1

incoming photon

scattered photon with reduced energy

interact with the medium

knocked out electron,

ionization and excitation

Chapter 5 Interactions of Ionizing Radiation

secondary electron, -ray

scattered electron

2

5.1 Ionization

Excitation: The energy lost by the incident particle is insufficient to cause ionization, but leaving the atom in an excited state.

Ionization: The energy lost by the incident particle is sufficiently large to remove an electron from the atom, resulting in an ion pair (negative charged electron & positive charged atom).

incident electron

scattered electron

scattered electron

3

5.1 Ionization (cont’d)

Directly ionizing radiation: charged particles (electrons, protons, -particles) produce large amount of ionization in its energy loss to the medium. (Example: it takes approx. 34 eV to produce 1 ion pair in air. Thus, for an electron to lose 1 MeV of its energy, approx. 30,000 ion pairs are produced.)

Indirectly ionizing radiation: neutral particles (photons, neutrons) themselves produce very little ion pairs. Instead, they eject directly ionizing particles from the medium. (Example: a 2-MeV photon, upon interacting with the medium, loses about 1-MeV of its energy, but producing only 1 pair of ions.)

4

5.2 Photon Beam Description

Fluence (): The quotient of dN by da where dN is the number of photons that enter an imaginary sphere of cross-sectional area da: dadN /

Fluence rate or flux density (): The fluence per unit of time:

Energy Fluence (): The quotient of dEfl by da, where dEfl is the energies of all photons that enter an imaginary sphere of cross-sectional area da: If all photons have the same energy (monoenergetic), then:

dtd /

dadE fl /hdNdE fl

Energy fluence rate, energy flux density, or intensity (): The energy fluence per unit of time: dtd /

da

dN

5

5.3 Photon Beam Attenuation

Incident photon fluence

transmitted photon fluence

scattered photons

detector

collimator

NdxdN

NdxdN

is the linear attenuation coefficient

xeIxI

dxI

dI

IdxdI

0)(

6

5.3 Photon Beam Attenuation (mono-energetic photon beam)

1

10

100

0 1 2 3 4 5

Absorber thickness (HVL)

50

1

10

100

0 2 4 6 8 10

Absorber thickness (cm)

50 693.0

HVL

HVL = 2cmTra

nsm

itted

inte

nsity

(%

)

nontransmissi 21

7

Example:

Suppose the HVL for a 6-MV beam is 1.4 cm cerrobend, what is the transmission through a 7 cm cerrobend block?

7 cm / 1.4 cm = 5, (that is, 5 HVLs)

Transmission = (1/2)5 = 1/32 ~ 3.1%

8

5.3 Photon Beam Attenuation (poly-energetic photon beam)

1

10

100

0 1 2 3 4 5

Absorber thickness (mm Al)

50

6

50

25

12.5

3rd HVL2nd HVL1st HVL

Tra

nsm

itted

inte

nsity

(%

)

9

5.4 Coefficients (attenuation coefficients)

Linear attenuation coefficient: (cm-1)

depends on photon energy and the nature of the material.

Mass attenuation coefficient: / (cm2/g)

Electronic attenuation coefficient: e = (cm2/electron)

N0 is the number of electrons per gram

atomic attenuation coefficient: a = (cm2/atom)

0

1

N

w

A

A

ZNN

0

0N

Z

10

5.4 Coefficients (energy transfer coefficients)

Energy transfer coefficient: (cm-1)

is the average energy transferred into kinetic energy of charged particle per interaction, hv is the original photon energy.

Mass Energy transfer coefficient: tr/ (cm2/g)

h

Etrtr

trE

11

5.4 Coefficients (energy absorption coefficients)

Energy absorption coefficient: en = tr (1-g) (cm-1)

‘g’ is the fraction of the energy of secondary charged particles that is lost to bremsstrahlung in the material.

Thus, en represents the energy absorbed locally in the material.

Mass Energy absorption coefficient: en/ (cm2/g)

In soft tissues (low Z materials), g 0. Thus, en tr .

12

5.5 Interactions of Photons with Matter

In the energy range of radiation therapy, 4 types of interaction of photons with matter are of interest:

Coherent scattering, photoelectric effect, Compton scattering, and pair production.

coh c

Incoming particle: 1 photonOutgoing particle(s):

coherent photoelectric comptonPair

production

1 photon 1 electron1 electron +

1 photon1 electron + 1 positron

13

5.6 Coherent Scattering

Also known as classical or Rayleigh scattering.

Scattered photon change direction, but no energy loss.

Only probable in high-Z material and at low photon energy.

Not important for radiation therapy.

Lord Rayleigh (1842-1919)

14

5.7 Photoelectric Effect discovered by Einstein in 1905

photo-electron

photonhv

K L MIncident photon absorbed by the atom, an electron is ejected with a kinetic energy equal to hv – EB.

The vacancy is filled by an outer shell electron, thereby emitting a characteristic x-ray.

The characteristic x-ray itself may be absorbed, and ejects an Auger electron.

Characteristic x-ray

Auger electron

Albert Einstein (1879-1955)

(hv – EB)

15

5.7 Photoelectric Effect (cont’d)

1 100.10.01

Photon energy (MeV)

0.01

0.1

1

10

100

Mas

s ph

otoe

lect

ric

atte

nuat

ion

coef

fici

ent

(

, cm

2 /g)

K-shell binding energy ~88 keV

L-shell binding energy ~15 keV

lead

water

31 E

3Z

33 EZ

16

5.8 Compton Effect

hv’

Incident photon interacts with a ‘free’ electron.

The electron is ejected at angle with energy E.

The photon is scattered at angle with a reduced energy hv’.

hv0

e- (Compton electron)

511.0/)(

/

)cos1(1

1'

0

200

0

MeVhv

cmhv

hvh

Arthur Compton (1892-1962)

17

5.8 Compton Effect (special cases)

Direct hit, = 0, = 180:

21

2,

21

10max0

'min

hEhh

Grazing hit, = 90, = 0: 0, max0'min Ehh

90 photon scatter ( = 90): hv’ 0.511 MeV

180 photon scatter ( = 180): hv’ 0.255 MeV

Low energy incident photons: hv0<<m0c2, then 0, hv’ hv

High energy incident photons: hv0>>m0c2, then >> 1,

18

5.8 Compton Effect (Dependence of Compton Effect on Energy and Atomic Number)

Compton effect decreases with increasing photon energy.

1 100.10.01

0.1

1

Com

pton

coe

ffic

ient

Photon energy (MeV)

Compton effect involves interaction of photon with individual electrons, therefore its coefficient depends on the number of electrons per gram.

ZNA/A

Since Z/A is nearly constant (1/2) for low-Z materials, it follows that is also nearly the same for all such materials.

19

5.9 Pair Production

The photon interacts with the electromagnetic field of the nucleus and gives up all its energy in the process of creating a pair of electron (e-) and positron (e+). hv>1.02 MeV

e- (electron)

Since the rest mass energy of each particle is 0.51 MeV, the photon energy must be greater than 1.02 MeV for this interaction to happen. The total kinetic energy carried by the pair is (hv – 1.02) MeV.

e+ (positron)

Carl D Anderson (1905-1991)

20

5.9 Pair Production (cont’d)

Annihilation: The positron loses its energy as it traverses through the medium. Near the end of its track, with almost no energy left, the positron combines with an electron and the total mass of these two particles is converted into two photons, each with 0.511 MeV, ejected in opposite directions.

(This is the principle on which PET works.)

e+

e-

hv=0.51 MeV

hv=0.51 MeV

21

5.9 Pair Production (cont’d)

Pair production coefficient increases with photon energy.

10 10010.1

0.1

1

Pai

r pr

oduc

tion

coe

ffic

ient

Photon energy (MeV)

aZ2

22

5.10 Relative Importance of Various Types of Interations

1 100.10.01

Photon energy (MeV)

0.1

1

10

Mas

s at

tenu

atio

n co

effi

cien

t (cm

2 /g)

K-shell binding energy ~88 keV

L-shell binding energy ~15 keV

lead

water

(for illustration only)

23

5.11 Interactions of Charged Particles

Interaction between the incident charged particle and:

atomic electrons ionization and excitation;

nucleus bremsstrahlung photons.

Electrons suffer much greater scattering than heavy particles.

Heavy charged particles may also cause nuclear reactions.

Stopping power S = dE/dx, defined as energy loss per unit path length (MeV/cm). For example, water’s stopping power for electrons is approx. 2 MeV/cm.

Mass stopping power is S/. (MeV cm2/g)

24

5.12 Interactions of Neutrons

Neutrons interacts in two processes:

• collision with the nucleus - protons from hydrogen & heavy nuclei from other elements.

• Nuclear disintegration.

Energy transfer is most efficient if the medium has light atomic weight. (e.g. paraffin is used for neutron shielding, water is used to slow down neutrons in nuclear reactor.)

Nuclear disintegration results in emission of heavy charged particles, neutrons, -rays.

25

5.13 Comparative Beam Characteristics (neutrons and Co-60)

Depth dose distribution for neutron beams is similar to that of Co-60.

26

5.13 Comparative Beam Characteristics (heavy charged particles)

Heavy charged particle beam is characterized by the Bragg peak, which may be modulated using filters to form a flat dose distribution at the peak region, followed by a sharp dropoff beyond the range.

27

5.13 Comparative Beam Characteristics (protons and electrons)

Electron beams also show constant dose region up to about half of the range, followed by a falloff, normally not as sharp as that of protons due to excessive scattering.