Guide The Compton Effect and Tertiary X-Radiation

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Clark GL, Duane W, Stifler WW. The Secondary and Tertiary Rays from Chemical Elements of Small Atomic Number Due to Primary X-Rays from a Molybdenum.
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Mass attenuation coefficient values are actually normalized with respect to material density, and therefore do not change with changes in density. Material density does have a direct effect on linear attenuation coefficient values. The total attenuation rate depends on the individual rates associated with photoelectric and Compton interactions.

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The respective attenuation coefficients are related as follows:. Let us now consider the factors that affect attenuation rates and the competition between photoelectric and Compton interactions.

Both types of interactions occur with electrons within the material. The chance that a photon will interact as it travels a 1-unit distance depends on two factors.

Interaction of Radiation with Matter

One factor is the concentration, or density, of electrons in the material. Increasing the concentration of electrons increases the chance of a photon coming close enough to an electron to interact. In a previous section Characteristics and Structure of Matter we observed that electron concentration was determined by the physical density of the material. Therefore, density affects the probability of both photoelectric and Compton interactions.

All electrons are not equally attractive to a photon. What makes an electron more or less attractive is its binding energy. The two general rules are:. Photoelectric interactions occur most frequently when the electron binding energy is slightly less than the photon energy. Compton interactions occur most frequently with electrons with relatively low binding energies.

In the previous section referred to above we observed that the electrons with binding energies within the energy range of diagnostic x-ray photons were the K-shell electrons of the intermediate- and high-atomic-number materials. Since an atom can have, at the most, two electrons in the K shell, the majority of the electrons are located in the other shells and have relatively low binding energies.

This can be considered from two perspectives. In a specific material with a fixed binding energy, a change in photon energy alters the match and the chance for photoelectric interactions. On the other hand, with photons of a specific energy, the probability of photoelectric interactions is affected by the atomic number of the material, which changes the binding energy.

This graph shows two significant features of the relationship. One is that the coefficient value, or the probability of photoelectric interactions, decreases rapidly with increased photon energy. This general relationship can be used to compare the photoelectric attenuation coefficients at two different photon energies.

The significant point is that the probability of photoelectric interactions occurring in a given material drops drastically as the photon energy is increased. The other important feature of the attenuation coefficient-photon energy relationship shown in the figure above is that it changes abruptly at one particular energy: the binding energy of the shell electrons. The K-electron binding energy is 33 keV for iodine.

This feature of the attenuation coefficient curve is generally designated as the K, L, or M edge. The reason for the sudden change is apparent if it is recalled that photons must have energies equal to or slightly greater than the binding energy of the electrons with which they interact. When photons with energies less than 33 keV pass through iodine, they interact primarily with the L-shell electrons. They do not have sufficient energy to eject electrons from the K shell, and the probability of interacting with the M and N shells is quite low because of the relatively large difference between the electron-binding and photon energies.

However, photons with energies slightly greater than 33 keV can also interact with the K shell electrons. This means that there are now more electrons in the material that are available for interactions. This produces a sudden increase in the attenuation coefficient at the K-shell energy.

In the case of iodine, the attenuation coefficient abruptly jumps from a value of 5.

X-Ray Physics: X-Ray Interaction with Matter and Attenuation

A similar change in the attenuation coefficient occurs at the L-shell electron binding energy. For most elements, however, this is below 10 keV and not within the useful portion of the x-ray spectrum. Photoelectric interactions occur at the highest rate when the energy of the x-ray photon is just above the binding energy of the electrons. An explanation for the increase in photoelectric interactions with atomic number is that as atomic number is increased, the binding energies move closer to the photon energy.

The general relationship is that the probability of photoelectric interactions attenuation coefficient value is proportional to Z3. In general, the conditions that increase the probability of photoelectric interactions are low photon energies and high-atomic-number materials. All electrons in low-atomic-number materials and the majority of electrons in high-atomic-number materials are in this category.

The characteristic of the material that affects the probability of Compton interactions is the number of available electrons. It was shown earlier that all materials, with the exception of hydrogen, have approximately the same number of electrons per gram of material. Since the concentration of electrons in a given volume is proportional to the density of the materials, the probability of Compton interactions is proportional only to the physical density and not to the atomic number, as in the case of photoelectric interactions.

The major exception is in materials with a significant proportion of hydrogen.

x ray interactions

In these materials with more electrons per gram, the probability of Compton interactions is enhanced. Although the chances of Compton interactions decrease slightly with photon energy, the change is not so rapid as for photoelectric interactions, which are inversely related to the cube of the photon energy. The direction in which an individual photon will scatter is purely a matter of chance.

There is no way in which the angle of scatter for a specific photon can be predicted. However, there are certain directions that are more probable and that will occur with a greater frequency than others. The factor that can alter the overall scatter direction pattern is the energy of the original photon.

In diagnostic examinations, the most significant scatter will be in the forward direction. This would be an angle of scatter of only a few degrees. However, especially at the lower end of the energy spectrum, there is a significant amount of scatter in the reverse direction, i. For the diagnostic photon energy range, the number of photons that scatter at right angles to the primary beam is in the range of one-third to one-half of the number that scatter in the forward direction.

Increasing primary photon energy causes a general shift of scatter to the forward direction. However, in diagnostic procedures, there is always a significant amount of back- and side-scatter radiation. The electron's kinetic energy is quickly absorbed by the material along its path. In other words, in a Compton interaction, part of the original photon's energy is absorbed and part is converted into scattered radiation.

The manner in which the energy is divided between scattered and absorbed radiation depends on two factors-the angle of scatter and the energy of the original photon. The relationship between the energy of the scattered radiation and the angle of scatter is a little complex and should be considered in two steps.

ECR 2016 / C-0007

The photon characteristic that is specifically related to a given scatter angle is its change in wavelength. It should be recalled that a photon's wavelength l and energy E are inversely related as given by:. Since photons lose energy in a Compton interaction, the wavelength always increases. The relationship between the change in a photon's wavelength, Dl , and the angle of scatter is given by:. For example, all photons scattered at an angle of 90 degrees, where the cosine has a value of 0, will undergo a wavelength change of 0. Photons that scatter back at an angle of degrees where the cosine has a value of -1 will undergo a wavelength change of 0.

This is the maximum wavelength change that can occur in a scattering interaction. It is important to recognize the difference between a change in wavelength and a change in energy. Since higher energy photons have shorter wavelengths, a change of say 0. All photons scattered at an angle of 90 degrees will undergo a wavelength change of 0. The change in energy can be found as follows. For a keV photon, the wavelength is 0. A scatter angle of 90 degrees will always increase the wavelength by 0.

Therefore, the wavelength of the scattered photon will be 0. The energy of a photon with this wavelength is 91 keV. Lower energy photons lose a smaller percentage of their energy. The photoelectric interaction captures all photon energy and deposits it within the material, whereas the Compton interaction removes only a portion of the energy, and the remainder continues as scattered radiation.

The combination of the two types of interactions produces the overall attenuation of the x-ray beam.

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We now consider the factors that determine which of the two interactions is most likely to occur in a given situation. The energy at which interactions change from predominantly photoelectric to Compton is a function of the atomic number of the material. The figure below shows this crossover energy for several different materials.

At the lower photon energies, photoelectric interactions are much more predominant than Compton.

A. Neutron Activation

We believe that this technique may be a breakthrough to improve X-ray radiography for medical diagnosis. Currently in the world photon counting detectors and their techniques have been progressing [1]. A CdTe detector [2] is widely used to measure the X-ray spectrum as shown in Fig. This detector has a high detection efficiency which is read by high density and high atomic number substances of cadmium Cd and tellurium Te Figure 3 indicates the concept of a response function; the response function is defined by an obtained spectrum when monoenergetic photons are introduced to the detector.

The effect of insufficient energy absorption is presented in the spectrum response function. The origin of response functions can be understood by considering the interactions between X-rays and the CdTe detector. As shown in Fig. The aim of this study is to evaluate the response function of the CdTe detector from the experiment and simulation.