Chapter 2

1. Chapter 2 Radiation Interactions with Matter LIU Yi-Bao School of Nuclear Engineering and Technology East China Institute of Technology

2. Contents • Introduction • Interaction of Heavy Charged Particles • Interaction of Fast Electrons • Interaction of Gamma Rays • Interaction of Neutrons • Radiation Exposure and Dose

3. Introduction The radiation detections based on: • Radiations interact with matter; • Radiations lose their energy in matter. Four major categories of radiations:

4. Detect for neutrons by the secondary heavy charged particles Heavy charged particles (characteristic distance~10-5m) Fast electrons (characteristic distance~10-3m) Detect for X-rays or -rays by the secondary electrons

5. 2.1 Interaction of Heavy Charged Particles A. Nature of the Interaction  electron Sufficient E to create ions Excited atoms Ion pairs

6. The maximum energy that can be transferred from a charged particle of mass m with kinetic energy E to an electron of mass mo in a single collision is 4Emo/m, or about 1/500 of the particle energy per nucleon.

7. B. Stopping Power The linear stopping power S for charged particles in a given absorber is simply defined as the differential energy loss for that particle within the material divided by the corresponding differential path length: Also called specific energy loss, or, “rate” of energy loss.

8. where： Bethe formula: Charge number of incident particles Average ionization potential of the absorber Atomic number of absorber atoms Velocity of particle Number density of the absorber atoms m0:electron rest mass

9. Figure 2.1 Variation of the specific energy loss in air versus energy of the charged particles.

10. C. Energy Loss characteristics C-1. The Braggcurve—A plot of the specific energy loss along the track of a charged particle such as in Fig. 2.2

12. C-2.Energy Straggling Energy spread of a beam of monoenergetic charged particles Energy loss is a statistical or stochastic process

13. D. Particle Range D-1. Definitions of Range

14. Mean range is defined as the absorber thichness that reduces the alpha particle count to exactly one-half of its value in the absence of the absorber. Path > Range Non-relativity

15. Fig. 2.6 Range –energy plot for alpha particles in air at standard temperature and pressure. (Calculated by Geant 4 in LIU Group)

16. Fig. 2.7 Range-energy curves calculated for different charged particles in silicon. (Calculated by Geant 4 in LIU Group)

17. Fig. 2.8 Range-energy curves calculated for alpha particles in different materials. (Calculated by Geant 4 in LIU Group)

18. D-2. Range straggling Defined as the fluctuation in path length for individual particles of the same initial energy. The same stochastic factors that lead to energy straggling at a given penetration distance also result in slightly different total path lengths for each particles. Range straggling

19. D-3. Stopping Time The time required to stop a charged particle in an absorber can be deduced from its range and average velocity. For non-relativity particle (mass M, kinetics E)：

20. k＝0.6 unit：u unit：s unit：m unit：MeV

21. D-4. Energy loss in thin absorbers For thin absorbers (or detectors) that are penetrated by a given charged particle, the energy deposited within the absorber can be calculated from 简单测厚仪原理：

22. 2.2 Interaction of fast electrons Characteristics of interaction of fast electrons: • Velocity faster; • Energy loss including ionization energy loss and radiation energy loss; • Scattering obvious and much more tortuous path.

23. A. Specific energy loss The total linear stopping power for electrons is the sum of the collisional and radiative losses。 Bethe formula

24. The linear specific energy loss through radiative process (bremsstrahlung) For electrons:

25. B. Electron Range an Transmission Curves B-1. Absorption of monoenergetic Electrons The concept of range is less definite for fast electrons than for heavy charged particles. Why?

26. Monoenergy electron

27. Fig.2.14 Range-energy plots for electrons in silicon and sodium iodide. (Calculated by Geant 4 in LIU Group)

28. B-2. Absorption of beta particles

30. Fig. 2.16 Beta particle absorption coefficient n in aluminum as a function of the endpoint energy Em, average energy Eav, and E`=0.5(Em+Eav) of different beta emitters.

31. B-3. Backscattering The fact that electrons often undergo large-angle deflections along their tracks leads to the phenomenon of backscattering. Backscattering is most pronounced for electrons with low incident energy and absorbers with high atomic number.

32. Fig.2.17 Fraction of normally incident electrons that are backscattered from thick slabs of various materials, as a function of incident energy E.

33. B-4. Pair Annihilation Positron Electron Two photons travel in exactly opposite directions 511 keV 511 keV E = mc2

34. 2.3 Interaction of gamma rays Three major types of gamma rays interaction mechanisms in radiation measurements: • Photoelectric absorption; • Compton scattering; • Pair production.

35. A. Interaction Mechanism A-1. Photoelectric absorption Photoelectric Effect In the photoelectric absorption process, a photon undergoes an interaction with an absorber atom in which the photon completely disappears. In its places, an energetic photoelectron is ejected by the atom from one of its bound shell. The interaction is with the atom as a whole and cannot take place with free electrons. Binding energy

37. E e ¢ ¢ h h v v A-2. Compton scattering Compton Effect The interaction process of Compton scattering takes place between the incident gamma ray photon and an electron in the absorbing material. Reciol electron Incident photon hv q q Scattered photon

38. 1) The relations between recoil electron and scattered photon Photon energy： Photon momentum Electron kinetic Electron momentum Relativity relation

40. 2) Compton scattering cross section

41. A-3. Pair Production The gamma ray energy exceeds twice the rest mass energy of an electron (1.02MeV). The interaction must take place in the coulomb field of nucleus Pair production is possible The gamma ray photon disappears and is replaced by an electron-positron pair. The positron will subsequently annihilate after slowing down in the matter, two annihilation photons are normally produced as secondary production of the interaction.

42. Summary

43. B. Gamma ray attenuation B-1. Attenuation coefficients Gamma ray transmission experiment

44. Linear attenuation coefficient Mass attenuation coefficient Mass thickness

45. B-2. Buildup source direct detector scattered Buildup factor, depends on the type of gamma ray detector and the geometry of the experiment.