Amanda Barry, Ph.D

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Amanda Barry, Ph.D

Interaction of Radiation with Matter

-

Lecture 2

For spRs sitting FRCR Part I Examinations

Interaction of Photons with
Matter

TO RECAP:

1.
Photons are indirectly ionising radiation

2.
They interact with matter via 5 processes:

1.
Elastic scattering

2.
Compton Effect

3.
Photoelectric effect

4.
Pair production

5.
Photonuclear interactions

TO RECAP:

1.
Photons are indirectly ionising radiation

2.
They interact with matter via 5 processes:

1.
Elastic scattering

2.
Photoelectric effect

3.
Compton Effect

4.
Pair production

5.
Photonuclear interactions

Interaction of Photons with
Matter

TO RECAP:

1.
Photons are indirectly ionising radiation

2.
They interact with matter via 5 processes:

1.
Elastic scattering

2.
Photoelectric effect


䑩a杮g獴楣s剡摩汯杹

3.
Compton Effect

4.
Pair production

5.
Photonuclear interactions

Interaction of Photons with
Matter

TO RECAP:

1.
Photons are indirectly ionising radiation

2.
They interact with matter via 5 processes:

1.
Elastic scattering

2.
Photoelectric effect


䑩a杮g獴楣s剡摩汯杹

3.
Compton Effect


剡d楯瑨敲慰礠

4.
Pair production

5.
Photonuclear interactions

Interaction of Photons with
Matter

Interaction of Photons with
Matter

TO RECAP:

1.
Photons are indirectly ionising radiation

2.
They interact with matter via 5 processes:

1.
Elastic scattering

2.
Photoelectric effect


䑩慧湯獴楣a剡摩汯杹

3.
Compton Effect


剡d楯瑨敲慰礠

4.
Pair production

5.
Photonuclear interactions

3.
Probability of interaction given by Linear Attenuation Coefficient


Dependent on Z, E and
r
e

Interactions of Radiation with
Matter

2.
Electromagnetic Radiation &


its interaction with Matter

1.
Elastic scattering

2.
Compton effect

2.
Photo
-
electric effect

3.
Pair production

4.
Photonuclear interactions

5.
Auger effect


6.
Scattered radiation

7.
Secondary electrons

8.
Linear energy transfer

9.
Range versus energy

3.
Interaction of sub atomic


particles with matter.

1.
Ionisation and excitation due


to charged particles

2.
Electrons

1.
collision loss

2.
radiative loss

3.
stopping power due to
each and total stopping
power,

4.
Particle range

5.
Bragg peak

3.
Bremsstrahlung

4.
Neutrons
-

elastic and inelastic
collisions.

5.
Protons, ionisation profile

6.
Elementary knowledge of pions
and heavy ions.

Scattered Radiation


= By
-
product of the interaction
of radiation with matter



Scattered radiation = radiation
(particulate or EM radiation)
that has changed direction with
or without a change in energy
during its passage through
intervening matter.



EXAMPLE: In radiotherapy,
scattered radiation comes from
the interaction of the primary
beam with the flattening filters,
primary and secondary
collimators, monitor chamber,
the patient.

V

Scattered Radiation

Energy Spectrum for Scattered Photon for
Scattered Photon Angles 0-180
o
0
1
2
3
4
5
6
Scattered Photon Energy (MeV)
0
20
40
60
80
100
180
EXAMPLE:1
o

beam

interacting via

the Compton Effect

Scattered Radiation

Average energy of scattered photons as a
function of scattering angle
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
0
20
40
60
80
100
120
140
160
180
Scattering Angle (degrees)
Average Energy (MeV)
Scattered Radiation


If energy of incoming radiation high


scatter mostly in forward
direction. Example: Therapy range (MV)



If energy of incoming radiation low


scatter in backwards
direction (= backscatter) increases. Example: Therapy range
(50


160 kV) or Diagnostic Imaging (typically 40


80 kV
p
)


Spatial distribution of

scattered x
-
rays

10 keV

100 keV

Scattering point

Not to scale

Scattered Radiation

Effects of Scattered Radiation:


In imaging it acts as a veil over the image.


bone

air

soft
tissue

bone

primary
diaphragm

film, fluorescent screen or
image intensifier

primary
radiological
image

intensity at
detector

scattered
radiation

grid

Image taken from: Johns & Cunningham, The Physics of Radiology, 4
th

Edition



In radiotherapy, adds to patient dose and has radiation protection


issues for staff

Secondary Electrons


When primary radiation interacts with matter, electrons may be
produced


these electrons are called “
secondary electrons



Secondary electrons are emitted close to the original point of


interaction.



If the secondary electron is given enough energy, it can create
its own separate track depositing energy along the way


d
-
ray



d
-
rays do not deposit energy in the immediate vicinity




consequences for determining Absorbed Dose



NOTE:
Electrons

follow tortuous paths undergoing many




interactions before coming to a stop.




Photons

travel in straight lines.



Range versus Energy


The furthest distance radiation travels in a medium is
called “
the range
”.


A

B

Medium

Range

Incoming

Radiation

A: starting point for


secondary e
-


B: stopping point for


secondary e
-

An electron follows a tortuous path undergoing

many interactions before coming to a stop

Range versus Energy


The range depends on:



the type and energy of the radiation



the density of the traversing medium

0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0.5
1
1.5
2.5
Initial Electron Energy (MeV)
Range (cm)
Bone
Muscle
Water
Fat
Data from: F. Attix, Introduction to Radiological Physics and Radiation Dosimetry

EXAMPLE: Electron range in tissues

Linear Energy Transfer



The LET is the rate at which energy is transferred to the medium


and therefore the density of ionisation along the track of the


radiation.



LET also referred to as “restricted stopping power” (L
D
)



LET is expressed in terms of keV per micron




Radiation

LET keV/
m
m

1 MeV
g
-
rays

100 kV
p

X
-
rays

20 keV
b
-
particles

5 MeV neutrons

5 MeV
a
-
particles

0.5

6

10

20

50

Table from: P. Dendy & B. Heaton, Physics for Diagnostic Radiology, 2
nd

Edition

dX
dE
LET
-

dE = energy lost by radiation

dX = length of track



Radiation that is easily


stopped has a high LET and


vice versa

Interaction of Charged Particles

with Matter
-

General


charged particles (e
-
, protons,
a
-
,
b
-
particles) lose energy in a manner


very different from uncharged radiation (X
-
rays,
g
-
rays, neutron)





WHY ? BECAUSE:



charged
-
particles are surrounded by an electrostatic field (= Coulomb
field)


they interact with electrons/nuclei of practically every atom they pass


The force between two particles is


Ze
2
/r
2


probability of charged particle passing through a medium without


interaction is ZERO


Example: a 1 MeV charged
-
particle typically undergoes 10
5



interactions before losing all its kinetic energy (K.E.)

HOW?

1.

soft collision
” when b >> a

2.

hard collision
” when b ~ a

3.

Coulomb
-
force interactions with


the external nuclear field
” when b << a

Charged

particle

b

a

Undisturbed

trajectory

Interactions characterised by:


impact parameter, b
” vs “
atomic radius, a


Interaction of Charged Particles
with Matter


Energy Loss

Collisional Energy Loss

Radiative Energy Loss

Interaction of Charged Particles
with Matter


Energy Loss

Soft Collisions (b >> a): Excitation and Ionisation

The electric field of the charged particle interacts with atomic electrons

causing them to accelerate and gain energy.


Passing charged particle

1.

Ejected electron

2.

1.

Excitation
: If the gain in electron energy


is equal to the difference in energy

between its own energy level and a

higher energy level, then the electron is

excited to the higher energy level.


2.

Ionisation
: If the gain in energy is

greater than the binding energy for the

electron, then an electron is removed

from its orbital. The atom is “ionised”.


Net effect
: transfer of a small amount of
energy (few eV) to atom of absorbing medium

Interaction of Charged Particles
with Matter


Energy Loss

Soft Collisions (b >> a)

Large b more probable than small b




“soft” collisions more likely than any other type of interaction




approx. 1/2 particle energy transferred to absorbing medium

Cerenkov radiation

in the core

of a reactor

Two additional effects:

1.
Polarisation of atoms in
absorbing medium


(more important for the


physicist!)



2.
Cerenkov radiation = emission of


bluish light (< 0.1 % of particle


energy spent in this way.


Unimportant in RT physics)

Interactions of Charged Particles
with Matter


Energy Loss

Hard Collisions (b ~ a): Ionisation,
d
-
牡祳Ⱐ
char. X
-
rays + Auger e
-

When b ~ a, more likely for CP to interact with single atomic e
-




“hard” collisions result in ejection of e
-





e
-

emitted with large K.E. =
d
-
ray





d
-
rays have sufficient energy to ionise other atoms





d
-
rays dissipate energy along separate track = spur

d
-
ray

Incoming

radiation

Bremsstrahlung

Main e
-

track

Ejected electron

Hard Collisions (b ~ a):
Ionisation,
d
-
rays
, char. X
-
rays + Auger e
-




char. X
-
rays and Auger electrons also emitted




some energy transferred to medium by
d
-
rays, char. x
-
rays and




Auger e
-

transported away from primary particle track




no. of hard collisions is small




BUT fraction of energy spent in hard + soft collision comparable



Interactions of Charged Particles
with Matter


Energy Loss

Incoming charged

particle

K radiation

E
-

h
n
k

Ejected

electron

K

L

M

L
-
shell to K
-
shell = K
a

radiation

M
-
shell to K
-
shell = K
b

radiation

Mean Energy Expended per Ion Pair, W

In measuring the energy absorbed extensive use is made of
ionisation.


Mean energy expended to form an ion pair: W = E/N


where


E = initial K.E. of the charged particle



N = mean no. of ion pairs formed when all energy is




used


EXAMPLE: W for dry air is 34 eV


Interaction of Charged Particles
with Matter


Energy Loss

Coulomb
-
force interactions with the external nuclear field” (b << a):






Bremsstrahlung

When charged particle comes very close to nucleus, its electric field interacts
with that of the nucleus.


Most important for electrons because: Prob.


Z
2

, 1/m
2



Most cases, elastic scattering results i.e. electron changes direction

but loses no energy


2
-
3% of cases, charged particle decelerates thereby losing energy and

changing direction


Up to 100 % particle energy lost as X
-
rays = Bremsstrahlung



continuous spectrum of Bremsstrahlung radiation

Incoming charged

particle


Bremsstrahlung,

h
n

E
-

h
n

Interaction of Charged Particles
with Matter


Energy Loss

Electrons

The interaction of electrons with matter is different from other charged
particles because the electron is very small:




m
e

= 9.11 e
-
31

kg



m
p

= 1.67 e
-
27

kg


Therefore, two important effects observed for electrons:


Relativistic effects


large changes in energy and angle


Rapid deceleration


Bremsstrahlung

Interaction of Charged Particles
with Matter


Energy Loss

Stopping Power, S


Stopping Power, S: The rate of energy loss per unit path
length by a charged particle having K.E. in a medium of
atomic number Z


Units: MeV/cm


Mass Stopping Power = S/
r
(indep. of density)


Total Stopping Power


collisional losses + radiative losses



r

r

r
rad
coll
S
S
S


Stopping Power depends on the absorbing medium, the


particle charge, the particle energy, the particle mass

Stopping Power, S


Stopping Power closely related to Absorbed Dose


To calculate Absorbed Dose we use the Restricted Stopping


Power (LET, L
D
)


The Restricted Stopping Power = fraction of S
coll
/
r

that


includes hard and soft collisions where the energy is absorbed


LOCALLY


Therefore, L
D



energy lost by charged particle traversing a


medium as a result of those collisions with atomic electrons


where energy lost is less than a certain threshold energy,
D



Conventionally,
D

= 100 eV


Stopping Power is related to Particle Range

Stopping Power, S

http://mightylib.mit.edu/Course%20Materials/22.01/Fall%202001

/heavy%20charged%20particles.pdf

Particle Range


Continuous Slowing Down Approximation:


dE
dx
dE
R
E









r

-
0
0
1


The stopping power and hence, the density of ionisation, usually


increases toward the end of particle range reaching a maximum,


called the
Bragg Peak
, shortly before the energy drops to zero.


This is of great practical importance for radiation therapy.




Electrons don’t have a Bragg Peak but Protons do.

Particle Range

0
10
20
30
40
50
60
70
80
90
100
0
0.5
1
1.5
2
2.5
3
3.5
Depth (cm)
% Depth Dose
0
20
40
60
80
100
0
2
4
6
8
10
Depth (cm)
% Depth Dose
9 MeV
12 MeV
15 MeV
18 MeV
6MeV
Example: Electron Depth Dose

6 MeV

R
100

R
50

R
P



Bragg Peak

Example: Proton Depth Dose

Summary


Scattered Radiation & Secondary electrons


sources of scatter and effects


Charged particle interactions


Hard and soft collisions and interactions with external nuclear
field


ionisation, excitation, bremsstrahlung


collisional losses, radiative losses


Stopping power and Restricted Stopping Power


Particle Range and Bragg Peaks


Electrons follow tortuous paths

End of Lecture 2