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

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Interaction of Ionizing Radiation with Matter

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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

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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

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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

Interaction of Ionizing Radiation 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

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Maximum ranges of different β-emitters

Interaction of electrons 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)

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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

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