarding the interactions of radiation with matter at energies being used, the two characteristic processes are the photoelectric effect and Compton scattering. Rayleigh scattering is also important to mention.

Compton scattering

Compton scattering is a physical process in which a photon interacts with the electron shell of an atom, as a result an electron is ejected and the photon is scattered, thus its direction of movement changes and its energy decreases.

 
It is important to know that the energy of the scattered photon is dependent on the scatter angle, and the scattering cross section is angle- and energy-dependent as well. At low energies the angle dependence of the cross section is symmetrical, which means that forward and backward scattering is similarly probable. However, as energy increases the probability curve changes and the probability of forward scattering gets typically much higher than that of backward scattering. At energies being used the angle dependence of the cross section is not significant as far as Compton scattering is concerned.

 
The photoelectric effect

The photoelectric effect is the physical process in which a photon knocks an electron out of the atom by transferring all its energy to the atom, the photon is absorbed, this way it pushes the atom.

 
The cross section of the photoelectric effect is directly proportional to the fourth power of the atomic number and inversely proportional to the third power of the energy. The average atomic numbers within the body are: Z(soft tissue)=7.5, Z(body)=8, Z(bones)=13. Studying the different types of interactions regarding their dependence on energy and on the atomic number we find that at the energies we use and for the atomic numbers we examine the characteristic process is Compton scattering.

 
Rayleigh scattering

This type of scattering is sometimes referred to as coherent scattering. In this case the photon scatters off the entire atom, thus the mass of the electron has to be replaced by the mass of the entire atom when making calculations. The process is of interest at low energies and in case of high atomic numbers, when the probability of Rayleigh scattering exceeds that of Compton scattering. Actually Rayleigh scattering is a small angled forward scattering in which the wavelength of the photon practically does not change. There are virtually no elements with high atomic numbers within the human body, but they can be found in collimators, so that is where Rayleigh scattering is important.

Half value thickness and tenth value thickness of lead

Nuclide	Energy (keV)	Half value thickness (cm)	Tenth value thickness (cm)
Tc-99m	140	0.03	0.1
I-123	156	0.04	0.13
I-131	364	0.3	1
F-18	511	0.7	2.3

 
The spectrum of a scintillator

A monoenergetic peak taken with a scintillator yields the spectrum visible in this figure:

A photopeak (or full energy peak) appears that looks nothing like the ideal photopeak visible in the image to the right, instead, the true photopeak is considerably widened. As a result of Compton scattering other signals belonging to lower energies appear, these form the Compton valley, the Compton edge and the Compton plateau.

The primary reason of the widening of the photopeak is statistics. The crystal converts ~10% of the in radiation into visible light (the value for NaI is 12%). A part of the light does not leave the crystal and reach the photocathode. In addition, the efficiency of the conversion of the photocathode is fairly low (~25%), therefore it is obvious that an incident gamma photon can produce very few electrons only, so there is no use in amplifying the signal with a PMT (photomultiplier tube) because the statistics will not be better. If the number of electrons is in the order of 1000, the statistical deviation is around 3%, thus the full width at half maximum is about 6-7%, which results in a 20 times worse energy resolution than that of a cooled semiconductor detector.

Photon scattering within the body

Photon scattering within the body can have several negative effects as far as the examination is concerned. It results in the decrease of the full energy peak and the increase of the Compton region in the spectrum. This way the chance for energy discrimination decreases because the peak-to-background ratio deteriorates considerably. As a consequence of the scattering the detectors sense photons that should not be detected if we intend to produce an accurate image, therefore scattered photons can have a negative effect on image quality. In case of gamma cameras only ‘luckily’ scattered photons are not sorted out by the collimator, still, the problem cannot be neglected. However, in PET a scattered photon can seriously affect the LOR (line of response; the line connecting the two detectors in coincidence).

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