Interaction BetweenIonizing Radiation And Matter,

Part 1 Photons, continued

Audun Sanderud

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Attenuation coefficientD

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• σ: Cross section target area; surface proportional with the probability of interaction

• µ/ρ: Mass attenuation coefficient; the number of photons with a single energy E and direction which interacts per length unit, ρ: mass density

• µ/ρ=(NA/A)aσ, µ/ρ=(NAZ/A)eσ, where

aσ: atomic cross section, eσ: electronic cross section (NA/A): is the number of atoms per mass unit(NAZ/A): is the number of electrons per mass unit

≈ constant for Z>1 (Hydrogen)

• Total mass attenuation coefficient:

Attenuation coefficient (2)D

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Rσμ τ σ κρ ρ ρ ρ ρ= + + +

• Mass energy-transfer coefficient: tr T

hμ μρ ρ ν=

tr tr tr trμ τ σ κρ ρ ρ ρ= + +

• Total mass energy-transfer coefficient:

Attenuation coefficients (3)D

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http://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html

http://physics.nist.gov/PhysRefData/Xcom/Text/XCOM.html

Braggs ruleD

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• Braggs rule for mixtures of n-atoms/elements:

1 1

1

, ,n n

tr tr ii i i n

i imix i mix ii

i

mf f fm

μ μμ μρ ρ ρ ρ= =

=

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎟ ⎟ ⎟ ⎟⎜ ⎜ ⎜ ⎜⎟ = ⎟ ⎟ = ⎟ =⎜ ⎜ ⎜ ⎜⎟ ⎟ ⎟ ⎟⎜ ⎜ ⎜ ⎜⎟ ⎟ ⎟ ⎟⎜ ⎜ ⎜ ⎜⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠∑ ∑ ∑

• Mass energy-absorption coefficient:g represent the average fraction of secondary electron energy lost to photons

( )1en tr gμ μρ ρ

⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜⎟= ⎟ −⎜ ⎜⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠

( )

1

1

1 ,

nen en

iimix i

nen tr

mix mix i iimix mix

f

g g f g

μ μρ ρ

μ μρ ρ

=

=

⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜⎟ ≅ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠⎛ ⎞ ⎛ ⎞⎟ ⎟⎜ ⎜⎟ ≡ ⎟ − =⎜ ⎜⎟ ⎟⎜ ⎜⎟ ⎟⎜ ⎜⎝ ⎠ ⎝ ⎠

∑

∑

• Braggs rule:

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o Photon Interaction• Five interaction processes between photons and matter:

Rayleigh scatteringCompton scatteringPhotoelectric effectPair- and triplet -productionPhoton-nuclear reactions

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o Rayleigh scattering

• Kinematics: hvi=hvfT = 0

• Atomic cross section:

• Mass Attenuation Coefficients:

• Mass Energy-Transfer Coefficients:

( )V r

0iψ θ

0fψ

( )

( ) ( )( )

22

2

2

2

cm atom

cm g

cm0 g

a R

a R

a R tr

Zh

Zh

σν

σρ ν

σρ

⎛ ⎞⎟⎜∝ ⎟⎜ ⎟⎜⎝ ⎠

∝

=

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o Compton scattering

hν e-

ϕθ

hν’

T

( )( )2 2, , cot 1 tan

21 1 cose

h em c

h hh T h hm cν

ν ν θν ν ν ϕθ

⎛ ⎞ ⎛ ⎞⎟⎜ ⎟⎜′ ′ ⎟= = − = +⎜ ⎟⎜⎟ ⎟⎜ ⎜⎟⎜ ⎝ ⎠⎝ ⎠+ −

• Kinematics:

• Electronic cross section:

• Atomic cross section:

• Mass Attenuation Coefficients:

• Mass Energy-Transfer Coefficients:

( )20 cm electrone Zσ ∝( )2cm atoma eZσ σ= ⋅( )2cm ga A eN ZA

σ σρ= ⋅

( )2cm ga tr a Thσ σρ ρ ν=

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o Photoelectric effect

• Kinematics:

• Atomic cross section:

• Mass Attenuation Coefficients:

• Mass Energy-Transfer Coefficients:

( ) ( )

( )

4 2

3

32

cm atom

cm g

a

a

Zh

Zh

τν

τρ ν

∝

⎛ ⎞⎟⎜∝ ⎟⎜ ⎟⎜⎝ ⎠

b a bT h E T hv Eν= − − −

( ) ( )21 cm gK K K K L L La tr a h P Y h P P Y hhν ν ντ τ

ρ ρ ν⎛ ⎞− − − ⎟⎜ ⎟∝ ⎜ ⎟⎜ ⎟⎜⎝ ⎠

Ta

θγ

e-X X+

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o Pair- and triplet -production

• Kinematics:

• Atomic cross section:

• Mass Attenuation Coef.:

• Mass Energy-Transfer Coef.:

( )22 cm, atoma par a triZ Zκ κ∝ ∝

Ta

−θγ

e-

+θe+

2 2min

2min

2 , : 2

: 4e e

e

h m c T T pair h m c

trip h m c

ν νν

+ −= + + ==

( )2 202 cm1 ga tr a m chκ κρ ρ ν

⎛ ⎞⎟⎜ ⎟= −⎜ ⎟⎜ ⎟⎜⎝ ⎠

( )20 cm, ga par a triZ Zκ κρ ρ∝ ∝

• Photon (energy above a few MeV) excites a nucleus

• Proton or neutron is emitted• (γ, n) interactions may lead to radiation protection

problems• Example: Tungsten W (γ, n)• Not important in dosimetry

Photonuclear interactionsD

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Photon Interaction Summary

( )( )

( )

2

2

1 / 1 cos

cot 1 tan 2

e

e

hhh m c

T h h

hm c

ννν θ

ν ν

ν θϕ

′=+ −

′= −⎛ ⎞⎟⎜= + ⎟⎜ ⎟⎜⎝ ⎠

2220 ' ' sin

2 'ed r

d θ

σ ν ν ν θν ν ν

⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎟⎜ ⎟ ⎟⎜ ⎜⎟= + −⎜ ⎟ ⎟⎜ ⎜⎟ ⎟ ⎟⎜ ⎜ ⎜⎟⎜ ⎝ ⎠ ⎝ ⎠Ω⎝ ⎠

( )1fe K K K K L L LT h P Y h P P Y hν ν ν= − − −

µtr/ρfeT

hτρ ν

'e tr ed d h hd d hθ θ

σ σ ν νν

−=Ω Ω

202h m c

hνκ

ρ ν⎛ ⎞− ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠

Photon interaction

Processes

Kinematics

Cross section

Meanenergy

transferred

2

a RZh

σν

⎛ ⎞⎟⎜∝ ⎟⎜ ⎟⎜⎝ ⎠

Compton Rayleigh Photo el.eff. Pair/triplet

T=0T = hν-Eb-Ta

= hν-Ebhν= 2m0c2 + Tˉ + T⁺

( )

4

3aZh

τν

∝2 2

0a par

a para tri

r Z P

CZ

κ ακκ

=

=

2

2

22

23

epar

etri

h m cT

h m cT

ν

ν

−=

−=

e tr

e

T h σνσ

=

Photon-nuclear reactions

SummaryD

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Interaction Between� Ionizing Radiation And Matter,� Part 1 Photons, continued ��Audun Sanderud���