Interaction Between Ionizing Radiation And Matter, Part 1 ... Interaction Between Ionizing Radiation

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Transcript of Interaction Between Ionizing Radiation And Matter, Part 1 ... Interaction Between Ionizing Radiation

  • Interaction Between Ionizing Radiation And Matter,

    Part 1 Photons, continued

    Audun Sanderud

    D ep

    ar tm

    en t o

    f P hy

    si cs

    U ni

    ve rs

    ity o

    f O sl

    o

  • Attenuation coefficient D

    ep ar

    tm en

    t o f P

    hy si

    cs U

    ni ve

    rs ity

    o f O

    sl o

    • 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

    ep ar

    tm en

    t o f P

    hy si

    cs U

    ni ve

    rs ity

    o f O

    sl o

    Rσμ τ σ κ ρ ρ ρ ρ ρ = + + +

    • Mass energy-transfer coefficient: tr T

    h μ μ ρ ρ ν =

    tr tr tr trμ τ σ κ ρ ρ ρ ρ = + +

    • Total mass energy-transfer coefficient:

  • Attenuation coefficients (3) D

    ep ar

    tm en

    t o f P

    hy si

    cs U

    ni ve

    rs ity

    o f O

    sl o

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

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

  • Braggs rule D

    ep ar

    tm en

    t o f P

    hy si

    cs U

    ni ve

    rs ity

    o f O

    sl o

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

    1 1

    1

    , , n n

    tr tr i i i i n

    i imix i mix i i

    i

    mf f f m

    μ μμ μ ρ ρ ρ ρ= =

    =

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

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

    ( )1en tr gμ μ ρ ρ

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

    ( )

    1

    1

    1 ,

    n en en

    i imix i

    n en tr

    mix mix i i imix mix

    f

    g g f g

    μ μ ρ ρ

    μ μ ρ ρ

    =

    =

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

    • Braggs rule:

  • D ep

    ar tm

    en t o

    f P hy

    si cs

    U ni

    ve rs

    ity o

    f O sl

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

    Rayleigh scattering Compton scattering Photoelectric effect Pair- and triplet -production Photon-nuclear reactions

  • D ep

    ar tm

    en t o

    f P hy

    si cs

    U ni

    ve rs

    ity o

    f O sl

    o Rayleigh scattering

    • Kinematics: hvi=hvf T = 0

    • Atomic cross section:

    • Mass Attenuation Coefficients:

    • Mass Energy-Transfer Coefficients:

    ( )V r

    0 iψ θ

    0 fψ

    ( )

    ( ) ( ) ( )

    2 2

    2

    2

    2

    cm atom

    cm g

    cm0 g

    a R

    a R

    a R tr

    Z h

    Z h

    σ ν

    σ ρ ν

    σ ρ

    ⎛ ⎞⎟⎜∝ ⎟⎜ ⎟⎜⎝ ⎠

    =

  • D ep

    ar tm

    en t o

    f P hy

    si cs

    U ni

    ve rs

    ity o

    f O sl

    o Compton scattering

    hν e-

    ϕ θ

    hν’

    T

    ( )( )2 2 , , cot 1 tan

    21 1 cos e

    h em c

    h hh T h h m cν

    ν ν θν ν ν ϕ θ

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

    • 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 σ ρ = ⋅

    ( )2cm ga tr a Th σ σ ρ ρ ν =

  • D ep

    ar tm

    en t o

    f P hy

    si cs

    U ni

    ve rs

    ity o

    f O sl

    o Photoelectric effect

    • Kinematics:

    • Atomic cross section:

    • Mass Attenuation Coefficients:

    • Mass Energy-Transfer Coefficients:

    ( ) ( )

    ( )

    4 2

    3

    3 2

    cm atom

    cm g

    a

    a

    Z h

    Z h

    τ ν

    τ ρ 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 hh ν ν ντ τ

    ρ ρ ν ⎛ ⎞− − − ⎟⎜ ⎟∝ ⎜ ⎟⎜ ⎟⎜⎝ ⎠

    Ta

    θ γ

    e-X X +

  • D ep

    ar tm

    en t o

    f P hy

    si cs

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    ve rs

    ity o

    f O sl

    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-

    +θ e+

    2 2 min

    2 min

    2 , : 2

    : 4 e e

    e

    h m c T T pair h m c

    trip h m c

    ν ν ν

    + −= + + = =

    ( )2 202 cm1 ga tr a m ch κ κ ρ 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 interactions D

    ep ar

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    t o f P

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  • Photon Interaction Summary

    ( )( )

    ( )

    2

    2

    1 / 1 cos

    cot 1 tan 2

    e

    e

    hh h m c

    T h h

    h m c

    νν ν θ

    ν ν

    ν θϕ

    ′= + −

    ′= − ⎛ ⎞⎟⎜= + ⎟⎜ ⎟⎜⎝ ⎠

    22 20 ' ' sin

    2 ' ed r

    d θ

    σ ν ν ν θ ν ν ν

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

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

    µtr/ρ feT

    h τ ρ ν

    'e tr ed d h h d d hθ θ

    σ σ ν ν ν

    −= Ω Ω

    2 02h m c

    h νκ

    ρ ν ⎛ ⎞− ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜⎝ ⎠

    Photon interaction

    Processes

    Kinematics

    Cross section

    Mean energy

    transferred

    2

    a R Z h

    σ ν

    ⎛ ⎞⎟⎜∝ ⎟⎜ ⎟⎜⎝ ⎠

    Compton Rayleigh Photo el.eff. Pair/triplet

    T=0 T = hν-Eb-Ta

    = hν-Eb hν= 2m0c2 + Tˉ + T⁺

    ( )

    4

    3a Z h

    τ ν

    ∝ 2 2

    0a par

    a par a tri

    r Z P

    CZ

    κ α κκ

    =

    =

    2

    2

    2 2

    2 3

    e par

    e tri

    h m cT

    h m cT

    ν

    ν

    −=

    −=

    e tr

    e

    T h σν σ

    =

    Photon- nuclear reactions

  • Summary D

    ep ar

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    t o f P

    hy si

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    ni ve

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