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PE and Compton Interactions, Complete absorption of the x-ray photon -…
PE and Compton Interactions
Photoelectric Effect
Incident (incoming) x-ray photon interacts with an
INNER SHELL
electron in an atom
All energy is transferred to the electron in the atom
An electron (now with higher energy) is ejected from the atom
Ejected Electron
Free Electron
Atom is now missing an electron = Ionized
Characteristic Cascade
An outer shell electron drops down to fill the hole in the inner shell producing secondary/characteristic radiation
Secondary Radiation
originates from irradiated matter outside of the x-ray tube
Most photons will be emitted as UV light, not x-rays
Low Z# in tissue
Low energy secondary radiation
Higher Z# with contrast agents
Higher energy secondary radiation
Example
A carbon atom in the patient’s body is ionized. What is the energy level of the characteristic photon emitted as an electron falls from the L-shell to the K-shell?
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Originates from irradiated matter outside of the x-ray tube.
Characteristic Radiation
The difference in binding energies between the two electron shells is emitted as an x-ray photon
When an electron falls from a higher orbit to fill the orbital vacancy, kinetic energy is lost and must be emitted as electromagnetic radiation
Photoelectron
Photoelectron velocity depends on energy transferred from the incident photon to the photoelectron
Ei = Eb + Eke
Ei = energy of the incident x-ray photon
Eb = binding energy of the electron
Eke = kinetic energy of the photoelectron
Determines photoelectron energy
When a PE interaction occurs in the body, most of the energy of the incident photon (Ei ) is transferred to the photoelectron as kinetic energy (Eke)
Examples
During an IVU exam, a 30 keV x-ray photon undergoes a PE interaction with an L shell electron in an atom of iodine (contrast).
What is the kinetic energy of the photoelectron speeding away from the atom?
Eke = Ei – Eb
X = 30 keV – 5 keV
X = 25 keV
The ejected photoelectron will have 25 keV of kinetic energy
Conditions
Type 1: Incident photon energy must be greater than (or equal to) the binding energy of the inner shell electron
Type 2: Incident photon energy and inner shell electron binding energy are similar
Mathematically described as an “inverse cubed relationship”
PE = 1/(Photon Energy)3
There is a significant decrease in the percentage of PE that occur at high kVp vs. low kVp
Doubling photon energy decreases the likelihood of PE by a factor of 8
As kVp increases:
The overall number of photon interactions decreases
More transmission occurs
Of the interactions that do occur:
The percentage of scatter increases
The percentage of PE interactions decreases
Type 3: More likely to occur in atoms with a high atomic number (Z#)
Higher atomic number (Z#) means more protons (more electrons)
Atoms with a higher atomic number have a higher electron binding energy (Eb)
PE is more likely to occur when an electron is tightly bound in its orbit
Mathematically described as a “direct cubed relationship”
PE = (Z)^3
Doubling the atomic number increases the chance of PE absorption interaction by factor of 8
Interacts with INNER SHELL
The average kV is approximately 1/3 of the kVp
Compton Scatter
Increased kVp
Increased % of Compton Scatter
Increasing kVp will reduce the total number of interactions
But a higher percentage of the interactions that occur will be Compton vs. PE
And the (higher energy) scatter produced is more likely to reach the IR
Increased Tissue Volume
Increased amount Compton scatter
The patient is the source of Compton scatter
Increasing the volume of tissue (area or thickness) will increase scatter production
Increased Atomic Number (Z#)
No effect on Compton scatter
Scatter is NOT related to atomic number, because Compton interactions occur with electrons in the outer shell
However, tissues with a high atomic numbers have more PE interactions
Therefore, increasing atomic number will decrease the percentage of the interactions that are Compton scatter
Same number of Compton interactions occur
But more PE interactions (more total interactions)
Interacts with OUTER SHELL
Ejects an electron
The incident photon continues on its way with less energy and in a different direction as a scattered photon
The scattered photon will travel until it causes additional interactions
The subsequent interactions can occur in the patient’s body or exit the body to interact with the IR, other people, or things in the room
An ion pair is formed
Compton/Recoil electron
Ei = Es + Eb + Eke
Ei = Energy of incident photon
Es = Energy of Compton scatter photon
Eb=Electron binding energy
Eke= Kinetic energy given to recoil electron
Incident photon energy (Ei) is distributed (not evenly divided) between the recoil electron (Eke) and the scattered photon (Es)
Examples
During a chest x-ray, a 40 keV x-ray photon undergoes a Compton interaction with an L shell electron within an atom of calcium
The recoil electron speeds away from the atom with 5keV of kinetic energy
What is the energy of the Compton scattered photon?
Es = Ei - Eb - Eke
Es = 40 keV - 0.438 keV - 5 keV
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A 30-keV x-ray ionizes an atom of barium by ejecting an O-shell electron with 12 keV of kinetic energy. What is the energy of the scattered x-ray?
Es = Ei - Eb - Eke (Rearranged formula)
Es = 30 keV - 0.03 keV - 12 keV
Scattered Photon energy is 17.97 keV
Higher Energy Incident Photon
Higher energy scattered photon
This all means that higher kVp not only creates a higher percentage of scatter, but the scatter produced is also more likely to reach the IR
Scattered photon travels in a more forward direction
Most scatter travels in a forward direction (toward the IR)
Especially true as incident photon energy increases (inner ring on image)
Higher keV photons, scatter in a more-forward direction
Scattered photons can be deflected at any angle
The scatter angle is determined by how much energy the incident photon gives up
Greater energy lost = Greater angle of deflection
Higher kVp produces scatter photons that continue traveling toward the IR
Deflection of 0°
No energy transferred to recoil electron (Photon is moving in the same direction)
Deflection of 180°
Transfers the most energy to recoil electron, less energy is retained with scattered photon
Lower frequency and increased wavelength of scattered photon
Backscatter
Scattered photons that are deflected back to the source
occurs when scattered x-rays are emitted at an angle of deflection that causes them to travel toward the tube (more than 90° backwards)
Backscatter Artifact
Outline of DR system electronics imposed on high-exposure image of large patients
Compton interactions are responsible for most of the scatter radiation in the diagnostic range
Increases noise (lower SNR)
Decreases radiographic contrast
No change to spatial resolution (that’s a geometric factor)
Things to Remember
Increased Tissue Volume
More matter more scatter
Increased amount of Compton Scatter
Increased amount of Photoelectric (PE) interactions
Increased Atomic Number (Z#)
No effect on Compton Scatter interactions as a total
Increased Photoelectric (PE) Interactions
Increased kVp
Fewer Total Number of Interactions
Increased % of Compton Scatter
Decreased % of Photoelectric Interactions
Compton = Outer-shell
"Recoil Electron"
Photoelectric = Inner Shell
"Photoelectron"
Formula's
Ei = Es + Eb + Eke
Es=Energy of Compton scatter photon
Eb=Electron binding energy
Eke= Kinetic energy given to recoil electron
Ei =Energy of incident photon
Direct Cubed Relationship
PE = (Z)^3
PE interaction increases when Z# increases
“Inverse Cubed Relationship”
PE = 1/(Photon Energy)^3
Photon energy increase PE decreases
Deflection of 0°
No energy transferred to recoil electron (Photon is moving in the same direction)
Deflection of 180°
Lower frequency and increased wavelength of scattered photon
Transfers the most energy to recoil electron, less energy is retained with scattered photon
Complete absorption of the x-ray photon
Photoelectric Interaction
Photoelectric Absorption
