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

Eγ [keV] 1 10 50 100 500 1000 2000ν [EHz = 1018 Hz] 0242 242 121 242 121 242 484λ [nm] 124 0124 0025 00124 00025 000124 000062

Grid spacing is in the order of 01 ndash 1 nm

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

Eγ [keV] 1 10 50 100 500 1000 2000ν [EHz = 1018 Hz] 0242 242 121 242 121 242 484λ [nm] 124 0124 0025 00124 00025 000124 000062

Grid spacing is in the order of 01 ndash 1 nm

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

Eγ [keV] 1 10 50 100 500 1000 2000ν [EHz = 1018 Hz] 0242 242 121 242 121 242 484λ [nm] 124 0124 0025 00124 00025 000124 000062

Grid spacing is in the order of 01 ndash 1 nm

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

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