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.)

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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

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Synopsis of interactions with the electron shell

photons photo effect compton effect

charged particles scattering, ionization

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Synopsis of interactions with the atomic nucleus

pair formation nuclear reaction

charged particles scattering, Bremsstrahlung, nuclear reaction

photons

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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+, …

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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

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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

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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:

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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

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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

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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

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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

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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