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

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

Introduction The radiation detections based on: 1.Radiations interact with matter; 2.Radiations lose their energy in matter. Four major categories of radiations: Charged Particulate RadiationsUncharged Radiations Heavy charged particles (characteristic distance~10 -5 m)  Neutrons (characteristic length ~10 -1 m) Fast electrons (characteristic distance~10 -3 m)  X-rays and Gamma rays (characteristic length ~10 -1 m)

Charged Particulate RadiationsUncharged Radiations  Neutrons (characteristic length ~10 -1 m)  X-rays and Gamma rays (characteristic length ~10 -1 m) Heavy charged particles (characteristic distance~10 -5 m) Detect for neutrons by the secondary heavy charged particles Detect for X-rays or  -rays by the secondary electrons Fast electrons (characteristic distance~10-3m)

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

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

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.

where ： Charge number of incident particles Velocity of particle Number density of the absorber atoms Atomic number of absorber atoms Average ionization potential of the absorber m 0 :electron rest mass Bethe formula:

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

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

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

D. Particle Range D-1. Definitions of Range

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

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

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

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

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

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) ：

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

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：

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.

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

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

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?

Monoenergy electron

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

B-2. Absorption of beta particles

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

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.

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

B-4. Pair Annihilation Positron 511 keV E = mc 2 Two photons travel in exactly opposite directions Electron

2.3 Interaction of gamma rays Three major types of gamma rays interaction mechanisms in radiation measurements: 1.Photoelectric absorption; 2.Compton scattering; 3.Pair production.

A. Interaction Mechanism A-1. Photoelectric absorption 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. Photoelectric Effect The interaction is with the atom as a whole and cannot take place with free electrons. Binding energy

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

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

2) Compton scattering cross section

A-3. Pair Production The gamma ray energy exceeds twice the rest mass energy of an electron (1.02MeV). Pair production is possible The interaction must take place in the coulomb field of nucleus 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.

Summary

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

Linear attenuation coefficient Mass attenuation coefficient Mass thickness

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