interaction of radiation

8/2/2019 Interaction of Radiation

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Interaction of Radiationwith matter

Dr. Ibrahim Idris Suliman

Sudan Atomic Energy Commission



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Interaction of Radiation

Charged particles (e-, p, )

directly ionizing radiationUncharged particles (, n)

indirectly ionizing radiation



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1. Light charged particles (electrons)

Excitation and ionization of atoms in absorber material(atomic effects)interaction with electrons in material (collision, scatter)deceleration by Coulomb interaction (Bremsstrahlung)

2. Heavy charged particles (Z>1)

• excitation and ionization of atoms in absorber

material (atomic effects)• Coulomb interaction with nuclei in material (collision,scatter) (long range forces)



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Interaction electrons

with matter

Energy-Loss Mechanisms

(a) Collisions with electrons

Ionization of atoms

Excitation of atoms

(b) Radiative losses

Bremsstrahlung (c) Could scatter elastically at low energies



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Interaction electrons

with matter Due to a small mass of an electron or positron:

They can transfer large fraction of their energy in a

single collision Can rapidly change their direction after a collision

Rather than Range (difficult to define), keep in mindtheir pathway

After loosing their kinetic energy, positrons willannihilate with electrons and produce 2 gamma rays.



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Charged particles Stopping power, S

Linear stopping S for a charged particle in agiven absorber is defined as the differentialenergy lost for that particle within the material

divided by the corresponding differential pathlength

(3.1)dE

Sdl

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S = linear stopping power

dE = energy lossincluding: electronic, radiative and nucleardl = path lengthunit: J m-1 or MeV cm-1



1 / (3.2)

dE S

dl

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Charged particles

Total mass stopping power

S = linear stopping power = densitydE = energy loss

including: electronic, radiative and nucleardl = path lengthunit: J m2 kg-1 or MeV cm2 g-1



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STOPPING POWER

The stopping power is defined as the kineticenergy loss by an electron or positron per unitpath length due to collisions or emitted radiation:



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electronic stopping ++

radiative stopping +

(only for e, for E > 1 MeV) nuclear stopping -

Relative importance

1 1

/ / / (3.3)el rad el rad

dE dE S S S

dl dl



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Collision vs bremsstrahlung

Energy lost is two process, collision and radiative.For heavy charged particles the radiative part hasno contribution and it is only the collision part which

plays and important role. For electrons the relative importance of the both

forms of energy loss can be approximated by theflowing conversion:

( / ) (3.5)( / ) 700

rad

cl

S EZ S

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Where E is the energy of the electron in MeV And Zthe atomic number of the material.



Bremsstrahlung

When mono-energetic electrons fall on absorbermaterial, a fraction of electron energy is converted toradiation (x-rays). This fraction is denoted with letter

g and it depend on the energy of the falling electronand the atomic number Z of absorber material.

For light materials and E>10 MeV. The fraction g canbe calculated from the empirical relation:

4

06.10 (3.6)g ZE

13



Bremsstrahlung

42.10 (3.7)ag ZE

14

Where Z is the atomic number of the absorbermaterial and E0 is the energy of the falling electron inMeV.

For x-rays emitted from radionuclide emittingradiation with maximum β energy Ea, it is valid:



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High LET radiation: -particlesLow LET radiation: electrons, photons

LET LSel

Linear Energy Transfer LET



Range of electrons There are many formulas for calculation of the

reduced range as a function of energy E ( for β-spectrum, the maximum energy Em is used).

1.265 0.0954ln0.412

E R E

0.542 0.133 R E

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0.5 R E

(0.02 ≤ E ≤ 2.0) ----------(2.9)

(0.6 ≤ E ≤ 20) ----------(2.10)

(E > 0.6 MeV) -------------(2.11)

Where the range Rρ is expressed in g cm-2 andthe energy in MeV



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Interaction of Heavy Charged Particles with Matter



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Interaction of heavy charged

particles with matter «Heavy» charged particles – all charged particlesother than the electron or positron

Include: muons (M = 207 me), pions (M = 270 me),kaons (M= 967 me), protons (M = 1836 me), alphaparticles, deuterons, tritons, fission fragments,other heavy ions

Energy-Loss Mechanisms

(a) collisions with electrons (b) radiative

Ionization of atoms Excitation of atoms



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Sketch of alpha particles paths in a

medium Can transfer only a small fraction of its energy in a

single collision with an electron. Thus, heavycharged particles

travel almost in straight lines (straight line trajectory) lose energy almost continuously in small amounts

have a very small range



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Ionization



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Maximum Energy Transfer in a

Single Collision Before After

Conservation of total kinetic energy and momentum:



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Single Collision From the first two equations we obtain

V1 = (M-m)/(M+m) V

and the maximum energy transfer is given byQmax = ½ MV² - ½ MV1

² = E[4mM/(M+m)²]

E = mV2 /2, the initial kinetic energy of incident particle



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Single Collision For incoming electron:

Qmax = E, if M = me

For muon

Qmax = [4me(207 me)/(208 me)2]E

Qmax = 0.0192 E



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Single Collision



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STOPPING POWER

Stopping power is defined as the average energy loss of acharged particle per unit path length:

where µ is the probability of collision per unit pathlength, and Qave is the average energy loss per collision.

The mass stopping power is given as:



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Bethe Formula

for stopping power

Where k o = 8.99 x 109 [N m² C-1]

Z – atomic number of heavy particle e - electron charge

n – number of electron per unit volume m – electron rest mass

c – speed of light in vacuum β – V/c – speed of the particle relative to c

I – mean excitation energy of the medium



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MEAN EXCITATION ENERGY OF

THE MEDIUM

For a compound or mixture, the stopping power can be calculated bysimpling adding the separate contributions from the individual

constituent elements:

where i corresponds to an individual element.



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Stopping power of water for

various heavy charged particles



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Bragg Curve

A curve showing the average number of ions per unitdistance along ( or

a specific ionization) a beam of initially monoenergeticionizing

particles, usually alpha particles, passing through a gas.Also known as a

Bragg ionization curve.



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Energy Deposition of Alpha particles

Specific ionization - SISI = (dE/dx)/EI

Number of ion pairs per unit path length

EI,air = 36 eV/ip

EI,tissue= 22 eV/ip



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RANGE

The range of a charged particle is the distance it travelsbefore coming to rest.

For a particles in air, the following approximate empiricalrelations exist:



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RANGE

The ranges of two heavy particles with the same initial speedcould be determined from the following ratio:

The range of other charged particles in terms of proton range:

For example, the range of alpha particle from 214Po decay(E=7.69 MeV) is

in air about 6cm

in tissue about 0.007 cm



Range of alpha particles and protons

The range of α-particles in air in standard condition(STP), Ra(α) expressed in cm and for initial energy E(MeV), is given by the following empirical formula.

3( ) (0.005 0.285)a R E E

3( ) 0.3a

R E

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(cm) -------------(2.12)

The eq. (2.12) can be written in more simpleform

(cm) --------------------(2.13)




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The range of α-particles in materials other than aircan be calculated by making use of Bragg- KleemanLaw

4( ) 3.2 10 a

A

AR R

(cm) -------------(2.14)

Where ρ in g cm-3 and Ra in cm




For a mixture of atoms with relative atomicmass’s A1, A2, ….. And weighted fractions f1, f2,….√A can be written as:

The range of protons in air ,Ra(p) can be given by

the following equation:

1 1 2 2 ...mixture A f A f A

1.8

( ) 1009.3

a

E R p

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-------------(2.15)

(cm) -------------(2.16)



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Bragg’s curve

0 5 0 1 00 1 5 0 2 00 2 5 0

Depth (mm )

0

2 0

4 0

6 0

8 0

1 00

R e l

a t i v e e n e r g y i m

p a r t e d ( % )

17 4 M eV pr ot on s in wat er

experiment

calculat ion



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Irradiation of a tumor in the brain

12

C particle beams at GSI



Interaction of photons with

matter

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fluence particle

ninteractioof y probabilit

Cross section (1)

SI unit: m2

special unit: barn (b)1 b = 10-28 m2



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Alternative definition:

1. Cross section may be bigger/smaller than the cross section ofthe atomic nucleus2. Type of interaction should be specified (σn,p or σ,e)

N partices per cm2

dx

Cross section (2)

2m per centresninteractioof number

ninteractiospecificatosubjected particlesincident theof fraction



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Interactions of photons

interaction

Energy loss

Atomicelectron

Nucleus Electric fieldof the nucleus

100% FotoelectricEffect

Photonuclearreactions

Pairproduction

0%<E < 100% ComptonEffect

- -

0% Coherent

Scattering

- -



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Photoelectric effect (1)

Entire energy transfer fromphoton to an atomic electron

KL

e-

h

3

4

,

h

Z e Cross section

Energy photo-electron:be E h E



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KL

e-

h

Fraction emitted X-rays (‘scattered’radiation)

K = cross section photoelectric effect in K shellK = fluorescence yield K shellEK

= mean bindings energy K electron

EK

hh

E

h

E L

L LK

K K ...

__

Photoelectric effect (2)



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Compton effect (1) h

h’

Ee-

Energy conservation:

Energy Compton electron:

Angular correlation:

)cos1(1

)cos1()(

2

2

2

cm

h

cm

h

E

e

e

e

'hv E hv e

Partial energy transferto a ‘free’ electron

2tan1)cot(

2

cm

h

e



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h

h’

Ee-

Angular distribution of thescattered photons

0

90

180

270

0 1 2

1 0M e V

1 M e V0.1 M e V

0.01 M e V

r icht ing invallend

f ot on

Compton effect (2)



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h

h’

Ee-

Cross section:

Fraction of the energy h transferred to compton electrons:

hh

h E f e

e

______

','1

5,0', h

Z C e

Compton effect (3)



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Pair production

Conversion of the photon into an (e-,e+) pair

h

e-

e+

Threshold energy: 2mc2 = 1,02 MeV

Scattered strongly forwards

Cross section:

h Z ee

2

,

hv

mc f

ee

2

,

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Fraction of the energy h transferred to (e-,e+) pair

Dependence of cross sections of



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Dependence of

Type of interaction

Energy

Z

cm2

/atom

Z

cm2

/gPhotoelectric Effect E-3.5 Z4 to Z5 Z3 to Z4

Compton Effect E-0.5 to E-1 Z independent

Pair Production E1 to ln E Z2 Z

Dependence of cross sections ofphoton energy and atomic number



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Interactions of photons

10 - 2 10 - 1 10 0 10 1 10 2

Pho ton ene rgy (M eV)

0

20

40

60

80

100

A t o m i c n u m b e r Z Pho to-Ele c t ric Ef fec t

d o m i n a n tPai r Prod uc t ion

d o m i n a n t

Com pton Ef fec t

d o m i n a n t C =

= C



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Attenuation and absorption

Narrow beam geometry



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Attenuation of photons

Suppose: parallel beam with fluence: 0

number of interaction centres per volume : N

dx

0

d

Probability on absorption per centre:

Number of centres per cm2

: N dxNumber of absorption per cm2 : N dxDecrease particle fluentie in dx d = - N dxIntegration yields:

(x)

x

x x N ee x

00)(



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Linear attenuation coefficient (cm-1) µ = N :

Mass attenuation coefficient (cm2 g-1): µ/ = N /

Number of centres (cm-3) N = NA/M

Correlation between micro- and macroscopic cross sections:

µ/ has the following component cross sections:

M

N A /

Attenuation of photons

def

/ / / / C

Photoelectric effect Compton effect pair production

I t ti f h t ith l d



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Interactions of photons with lead

10 1 10 2 10 3 10 4 10 5

Energy (k eV)

10 - 3

10- 2

10 - 1

10 0

10 1

10 2

æ / Ò ( c m

2 g

- 1 )

pa ir p r o duc t ion /

Coher ent e scat .c o h

/

I t ti f h t ith i



Interactions of photons with air

10 1 10 2 10 3 10 4 10 5

Energy (keV)

10 - 3

10 - 2

10 - 1

10 0

10 1

µ / ( c m

2 g

- 1 )

interaction of radiation

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