Interaction of Ionizing Radiation with Matter
1
Type of radiationcharged particles
photonenneutronen Uncharged bdquoparticlesldquo
Charged particleselectrons (β-)
He2+ (α) H+(p) D+ (d)Recoil nuclidesFission 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
2
Radiation deceleration decrease of energy
Matter physical chemical andor biological effects
Important parameters
Practical consequences of the interaction with matter
particle mass chargespeed kinetic energyspin
matter
atom mass Atom number Znumber of e- per volumedensityionization potential
Interaction of Ionizing Radiation with Matter
3
Synopsis of interactions with the electron shell
photonsphoto effectcompton effect
charged particles scattering ionization
Interaction of Ionizing Radiation with Matter
4
Synopsis of interactions with the atomic nucleus
pair formationnuclear reaction
charged particles scattering Bremsstrahlung nuclear reaction
photons
Interaction of Ionizing Radiation with Matter
5
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+ hellip
Interaction of Ionizing Radiation with Matter
6
Charged particles deceleration by inelastic scattering
Ionization and Excitation
Ionizing radiation
Interaction of Ionizing Radiation with Matter
7
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 3385eVIP
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
8
Ionizing radiation
The lower the energy the higher the SI since probability of interaction with shell electron increases
Bragg Peak
Interaction of Ionizing Radiation with Matter
9
241 Am was in smoke detectors Eα= 548 MeV
specific ionization (SI) = 34sdot104 IPcm
LET = 34middot104middot338 = 12 MeVcm
Range = = = 48 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
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
2
Radiation deceleration decrease of energy
Matter physical chemical andor biological effects
Important parameters
Practical consequences of the interaction with matter
particle mass chargespeed kinetic energyspin
matter
atom mass Atom number Znumber of e- per volumedensityionization potential
Interaction of Ionizing Radiation with Matter
3
Synopsis of interactions with the electron shell
photonsphoto effectcompton effect
charged particles scattering ionization
Interaction of Ionizing Radiation with Matter
4
Synopsis of interactions with the atomic nucleus
pair formationnuclear reaction
charged particles scattering Bremsstrahlung nuclear reaction
photons
Interaction of Ionizing Radiation with Matter
5
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+ hellip
Interaction of Ionizing Radiation with Matter
6
Charged particles deceleration by inelastic scattering
Ionization and Excitation
Ionizing radiation
Interaction of Ionizing Radiation with Matter
7
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 3385eVIP
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
8
Ionizing radiation
The lower the energy the higher the SI since probability of interaction with shell electron increases
Bragg Peak
Interaction of Ionizing Radiation with Matter
9
241 Am was in smoke detectors Eα= 548 MeV
specific ionization (SI) = 34sdot104 IPcm
LET = 34middot104middot338 = 12 MeVcm
Range = = = 48 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
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
3
Synopsis of interactions with the electron shell
photonsphoto effectcompton effect
charged particles scattering ionization
Interaction of Ionizing Radiation with Matter
4
Synopsis of interactions with the atomic nucleus
pair formationnuclear reaction
charged particles scattering Bremsstrahlung nuclear reaction
photons
Interaction of Ionizing Radiation with Matter
5
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+ hellip
Interaction of Ionizing Radiation with Matter
6
Charged particles deceleration by inelastic scattering
Ionization and Excitation
Ionizing radiation
Interaction of Ionizing Radiation with Matter
7
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 3385eVIP
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
8
Ionizing radiation
The lower the energy the higher the SI since probability of interaction with shell electron increases
Bragg Peak
Interaction of Ionizing Radiation with Matter
9
241 Am was in smoke detectors Eα= 548 MeV
specific ionization (SI) = 34sdot104 IPcm
LET = 34middot104middot338 = 12 MeVcm
Range = = = 48 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
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
4
Synopsis of interactions with the atomic nucleus
pair formationnuclear reaction
charged particles scattering Bremsstrahlung nuclear reaction
photons
Interaction of Ionizing Radiation with Matter
5
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+ hellip
Interaction of Ionizing Radiation with Matter
6
Charged particles deceleration by inelastic scattering
Ionization and Excitation
Ionizing radiation
Interaction of Ionizing Radiation with Matter
7
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 3385eVIP
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
8
Ionizing radiation
The lower the energy the higher the SI since probability of interaction with shell electron increases
Bragg Peak
Interaction of Ionizing Radiation with Matter
9
241 Am was in smoke detectors Eα= 548 MeV
specific ionization (SI) = 34sdot104 IPcm
LET = 34middot104middot338 = 12 MeVcm
Range = = = 48 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
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
5
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+ hellip
Interaction of Ionizing Radiation with Matter
6
Charged particles deceleration by inelastic scattering
Ionization and Excitation
Ionizing radiation
Interaction of Ionizing Radiation with Matter
7
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 3385eVIP
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
8
Ionizing radiation
The lower the energy the higher the SI since probability of interaction with shell electron increases
Bragg Peak
Interaction of Ionizing Radiation with Matter
9
241 Am was in smoke detectors Eα= 548 MeV
specific ionization (SI) = 34sdot104 IPcm
LET = 34middot104middot338 = 12 MeVcm
Range = = = 48 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
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
6
Charged particles deceleration by inelastic scattering
Ionization and Excitation
Ionizing radiation
Interaction of Ionizing Radiation with Matter
7
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 3385eVIP
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
8
Ionizing radiation
The lower the energy the higher the SI since probability of interaction with shell electron increases
Bragg Peak
Interaction of Ionizing Radiation with Matter
9
241 Am was in smoke detectors Eα= 548 MeV
specific ionization (SI) = 34sdot104 IPcm
LET = 34middot104middot338 = 12 MeVcm
Range = = = 48 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
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
7
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 3385eVIP
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
8
Ionizing radiation
The lower the energy the higher the SI since probability of interaction with shell electron increases
Bragg Peak
Interaction of Ionizing Radiation with Matter
9
241 Am was in smoke detectors Eα= 548 MeV
specific ionization (SI) = 34sdot104 IPcm
LET = 34middot104middot338 = 12 MeVcm
Range = = = 48 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
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
8
Ionizing radiation
The lower the energy the higher the SI since probability of interaction with shell electron increases
Bragg Peak
Interaction of Ionizing Radiation with Matter
9
241 Am was in smoke detectors Eα= 548 MeV
specific ionization (SI) = 34sdot104 IPcm
LET = 34middot104middot338 = 12 MeVcm
Range = = = 48 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
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
9
241 Am was in smoke detectors Eα= 548 MeV
specific ionization (SI) = 34sdot104 IPcm
LET = 34middot104middot338 = 12 MeVcm
Range = = = 48 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
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
10
RSP = RairRabs (R = Range)
RSP values for some materials and particles
SI is a characteristic feature of a specific material since the e--density changesTo compare different materials the relative stopping power is useful
Ionizing radiation
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
11
Ionizing radiation
Ranges in air for different particles and energies
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
12
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 bdquosimpleldquo 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
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
13
me = rest mass of an electronε0 = dielectric constant (vacuum)ν = velocity of the electronT = mean ionization density of the matterial
e- are light particles relativistic effects have to be considered
E = 100 keVE = 1000 keV
v = 055 cv = 094 c
m = 12 ∙ mo
m = 3 ∙ mo
for lower energies the relativistic effects can be neglected
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
14
The formula predict a minimum value
depending only on the mass of the particle
The slower the particle the more ionization per length
dEdx at a certain energy
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
15
Typical β- decay shows a continuous energy distribution hence it has many low energy electrons
Ψ(x) = Ψ(0) ∙ e-micro∙x
with micro = konst
or N(x) = N0 ∙ e-micro∙x
with micro = 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
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
16
The absorption of electrons decreases linearly
Often instead of path x one takes mass-equivalent range d = δ∙ x
then
with microδ = 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
micro is a function of the electron energy and the material
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
17
Example equivalent range of e- in Al
one can easily calculate the path for reducing the e--flux to 50
x12 can be determined experimentally and micro be calculated for a particular material
andx12 = ln2micro
d12 = (ln2)(micro8)
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
18
Semiempirical relationships for connecting range with electron energy
(015 lt Eβ lt 08 MeV)
Interaction of electrons with matter
Semiempirical relationship between micro δ and Emax
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
19
Maximum ranges of different β-emitters
Interaction of electrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
20
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 frac12 Mimiddotv12 = frac12 Mimiddotv2
2 + frac12 memiddot ve2
momentum Mi middotv1 = Miv2 + memiddotve (non-relativistic)
Interaction of charged particles with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
21
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 = 9109∙10-31 kg mα = 6646∙10-27 kg 5468 ∙10-4 u 40026 u
QmaxE = = 000054 = 005 heavy particles travel straight
Maximum energy transfer (MET)
Example
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
22
Examples for protons H
Proton KineticEnergy E(MeV)
011
10100
103
104
105
106
107
Qmax(MeV)
00002200022002190229333136106 x 104
538 x 105
921 x 106
Maximum percentageenergy transfer
100QmaxE
02202202202303314
106538921
Maximum energy transfer (MET)
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
23
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
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
24
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
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
25
The following formula gives this ratio
Example Pb shielded source of 90Y(Emax = 228MeV) produces 10 Bremsstrahlung
Bremsstrahlung
The stopping efficiency by Bremsstrahlung increases by z2 but the stopping by ionization only by z
The formation of Bremsstrahlung increases with the energy of the electron
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
26
Bremsstrahlung
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
27
Example
Bremsstrahlung
Pb shielded source of 90Y(Emax = 228MeV) produces asymp10 Bremsstrahlung
Donlsquot shield β-emitters with lead
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
28
The Bremsstrahlung is used to produce synchrotron radiation
Bremsstrahlung
Synchrotron Lichtquelle Schweiz SLS
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
29
Photo Effect
Compton EffectPair Formation
Three principle modes of interaction
Photons do not steadily lose energy as they penetrate matter
The distance the photons can travel before they interact with anatom is governed statistically by a probability which depends onthe specific medium and on the photon energy
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
30
electron gap filled by an outer-sphere electron (X-ray fluorescence secondary radiation)
Photo effect
incoming γ-quant
photoelectron
interaction between γ - quanta and electrons of the inner shellsemission of a photoelectron (ionization)dominates with low photon energiesabsorption of the γ -quant
Electron of the shell
higher energy level
lower energylevel γ-quant
radiation
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
31
The photoelectron contains the complete energy of the γ ndash quant minus anenergy ϕ that the electron expends in escaping the atom
Every γ-rays emitting nucleus emits γ-quanta with a distinct energies (fingerprint)
γ ndash spectroscopy
ϕν minus= hT
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Photo effect
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
32
The photo effect depends strongly on the atomic number Z and theenergy hν of the photons
3)(4
νhZyprobabilit =
Photo effect
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
33
interaction between γ -quanta and e- of the outer electron shells (Compton electrons)
emission of a Compton electron (ionization)
γ -quant loses energy (shift to longer wavelengths Compton shift)
the Compton shift only depends on the scattered angle not on the wave length of the incident-photon
resulting quant can undergo more Compton reaction or finally photo reactions
Compton effect
Incomingγ-quant
scatteredγ-quant
compton electron
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
34
The emitted Compton electrons have no defined energy (Compton continuum)
Compton continuum
httpenwikipediaorgwikiFileGammaspektrum_Uranerzjpg
Compton effect
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
35
Never forget 2cmE sdot=
A photon with an energy of at least 1022 MeV can be converted into an e+ e-
pair in the field of an atomic nucleus
22 cemh geν
Excess energy is kinetic energy of the products
The distribution of the excess energy is continuous
Pair formation
incoming γ-quant
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
36
Pair production becomes more likely with increasing photon energy
The probability also increases with the atomic number
2Zyprobabilit asymp
Pair formation
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
37
The produced positron immediately reacts with an electron
νhee =minus++
Since the total momentum before the decay is zero two photons mustbe produced in order to conserve momentum
The produced photons going off in opposite directions
νhcem =22Due to the photon energy is 511 keV (1022 MeV2)
Annihilation of positrons
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
38
The presents of 511 keV annihilation photons around any positron source is always a potential radiation hazard
Disadvantage
AdvantagesPair Formation helps to convert high energy photons (gt 1022 MeV) into photons with less energy (511 keV)
rArr easier to shield
Question How would you shield a γ-emitter
Pair formation
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
12032018
Interaction of γ-radiation and x-rays with matter
Interaction of Ionizing Radiation with Matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
40
Neutrons have no charge and donlsquot interact with the shell electron (no direct ionization)
Classification of Neutrons
Thermal Neutrons Energy distribution according to the Maxwell ndash Boltzmann equationEnergy asymp 0025 eV
(most probable energy in the distribution at 20degC)
Slow Neutrons Also called ldquointermediaterdquo of ldquoresonancerdquo neutronsEnergy le 01 MeV
Fast Neutrons Energy le 20 MeV
Relativistic Neutrons Energy gt 20 MeV
Interaction of neutrons with matter
Interactions between neutrons and matter are interactions with nuclei (only secondary ionization processes)
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
41
energy range 1 - 10 MeVemission of excess energy as γ-quants
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
fast neutronW1
slow neutronW2
Backscattered nucleus W3 γ-quant
Inelastic scattering
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
42
Interaction of neutrons with matter
fast neutronW1
slow neutronW2
Backscattered nucleusW3
Elastic scattering
2)(4
max mMnmMEQ
+=
M = Mass of a neutronm = Mass of the recoil nucleusEn = Kinetic energy of the neutron
Maximum Fraction of Energy Lost Qmax En
energy range 10 keV - 1 MeV
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Interaction of Ionizing Radiation with Matter
43
If a neutron reaches thermal energies it will move about randomly by elastic scattering until absorbed by a nucleus
Slowing-down neutrons is called neutron moderation
Nuclear reaction (np) (n 2n) (n α) (n γ)
Neutron Activation Analysis
Interaction of neutrons with matter
Top Related