Chapter 12 Lecture Notes

X-Ray Interactions

Five X-Ray Interactions with Matter

There are 5 interactions with matter that must be learned in this class. The five interactions are:
1. Coherent Scattering
2. Photodisintegration
3. Pair Production
4. Compton Effect or scattering
5. Photoelectric Effect

 

thomson

Coherent Scattering - a term sometimes used for Rayleigh scattering and Thomson scattering. They are both examples of coherent scattering, in which the incident photon undergoes a change in direction without a change in wavelength.

Notice in this diagram that the direction of the photon is changed but the wavelength remains the same.

coherent

This is another diagram showing that the wavelength does not change.

coherent

**Coherent scattering contributes slightly to film fog.

 

 

photo disintegration

Photodisintegration - collision of a high energy photon with an atomic nucleus. The photon is completely absorbed in the process, and a neutron, proton, or alpha particle is ejected from the excited nucleus.

This diagram shows an x-ray interacting with the nucleus of an atom and expelling a piece of the nucleus.

photo disintegration

photo disintegration

**Need at least 10 MeV for photodisintegration. This is more energy than a normal x-ray.

 

pair production

Pair Production - the process in which a high-energy photon is completely transformed into an electron and a positron. Thus, this is a process whereby energy is transformed into matter. It occurs only in the vicinity of atoms which act as a sort of "catalyst". Since according to Einstein's theory of relativity, the energy (E) and the mass (m) are proportional to each other with the constant of proportionality being the square of the velocity of light (c),


emc

and the resting masses of electron and positron are 511 keV each, the minimum photon energy required for pair production to occur is 1.022 MeV. The inverse reaction to pair production is the annihilation reaction. This is also more energy than normal x-ray.

Pair Production applet

In this applet, first click on the button by the pair production in the lower right hand corner. Then click on the green arrow to start the applet. Notice that the photon comes in from the left and at some point splits into two particles, an electron and a positron. Then the positron annihilates an electron and ionizes the atom.

 

compton

Compton Effect - During Compton scattering, a photon impinges on an electron in matter, and in this process transfers part of its energy to it. The excited electron is termed a Compton electron and is ejected or moved into an excited atomic state, while due to the law of conservation of energy the photon energy is reduced.

This diagram shows a photon interacting with an electron, ejecting it and giving some of its energy to the electron. The photon is scattered by an angle, luckily we do not have to calculate the angle, and the wavelength is changed.

compton

compton

Compton Effect applet

This is the same applet as before, just click on the Compton Effect.

Compton Effect applet 2

This one is on the bottom of the page. It is a little more technical than the first one. If you follow the instructions you will see some interesting information.

 

Compton Effect - The math of the Compton Effect.

compton

where ei = energy of the incident x-ray, es = energy of the scattered x-ray, eb = electron binding energy, and eke = kinetic energy of the electron.

Example 1

What is the energy of the scattered x-ray under Compton scattering if it originally had 45 keV and the binding energy of the Compton electron is 15 keV and its kinetic energy is 5 keV?

First we use the formula above and plug in the values.

example 1

Then solve for the energy of the scattered electron.

example 2

example 1

 

Example 2

What was the energy of the original x-ray if the scattered x-ray has energy of 19 keV and the binding energy of the N-shell tungsten electron is 0.6 keV and the Compton electron has kinetic energy of 27.2 keV?

Plug in the values in the formula.

example 2

Simplify.

example 2

 

Example 3

3. What is the kinetic energy of the Compton electron, it was an M-shell electron in tungsten and the energy of the scattered x-ray is 2.9 keV and the original x-ray had an energy of 7.2 keV?

Plug in the values. Remember that an M-Shell electron has a binding energy of 3 keV.

example 3

Solve for the kinetic energy of the electron.

example 3

example 3

 

This is a diagram showing Coherent and Compton scattering. It shows the possible scattering angles and the probability of when the scattering will occur.

compton scatter

Backscatter radiation - Some of the radiation after entering the tissue will scatter back toward the surface. This portion of the radiation is called backscatter.

The probablility of the Compton effect is inversely proportional to energy compton and independent of atomic number.

compton

 

Compton effect reduces the contrast in an x-ray image.

Features of Compton Scattering
Most likely to occur

a) with outer-shell electrons
b) with loosely bound electrons

As x-ray energy increases

a) Increased penetration through tissue without interaction
b) Increased Compton scattering relative to photoelectric effect

As atomic number of absorber increases No effect on Compton scattering
As mass density of absorber increases Proportional increase in Compton scattering

 

photoelectric

Photoelectric Effect - effect discovered by Einstein (for which he received the Nobel prize in 1921) in which a photon transfers its entire energy to an electron in the material on which it impinges. The electron thereby acquires enough energy either to free itself from the material to which it is bound or to be elevated into the conduction band of a semiconductor or insulator (solid).

This diagram shows a photon interacting with an electron and giving all of its energy to the electron. The electron is then ejected from the atom.

photoelectric

This series of diagrams shows the photoelectric effect. Notice that the hole will then be filled by electrons and give off characteristic x-rays if filled correctly.

photoelectric

photoelectric

Photoelectric effect applet

This applet is the same one as before, just select the photoelectric effect.

 

Photoelectric Effect - The Math of the Photoelectric Effect.

photoelectric

where ei = energy of the incident x-ray, eb = electron binding energy, and eke = kinetic energy of the electron.

Example 4

If the binding energy for sodium is 2.28 eV and the energy of the x-ray is 4.14 eV what is the kinetic energy of the photoelectron?

Using the equation above plug in the values.

example 4

Solve for the kinetic energy.

example 4

 

Example 5

If the kinetic energy of the photoelectron is 1 eV and the frequency of the x-ray is ex 2 what is the binding energy of cesium?

First the energy of the x-ray photon needs to be calculated. This is done by using Planck's Equation.

example 5

example 5

example 5

This is the energy of the x-ray photon. Now use the equation to solve for the binding energy.

example

Solve for the binding energy.

example 5

 

Example 6

If the frequency of an x-ray is ex 2 and the binding energy of lithium is 2.3 eV what is the kinetic energy of the photoelectron?

First the energy of the x-ray photon needs to be calculated. This is done by using Planck's Equation.

example 5

example 5

example 5

Next use the eqation to find the kinetic energy.

example 6

Solve for the kinetic energy.

example 6

 

 

The probability of the photoelectric effect is inversely proportional to the cube of the x-ray energy photoelectric.

probability

The probability of photoelectric effect is directly proportional to the cube of the atomic number of the absorbing material cubed.

Effective Atomic Numbers
Types of Substance
Effective Atomic Number
Human Tissue  
Fat
6.3
Soft Tissue
7.4
Lung
7.4
Bone
13.8
Contrast Material
Air
7.6
Iodine
53
Barium
56
Other
Concrete
17
Molybdenum
42
Tungsten
74
Lead
82

 

Features of Photoelectric Effect
Most likely to occur a) With inner-shell electrons
b) With tightly bound electrons
c) When x-ray energy is just higher than electron-binding energy
As x-ray energy increases

a) Increased penetration through tissue without interaction
b) Less photoelectric effect relative to Compton effect
c) Reduced absolute photoelectric effect

As atomic number of absorber increases Increases proportionately with the cube of the atomic number cubed
As mass density of absorber increases Proportional increase in photoelectric absorption

 

Differential Absorption

Differential Absorption occurs because of Compton scattering, photoelectric effect, and x-rays transmitted through the patient.

scatterin

scattering

 

Radiopaque - or opaque, the relative capacity of matter to obstruct the transmission of radiant energy. When x-rays are obstructed the film is light, for example from bone.

Radiolucent - or nonopaque, being permeable to radiation or penetrable by X-rays. The opposite term is radiopaque. When x-rays are not obstructed the film is dark.

The difference between the radiopaque and the radiolucent areas of the body give the contrast or differential absorption.

Differential absorption increases as the kVp is reduced.

 

Dependence on Atomic Number

probability

How much more likely is an x-ray to interact with a lung than fat?

problem 1

 

 

Dependence on Mass Density

Mass density is the mass per unit volume of a substance.

 

The interaction between x-rays and tissue is proportional to the mass density of the tissue.

Mass Density of Materials in Radiology
Substance
Mass Density mass density
Human Tissue  
Lung
320
Fat
910
Soft tissue, muscle
1000
Bone
1850
Contrast Material
Air
1.3
Barium
3500
Iodine
4930

Other

Calcium
1550
Concrete
2350
Molybdenum
10,200
Lead
11,350
Rhenium
12,500
Tungsten
19,300

 

Characteristics of Differential Absorption
As x-ray energy increases a) Fewer Compton interactions
b) Many fewer photoelectric interactions
c) More transmission through tissue
As tissue atomic number increases a) No change in Compton interactions
b) Many more photoelectric interactions
c) Less x-ray transmission
As tissue mass density increases a) Proportional increase in Compton interactions
b) Proportional increase in photoelectric interaction
c) Proportional reduction in x-ray transmission

 

Contrast Examination

Barium and iodine compounds are use as contrast agents to enhance the contrast on a radiograph.

 

Exponential Attenuation

Attenuation - process by which radiation loses power as it travels through matter and interacts with it. Beam attenuation is the basis of the contrast observed in all X-ray based imaging methods.

attenuation