Charged particle therapy, ion range verification, prompt radiation

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Submitted on 15 Feb 2011

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Charged particle therapy, ion range verification, prompt

radiation

Mauro Testa

To cite this version:

THESE DE L‘UNIVERSITE DE LYON Délivrée par

L’UNIVERSITE CLAUDE BERNARD LYON 1

ECOLE DOCTORALE PHAST

DIPLOME DE DOCTORAT

Présentée à Lyon le 14 octobre 2010

par

Mauro TESTA

Physical measurements for ion range verification in charged particle therapy

Directeur de thèse : M. Chevallier

Jury : M. M. Chevallier Directeur de thèse M. R. Ferrand

M. F. Haas Rapporteur

M. C. Lacasta

M. J-M. Moreau Président du jury

Mme K. Parodi

M. C. Ray

M. D. Schardt Rapporteur

1 1 1 23456789AB9C95DE1

Acknowledgements

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Contents

1 Overview ... 3

1.1 Particle radiation therapy... 3

1.2 Prompt 1-camera for dose verification and ion range monitoring in particle therapy. ... 4

1.3 Outline of the thesis... 6

2 Radiation therapy: introduction ... 7

2.1 Physical rationale for particle radiation therapy... 8

2.2 Radiobiological rationale for particle radiation therapy... 10

2.3 Particle vs conventional radiation therapy: clinical results and cost analysis 12 2.3.1 Clinical results ... 13

2.3.2 Cost analysis ... 15

2.4 Current and future ion therapy centers ... 16

3 Radiation therapy with ion beams ... 18

3.1 The physics of interaction of ions with matter ... 18

3.1.1 Inverse depth dose profile: stopping of ions in matter ... 18

3.1.2 Range scattering ... 20

3.1.3 Lateral scattering ... 22

3.1.4 Ion fragmentation: models and fragments ... 23

3.2 The physics of interaction of photons with matter ... 26

3.2.1 Photoelectric effect, Compton scattering, Pair production... 26

3.3 The physics of interaction of neutrons with matter ... 30

4 Current and proposed methods for dose verification and monitoring in particle therapy ... 32

4.1 PET and TOF-PET ... 32

4.1.1 Ion range verification with PET ... 36

4.2 Prompt photon radiation ... 37

4.2.1 Collimated Prompt Gamma Camera... 41

4.2.1 Compton Camera... 43

4.3 Interaction Vertex Imaging (IVI) ... 45

5 Physical measurements of the prompt radiation originated from ion fragmentation ... 48

5.1 Properties of scintillation detectors ... 48

5.1.1 Characteristics of BaF2 – NaI(Tl) – LYSO – BC501 scintillators ... 50

5.1.2 Pulse shape discrimination (PSD) for BaF2 and BC501 scintillators... 54

5.1.2.1 PSD test measurements with a 241Am-Be source ... 54

5.1.2.2 PSD test measurements with 14 MeV neutrons ... 58

5.2 Measurements of prompt 1-rays produced from C-ion fragmentation ... 61

5.2.1 GANIL and GSI single-detector experimental set-up ... 61

5.2.1.1 Calculation of detection solid angle and field pf view ... 64

5.2.2 GANIL multi-detector experimental set-up ... 66

5.3 Results and discussion ... 68

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5.3.2.1 Time of flight (TOF) spectra analysis ... 84

5.3.2.2 Multi detector prompt photon scan profiles ... 86

5.4 Conclusions and perspectives... 88

6 Geant4 Monte Carlo simulations for the design of a multi-detector multi-collimator Prompt Gamma Camera... 92

6.1 Application of Monte Carlo simulation codes in medical physics... 92

6.1.1 A short overview of the code architecture and physical models used in Geant4………..93

6.2 Simulations of a simplified multi-collimated and multi-detector Prompt Gamma Camera ... 94

6.2.1 Basic principles of collimator design ... 94

6.2.2 Description of the simulation set-up... 95

6.2.3 Basic description of collimator imaging properties... 99

6.3 Simulations results and discussion ... 101

6.3.1 Influence of the collimator design on the detection efficiency ... 101

6.3.1.1 Influence of the collimator thickness and position on the visibility of the collimator slit-pattern ... 101

6.3.1.2 Influence of the collimator thickness and position on the detection efficiency ... 104

6.3.1.3 Influence of the collimator tiles and slit dimension on the detection efficiency ... 108

6.3.2 Influence of the collimator design on the spatial resolution... 109

6.3.2.1 Influence of the collimator position on the spatial resolution ... 111

6.3.2.2 Influence of the crystal detector width on the spatial resolution... 115

6.3.2.3 Influence of the detection statistics on the spatial resolution ... 116

6.3.3 Conclusions and perspectives... 117

7 Summary and outlook... 121

8 Appendix... 124

8.1 NaI(Tl) calibration for beam intensity monitoring ... 124

8.2 Electronics and acquisition set-up ... 125

8.2.1 GANIL single-detector experiment ... 125

8.2.2 GSI single-detector experiment ... 127

8.2.3 GANIL multi-detector experiment ... 127

Bibliography ... 129

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1 Overview

1.1 Particle radiation therapy

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1.2 Prompt

1

-camera for dose verification and ion range

monitoring in particle therapy

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1.3 Outline of the thesis

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2 Radiation therapy: introduction

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2.1 Physical rationale for particle radiation therapy

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figure 2-1: Comparison of depth-dose profiles for carbon ions and photons from (Schardt et al. 2010). The inverse depth dose profile of carbon ions compared to photons is favorable to treat deep-seated tumours.

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figure 2-2: Superposition of several C-ions Bragg-curves with different energies (red lines) to produce a Spread-Off-Bragg-Peak SOBP (blue line) from (www.gsi.de/forschung/bio/).

2.2 Radiobiological rationale for particle radiation therapy

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figure 2-3: Up: homogenous biological effective dose distribution (green line) and inhomogeneous physical dose distribution (blue line) obtain by superposition of different C-ion Bragg-peak curves.

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2.3 Particle vs conventional radiation therapy: clinical results

and cost analysis

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8

figure 2-4: Comparison of treatment plans for large tumour volumes in the base of the skull. Left: plan for carbon ions, two fields of irradiation. Right: plan for IMRT nine fields of irradiation. The irradiation with C-ions results in a substantial reduction of the integral dose to normal tissue and better spare of critical structures. Picture from (Durante & Loeffler 2009).

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2.3.1 Clinical results

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8

Indication End point Results Photons Results Ions NIRS Results Ions GSI Nasopharynx carcinoma (advanced state) 5 year survival 40 - 50 % 63 %

Chordoma Local control rate 30 - 50 % 65 % 70 % Chondrosarcoma Local control rate 33 % 88 % 89 %

Glioblastoma Average survival

time 12 month 16 month

Choroid melanoma 5 year survival 95 %

96 % preservation of

eyesight Paranasal sinuses

Tumours Local control rate 21 % 63 % Pancreatic

carcinoma

Average survival

time 6.5 month 7.8 month Liver tumours 5 year survival 23 % 100 % Salivary gland

tumours Local control rate 24 - 28 % 61 % 77.5 % Soft-tissue

carcinoma 5 year survival 31 - 75 % 52 - 83 %

Table 2-1 Comparison of clinical results for conventional radiation therapy with photons and C-ion treatments performed at NIRS and GSI. C-ions are superior to photons for all the end points under consideration; from (www.gsi.de/forschung/bio/).

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2.3.2 Cost analysis

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A3BC35CDE8526734F8CE57DB5CDE8

8

figure 2-5: Comparative average costs for different cancer treatments. Proton and carbon ion therapies are slightly more expensive than the average cost of cancer treatment in France but nevertheless cheaper than regularly employed chemotherapy treatments; adapted from (www.etoile.org).

2.4 Current and future ion therapy centers

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Comparative average cost for different cancer treatments

2 500 € 6 400 € 24 000 € 25 000 € 30 000 € 40 000 € 50 000 € 0 10 000 € 20 000 € 30 000 € 40 000 € 50 000 € Conventional RT

IMRT Average cost for cancer treatment in France One year chemotherapy with Herceptin Proton therapy Carbon ion therapy One year chemotherapy with Nexavar

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3 Radiation therapy with ion beams

3.1 The physics of interaction of ions with matter

3.1.1 Inverse depth dose profile: stopping of ions in matter

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,2A5 E235 939AE945 )9%2&5 5 29D5 9%B47EF5 F2%%E4E2345 &E785 7BA975 4FA99393DF%9E5 )9E35725F237AE)D7954E3E6EFB37%#57257895939A#%2445B352E3B7957895472CCE35 CA2F9445 B75 7895 $9A#5 935 265 7895 CBA7EF%95 CB785 '%B475 69&5 9(5 8E45 49F235 9F8B3E45 265 939A#%2445 E45 F223%#5 FB%%95 3DF%9BA5 472CCE35 C2&9A5 1745 $B%D945BA95A9C2A795B45B4895%E3945E356EDA95562A5E2345265789ABC9D7EF5E379A9475 '$B%D94562A5CA272345BA953275482&35)9FBD49572254B%%57256E75E3578952AE3B7954FB%9(11 5

5

figure 3-1: Electronic (full lines) and nuclear (dashed lines) energy-loss per unit path length dE/dx for ions of therapeutic interest in water. dE/dx values are calculated with SRIM code (Ziegler 2004).

123425467859AB2CD8E45984678FA28

[ ]

[ ]

1 2 3 4 5 6 × × 1 2 3 4 5 6 × × = − − g cm cm F m keV dx dE Gy D 3 2 9 1 10 6 . 1 ρ µ 5 3-4 5 1359DB7E23557895B)42A)952495E45FB%FD%B795E35:AB#5;:#<=2>5B35 !5 "5 A9CA94937457895727B%5939A#5%2445265CBA7EF%945 895727B%5CB785%937857AB$9%%95E35B59ED5)#5B35E235&E785E3E7EB%5939A#5!85FB35 )95FB%FD%B795)#5E379AB7E357895727B%5939A#%2445B45A9C2A795E359DB7E23585

( )

7

8− 9 A B C D = 0 1 0 E dE dx dE E R 5 3-5 5 ,2A5 89B$#5 F8BA95 E2345 7895 E379AB%5 482&35 E35 9DB7E235 85 A9CA9493745 B5 $9A#5 F%2495BCCA21EB7E23526578959B35CA2-9F795AB3951#B52657895CBA7EF%9454E3F95E2345 BA95 $9A#5 %E77%95 4FB779A95 B35 7AB$9%5 B%2475 E35 B5 47ABE875 %E395 135 6EDA95 5 &95 482&5 B5 F2CBAE4235 )97&9935 7895 CA2-9F795 AB3945 E35 &B79A5 62A5 E2345 265 789ABC9D7EF5E379A9475175FB35)953279578B757895AB395265E2345&E78578954B954C9FE6EF5 939A#5 4FB%945 &E785 B5 6BF72A5 265 $5E_{5 '&89A95 $5 9327945 7895 B445 3D)9A5 B35 E5}

7895B72EF53D)9A52657895CBA7EF%9(5B35789A962A95CA272345B35α5CBA7EF%945482&5

78954B95CB785E35&B79A5&8935C%27795B45B56D3F7E235265789EA54C9FE6EF5939A#5

5

figure 3-2: Projected mean range for ions of therapeutic interest calculated in water with SRIM code (Ziegler 2004).

3.1.2 Range scattering

545 E75 FB35 )95 49935 E35 6EDA95 5 7895 AB7E25 )97&9935 7895 472CCE35 C2&9A5 B75 7895 *ABC9B25 B35 B75 939AE945 265 49$9AB%5 8D3A945 9D5 FB35 AE495 725 6BF72A5 265 8D3A945 8E45 E45 F234E479375 &E785 7895 939A#%2445 $B%D945 &8EF85 FB35 )95 FB%FD%B795&E7859DB7E2355)D75E35A9B%E7#547B7E47EFB%56%DF7DB7E23452657895939A#

92C5AB88

%2445 BA2D35 E745 B$9AB95 $B%D95 2FFDA5 E35 7895 %BA95 3D)9A5 265 F2%%E4E2345 265 7895 4%2&E32&35 CA2F9445 8E45 C893293235 E45 232&35 B45 AB395 2A5 939A#5 47AB%E35 B35 E75 E45 A94C234E)%95 62A5 7895 %BA9A5 *ABC9B25 9B4DA95 62A5 B35 E235 )9B5 &E785 A94C9F75 725 7895 FB%FD%B7E235 )B495 235 7895 B$9AB95 939A#%2445 265 B5 4E3%95CBA7EF%95B45A9CA9493795E356EDA9555895AB39547AB%E35E3FA9B4945&E785 7895 C9397AB7E235 9C785 E35 B5 E$935 B79AEB%5 A94D%7E35 E35 *ABC9B245 265 %BA9A5 &E785 B35 4B%%9A5 89E875 62A5 8E89A5 E3E7EB%5 939A#5 265 7895 4B95 E2345 B45 A9CA9493795E356EDA95855

2A92$9A57895AB39547AB%E359C9345B%4252357895B4452657895CA2-9F7E%95895 CA27235 *ABC9B25 482&35 E35 6EDA95 5 E45 %BA9A5 78B35 7895 FBA)235 *ABC9B25 78B75 BAE4945 B75 7895 4B95 9C785 E35 &B79A5 )9FBD495 62A5 E669A9375 E235 4C9FE945 7895 AB395 47AB%E35 BCCA21EB79%#5 $BAE945 B45 7895 E3$9A495 265 7895 4DBA95 A2275 265 7895 CBA7EF%95B445'?F8BA75975B%5(513995789547B7E47EFB%56%DF7DB7E2345235$E2%9375 )E3BA#5 E379ABF7E2345 )97&9935 7895 E3F2E35 CBA7EF%95 B35 9%9F7A2345 6A25 7895 9ED5 BA95 7895 BE35 A94C234E)%95 62A5 AB395 47AB%E35 B35 789#5 BA95 CA2C2A7E23B%57257895AB7E25)97&993578959%9F7A235B35 E235B445589A962A95B757895 4B95 C9397AB7E235 9C785 89B$E9A5 E2345 918E)E75 B5 3BAA2&9A5 *ABC9B25 &E785 B5 4799C9A5E47B%56B%%266525E$95B3591BC%957895A9%B7E$95AB39547AB%E35E357E44D95 B2D3745725B)2D75@526578959B35AB39562A5CA272345B3523%#5725@562A5 E2345 'ABA2E5 (5 135 F%E3EFB%5 CABF7EF95 82&9$9A5 7895 CA26E%95 265 7895 *ABC9B25 E45 )A2B9A5BE3%#5D957257895934E7#5E3822939E7E9452657895C9397AB7957E44D94562A5 39E8)2DAE35 7AB-9F72AE945 265 7895 6E3E795 )9B5 4E.95 '?F8BA75 975 B%5 (5 "DF%9BA5 6AB937B7E235 78B75 &E%%5 )95 E4FD4495 E35 7895 39175 CBABABC85 B%425 8B45 B35 EC2A7B375 E36%D93F95 235 7895 *ABC9B25 CA26E%95 &82495 C9B25 725 937AB3F95 AB7E25 )9F2945 ABDB%%#5 4B%%9A5 &E785 E3FA9B4E35 CBA7EF%95 939A#5 D95 725 789EA5 8E89A5 6AB937B7E235 AB795 ,E3B%%#5 E75 FB35 )95 F23F%D95 78B75 7895 9669F75 265 AB395 47AB%E35235789ABC#5BCC%EFB7E2345E45B%&B#454B%%9A578B3552A5F2CBAB)%95&E785 7895 D3B$2EB)%95 2937D5 E4C9A4E235 265 7895 )9B5 6A25 7895 BFF9%9AB72A5 9%E$9A#54#4795'ABA2E5(52A92$9A562A54FB33E35)9B59%E$9A#54#47945 D4E354%EF95)#54%EF95EAABEB7E23526578957BA975$2%D95E75FB35)959$935B$B37B92D45 725&E935789548BAC5*ABC9B25725A9DF9578953D)9A5265939A#5479C45%9BE35725 4E3E6EFB375 482A79A5 2$9AB%%5 EAABEB7E235 7E945 B35 B5 8E89A5 CBA7EF%95 6%D93F95 C9A5 %B#9A5'B5C9)9A535:57AB675+++(5

123425467859AB2CD8E45984678FA28

figure 3-3: Comparison of measured Bragg curves of proton and C-ions having the same mean range. The measurements are performed in water with an ionization chamber and are normalized to the same peak height, from (Schardt et al. 2007)

3.1.3 Lateral scattering

8BA95 CBA7EF%945 CB44E35 78A2D85 B5 9ED5 91C9AE93F95 3275 23%#5 E379ABF7E2345 &E7857BA9759%9F7A2345)D75B%425D%7EC%959%B47EF5F2%%E4E2345&E7857BA9753DF%9E5895 47B7E47EFB%5 A9C97E7E235 265 789495 D%7EC%95 E379ABF7E2345 )97&9935 E2345 B35 7BA975 3DF%9E5 A94D%745 E35 B5 %B79AB%5 4CA9B5 265 7895 E235 )9B5 F223%#5 FB%%95 %B79AB%5 4FB779AE358953975B3D%BA5E47AE)D7E23526578952D7F2E35CBA7EF%945B679A5B578EF25 B)42A)9A5&E785A94C9F757257895E3FE9375EA9F7E235FB35)95E379ACA9795B457895A94D%745 6A25 49$9AB%5 8E8%#5 CA2)B)%95 96%9F7E2345 )#5 4B%%5 B3%945 B35 E75 E45 &9%%5

BCCA21EB795&E785B5:BD44EB3548BC95&E785B547B3BA59$EB7E235σθ5E$935)#57895 9CEAEFB%562AD%B5CA2C2495)#5'0E8%B35+D8(5B35A9C2A795E359DB7E235!5 88 9 A BB C D + = rad rad p L x L d Z pc MeV 10 log 9 1 1 1 . 14 β σθ 5 3-6

&89A95F5E4578952937D52657895CBA7EF%95 5789578EF2394452657895B)42A)9A5B35%&' 5

7895 ABEB7E235 %93785 265 7895 9ED5 175 62%%2&45 78B75 7895 B3D%BA5 4CA9B5 265 E2345 E3FA9B4945 B45 7895 CBA7EF%95 939A#5 9FA9B4945 D95 725 7895 2F65 79A5 B75 7895 932E3B72A5 265 9DB7E235 !5 135 6EDA95 5 &95 CA949375 B5 F2CBAE4235 265 %B79AB%5 4FB779AE3562A5E669A9375E2354C9FE945265789ABC9D7EF5E379A9475*9B45265FBA)235B35 89B$E9A5E2345482&5%E77%95%B79AB%54FB779AE35'E55(5&8E%957895B3D%BA54CA9B5265 CA272345 E45 235 B$9AB95 78A995 7E945 %BA9A5 895 4B%%5 %B79AB%5 96%9F7E235 265 89B$#5 E2345 C9397AB7E35 78A2D85 B5 78EF25 B)42A)9A5 E45 B5 CBA7EFD%BA5 B$B37B95 265 89B$#5 E2345 E35 F2CBAE4235 725 CA272345 4E3F95 789#5 B%%2&5 B5 4B69A5 BCCA2BF85 725 4934E7E$95 47ADF7DA945B35B56DA789A5ECA2$99375E3578952495E47AE)D7E235E3578957BA975BA9B5 '?F8BA75975B%5(5895%B79AB%5)9B54FB779AE35E45B%425265F%E3EFB%5A9%9$B3F9562A5 78957A9B793752657D2DA45E35F%2495$EFE3E7#57252AB345B75AE425'F5G(51399562A5 7895 96E3E7E235 265 7895 EA9F7E235 B35 C24E7E235 265 7895 EAABEB7E35 C2A745 7895 %B79AB%5 4CA9BE352657895)9B5979AE39457895E3ED5E47B3F95B75&8EF85B35F5G5FB35 )95BCCA2BF895

92C5AB88

5

figure 3-4: Lateral scattering in water for ions of therapeutic interest calculated with SRIM code (Ziegler 2004). The small lateral deflection of carbon and heavier ions allow a closer approach to organs at risk (OAR) compared to proton beams.

3.1.4 Ion fragmentation: models and fragments

0E85939A#5E2345C9397AB7E35B578EF25B)42A)9A5327523%#5E379ABF75&E78578957BA975 3DF%9E54('59%9F7A2B397EF5E379ABF7E2345B4594FAE)95E357895CA9$E2D45CBABABC85 )D75 789#5 91C9AE93F95 B45 &9%%5 47A235 3DF%9BA5 62AF95 E379ABF7E2345 A94D%7E35 E35

CA2-9F7E%95B32A57BA9753DF%9E56AB937B7E235895727B%5A9BF7E235FA244549F7E235HG5

94FAE)9457895CA2)B)E%E7#562A5B35E235265D39A2E353DF%9BA56AB937B7E235B35E75 E45B%2475F2347B3752$9A5B5&E95939A#5AB3952&35725B)2D7559D5'7215975 B%5 +ID(5 13995 E35 78E45 939A#5 A9E235 HG5 E45 BE3%#5 E$935 )#5 7895 9297AEFB%5

FA2445 49F7E2345 265 2$9A%BCCE35 3DF%9E5 F35 7895 2789A5 8B35 B75 %2&9A5 939AE945 HG5

AE4945 D95 725 7895 F237AE)D7E235 265 2789A5 A9BF7E235 9F8B3E445 %E295 99CE39%B47EF5 F2%%E4E235 2A5 6D4E235 A9BF7E2345 '?F8BA75 975 B%5 (5 575 49$9AB%5 8D3A945 9D5 $E2%9375 4CB%%B7E235 A9BF7E2345 B#5 A94D%75 E35 7895 F2C%9795 E4E379AB7E235 265 )2785 CA2-9F7E%95 B35 7BA975 3DF%9E5 135 7895 CA27235 FB495 23%#5 7BA975 6AB937B7E235 E45 C244E)%95 ,2A5 7895 4B295 265 F2C%97939445 &95 937E235 78B75 3DF%9BA5 A9BF7E2345 E3DF95)#59%9F7A2B397EF5E379ABF7E2345BA95B%425C244E)%95)D75B%&B#4539%EE)%95 E35 7895 939A#5 AB395 265 E2345 D495 E35 CBA7EF%95 789ABC#5 5E7E23B%%#5 3DF%923EF5 A9BF7E2345 %9BE35 725 CE235 CA2DF7E2345 BA95 B%425 C244E)%95 B75 7895 8E89475 E235 939AE945 D495 E35 8BA23789ABC#5 )D75 789#JA95 ABA95 932D85 725 )95 F2C%979%#5 EAA9%9$B37562A5CABF7EFB%5CDAC24945

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123425467859AB2CD8E45984678FA28

CA2F9445 'F%E$9EAB5 975 B%5 +D+(5 135 7895 6EA475 479C5 3DF%92345 BA95 B)AB795 E35 7895

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47DE945 &9A95 C9A62A95 B75 015 5 6BFE%E7#5 '?F8B%%5 975 B%5 ++!(5 :5"1S5 6BFE%E7#5 '*ABD335 975 B%5 (5 B35 ?1?I5 4#3F8A27A235 B75 :?15 '?F8BA75 975 B%5 ++!(5 62A5  E2345B2352789A54C9FE9458A995BE35F23F%D4E2345FB35)95AB&3562A578959669F745 2656AB937B7E235A9%9$B375725ABE2789ABC#5&E7858E8939A#5E235)9B45'?F8BA75 975B%5(K5

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92C5AB88

5

figure 3-5: Measured Bragg-curves for C-ions of different energies stopping in water. The measurements are performed with an ionization chamber in water; from (Schardt et al. 2010).

135 939AB%5 89B$#E235 3DF%9BA5 6AB937B7E2345 BA95 A94C234E)%95 62A5 7895 979AE2AB7E235 265 7895 2495 E47AE)D7E235 )2785 E35 7895 %23E7DE3B%5 B35 7AB34$9A4B%5 E934E2345 94C9FEB%%#5 E35 7895 *ABC9B25 A9E235 "9$9A789%9445 62A5 E2345 7895 6AB937B7E235 E45 47E%%5 &E78E35 B35 BFF9C7B)%95 %EE75 94C9FEB%%#5 &8935 D4E35 BF7E$95 )9B5 9%E$9A#5 4#47945 725 B$2E5 CA2-9F7E%95 6AB937B7E235 )962A95 9379AE35 7895

CB7E9375'ABA2E5(5,DA789A2A957895C24E7A2359E77E36AB93745%E295 _5B35

 _{5 FB35 )95 D7E%E.95 62A5 ()C 4(4*5 AB395 23E72AE35 &E785 C24E7A235 9E44E235}

722ABC8#5 'A/(5 B45 E75 &E%%5 )95 94FAE)95 E35 2A95 97BE%5 E35 7895 39175 F8BC79A5 8BA956AB9374594FBCE356A257895CB7E9375'BE3%#5CA272345B3509E234(5BA95 FDAA937%#5 CA2C2495 62A5 &'+,(C (),4(4*5 AB395 $9AE6EFB7E235 &E785 7895 E379ABF7E235 $9A7915 EBE35 '11(5 79F83ED95 '4995 F8BC79A5 (5 B45 &9%%5 B45 CA2C75 RAB#45 99AE352A78223B%%#57257895)9B5EA9F7E2358B$95)9935CA2$95725)95F2AA9%B795 &E785 7895 CAEBA#5 E235 CB785 )2785 62A5 CA27235 )9B45 'E35 975 B%5 !(5 B35 E235 )9B45'/5947B5975B%5I(5

,E3B%%#5 DAE35 B5 CBA7EF%95 EAABEB7E235 B5 F234E9AB)%95 B2D375 265 39D7A2345 BA95 CA2DF95 &E785 B5 $9A#5 )A2B5 B3D%BA5 4C9F7AD5 '/5 947B5 975 B%5 +(5 B35 B%782D85789#5FB33275)9591C%2E79562A5CAEBA#5AB395$9AE6EFB7E2354E3F95789#5BA95 D3F2AA9%B795&E7857895E235CB785'5947B5975B%5(54295E4FD44E23458B$95)9935 ABE495 B)2D75 7895 A2%95 265 789495 39D7A2345 62A5 7895 AE425 265 %B795 9669F745 B35 E3DF99375 265 49F23BA#5 FB3F9A5 'ABB3977E5 975 B%5 !(5 /$935 782D85 E75 &B45 C2E3795 2D75 78B75 7895 39D7A235 2495 9C9345 235 7895 )9B5 9%E$9A#5 4#4795 ':2774F8B%25 !(5 &E785 4FB3395 CA27235 )9B45 B5 39%EE)%95 39D7A235 2495 265 5

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3.2 The physics of interaction of photons with matter

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3.2.1 Photoelectric effect, Compton scattering, Pair production

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b e h E

E = ν − 5 3-7

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