Gamma ray interaction with matter A) Primary interactions 1) Coherent scattering (Rayleigh scattering) 2) Incoherent scattering (Compton scattering) 3) Photoelectric effect 4) Production of electron and positron pairs 5) Interactions with small contributions 6) Total attenuation of gamma rays at matter B) Secondary interactions 1) X-rays 2) Auger electrons 3) Annihilation of positron and electron 4) Bremsstrahlung radiation γ e - e - γ e - γ e + e - γ
e -. γ. e -. e -. γ. γ. e +. γ. e -. Gamma ray interaction with matter. A) Primary interactions 1) Coherent scattering (Rayleigh scattering) 2) Incoherent scattering (Compton scattering) 3) Photoelectric effect - PowerPoint PPT Presentation
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Transcript
Gamma ray interaction with matter
A) Primary interactions
1) Coherent scattering (Rayleigh scattering) 2) Incoherent scattering (Compton scattering) 3) Photoelectric effect 4) Production of electron and positron pairs 5) Interactions with small contributions 6) Total attenuation of gamma rays at matter
B) Secondary interactions
1) X-rays 2) Auger electrons 3) Annihilation of positron and electron 4) Bremsstrahlung radiation
γ e-
e-
γ
e-
γ
e+
e-
γ
Coherent scatteringCoherent scattering on bounded electrons (whole atom) (energy is not transfered only direction of momentum is changed) ndash in the limit Rayleigh scattering
Thomson scattering ndash scattering on free electrons in classical limit (coherent as well as incoherent)
Polar graph of cross-section without inclusion of F(qZ) influence classical limit of Thomson scattering
F(qZ) ndash probability of momentum transfer on Zelectron atom without energy transfer
High energy rarr scattering to small angles
r0 ndash classical electron radius (SI units)
282fmcm
cαm10282
cm4π
er
2e
152
e0
2
0
)cos1(2
1 220
r
d
d TbarnmrT 665010656
3
8 22920 Unpolarized
Polarized TTP r 203
8
20
2220
4
20
2220
42
03
8
TR r
)()cos1(2
1 220 ZqFr
d
d R
TR
TR
TR
0
20
20
0
40
4
0
Eγ ν
Eγ` νacute
Θ
220 sinr
d
d TP
Eγ = Eγacuteν = νacute
α = 1137ħc = 197 MeVfmmec2 = 0511 MeV
Diffraction on crystal lattice
Usage of interference during coherent scattering on layers of crystal lattice
Bragg law nλ = 2dsin Θ
d ndash grid spacingλ ndash radiation wave lengthn ndash diffraction order
Dependency of first diffraction maximum angle onX-ray and gamma ray energies for two grid spacings
Spectrometers with sizes up to ten meters were built
Eγ = 1000 keV d = 06 nm r = 10 m rarr Θ = 0059O x = 10 mmEγ = 100 keV rarr Θ = 059O x = 100 mm
Incoherent (Compton scattering)
cos11
EE
2cm
E
e
Where parameter
Relation between scattered photon energy Eγ and scattering angle Θ
We obtain relations between energies and angles of scattering and reflection from the energy and momentum conservation laws
We assumed 1) scattering on free electron (EγgtgtBe) 2) electron is in the rest
Θ
φ
Eγ pγ=Eγc
Eγrsquo pγrsquo=Eγrsquoc
mec2 pe= 0
222
2
cmc
EpE e
eee
Scattered photon energy
211800 E
E
Reflected electron energy
Reflection angle
cos11
cos1
EEEEe
21
21800 E
Ee
2
tan1cot
Polar graph of cross-section without inclusion of S(qZ) influence In the limit E rarr 0 we obtain graph for coherent scattering
2
2
20 sin
2
1
E
E
E
E
E
EZr
d
d C
cos11
cos1cos1
cos11
1
2
1 222
22
0
Zrd
d C
222
021
3121ln
2
121ln
1
21
1212
ZrC
Diferential cross-section is described by Klein-Nishin equation (on free electrons)
We introduce energy of scattered photon
inclusion of influence of electron binding at atom rarr multiplying by function S(qZ) ndash probability of momentum q transfer to electron during ionization or excitation
Total cross section (can be obtained by integration)
Distribution of energy transferred to electrons
Eγ gt mec2 rarr ζ gt 1
E
ZZC ~~
Scattering of high energy electron and low energy photon ndash inverse Compton scattering (see exercise)
Photoelectric effect
Can pass only on bounded electron
Total photon energy is transfered
Electron energy Ee = Eγ - Be
and so σF = ~ Z5Eγ-35 near to K-shell σF = ~ Z45Eγ
-3
Cross-section (for Eγ ltlt mec2)
Accurate calculation of photoeffect process (solution of Dirac equation) is very sophisticated
γ e-
27
54 124
TF Z
If it is enough energy (Eγ gt BeK binding energy on K-shell) the photoeffect will pass almost only on these electrons
137
1
4 0
2
c
e
where is fine structure constant
More accurate equation for σF near to K-shell see Leo
Dependency of K-shell electron binding energy on proton number Z of atom (Si ndash 18389 keV Ge ndash 111031 keV Pb ndash 880045 keV)
Production of electron and positron pairs
e+
e-
γ
σP ~ Z2ln(2Eγ)
Transformation of photon to electron and positron pair
Energy and momentum conservation laws rarr only In nucleus field (mostly) Eγ gt 2mec2 = 1022 keVeventually electrons Eγ gt 4mec2 = 2044 keV (je 1-2Z smaller)
31222
ZcmEcm e
e
312ZcmE e
where f(Z) is coulomb correction of order α2
Dependency of σP on Z and Eγ is(for bdquolower energiesldquo range)
There is valid for cross-section in special cases
Without screening
Complete screening
54
109)(2ln
9
74 2
02 ZfrZP
54
1)(183ln
9
74 312
02 ZfZrZP
Production in the electron field(bdquotripletldquo production)
252
20 432
3
Zr
PT
Eγgtgtmec2 electrons and positrons are peaked forward Θ asymp 1ζ Cross-section dependency On photon energy
Description is equivalent to description of bremsstrahlung radiation (necessity to include screening influence predominance of pair production near nucleus ndash without screening)
Interaction with small contribution
Photonuclear reactions ndash resonance processes with small probability
Photon interaction with coulomb field of nucleus (Delbruumlck scattering) ndashwe can look on it as on virtual pair production and following annihilation
Photonuclear reactions in order of mbarn up to barn in narrow energy rangeinteraction with electrons in order of barns up to 105 barns in broad energy range
Nuclear Rayleigh scattering Nuclear Thomson scattering ndash substitutions e rarrZe me rarr Mj
and then mA
Z
cM
eZrr
Jj
182
20
22
0 10514
Nuclear resonance scattering ( for example giant dipole resonance)
Total cross-sections barnA
Zm
A
Zr jTJ 126010612
3
82
4236
2
42
X-ray
Auger electrons
proton
zaacuteřeniacute gamaelektron
XA
X
NN
N
Fluorescent efficiency (coefficient)
Bremsstrahlung radiation during movement of electrons and positrons
NX ndash X-ray photons NA ndash Auger electrons
Released energy is transferred during electron transition at atomic cloud on other electron
Passage of electrons and positrons1) Ionization losses2) Bremsstrahlung radiation
Charged particle moves in nuclear field with acceleration rarr it emits photons
Annihilation of positron and electron
Positrons are stopped by ionization losses and they annihilate in the rest rarr 2 quanta of 511 keV (they are not fully in the rest rarr energy smearing of annihilation quanta)
Secondary processes
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range
Equation for decreasing of photon number xe
I
I
0
For compound or mixture Bragg rule is valid
2
22
1
11
ww
Total cross-section
dI = -μIdx
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Coherent scatteringCoherent scattering on bounded electrons (whole atom) (energy is not transfered only direction of momentum is changed) ndash in the limit Rayleigh scattering
Thomson scattering ndash scattering on free electrons in classical limit (coherent as well as incoherent)
Polar graph of cross-section without inclusion of F(qZ) influence classical limit of Thomson scattering
F(qZ) ndash probability of momentum transfer on Zelectron atom without energy transfer
High energy rarr scattering to small angles
r0 ndash classical electron radius (SI units)
282fmcm
cαm10282
cm4π
er
2e
152
e0
2
0
)cos1(2
1 220
r
d
d TbarnmrT 665010656
3
8 22920 Unpolarized
Polarized TTP r 203
8
20
2220
4
20
2220
42
03
8
TR r
)()cos1(2
1 220 ZqFr
d
d R
TR
TR
TR
0
20
20
0
40
4
0
Eγ ν
Eγ` νacute
Θ
220 sinr
d
d TP
Eγ = Eγacuteν = νacute
α = 1137ħc = 197 MeVfmmec2 = 0511 MeV
Diffraction on crystal lattice
Usage of interference during coherent scattering on layers of crystal lattice
Bragg law nλ = 2dsin Θ
d ndash grid spacingλ ndash radiation wave lengthn ndash diffraction order
Dependency of first diffraction maximum angle onX-ray and gamma ray energies for two grid spacings
Spectrometers with sizes up to ten meters were built
Eγ = 1000 keV d = 06 nm r = 10 m rarr Θ = 0059O x = 10 mmEγ = 100 keV rarr Θ = 059O x = 100 mm
Incoherent (Compton scattering)
cos11
EE
2cm
E
e
Where parameter
Relation between scattered photon energy Eγ and scattering angle Θ
We obtain relations between energies and angles of scattering and reflection from the energy and momentum conservation laws
We assumed 1) scattering on free electron (EγgtgtBe) 2) electron is in the rest
Θ
φ
Eγ pγ=Eγc
Eγrsquo pγrsquo=Eγrsquoc
mec2 pe= 0
222
2
cmc
EpE e
eee
Scattered photon energy
211800 E
E
Reflected electron energy
Reflection angle
cos11
cos1
EEEEe
21
21800 E
Ee
2
tan1cot
Polar graph of cross-section without inclusion of S(qZ) influence In the limit E rarr 0 we obtain graph for coherent scattering
2
2
20 sin
2
1
E
E
E
E
E
EZr
d
d C
cos11
cos1cos1
cos11
1
2
1 222
22
0
Zrd
d C
222
021
3121ln
2
121ln
1
21
1212
ZrC
Diferential cross-section is described by Klein-Nishin equation (on free electrons)
We introduce energy of scattered photon
inclusion of influence of electron binding at atom rarr multiplying by function S(qZ) ndash probability of momentum q transfer to electron during ionization or excitation
Total cross section (can be obtained by integration)
Distribution of energy transferred to electrons
Eγ gt mec2 rarr ζ gt 1
E
ZZC ~~
Scattering of high energy electron and low energy photon ndash inverse Compton scattering (see exercise)
Photoelectric effect
Can pass only on bounded electron
Total photon energy is transfered
Electron energy Ee = Eγ - Be
and so σF = ~ Z5Eγ-35 near to K-shell σF = ~ Z45Eγ
-3
Cross-section (for Eγ ltlt mec2)
Accurate calculation of photoeffect process (solution of Dirac equation) is very sophisticated
γ e-
27
54 124
TF Z
If it is enough energy (Eγ gt BeK binding energy on K-shell) the photoeffect will pass almost only on these electrons
137
1
4 0
2
c
e
where is fine structure constant
More accurate equation for σF near to K-shell see Leo
Dependency of K-shell electron binding energy on proton number Z of atom (Si ndash 18389 keV Ge ndash 111031 keV Pb ndash 880045 keV)
Production of electron and positron pairs
e+
e-
γ
σP ~ Z2ln(2Eγ)
Transformation of photon to electron and positron pair
Energy and momentum conservation laws rarr only In nucleus field (mostly) Eγ gt 2mec2 = 1022 keVeventually electrons Eγ gt 4mec2 = 2044 keV (je 1-2Z smaller)
31222
ZcmEcm e
e
312ZcmE e
where f(Z) is coulomb correction of order α2
Dependency of σP on Z and Eγ is(for bdquolower energiesldquo range)
There is valid for cross-section in special cases
Without screening
Complete screening
54
109)(2ln
9
74 2
02 ZfrZP
54
1)(183ln
9
74 312
02 ZfZrZP
Production in the electron field(bdquotripletldquo production)
252
20 432
3
Zr
PT
Eγgtgtmec2 electrons and positrons are peaked forward Θ asymp 1ζ Cross-section dependency On photon energy
Description is equivalent to description of bremsstrahlung radiation (necessity to include screening influence predominance of pair production near nucleus ndash without screening)
Interaction with small contribution
Photonuclear reactions ndash resonance processes with small probability
Photon interaction with coulomb field of nucleus (Delbruumlck scattering) ndashwe can look on it as on virtual pair production and following annihilation
Photonuclear reactions in order of mbarn up to barn in narrow energy rangeinteraction with electrons in order of barns up to 105 barns in broad energy range
Nuclear Rayleigh scattering Nuclear Thomson scattering ndash substitutions e rarrZe me rarr Mj
and then mA
Z
cM
eZrr
Jj
182
20
22
0 10514
Nuclear resonance scattering ( for example giant dipole resonance)
Total cross-sections barnA
Zm
A
Zr jTJ 126010612
3
82
4236
2
42
X-ray
Auger electrons
proton
zaacuteřeniacute gamaelektron
XA
X
NN
N
Fluorescent efficiency (coefficient)
Bremsstrahlung radiation during movement of electrons and positrons
NX ndash X-ray photons NA ndash Auger electrons
Released energy is transferred during electron transition at atomic cloud on other electron
Passage of electrons and positrons1) Ionization losses2) Bremsstrahlung radiation
Charged particle moves in nuclear field with acceleration rarr it emits photons
Annihilation of positron and electron
Positrons are stopped by ionization losses and they annihilate in the rest rarr 2 quanta of 511 keV (they are not fully in the rest rarr energy smearing of annihilation quanta)
Secondary processes
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range
Equation for decreasing of photon number xe
I
I
0
For compound or mixture Bragg rule is valid
2
22
1
11
ww
Total cross-section
dI = -μIdx
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Diffraction on crystal lattice
Usage of interference during coherent scattering on layers of crystal lattice
Bragg law nλ = 2dsin Θ
d ndash grid spacingλ ndash radiation wave lengthn ndash diffraction order
Dependency of first diffraction maximum angle onX-ray and gamma ray energies for two grid spacings
Spectrometers with sizes up to ten meters were built
Eγ = 1000 keV d = 06 nm r = 10 m rarr Θ = 0059O x = 10 mmEγ = 100 keV rarr Θ = 059O x = 100 mm
Incoherent (Compton scattering)
cos11
EE
2cm
E
e
Where parameter
Relation between scattered photon energy Eγ and scattering angle Θ
We obtain relations between energies and angles of scattering and reflection from the energy and momentum conservation laws
We assumed 1) scattering on free electron (EγgtgtBe) 2) electron is in the rest
Θ
φ
Eγ pγ=Eγc
Eγrsquo pγrsquo=Eγrsquoc
mec2 pe= 0
222
2
cmc
EpE e
eee
Scattered photon energy
211800 E
E
Reflected electron energy
Reflection angle
cos11
cos1
EEEEe
21
21800 E
Ee
2
tan1cot
Polar graph of cross-section without inclusion of S(qZ) influence In the limit E rarr 0 we obtain graph for coherent scattering
2
2
20 sin
2
1
E
E
E
E
E
EZr
d
d C
cos11
cos1cos1
cos11
1
2
1 222
22
0
Zrd
d C
222
021
3121ln
2
121ln
1
21
1212
ZrC
Diferential cross-section is described by Klein-Nishin equation (on free electrons)
We introduce energy of scattered photon
inclusion of influence of electron binding at atom rarr multiplying by function S(qZ) ndash probability of momentum q transfer to electron during ionization or excitation
Total cross section (can be obtained by integration)
Distribution of energy transferred to electrons
Eγ gt mec2 rarr ζ gt 1
E
ZZC ~~
Scattering of high energy electron and low energy photon ndash inverse Compton scattering (see exercise)
Photoelectric effect
Can pass only on bounded electron
Total photon energy is transfered
Electron energy Ee = Eγ - Be
and so σF = ~ Z5Eγ-35 near to K-shell σF = ~ Z45Eγ
-3
Cross-section (for Eγ ltlt mec2)
Accurate calculation of photoeffect process (solution of Dirac equation) is very sophisticated
γ e-
27
54 124
TF Z
If it is enough energy (Eγ gt BeK binding energy on K-shell) the photoeffect will pass almost only on these electrons
137
1
4 0
2
c
e
where is fine structure constant
More accurate equation for σF near to K-shell see Leo
Dependency of K-shell electron binding energy on proton number Z of atom (Si ndash 18389 keV Ge ndash 111031 keV Pb ndash 880045 keV)
Production of electron and positron pairs
e+
e-
γ
σP ~ Z2ln(2Eγ)
Transformation of photon to electron and positron pair
Energy and momentum conservation laws rarr only In nucleus field (mostly) Eγ gt 2mec2 = 1022 keVeventually electrons Eγ gt 4mec2 = 2044 keV (je 1-2Z smaller)
31222
ZcmEcm e
e
312ZcmE e
where f(Z) is coulomb correction of order α2
Dependency of σP on Z and Eγ is(for bdquolower energiesldquo range)
There is valid for cross-section in special cases
Without screening
Complete screening
54
109)(2ln
9
74 2
02 ZfrZP
54
1)(183ln
9
74 312
02 ZfZrZP
Production in the electron field(bdquotripletldquo production)
252
20 432
3
Zr
PT
Eγgtgtmec2 electrons and positrons are peaked forward Θ asymp 1ζ Cross-section dependency On photon energy
Description is equivalent to description of bremsstrahlung radiation (necessity to include screening influence predominance of pair production near nucleus ndash without screening)
Interaction with small contribution
Photonuclear reactions ndash resonance processes with small probability
Photon interaction with coulomb field of nucleus (Delbruumlck scattering) ndashwe can look on it as on virtual pair production and following annihilation
Photonuclear reactions in order of mbarn up to barn in narrow energy rangeinteraction with electrons in order of barns up to 105 barns in broad energy range
Nuclear Rayleigh scattering Nuclear Thomson scattering ndash substitutions e rarrZe me rarr Mj
and then mA
Z
cM
eZrr
Jj
182
20
22
0 10514
Nuclear resonance scattering ( for example giant dipole resonance)
Total cross-sections barnA
Zm
A
Zr jTJ 126010612
3
82
4236
2
42
X-ray
Auger electrons
proton
zaacuteřeniacute gamaelektron
XA
X
NN
N
Fluorescent efficiency (coefficient)
Bremsstrahlung radiation during movement of electrons and positrons
NX ndash X-ray photons NA ndash Auger electrons
Released energy is transferred during electron transition at atomic cloud on other electron
Passage of electrons and positrons1) Ionization losses2) Bremsstrahlung radiation
Charged particle moves in nuclear field with acceleration rarr it emits photons
Annihilation of positron and electron
Positrons are stopped by ionization losses and they annihilate in the rest rarr 2 quanta of 511 keV (they are not fully in the rest rarr energy smearing of annihilation quanta)
Secondary processes
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range
Equation for decreasing of photon number xe
I
I
0
For compound or mixture Bragg rule is valid
2
22
1
11
ww
Total cross-section
dI = -μIdx
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Incoherent (Compton scattering)
cos11
EE
2cm
E
e
Where parameter
Relation between scattered photon energy Eγ and scattering angle Θ
We obtain relations between energies and angles of scattering and reflection from the energy and momentum conservation laws
We assumed 1) scattering on free electron (EγgtgtBe) 2) electron is in the rest
Θ
φ
Eγ pγ=Eγc
Eγrsquo pγrsquo=Eγrsquoc
mec2 pe= 0
222
2
cmc
EpE e
eee
Scattered photon energy
211800 E
E
Reflected electron energy
Reflection angle
cos11
cos1
EEEEe
21
21800 E
Ee
2
tan1cot
Polar graph of cross-section without inclusion of S(qZ) influence In the limit E rarr 0 we obtain graph for coherent scattering
2
2
20 sin
2
1
E
E
E
E
E
EZr
d
d C
cos11
cos1cos1
cos11
1
2
1 222
22
0
Zrd
d C
222
021
3121ln
2
121ln
1
21
1212
ZrC
Diferential cross-section is described by Klein-Nishin equation (on free electrons)
We introduce energy of scattered photon
inclusion of influence of electron binding at atom rarr multiplying by function S(qZ) ndash probability of momentum q transfer to electron during ionization or excitation
Total cross section (can be obtained by integration)
Distribution of energy transferred to electrons
Eγ gt mec2 rarr ζ gt 1
E
ZZC ~~
Scattering of high energy electron and low energy photon ndash inverse Compton scattering (see exercise)
Photoelectric effect
Can pass only on bounded electron
Total photon energy is transfered
Electron energy Ee = Eγ - Be
and so σF = ~ Z5Eγ-35 near to K-shell σF = ~ Z45Eγ
-3
Cross-section (for Eγ ltlt mec2)
Accurate calculation of photoeffect process (solution of Dirac equation) is very sophisticated
γ e-
27
54 124
TF Z
If it is enough energy (Eγ gt BeK binding energy on K-shell) the photoeffect will pass almost only on these electrons
137
1
4 0
2
c
e
where is fine structure constant
More accurate equation for σF near to K-shell see Leo
Dependency of K-shell electron binding energy on proton number Z of atom (Si ndash 18389 keV Ge ndash 111031 keV Pb ndash 880045 keV)
Production of electron and positron pairs
e+
e-
γ
σP ~ Z2ln(2Eγ)
Transformation of photon to electron and positron pair
Energy and momentum conservation laws rarr only In nucleus field (mostly) Eγ gt 2mec2 = 1022 keVeventually electrons Eγ gt 4mec2 = 2044 keV (je 1-2Z smaller)
31222
ZcmEcm e
e
312ZcmE e
where f(Z) is coulomb correction of order α2
Dependency of σP on Z and Eγ is(for bdquolower energiesldquo range)
There is valid for cross-section in special cases
Without screening
Complete screening
54
109)(2ln
9
74 2
02 ZfrZP
54
1)(183ln
9
74 312
02 ZfZrZP
Production in the electron field(bdquotripletldquo production)
252
20 432
3
Zr
PT
Eγgtgtmec2 electrons and positrons are peaked forward Θ asymp 1ζ Cross-section dependency On photon energy
Description is equivalent to description of bremsstrahlung radiation (necessity to include screening influence predominance of pair production near nucleus ndash without screening)
Interaction with small contribution
Photonuclear reactions ndash resonance processes with small probability
Photon interaction with coulomb field of nucleus (Delbruumlck scattering) ndashwe can look on it as on virtual pair production and following annihilation
Photonuclear reactions in order of mbarn up to barn in narrow energy rangeinteraction with electrons in order of barns up to 105 barns in broad energy range
Nuclear Rayleigh scattering Nuclear Thomson scattering ndash substitutions e rarrZe me rarr Mj
and then mA
Z
cM
eZrr
Jj
182
20
22
0 10514
Nuclear resonance scattering ( for example giant dipole resonance)
Total cross-sections barnA
Zm
A
Zr jTJ 126010612
3
82
4236
2
42
X-ray
Auger electrons
proton
zaacuteřeniacute gamaelektron
XA
X
NN
N
Fluorescent efficiency (coefficient)
Bremsstrahlung radiation during movement of electrons and positrons
NX ndash X-ray photons NA ndash Auger electrons
Released energy is transferred during electron transition at atomic cloud on other electron
Passage of electrons and positrons1) Ionization losses2) Bremsstrahlung radiation
Charged particle moves in nuclear field with acceleration rarr it emits photons
Annihilation of positron and electron
Positrons are stopped by ionization losses and they annihilate in the rest rarr 2 quanta of 511 keV (they are not fully in the rest rarr energy smearing of annihilation quanta)
Secondary processes
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range
Equation for decreasing of photon number xe
I
I
0
For compound or mixture Bragg rule is valid
2
22
1
11
ww
Total cross-section
dI = -μIdx
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Polar graph of cross-section without inclusion of S(qZ) influence In the limit E rarr 0 we obtain graph for coherent scattering
2
2
20 sin
2
1
E
E
E
E
E
EZr
d
d C
cos11
cos1cos1
cos11
1
2
1 222
22
0
Zrd
d C
222
021
3121ln
2
121ln
1
21
1212
ZrC
Diferential cross-section is described by Klein-Nishin equation (on free electrons)
We introduce energy of scattered photon
inclusion of influence of electron binding at atom rarr multiplying by function S(qZ) ndash probability of momentum q transfer to electron during ionization or excitation
Total cross section (can be obtained by integration)
Distribution of energy transferred to electrons
Eγ gt mec2 rarr ζ gt 1
E
ZZC ~~
Scattering of high energy electron and low energy photon ndash inverse Compton scattering (see exercise)
Photoelectric effect
Can pass only on bounded electron
Total photon energy is transfered
Electron energy Ee = Eγ - Be
and so σF = ~ Z5Eγ-35 near to K-shell σF = ~ Z45Eγ
-3
Cross-section (for Eγ ltlt mec2)
Accurate calculation of photoeffect process (solution of Dirac equation) is very sophisticated
γ e-
27
54 124
TF Z
If it is enough energy (Eγ gt BeK binding energy on K-shell) the photoeffect will pass almost only on these electrons
137
1
4 0
2
c
e
where is fine structure constant
More accurate equation for σF near to K-shell see Leo
Dependency of K-shell electron binding energy on proton number Z of atom (Si ndash 18389 keV Ge ndash 111031 keV Pb ndash 880045 keV)
Production of electron and positron pairs
e+
e-
γ
σP ~ Z2ln(2Eγ)
Transformation of photon to electron and positron pair
Energy and momentum conservation laws rarr only In nucleus field (mostly) Eγ gt 2mec2 = 1022 keVeventually electrons Eγ gt 4mec2 = 2044 keV (je 1-2Z smaller)
31222
ZcmEcm e
e
312ZcmE e
where f(Z) is coulomb correction of order α2
Dependency of σP on Z and Eγ is(for bdquolower energiesldquo range)
There is valid for cross-section in special cases
Without screening
Complete screening
54
109)(2ln
9
74 2
02 ZfrZP
54
1)(183ln
9
74 312
02 ZfZrZP
Production in the electron field(bdquotripletldquo production)
252
20 432
3
Zr
PT
Eγgtgtmec2 electrons and positrons are peaked forward Θ asymp 1ζ Cross-section dependency On photon energy
Description is equivalent to description of bremsstrahlung radiation (necessity to include screening influence predominance of pair production near nucleus ndash without screening)
Interaction with small contribution
Photonuclear reactions ndash resonance processes with small probability
Photon interaction with coulomb field of nucleus (Delbruumlck scattering) ndashwe can look on it as on virtual pair production and following annihilation
Photonuclear reactions in order of mbarn up to barn in narrow energy rangeinteraction with electrons in order of barns up to 105 barns in broad energy range
Nuclear Rayleigh scattering Nuclear Thomson scattering ndash substitutions e rarrZe me rarr Mj
and then mA
Z
cM
eZrr
Jj
182
20
22
0 10514
Nuclear resonance scattering ( for example giant dipole resonance)
Total cross-sections barnA
Zm
A
Zr jTJ 126010612
3
82
4236
2
42
X-ray
Auger electrons
proton
zaacuteřeniacute gamaelektron
XA
X
NN
N
Fluorescent efficiency (coefficient)
Bremsstrahlung radiation during movement of electrons and positrons
NX ndash X-ray photons NA ndash Auger electrons
Released energy is transferred during electron transition at atomic cloud on other electron
Passage of electrons and positrons1) Ionization losses2) Bremsstrahlung radiation
Charged particle moves in nuclear field with acceleration rarr it emits photons
Annihilation of positron and electron
Positrons are stopped by ionization losses and they annihilate in the rest rarr 2 quanta of 511 keV (they are not fully in the rest rarr energy smearing of annihilation quanta)
Secondary processes
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range
Equation for decreasing of photon number xe
I
I
0
For compound or mixture Bragg rule is valid
2
22
1
11
ww
Total cross-section
dI = -μIdx
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Photoelectric effect
Can pass only on bounded electron
Total photon energy is transfered
Electron energy Ee = Eγ - Be
and so σF = ~ Z5Eγ-35 near to K-shell σF = ~ Z45Eγ
-3
Cross-section (for Eγ ltlt mec2)
Accurate calculation of photoeffect process (solution of Dirac equation) is very sophisticated
γ e-
27
54 124
TF Z
If it is enough energy (Eγ gt BeK binding energy on K-shell) the photoeffect will pass almost only on these electrons
137
1
4 0
2
c
e
where is fine structure constant
More accurate equation for σF near to K-shell see Leo
Dependency of K-shell electron binding energy on proton number Z of atom (Si ndash 18389 keV Ge ndash 111031 keV Pb ndash 880045 keV)
Production of electron and positron pairs
e+
e-
γ
σP ~ Z2ln(2Eγ)
Transformation of photon to electron and positron pair
Energy and momentum conservation laws rarr only In nucleus field (mostly) Eγ gt 2mec2 = 1022 keVeventually electrons Eγ gt 4mec2 = 2044 keV (je 1-2Z smaller)
31222
ZcmEcm e
e
312ZcmE e
where f(Z) is coulomb correction of order α2
Dependency of σP on Z and Eγ is(for bdquolower energiesldquo range)
There is valid for cross-section in special cases
Without screening
Complete screening
54
109)(2ln
9
74 2
02 ZfrZP
54
1)(183ln
9
74 312
02 ZfZrZP
Production in the electron field(bdquotripletldquo production)
252
20 432
3
Zr
PT
Eγgtgtmec2 electrons and positrons are peaked forward Θ asymp 1ζ Cross-section dependency On photon energy
Description is equivalent to description of bremsstrahlung radiation (necessity to include screening influence predominance of pair production near nucleus ndash without screening)
Interaction with small contribution
Photonuclear reactions ndash resonance processes with small probability
Photon interaction with coulomb field of nucleus (Delbruumlck scattering) ndashwe can look on it as on virtual pair production and following annihilation
Photonuclear reactions in order of mbarn up to barn in narrow energy rangeinteraction with electrons in order of barns up to 105 barns in broad energy range
Nuclear Rayleigh scattering Nuclear Thomson scattering ndash substitutions e rarrZe me rarr Mj
and then mA
Z
cM
eZrr
Jj
182
20
22
0 10514
Nuclear resonance scattering ( for example giant dipole resonance)
Total cross-sections barnA
Zm
A
Zr jTJ 126010612
3
82
4236
2
42
X-ray
Auger electrons
proton
zaacuteřeniacute gamaelektron
XA
X
NN
N
Fluorescent efficiency (coefficient)
Bremsstrahlung radiation during movement of electrons and positrons
NX ndash X-ray photons NA ndash Auger electrons
Released energy is transferred during electron transition at atomic cloud on other electron
Passage of electrons and positrons1) Ionization losses2) Bremsstrahlung radiation
Charged particle moves in nuclear field with acceleration rarr it emits photons
Annihilation of positron and electron
Positrons are stopped by ionization losses and they annihilate in the rest rarr 2 quanta of 511 keV (they are not fully in the rest rarr energy smearing of annihilation quanta)
Secondary processes
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range
Equation for decreasing of photon number xe
I
I
0
For compound or mixture Bragg rule is valid
2
22
1
11
ww
Total cross-section
dI = -μIdx
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Production of electron and positron pairs
e+
e-
γ
σP ~ Z2ln(2Eγ)
Transformation of photon to electron and positron pair
Energy and momentum conservation laws rarr only In nucleus field (mostly) Eγ gt 2mec2 = 1022 keVeventually electrons Eγ gt 4mec2 = 2044 keV (je 1-2Z smaller)
31222
ZcmEcm e
e
312ZcmE e
where f(Z) is coulomb correction of order α2
Dependency of σP on Z and Eγ is(for bdquolower energiesldquo range)
There is valid for cross-section in special cases
Without screening
Complete screening
54
109)(2ln
9
74 2
02 ZfrZP
54
1)(183ln
9
74 312
02 ZfZrZP
Production in the electron field(bdquotripletldquo production)
252
20 432
3
Zr
PT
Eγgtgtmec2 electrons and positrons are peaked forward Θ asymp 1ζ Cross-section dependency On photon energy
Description is equivalent to description of bremsstrahlung radiation (necessity to include screening influence predominance of pair production near nucleus ndash without screening)
Interaction with small contribution
Photonuclear reactions ndash resonance processes with small probability
Photon interaction with coulomb field of nucleus (Delbruumlck scattering) ndashwe can look on it as on virtual pair production and following annihilation
Photonuclear reactions in order of mbarn up to barn in narrow energy rangeinteraction with electrons in order of barns up to 105 barns in broad energy range
Nuclear Rayleigh scattering Nuclear Thomson scattering ndash substitutions e rarrZe me rarr Mj
and then mA
Z
cM
eZrr
Jj
182
20
22
0 10514
Nuclear resonance scattering ( for example giant dipole resonance)
Total cross-sections barnA
Zm
A
Zr jTJ 126010612
3
82
4236
2
42
X-ray
Auger electrons
proton
zaacuteřeniacute gamaelektron
XA
X
NN
N
Fluorescent efficiency (coefficient)
Bremsstrahlung radiation during movement of electrons and positrons
NX ndash X-ray photons NA ndash Auger electrons
Released energy is transferred during electron transition at atomic cloud on other electron
Passage of electrons and positrons1) Ionization losses2) Bremsstrahlung radiation
Charged particle moves in nuclear field with acceleration rarr it emits photons
Annihilation of positron and electron
Positrons are stopped by ionization losses and they annihilate in the rest rarr 2 quanta of 511 keV (they are not fully in the rest rarr energy smearing of annihilation quanta)
Secondary processes
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range
Equation for decreasing of photon number xe
I
I
0
For compound or mixture Bragg rule is valid
2
22
1
11
ww
Total cross-section
dI = -μIdx
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Interaction with small contribution
Photonuclear reactions ndash resonance processes with small probability
Photon interaction with coulomb field of nucleus (Delbruumlck scattering) ndashwe can look on it as on virtual pair production and following annihilation
Photonuclear reactions in order of mbarn up to barn in narrow energy rangeinteraction with electrons in order of barns up to 105 barns in broad energy range
Nuclear Rayleigh scattering Nuclear Thomson scattering ndash substitutions e rarrZe me rarr Mj
and then mA
Z
cM
eZrr
Jj
182
20
22
0 10514
Nuclear resonance scattering ( for example giant dipole resonance)
Total cross-sections barnA
Zm
A
Zr jTJ 126010612
3
82
4236
2
42
X-ray
Auger electrons
proton
zaacuteřeniacute gamaelektron
XA
X
NN
N
Fluorescent efficiency (coefficient)
Bremsstrahlung radiation during movement of electrons and positrons
NX ndash X-ray photons NA ndash Auger electrons
Released energy is transferred during electron transition at atomic cloud on other electron
Passage of electrons and positrons1) Ionization losses2) Bremsstrahlung radiation
Charged particle moves in nuclear field with acceleration rarr it emits photons
Annihilation of positron and electron
Positrons are stopped by ionization losses and they annihilate in the rest rarr 2 quanta of 511 keV (they are not fully in the rest rarr energy smearing of annihilation quanta)
Secondary processes
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range
Equation for decreasing of photon number xe
I
I
0
For compound or mixture Bragg rule is valid
2
22
1
11
ww
Total cross-section
dI = -μIdx
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
X-ray
Auger electrons
proton
zaacuteřeniacute gamaelektron
XA
X
NN
N
Fluorescent efficiency (coefficient)
Bremsstrahlung radiation during movement of electrons and positrons
NX ndash X-ray photons NA ndash Auger electrons
Released energy is transferred during electron transition at atomic cloud on other electron
Passage of electrons and positrons1) Ionization losses2) Bremsstrahlung radiation
Charged particle moves in nuclear field with acceleration rarr it emits photons
Annihilation of positron and electron
Positrons are stopped by ionization losses and they annihilate in the rest rarr 2 quanta of 511 keV (they are not fully in the rest rarr energy smearing of annihilation quanta)
Secondary processes
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range
Equation for decreasing of photon number xe
I
I
0
For compound or mixture Bragg rule is valid
2
22
1
11
ww
Total cross-section
dI = -μIdx
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Total absorption of gamma rays at matters
Review of main processes
σ = σF + σC + σPTotal cross-sections
Multiply by number of atoms per volume unit N
A
NN a
where Na ndash Avogadro constant A ndash atomic massρ ndash material density
μ ndash total absorption coefficient ndash inverse value of mean free path of photon at material
Photon can loss big part (even all) its energy in oneinteraction rarr beam weakens it has not fixed range