Compton Scattering and Photon Interactions with Matter

These flashcards help to review key concepts related to Compton scattering and photon interactions with matter, relevant for exam preparation.

Compton scattering

An interaction where an incoming photon strikes an outer shell electron, transferring energy and knocking the electron out of its orbit.

Compton scattered photon

The photon that exits the atom in a different direction after interacting with an electron; it has less energy than the incident photon.

Photon energy relation in Compton scattering

Ei = Es + Eb + Eke, where Ei is the energy of the incident photon, Es is the energy of the scattered photon, Eb is the electron binding energy, and Eke is the kinetic energy of the ejected electron.

Impact of Compton scattering on patient dose

Results in ionization, biological damage, and increases patient dose due to absorbed scattered photons in tissues.

Impact of Compton scattering on occupational dose

Creates scatter that exposes healthcare professionals, being the main source of occupational dose.

Image quality effects of Compton scattering

Decreases image contrast due to the combination of photoelectric effect and transmission, leading to noise in the image.

Effect of patient thickness on Compton scattering

Increased patient thickness results in more matter, leading to more scatter.

Effect of collimation on Compton scattering

Decreased collimation results in more field size and increased scatter, while increased collimation leads to less scatter.

Photoelectric effect

Predominates in lower energies (25–45 keV) and when using high atomic number contrast agents, resulting in a high-contrast image.

Attenuation

Reduction in x-ray beam intensity due to absorption and scatter in matter; more tissue thickness leads to more attenuation.

Factors affecting beam attenuation

Include tissue thickness, tissue density, atomic number, and beam energy.

Differential Absorption

The process by which different tissues absorb varying amounts of radiation, affecting the resultant image clarity.

Characteristic cascade

A sequence of interactions leading to the ejection of an electron and the production of secondary radiation.

Coherent scattering

Occurs at low energy levels (10 keV and less) and does not ionize atoms; it primarily results in minimal patient dose and noise.

Probability of photoelectric interactions

Inversely proportional to the cube of the energy of the beam and increases with higher atomic number.

Relationship between kVp and photon interactions

As kVp increases, the probability of Compton interactions increases while that of photoelectric interactions decreases.

Compton scattering

An interaction between an incoming high-energy photon (typically in the diagnostic x-ray range) and a loosely bound outer-shell electron of an atom. During this interaction, the photon transfers only a part of its energy to the electron, causing the electron to be ejected from its orbit (Compton electron), thus ionizing the atom. The incident photon, now with reduced energy and a longer wavelength, changes its direction of travel and is known as a Compton scattered photon.

Compton scattered photon

This is the original incident photon after it has undergone a Compton scattering event. It has interacted with an outer-shell electron, transferred some of its initial energy to that electron, and subsequently changed its direction of travel. As a result, the Compton scattered photon possesses less energy, a longer wavelength, and a lower frequency compared to the incident photon before the interaction.

Photon energy relation in Compton scattering

The conservation of energy in a Compton scattering event is quantitatively expressed by the equation:Ei = Es + Eb + Eke
Where:

• Ei = the initial energy of the incident photon.
• Es = the energy of the scattered photon after the interaction.
• Eb = the binding energy of the ejected outer-shell electron (which is typically very low and often negligible compared to photon energies in diagnostic radiology).
• Eke = the kinetic energy imparted to the Compton electron as it is ejected from the atom.

Impact of Compton scattering on patient dose

Compton scattering significantly contributes to patient radiation dose. When scattered photons interact with and are subsequently absorbed by other tissues within the patient's body, they deposit their remaining energy, leading to further ionizations and potential biological damage. This indirect absorption of scattered photons adds to the overall radiation burden on the patient.

Impact of Compton scattering on occupational dose

Compton scattering is considered the primary source of occupational radiation dose for healthcare professionals in an imaging environment. The scattered photons travel in various, unpredictable directions, dispersing radiation throughout the imaging room. This diffused radiation necessitates the use of lead aprons, gloves, and other shielding devices for personnel to minimize their exposure.

Image quality effects of Compton scattering

Compton scattered photons originate from the patient and travel randomly in all directions. When these spurious photons reach the image receptor, they carry no useful diagnostic information about the anatomy being imaged. Instead, they produce a generalized graying or fogging effect on the image, acting as a form of noise. This noise effectively reduces the signal-to-noise ratio and consequently degrades image contrast, making it challenging to differentiate subtle tissue variations.

Effect of patient thickness on Compton scattering

As the thickness of the patient increases, there is a greater volume of tissue available for x-ray photons to interact with. This larger amount of matter leads to a higher probability of Compton interactions occurring. Consequently, an increase in patient thickness directly results in a greater amount of scatter radiation being produced and emitted from the patient.

Effect of collimation on Compton scattering

Collimation is the process of restricting the size and shape of the x-ray beam. When collimation is decreased (meaning a larger field size is selected), a greater volume of the patient's tissue is irradiated. This expanded irradiated volume provides more opportunities for Compton interactions, thereby increasing the amount of scatter radiation. Conversely, increasing collimation (reducing field size) limits the irradiated volume, which in turn reduces the number of Compton interactions and thus decreases scatter radiation.

Photoelectric effect

This is an interaction where an incident x-ray photon is completely absorbed by an inner-shell electron of an atom, causing that electron (now called a photoelectron) to be ejected from its orbit. This effect is highly dependent on the energy of the incident photon and the atomic number of the absorbing material. It predominates at lower x-ray energies (typically in the range of 25–45 keV used in diagnostic imaging) and in materials with high atomic numbers (e.g., bone, iodine, barium contrast agents). The complete absorption of photons in certain tissues (e.g., bone) relative to others (e.g., soft tissue) is crucial for generating high-contrast images.

Attenuation

Attenuation refers to the overall reduction in the intensity of an x-ray beam as it passes through matter. This reduction occurs due to two primary processes: absorption (where photons are entirely removed from the beam, as in the photoelectric effect) and scatter (where photons change direction and lose energy, as in Compton scattering). The more matter an x-ray beam traverses, or the denser that matter is, the greater the degree of attenuation the beam will undergo.

Factors affecting beam attenuation

The extent to which an x-ray beam is attenuated is influenced by several key factors:

• Tissue thickness: Thicker tissues present more material for x-ray photons to interact with, leading to greater attenuation.
• Tissue density: Denser tissues contain more atoms per unit volume than less dense tissues, increasing the probability of interactions and thus enhancing attenuation.
• Atomic number (Z): Materials with a higher effective atomic number exhibit increased attenuation, particularly due to a significantly higher probability of photoelectric absorption.
• Beam energy (kVp): The energy of the x-ray beam. Lower energy beams are more readily attenuated (especially by the photoelectric effect), while higher energy beams possess greater penetrability, leading to less attenuation for a given tissue thickness.

Differential Absorption

Differential absorption is the fundamental principle that underlies the formation of an x-ray image. It describes the process by which different tissues within the body absorb varying amounts of incident x-ray radiation based on their unique characteristics (such as atomic number, density, and thickness). This variation in absorption creates distinct differences in the number of photons reaching the image receptor, thereby generating the contrast and structural detail necessary to form a diagnostic image.

Characteristic cascade

When an electron is ejected from an inner shell of an atom (e.g., following a photoelectric interaction), it leaves a vacancy. This unstable state is resolved as an electron from an outer, higher-energy shell drops into the vacant inner shell. To release the excess energy, the atom emits either a characteristic x-ray photon (radiation) or an Auger electron. This process can continue as outer shells fill inner vacancies, creating a 'cascade' of electron transitions and secondary radiation until the atom returns to a stable state.

Coherent scattering (Thomson or Rayleigh scattering)

Coherent scattering is an interaction that occurs at very low x-ray photon energies (typically below 10 keV), where the incident photon interacts with the entire atom rather than a single electron. The atom absorbs the photon's energy and immediately re-emits a photon of identical energy and wavelength in a slightly different direction, without causing any ionization of the atom. While it contributes minimally to patient dose and is generally considered insignificant in diagnostic radiography, it does not produce image noise or useful image information.

Probability of photoelectric interactions

The likelihood of a photoelectric interaction occurring is exquisitely sensitive to both the energy of the x-ray beam and the atomic number of the absorbing material:

• It is inversely proportional to the cube of the energy (E) of the x-ray beam: P_{PE} \propto \frac{1}{E^3}. This means a small increase in beam energy leads to a significant decrease in photoelectric interactions.
• It is directly proportional to the cube of the atomic number (Z) of the absorbing material: P_{PE} \propto Z^3. This implies that materials with higher atomic numbers (e.g., bone, contrast media) are substantially more likely to undergo photoelectric absorption.

Relationship between kVp and photon interactions

As the kilovoltage peak (kVp) of the x-ray beam increases, the average energy of the photons within the beam also increases. This change in beam energy directly influences the predominant type of photon interaction:

• The probability of photoelectric interactions significantly decreases because they are highly energy-dependent (inversely proportional to the cube of the energy).
• The probability of Compton scattering increases relative to the photoelectric effect. At higher energies, photons