Interactions of EM Radiation with Matter

Manos PapadopoulosNuclear Medicine DepartmentCastle Hill HospitalHull & East Yorkshire Hospitals NHS Trust

ELECTROMAGNETIC RADIATION

Light is electromagnetic radiation

a form of energy

Has both electric and magnetic components

Characterised by

wavelength (λ)

frequency (ν)

WAVE CHARACTERISTICS

Wavelength (λ): The distance between two consecutive peaks in the wave

WAVE CHARACTERISTICS

Frequency (ν): The number of waves (or cycles) per unit time

WAVE CHARACTERISTICS

The product of wavelength (λ) and frequency (ν) is constant

PARTICLE CHARACTERISTICS

Particle-like properties

Photons or quanta

Ε = hν = hc/λ

where h is Planck’s constant

For a typical diagnostic X-ray

λ = 2·10-11 m photon energy is 62 keV

ELECTROMAGNETIC SPECTRUM

ELECTROMAGNETIC SPECTRUM

Name (m) (Hz) Interesting Facts

Radio/TV 10-1 – 10-4 109 – 104 Low “”are reflected from earth’s atmosphere

Microwaves 10-3 – 10-1 1011 – 109 Cellular phones, Radar

Infrared 10-7 – 10-3 1014 – 109 “Heat” radiation

Visible 4·10-7 – 7·10-7 7.5·1014 – 4.3·1014 ~ 1/40 of total spectrum

Ultraviolet 10-8 – 7x10-7 1016 – 1014 “Burning rays” of sun

X-rays 10-11 – 10-8 1019 – 1016 tissue damage, ionisation

Gamma rays <10-11 >1019 tissue damage, ionisation

GENERAL PROPERTIES

Intensity (I) of a beam of radiation

rate of flow of energy per unit area (A) perpendicular to

the beam

Reduction in intensity by

the inverse square law

attenuation by interaction with matter

INVERSE SQUARE LAW

The intensity of a beam of radiation decreases as the inverse of

the square of the distance (r) from that source

where E is the rate of energy emission of the source

Applies to all radiations under defined conditions

for a point source

in the absence of attenuation

24 r

EI

INVERSE SQUARE LAW

PHOTON ATTENUATION

The removal of photons from a beam of photons

as it passes through matter

Attenuation is caused by

absorption

scattering of primary beam

ATTENUATION COEFFICIENT

Linear Attenuation Coefficient (μ) is defined as

the fraction of photons removed from a beam of X- or γ- rays per

unit thickness

n: number of photons removed from the beam

N: number of photons incident on the material

Δx: thickness of the material (cm)

1

cm

xN

n

ATTENUATION COEFFICIENT

Absorber 100 keV 200 keV 500 keV

Air 0.000195 0.000159 0.000112

Water 0.167 0.136 0.097

Carbon 0.335 0.274 0.196

Aluminium 0.435 0.324 0.227

Iron 2.72 1.09 0.655

Copper 3.8 1.309 0.73

Lead 59.7 10.15 1.64

Linear attenuation coefficients (in cm-1) for a range of materials at γ-ray energies of 100-, 200- and 300 keV

PHOTON ATTENUATION

xeNN 0

HALF-VALUE LAYER

The half-value layer (HVL) is defined as:

the thickness of material required to reduce the intensity of a beam to

one half of its initial value

μ and HVL are related as follows:

HVL is a function of

photon energy

attenuating material

geometry

HVLHVL

693.02ln

HALF-VALUE THICKNESS

INTERACTIONS WITH MATTER

Rayleigh scattering

Compton scattering

Photoelectric effect

Pair production

RAYLEIGH SCATTERING

Incident photon interacts with and excites an atom

Atom is excited emission of a photon

Emitted photon

same energy

different direction scattered photon

RAYLEIGH SCATTERING

RAYLEIGH SCATTERING

RAYLEIGH SCATTERING

RAYLEIGH SCATTERING

Electrons are not ejected no ionisation

In medical imaging detection of scattered photons

impairs image quality

Scattering angle increases as the photon energy decreases

Occurs with very low-energetic diagnostic X-rays

Low probability of occurrence in diagnostic energies ~ 12% of interactions at 30 keV

~ 5% of interactions above 70 keV

COMPTON SCATTERING

Inelastic scattering

Photon interacts with an outer-shell (valence) electron

scattered photon – reduced energy

Compton electron

Through conservation of energy:

esc EEE 0

COMPTON SCATTERING

cos11 20

0

mcE

EEsc

0

20

0(max)

20

0(min)

0

00

2

2

21

180

00

Emc

EEEEand

mcE

EE

EandEE

sce

sc

esc

COMPTON SCATTERING

Compton electron loses its kinetic energy through

excitation and ionisation of surrounding atoms

Scattered photon may traverse the medium

without interaction or

may undergo subsequent interactions

Scattered photons detected by image receptor

image quality is impaired

COMPTON SCATTERING

Incident photon energy increases

scattered photons

Compton electrons

For higher energy incident photons

majority of energy transferred to scattered electron

Probability of a Compton interaction

increases with the incident photon energy (E)

is independent of atomic number (Z)

scattered more towards the forward direction

PHOTOELECTRIC EFFECT

Photon interacts with orbital

electron

Electron absorbs all of photon energy

Electron is ejected

now called a photoelectron

Through conservation of energyboe

EEE

PHOTOELECTRIC EFFECT

PHOTOELECTRIC EFFECT

The incident photon energy must be

≥ to the binding energy of the ejected electron

Following a photoelectric interaction

the atom is ionised

a vacancy is created electron cascade

Characteristic X-rays or Auger electrons

Probability of a photoelectric interaction

decreases with increasing photon energy (E)

increases with atomic number (Z)

PAIR PRODUCTION

X- or γ-ray photon interacts with electric field of nucleus

energy of photon transformed into an electron-positron pair

Pair production has a threshold energy

equal to 1.022 MeV - the rest mass energies of the β-particles

The beta particles lose their kinetic energy via

excitation and ionisation

When the positron comes to rest

interacts with an electron annihilation radiation

PAIR PRODUCTION

DOMINANT REGIONS

SUMMARY I

Light is electromagnetic radiation

energy propagated as a pair of electric and magnetic fields

Duality of light

wave-properties

particle-properties

Reduction in intensity by

the inverse square law

attenuation by interaction with matter

SUMMARY II Interactions of photons with matter

Rayleigh scattering

incident photon excites the entirety of the atom

Compton scattering

part of the incident photon’s electron absorbed by free electron

Photoelectric effect

all of incident electron absorbed by inner-shell electron

Pair production

X- or γ-ray photon interacts with electric field of nucleus

electron – positron pair created

THE END

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