Interaction of Photons W

Matte

r

7/5/2011
General Stuff
Objectives

• To review three principal interactions 

photons with matter.

• To examine the factors affecting the 

probability of photon interactions. 

• To introduce the linear and mass 

attenuation coefficients as useful measures of the probability of intera
Introduction

• Understanding how radiation interac

matter is essential to understanding

– How instruments detect radiation– How dose is delivered to tissue– How to design an effective shield
Properties of Photons

• A photon is a “packet” of electromag

energy.

• It has no mass, no charge, and trave

straight line at the speed of light.

Properties of Photons (con

This discussion is limited to photons enough energy to ionize matter: 

• X-rays: characteristic x-rays

bremsstrahlung

• gamma rays • annihilation radiation (511 keV)
Photon Interactions

• Photons interact differently in matte

charged particles because photons no electrical charge.

• In contrast to charged particles, ph

do not continuously lose energy whthey travel through matter.
Photon Interactions (cont

• When photons interact, they transfe

energy to charged particles (usuallelectrons) and the charged particle

i th i i d

give up th

eir energy via secon

dary 

interactions (mostly ionization).

• The interaction of photons with ma

probabilistic, while the interaction ocharged particles is certain.
+++++

------- alpha

Beta

-+

Possible Gamma

Interactions 
Gamma 

e

-
Gamma ?
Photon Interactions (cont

• The probability of a photon interactin

depends upon:

– The photon energy

– The atomic number and density of t

material (electron density of the absmatter).
Photon Interactions (cont

• The three principal types of photon 

interactions are:

Ph t l t i ff t

– Ph

o

toelec

t

ric effec

t

– Compton scattering 

(incoherent scattering)

– Pair production
Photon Interactions (cont

• There are a number of less important 

mechanisms by which photons interact matter. The most important of the unimphoton interactions are:

– Rayleigh scattering (coherent sca– Thomson scattering (coherent sca– Photonuclear reactions
Photoelectric Interaction
• In the photoelectric (PE) interaction, the p

absorbed by an inner shell (e.g., K shell) of an atom.

Photoelectric Interactio

• All the photon energy is transferred to the 

electron so that the photon disappears.

• The electron is ejected from the atom. Th

leaves a vacancy in the shell that the elecoriginally occupied.
Photoelectric Interactio

• Some of the 

photon’s energy is used to overcome 

the binding energythe binding energy

of the electron 

• The rest of its 

energy is given to the electron as kinetic energy

e

-

e

-

PE
Photoelectric Interaction

• The vacancy created in the electro

shell is then filled by an electron fafrom a hi

gher energy shellg gy

• When this happens, either a 

characteristic x-ray or an auger eleis emitted
e

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e- e- 

e
e

e- e- 

e
Characterist

x-ray

e

-

e

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e

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e

-
Photoelectric Interaction

• PE interactions are desirable in shi

for photons since the photons are com

pletel

y absorbed. 

p y

• On the other hand, PE interactions 

not desirable from the standpoint oabsorbed dose to human tissue.
Photoelectric Interaction

• The PE interaction is most probable 

– Low energy photons (as long as 

Low energy photons (as long as 

photon energy exceeds the electbinding energy)

– High atomic number and high de

materials (i.e., high electron dens
Photoelectric Interaction

• Lead is widely used for shielding gamma 

and x-rays because it has a high atomic n(Z = 82) and it is inexpensive.

• Tungsten has a lower atomic number (Z 

but is a better shield because it has a muhigher density (18-19 g/cm

3) than lead (1

• Uranium can be an even better shield. Its 

number is 92 and its density is 18 g/cm

3
Compton Scattering
Compton Scattering

• In Compton scattering, a photon transfe

portion of its energy to a loosely bound shell electron of an atom (the binding en

f th l t i id d li ibl )

o

f the elec

tron is considere

d negli

gibl

e

)

• The photon loses energy and changes 

direction. This is known as incoherent scattering.
E

(’

E

(

2

e

-

e

-

e

-

e

-
• The following equation is used to calcul

energy of the scattered photon (E’

(

)

Compton Scattering
• The following equation is then used to cal

the energy of the scattered electron (E

e

)

Compton Scattering
• The division of energy between the electr

scattered photon depends on the angle o(

2

)

Compton Scattering

• The photon loses the least amount of its 

when 

2 is small

• The photon loses the largest amount of it

energy when 

2 is 180 degrees
• For example, lets calculate the en

the scattered photon (E’

() when a 

photon 

(

E

(

) scatters at an an

gle of

Compton Scattering

p

(

() g

– 10 o – 180 o 
E(’ (?)

E( (1 MeV)

e- e- ee-
Compton Scattering

E = 1 MeV, and 2 = 10o and 180o 
10 Degree Scattering Angle
180 Degree Scattering Angle
Bonus calculation! We will now calculat

energy of 2 MeV photons scattered at 1
• In most situations, the energy of ga

rays scattered at 180 o is close to 2keV.

Compton Scattering

• As the energy of the original photo

decrease, the energy of the scatterphotons decrease.
• Compton scattering occurs at all ph

energies and in all materials.

Compton Scattering

• The potential for Compton scatterin

always present. 

• It is usually the most probable type 

interaction
• The photons are scattered in all 

directions by the scattering object. 

Compton Scattering

• The more energetic the incident ph

the more forward the scatter (smal

• Lower energy photons are more lik

scatter at an angle of 90o or higher
– The photon loses the greatest am

of energy when 

2 = 180o.

Compton Scattering

– The scattered electron has the 

greatest amount of energy when 180o.
e

-

e

-

e

-

e

e

-
e

-

E (1 MeV)

e

-

e

-

e

e

-
e

E (1 MeV)e- e- 

e e-
180 degrees

E’ (0.2MeV) (

ee- 

e-
E’

E’ (0.2MeV) (

e

-

e

-

e

-
e

-

e

-

e

-
• In some radiation safety application

exposure to Compton scattered phcan be a si

gnificant source of ex

po

Compton Scattering

g p

for example, to medical personnel present during radiological procedu
• In most applications Compton scattering 

undesirable, e.g.,

– Gamma spectroscopy

Compton Scattering

Gamma spectroscopy

– Diagnostic x-ray imaging

• However, the absorbed dose to a tumor 

photons in radiation therapy is actually dby the Compton scattered electrons.
Pair Production
Pair Production

• In pair production, a photon interac

with the electric field of the nucleus an atom.

• The photon completely disappears 

an electron and a positron are produced.
Pair Production

e

-

• Since the electron and positron each have 

energy equivalence of 511 keV, the incomphoton must have an energy of at least 10for pair production to take place. 

nucleus

PP

e

+
• Any additional photon energy above 1022 

given to the positron and the electron as kenergy. 

• The kinetic energy of the electron and the 

t il th

Pair Production

are no

t necessarily the same.

• PP is most likely to occur with relatively h

photon energies and high atomic number materials (larger nuclei).
• The electron and positron will give up thei

energy via ionization, excitation and/or bremsstrahlung.

• Ultimately the positron will annihilate itse

Pair Production

Ultimately, the positron will annihilate itse

electron, most likely after it has given up akinetic energy. The result is the productio511 keV annihilation photons.

• If the positron comes to rest before its ann

(the most probable case), the two photons emitted 180 degrees from each other.
nucleus
nucleus
nucleus
e

nucleus e+
nucleus
e+

eInnocent bystander
e+

eInnocent bystander
e+

eInnocent bystander
511 keV 511 keV

511 keV 511 keV
• In shielding, spectroscopy, or dosim

applications, the two 511 keV photocreated after 

pair 

production must 

Pair Production

p p

always be considered.
• A fanciful thought: The 

positron can be thought of as the electron moving 

backward in time!

+

Pair Production

backward in time!

e

e

+

TIME
The Most Important of t

Unimportant Photon 

Interactions with Matte
• Raleigh scattering is a type of coherent s

whereas Compton scattering is incoheren

• With coherent scattering, the photon chan

Raleigh Scattering

direction but does not lose energy. Its wais unaffected.

• Because it can be explained in terms of a 

particle interaction, it is sometimes referre“classical scattering.” The photon is the wthe electron is the particle.
• The photon is viewed as electric and mag

waves oscillating in two planes at right aneach other. The intersection of the two pladefined by the trajectory of the photon. 

Raleigh Scattering

Pho

Traje

Magnetic vector of 

electromagnetic 

wave

Electric vector of 

electromagnetic 

wave
• The electric field of the passing photon causes t

electrons of an atom to oscillate. These vibrating emit their own electromagnetic radiation and retoriginal undisturbed state. The electromagnetic of the atom’s electrons to combine to produce a (electromagnetic wave) that leaves in a direction 

Raleigh Scattering

(electromagnetic wave) that leaves in a direction 

from that of the incident photon.

• Raleigh scattering is most important when the p

energy is low and the atomic number is high. In case, the binding energy of the outer electrons icompared to the photon energy - this limits the of Compton scattering.
• In the case of lead, Raleigh scattering can be m

probable than Compton scattering at energies ukeV or so. In water, this is true up to about 10 kthese low energies, the photoelectric effect is faprobable than either type of scattering.

Raleigh Scattering

• The scattering angle is quite small. • The net effect of coherent scattering (in shieldin

imaging, etc.) is essentially the same as Comptoscattering at shallow angles where little energy ithe photon.
• Thomson scattering is another type of coherent 

It is of even less interest than Raleigh scattering

• In Thomson scattering, only a single “free” elect

involved rather than all the electrons of the atom 

the case with Raleigh scattering

Thomson Scattering

the case with Raleigh scattering.

• Once again, the electromagnetic wave of the ph

causes the vibration of the electron. Note, this is case of “excitation” where the electron is moved higher energy level.

• The original photon disappears and a new photo

same energy is emitted in a different direction.
• In photonuclear reactions, the photon is absorbe

nucleus of the atom and a nuclear particle (neutproton, alpha) is ejected. Photon induced fission an extreme example. Of these, photo-neutron reare the most common.

Photonuclear Reactions

• For these reactions to occur, the photon energy 

exceed the binding energy of the particle. 

• Usually this threshold energy is on the order of 7 

MeV. There are exceptions however. 
Probability of Interactio
Probability of Interaction

• Charged particles (e.g., alphas and beta

continuously interact with the material thtravel through. Photons occasionally int

• We will now consider the factors that aff

probability of photon interactions (photoeffect, compton scattering, pair producti
• The two most important factors 

influencing the probability of a givetype of interaction are:

Probability of Interaction

- the energy of the photon (E) - the atomic number (Z) and densit

material (i.e., the electron density
• The next slide shows the probability 

interaction as a function of the photoenergy in a low-Z material 

(water

).

Probability of Interaction

gy ( )

• Note that the probability of the 

photoelectric effect decreases dramas the the photon energy increases.

• The next slide shows the probabilit

interaction as a function of the phoenergy for a hi

gh-Z material 

(lead

).

Probability of Interaction

gy g ( )

• Again, look at the probability of the 

photoelectric effect.

• In general, the curves for water and lead 

the same shape: as the photon energy increases, the probability of a PE intera

d

Probability of Interaction

ecreases.

• But, on the curve for lead, there are thre

sudden increases (or decreases dependhow you look at it) in the probability of a interaction.
• The “spikes” or sudden increases in the 

probability of PE interactions are called thand M edges.

• Goin

g from lower to hi

gher ener

gies, ther

Probability of Interaction

g g g,

sudden increases in the probability of intebecause the photon “gains” enough enereject the M, L and K shell electrons, resp

• The electron binding energies are approx

keV (M shell), 15 keV (L shell) and 88 keV shell).
K edge

L edge

M edge
• It is sometimes said that an element is transpare

own radiation. This means is that a material is smore effective at absorbing photon energies belabove the energies of its own characteristic x-ra

• For example the energy of lead’s K

x

-ray is 75 

Probability of Interaction

For example, the energy of lead s

K

"

x ray is 75 

indicated in the previous figure, absorption by leincreases as the photon energy decreases below At the same time, absorption increases when thenergy exceeds 88 keV (at the K-edge).

• This effect of increasing energy is somewhat sh

Absorption is greater at 75 keV than at energies 120 keV or so. 

• The previous slide shows how the photo

effect is dominant at low energies in higmaterials.

Probability of Interaction

• Compton scattering occurs at all energie

materials, but is the dominant interactiomedium energy range.

• Pair production only occurs at energies 

1.022 MeV. Pair production becomes mprobable as the photon energy and the number of the material increase.
• There are two common quantities u

to describe the probabilities of thesinteractions:

Probability of Interaction

linear attenuation coefficient (

:).

mass attenuation coefficient (

:

/

D
• The linear attenuation coefficient (

:) is t

probability of an interaction per linear ditraveled by the photon.

Probability of Interaction

• It is actually the sum of the probabilities 

photoelectric effect (

J), compton scatter

and pair production (

6

)

: = 

J + 

F + 

6
• The greater the number of atoms 

encountered per centimeter travelelar

ger the value of 

: and the more 

Probability of Interaction

g

probable a given type of interaction

• The units of 

: are cm-1. 
• : is the sum of the individual attenuation 

coefficients for the photoelectric effect, Cscattering, and pair production. 

Probability of Interaction

• The value of : depends on photon ener

type and the atomic number (and densitmaterial.

• Values of : can be hard to find in the lite
• A more common quantity for expre

the probability of an interaction is thmass attenuation coefficient (

:

/

D

)

Probability of Interaction

• It is equal to the linear attenuation 

coefficient (

:), divided by the densi

the material (

D). The units of 

:

/

D ar

cm

2/g.
• The mass attenuation coefficient can 

thought of as the fraction of the photointeracting per unit density thickness

Probability of Interaction

• Values of 

:

/

D are found in:

PTP’s Radiological Health Handb(beginning on page 90)http://physics.nist.gov/PhysRefDaayMassCoef/cover.html


• Should it be necessary to convert f

:

/

D to 

:, the densities of common 

materials can found in PTP’s 

R di l i l H lth H db k

Probability of Interaction

R

adi

ological Health

Handboo

k on p

5 and the RHH pg. 65, or the HHPRpp. 5-50—5-51.
• Photoelectric effect

The probability varies approximately w

Probability of Interaction

The probability varies approximately w
• Compton Scattering

The probability per atom varies 

Probability of Interaction

approximately with Z The probability varies approximatewith 1/E
• Pair Production

The probability per atom varies 

2

Probability of Interaction

approximately with ZThe probability varies approximatewith the natural log of E
• A related quantity is the mass energy 

absorption coefficient (

:en

/

D). The un

the same as those of the mass attenu

ffi i t (

2/ )

Probability of Interaction

coeffi

cien

t

(cm

2

/

g

).

• The mass energy absorption coefficie

be thought of as the fraction of the phenergy that is absorbed per unit densthickness
• The mass energy absorption coefficie

(

:en

/

D) is smaller than the mass atten

coefficient 

(

:

/

D

)

Probability of Interaction

(

:

D

)

• Values of 

:en

/

D are found in:

PTP’s Radiological Health Handbook 

(beginning on page 90)

http://physics.nist.gov/PhysRefData/XrayMassCoef/cover.html
• The mass attenuation coefficient (

:

/

D 

normally used in shielding calculation

Probability of Interaction

• The mass energy absorption coefficie

(

:en

/

D) is normally used in dosimetry 

calculations
No interacti

Photoelectric E

511 keV

Compton Scatt

Pair Producti