Interaction of Ionizing Radiation with Matter 95d7c5c8-704c-48bc... · PDF file...

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Transcript of Interaction of Ionizing Radiation with Matter 95d7c5c8-704c-48bc... · PDF file...

  • Interaction of Ionizing Radiation with Matter

    1

    Type of radiation charged particles

    photonen neutronen Uncharged „particles“

    Charged particles electrons (β-)

    He2+ (α), H+(p) D+ (d) Recoil nuclides Fission fragments

    Interaction of ionizing radiation with matter can be described at the molecular level (molecular process)

    or as macroscopic effects ( decrease, absorption, scattering, etc.)

  • Interaction of Ionizing Radiation with Matter

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    Radiation: deceleration, decrease of energy

    Matter: physical, chemical, and/or biological effects

    Important parameters:

    Practical consequences of the interaction with matter

    particle mass, charge speed, kinetic energy spin

    matter

    atom mass Atom number Z number of e- per volume density ionization potential

  • Interaction of Ionizing Radiation with Matter

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    Synopsis of interactions with the electron shell

    photons photo effect compton effect

    charged particles scattering, ionization

  • Interaction of Ionizing Radiation with Matter

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    Synopsis of interactions with the atomic nucleus

    pair formation nuclear reaction

    charged particles scattering, Bremsstrahlung, nuclear reaction

    photons

  • Interaction of Ionizing Radiation with Matter

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    Energy is high enough to ionize by collision

    Indirect ionizing radiation: n, γ

    Ionization as a consequents of nuclear reactions in the absorbing matter

    In the context of radiation absorption, two definitions are important:

    linear stopping power

    and linear energy transfer

    Without Bremsstrahlung SI and LI are equal, otherwise there will be a substantial difference

    also important

    Ionizing radiation

    Direct ionizing radiation: α, β-, β+, …

  • Interaction of Ionizing Radiation with Matter

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    Charged particles: deceleration by inelastic scattering

    Ionization and Excitation

    Ionizing radiation

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    By collision with electrons, the incident particle ionizes matter

    The mean energy to remove an electron is called the W-factor

    W-factor for air is 33.85eV/IP

    When the charged particle travels through matter, it makes an energy dependent number of ionization / length

    this is called specific ionization (SI)

    The mean energy loss per path length (LET) can determined by:

    LET = SI∙W LET = Linear Energy Transfer

    Ionizing radiation

  • Interaction of Ionizing Radiation with Matter

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    Ionizing radiation

    The lower the energy, the higher the SI since probability of interaction with shell electron increases

    Bragg Peak

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    241 Am was in smoke detectors Eα= 5.48 MeV

    specific ionization (SI) = 3.4⋅104 IP/cm

    LET = 3.4·104·33.8 = 1.2 MeV/cm

    Range = = = 4.8 cm

    This is the maximum range, the SI increases dramatically at the end of the path.

    Ionizing radiation

    Example

  • Interaction of Ionizing Radiation with Matter

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    RSP = Rair/Rabs (R = Range)

    RSP values for some materials and particles

    SI is a characteristic feature of a specific material, since the e--density changes. To compare different materials, the relative stopping power is useful.

    Ionizing radiation

  • Interaction of Ionizing Radiation with Matter

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    Ionizing radiation

    Ranges in air for different particles and energies

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    Since not every collision leads to ionization, the average energy loss for ionization is larger than the minimal Ie of the atoms

    Bethe and Bloch proposed a „simple“ formula for energy loss along a track, considering the nature of the absorber

    The most important interaction of electrons with matter is inelastic scattering with electrons from the shells.

    Interaction of electrons with matter

    ionization

  • Interaction of Ionizing Radiation with Matter

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    me = rest mass of an electron ε0 = dielectric constant (vacuum) ν = velocity of the electron T = mean ionization density of the matterial

    e- are light particles, relativistic effects have to be considered

    E = 100 keV E = 1000 keV

    v = 0.55 c v = 0.94 c

    m = 1.2 ∙ mo m = 3 ∙ mo

    for lower energies, the relativistic effects can be neglected

    Interaction of electrons with matter

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    The formula predict a minimum value

    ...depending only on the mass of the particle

    The slower the particle the more ionization per length.

    dE dx at a certain energy....

    Interaction of electrons with matter

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    Typical β- decay shows a continuous energy distribution, hence it has many low energy electrons

    Ψ(x) = Ψ(0) ∙ e-µ∙x

    with µ = konst

    or N(x) = N0 ∙ e-µ∙x

    with µ = linear absorption coefficient (see x-ray crystallography)

    The Bethe-Bloch formula is an exponential formula

    Interaction of electrons with matter

    Empirically, it can be described:

  • Interaction of Ionizing Radiation with Matter

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    The absorption of electrons decreases linearly

    Often, instead of path x one takes mass-equivalent range d = δ∙ x

    then

    with µ/δ = mass absorption coefficient

    it allows to calculate the maximum range of electrons in a material

    it allows to calculate the thickness of materials for shielding

    Interaction of electrons with matter

    µ is a function of the electron energy and the material

  • Interaction of Ionizing Radiation with Matter

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    Example: equivalent range of e- in Al

    one can easily calculate the path for reducing the e--flux to 50%

    x1/2 can be determined experimentally and µ be calculated for a particular material

    andx1/2 = ln2 µ

    d1/2 = (ln2)/(µ/8)

    Interaction of electrons with matter

  • Interaction of Ionizing Radiation with Matter

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    Semiempirical relationships for connecting range with electron energy

    (0.15 < Eβ < 0.8 MeV)

    Interaction of electrons with matter

    Semiempirical relationship between µ, δ and Emax

  • Interaction of Ionizing Radiation with Matter

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    Maximum ranges of different β-emitters

    Interaction of electrons with matter

  • Interaction of Ionizing Radiation with Matter

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    How much energy can be lost in a single collision?

    Of particular interest: collision with a shell electron

    Maximum energy transfer

    incoming particle : mass Mi, speed Vi1 electron : mass me speed 0

    after collision : Mi, v2, me, ve

    Energy: ½ Mi·v12 = ½ Mi·v22 + ½ me· ve2

    momentum: Mi ·v1 = Mi·v2 + me·ve (non-relativistic)

    Interaction of charged particles with matter

  • Interaction of Ionizing Radiation with Matter

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    speed of reflected particle

    MET Qmax = nicht relativistisch

    If Mi = me (electron on electron)

    then Qmax = E

    This explains why light particles have a zigzag pass in matter

    α-particle colliding with an e-

    me = 9.109∙10-31 kg mα = 6.646∙10-27 kg 5.468 ∙10-4 u 4.0026 u

    Qmax/E = = 0.00054 = 0.05 % !! heavy particles travel straight

    Maximum energy transfer (MET)

    Example:

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    Examples for protons H

    Proton Kinetic Energy E (MeV)

    0.1 1

    10 100

    103 104 105 106 107

    Qmax (MeV)

    0.00022 0.0022 0.0219 0.229 3.33 136 1.06 x 104 5.38 x 105 9.21 x 106

    Maximum percentage energy transfer

    100Qmax/E

    0.22 0.22 0.22 0.23 0.33 1.4

    10.6 53.8 92.1

    Maximum energy transfer (MET)

  • Interaction of Ionizing Radiation with Matter

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    Which results in the emission of Bremsstrahlung

    Bremsstrahlung

    Besides inelastic scattering at the electron shell, inelasting scattering at the nucleus is the most important interaction.

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    The stopping power of atoms or materials does not only depend on ionization but also on direct electron-target nucleus interactions

    This energy loss generates photons, so called Bremsstrahlung

    total stopping power

    From Bethe-Formula, the ratio between collision and radiation is

    The higher the atomic number, the more Bremsstrahlung

    Bremsstrahlung

    The higher the energy, the more Bremsstrahlung

  • Interaction of Ionizing Radiation with Matter

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    The following formula gives this ratio

    Example: Pb shielded source of 90Y(Emax = 2.28MeV) produces 10% Bremsstrahlung

    Bremsstrahlung

    The stopping efficiency by Bremsstrahlung increases by z2, but the stopping by ionization only by z.

    The formatio