Compton scattering and KleinNishina formula Shibata lab 1214594

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コンプトン散乱とクライン-仁科の公式 Compton scattering and Klein-Nishina formula Shibata lab. 12_14594 Yazawa Yukitaka 1

コンプトン散乱とクライン-仁科の公式 Compton scattering and Klein-Nishina formula Shibata lab. 12_14594 Yazawa Yukitaka 1

1. Introduction • The purpose of this research is Øto understand the interaction between

1. Introduction • The purpose of this research is Øto understand the interaction between gamma ray and matter, especially Compton scattering Øto verify differential cross section of Compton scattering, Klein-Nishina formula • Arthur H. Compton was awarded the Nobel prize in 1927 for the discovery of Compton effect. • Compton effect confirms that light also follows laws of kinematics in the same way as particles do. 2

2. Compton scattering Law of energy and momentum conservation : Momentum : Energy :

2. Compton scattering Law of energy and momentum conservation : Momentum : Energy : Lorentz factor Energy [ke. V] Energy of incident photon: 662 ke. V Energy of scattered photon Energy of recoil electron 662 ke. V 3

Differential cross section Klein-Nishina formula shows differential cross section for photons scattered by single

Differential cross section Klein-Nishina formula shows differential cross section for photons scattered by single electron p’ electron p position time photon k’, ε’(k’) electron p’ photon k, ε(k) Feynman diagram of Compton scattering Klein-Nishina formula: electron p photon k’, ε’(k’) 4

 1176 ke. V 662 ke. V position Yields (180 sec) p n time

1176 ke. V 662 ke. V position Yields (180 sec) p n time u d u u d d Photoelectric peak (662 ke. V) ADC channel 5

4. Setup for measurement of Compton scattering 5 cm 10 cm θ Lead 5

4. Setup for measurement of Compton scattering 5 cm 10 cm θ Lead 5 cm 25 cm This process is measured in coincidence by Na. I 1 and 2 scintillator with CAMAC/NIM modules. 6

5. Results 5. 1 Identification of the process Counts cc cc cc Peak on

5. Results 5. 1 Identification of the process Counts cc cc cc Peak on ADC channel of Na. I 1 + Na. I 2 →Determine counts and energy of the event. 7

5. 2 Angle dependence of energy Theoretical energy of recoil electron Theoretical energy of

5. 2 Angle dependence of energy Theoretical energy of recoil electron Theoretical energy of scattered photon Energy measured by Na. I 1 Projection to channel of Na. I 1 and Na. I 2 Energy[ke. V] Energy measured by Na. I 2 Sum of energy (Na. I 1+ Na. I 2) 662 ke. V Detected energy agrees with expected value at the most scattering angles. 8

 5. 3 Differential cross section Luminosity Real data d Klein-Nishina formula θ Vertical

5. 3 Differential cross section Luminosity Real data d Klein-Nishina formula θ Vertical bar: Statistic error Horizontal bar: Maximum range of scattering angle Real data don’t agree with Klein. Nishina formula. The reason for discrepancy is being investigated. But, angular dependence follows Klein-Nishina formula. 9

6. Summary • 10

6. Summary • 10

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Appendix A: Intrinsic Detection Efficiency Energy of gammra ray [Me. V] 13

Appendix A: Intrinsic Detection Efficiency Energy of gammra ray [Me. V] 13

Appendix B: Energy calibration Calibration of Na. I 2 scintillator Calibration of Na. I

Appendix B: Energy calibration Calibration of Na. I 2 scintillator Calibration of Na. I 1 scintillator ADC Channel Energy [ke. V] = 1. 5 × Channel - 51 Energy [ke. V] = 1. 5 × Channel - 41 14

Appedix B: Energy Calibration 2 Na. I scintillator 2 Na. I scintillator 1 ADC

Appedix B: Energy Calibration 2 Na. I scintillator 2 Na. I scintillator 1 ADC channel Energy of gamma ray [ke. V] Energy [ke. V] = 1. 3 × Channel – 4. 4 Energy of gamma ray [ke. V] Energy [ke. V] = 1. 3 × Channel + 38 15

Energy in case of new energy calibration (6 peaks) Theoretical energy of recoil electron

Energy in case of new energy calibration (6 peaks) Theoretical energy of recoil electron Theoretical energy of scattered photon Energy measured by Na. I 1 Energy [ke. V] Energy measured by Na. I 2 Sum of energy (Na. I 1+ Na. I 2) 662 ke. V 16

Appendix C: Reason of discrepancy (Energy) Na. I 1 scintillator ② Compton forward scattering

Appendix C: Reason of discrepancy (Energy) Na. I 1 scintillator ② Compton forward scattering → Gamma ray loses energy. Scattering angle becomes larger when the gamma ray is scattered above and below the center of Na. I 1 scintillator. Na. I 2 scintillator 17

Appendix D: 2 dimensional plot ADC channel of Na. I 2 scintillator ADC channel

Appendix D: 2 dimensional plot ADC channel of Na. I 2 scintillator ADC channel of Na. I 1 scintillator 18

Appendix E: Histgram of ADC 1 + ADC 2 channel Counts Sum of ADC

Appendix E: Histgram of ADC 1 + ADC 2 channel Counts Sum of ADC channel (ADC 1 + ADC 2) 19

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