4/2003 Rev 2 I.3.4 – slide 1 of 24

Session I.3.4

Part I Review of Fundamentals

Module 3 Interaction of Radiation with Matter

Session 4 Photon Interactions

IAEA Post Graduate Educational CourseRadiation Protection and Safety of Radiation Sources

4/2003 Rev 2 I.3.4 – slide 2 of 24

In this session we will discuss photon interactions including:

Photoelectric effect Compton scattering Pair production

Overview

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Photoelectric Effect

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Photoelectric Effect

-Example: Eincident photon = 80 keV

Ebinding energy = 20 keVEphotoelectron = 60 keV

Ephotoelectron = Eincident photon – Ebinding energy

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Photoelectric Effect

The photoelectric effect is predominant for:

Low energy photons High atomic number “Z” materials

Probability is proportional to: Z4

E3

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Photoelectric Effect

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Compton Scattering

incidentphoton (Eip)

scatteredphoton (Esp)

scatteredelectron (Ese)

loosely boundelectron (Eie)

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Compton Scattering

Eie = moc2 Ese = mc2

Eip =hcip

E*sp =hcsp

Conservation of Energy: hcip

+ moc2 = hcsp

+ mc2

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Compton Scattering

Pse = mv

Pip = hip

P*sp = hsp

Conservationof Momentum:

hip

= hsp

cos + mv cos

0 = hsp

sin + mv sin

horizontal

vertical

Pie = 0

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Compton Scattering

(1 - cos) = sp - ip =h

moc

Solving both the energy and momentum equations yields:

The energy transferred to the scattered electron is:

Ese = Eip – Esp = -hcip

hcsp

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Compton Scattering

Substituting E =hc

into the momentum equations gives the energy of the scattered photon:

Esp =1 + (1 - cos)

Eip

moc2

Eip

moc2 = rest mass energy of the electron = 0.511 MeV

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Compton Scattering

Esp =1 + (1 - cos)

Eip

moc2

Eip For simplicity let

Eip

moc2= f

Esp =1 + f (1 - cos)

Eip

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Compton Scattering

When = 90º, Esp = the energy of the scattered photon is reduced

When = 180º, Esp = the energy of the scattered photon is minimum

When = 0º, Esp = Eip there is no interaction

Eip

(1+f)

Eip

(1+2f)

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Compton Scattering

Example 1: A low energy photon (10 keV) scattered by 90º and 180º

f = 10 keV/511 keV = 0.02; cos 90º = 0; cos 180º = -1

Esp =1 + 0.02 (1 - 0)

10 keV= 10/1.02 = 9.8 keV

Esp =1 + 0.02 (1 - -1)

10 keV= 10/1.04 = 9.6 keV

the scattered electron

receives only 2-4% of the

incident energy

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Compton Scattering

Example 2: A high energy photon (1000 keV) scattered by 90º and 180º

f = 1000 keV/511 keV = 1.96; cos 90º = 0; cos 180º = -1

Esp =1 + 1.96 (1 - 0)

1000 keV= 1000/2.96 = 340 keV

Esp =1 + 1.96 (1 - -1)

1000 keV= 1000/4.92 = 200 keV

the scattered electron receives

about 66-80% of the incident

energy

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Compton Scattering

Example 3: What is the maximum energy of a photon scattered through 90º and 180º for a very high energy incident photon

If f = Eip/511 keV >> 1 then (1 + f) f

1 + f

Eip

f

EipEsp = = 511 keV= =

Eip

Eip

511

(90º)

(180º)1 + 2f

Eip

2f

EipEsp = = = = = 255 keV

511

2

Eip

2Eip

511

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Compton Scattering

E =hc

h = 6.62 x 10-34 J-secc = 3 x 108 m/sec

E =(6.62 x 10-34 J-sec)(3 x 108 m/sec)

(1.6 x 10-19 J/eV)(103 eV/kev)

E = 1.24 x 10-9 keV-m (m)

The energy of a photon relative to its wavelength:

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Pair Production

Photon converted into two particles

(energy into mass)

electron (-)positron (+)

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Pair Production

The rest mass energy of a positive or negative electron is 0.511 MeV

To create these two particles requires a minimum energy of 2 x 0.511 MeV = 1.02 MeV

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Pair Production

A positron cannot exist at rest. It combines with an electron. The two particles annihilate each other converting mass back into energy.

Since the rest mass energy of each particle is 0.511 MeV, the two photons created must each possess an energy of 0.511 MeV. Two photons must be created, traveling in opposite directions, to satisfy the Law of Conservation of Momentum.

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Photon Energy (MeV)

PairProduction

Compton

Photoelectric

Combined

Pro

bab

ility

WATER

Photon Interactions

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Photon Energy (MeV)Pair

Production

Compton

Photoelectric

Combined

Pro

bab

ility

LEAD

K shellBindingEnergy

Photon Interactions

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Summary

We have discussed Photon Interactions including:

Photoelectric Effect low energy photons photon electron

Compton Scattering medium energy photons photon electron + new photon

Pair Production photon ( 1.02 MeV) photon e- + e+ 2 photons (0.511 MeV each)

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Where to Get More Information

Cember, H., Johnson, T. E., Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2008)

Martin, A., Harbison, S. A., Beach, K., Cole, P., An Introduction to Radiation Protection, 6th Edition, Hodder Arnold, London (2012)

Jelley, N. A., Fundamentals of Nuclear Physics, Cambridge University Press, Cambridge (1990)

Firestone, R.B., Baglin, C.M., Frank-Chu, S.Y., Eds., Table of Isotopes (8th Edition, 1999 update), Wiley, New York (1999)