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Interaction of Radiation with Matter

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Interaction of Radiation with Matter INTERACTION OF RADIATION WITH MATTER OBJECTIVES Aims From this chapter you should develop your understanding of the various ways that photons, charged particles and neutrons can interact with matter and the concepts, such as mass attenuation coefficient, stopping power and range, that have been invented in order to aid that understanding. These ideas are the basis for the later study of the effects of x rays, gamma radiation and other ionising radiations on living things. Minimum learning goals When you have finished studying this chapter you should be able to do all of the following. 1. Explain, use and interpret the terms linear attenuation coefficient, mass attenuation coefficient, attenuation length, mean free path, half thickness, density-thickness, build-up, secondary particles, photoelectric effect, atomic photoelectric effect, photoelectrons, photoionisation, absorption edges, Compton effect [Compton scattering], Compton edge, pair production, rate of energy loss, linear stopping power, mass stopping power, minimum ionisation, range, straggling, bremsstrahlung [braking radiation], Cherenkov radiation, elastic scattering. 2. State, explain and apply the exponential attenuation law for a beam of particles suffering all-or- nothing interactions. 3. State, explain and apply the relations among linear attenuation coefficient, mass attenuation coefficient, density and composition of materials. 4. Distinguish between absorption of energy and the attenuation of a beam of photons and describe the build-up of secondary particles. 5. (a) Describe and compare the processes (photoelectric effect, Compton effect, Rayleigh scattering, pair production) by which photons interact with matter. (b) Describe and explain in general terms how attenuation coefficients and the relative importance of those processes vary with photon energy and explain the origin of absorption edges. (c) Explain why pair production occurs only for photons with sufficiently high energy. 6. (a) Describe the processes (excitation and ionisation, bremsstrahlung and Cherenkov radiation) by which a beam of energetic charged particles loses energy as it passes through bulk matter. (b) Describe and explain how the speeds, charges, kinetic energies and masses of particles affect their interactions with an absorber. 7. Describe how linear stopping power and mass stopping power depend on particle energy and the composition of the absorber. 8. Describe and explain how the number of particles in a monoenergetic beam of charged particles varies with depth of penetration into an absorber. 9. Describe some examples of how neutrons interact with bulk matter. TEXT 1-0 INTRODUCTION This chapter is all about the interactions between radiation and matter. Here radiation is defined broadly to include charged particles such as alpha and beta radiation, beams of charged particles created by accelerating machines as well as electromagnetic radiation or photons. We even include beams of neutral particles such as neutrons. There are two kinds of interesting questions. Firstly, we can ask questions about what happens to the radiation, how far it travels and how its strength is affected. It will be necessary to define carefully what we mean by strength. When a beam of radiation of any kind penetrates matter some of the radiation may be absorbed completely, some may be scattered and some may pass straight through without any interaction at all. The processes of absorption and scattering can be described and explained in terms of interactions between particles. Particles in the beam of radiation strike particles in the material and are either stopped or scattered. There are two broad kinds of process by which a particle travelling through matter can lose energy. In the first kind the energy loss is gradual; the particle loses energy nearly continuously through many interactions with the surrounding material. In the second kind the energy loss is catastrophic; the particle moves without any interaction at all through the material until, in a single collision, it loses all its energy. The motion of charged particles through matter is characterised by gradual energy loss whereas photon interactions are of the "all-or-nothing" type. In this chapter we will start by considering the interaction of photons with matter and then proceed to look at the absorption of material particles. 1-1 ATTENUATION COEFFICIENTS If the interactions are of the "all-or nothing" type then the attenuation of a beam of particles with identical energies, all travelling in the same direction, is described by an exponential law. If at some distance into the material N0 particles are moving through a slab of material, then after penetrating an extra distance x it is found that the number of particles in the beam is reduced to −µl x N(x) = N0 e ... (1.1). This exponential attenuation law follows from the fact that, over any short distance, the probability of losing a particle from the beam is proportional to the number of particles left. Where there are many particles many will be lost,€ but as the number left decreases so does the rate of loss. -1 µ = 50 m 100 mm Figure 1.1 Attenuation of a photon beam - schematic The original photons interact at random. In this example the attenuation coefficient, µ = 50 m-1. The quantity µl is known as the linear attenuation coefficient; it is a measure of how rapidly the original photons are removed from the beam. A large value of µl means that the original photons are removed after travelling only a small distance. It is important to remember that the exponential attenuation law does not describe what happens to the energy carried by the photons removed from the beam - it is possible that some of that energy may be carried through the medium by other particles, including some new photons. Example 3 The linear attenuation coefficient for 200 keV x rays in lead is 1.0 × 10 m-1. What is the fraction of such photons remaining after penetrating a lead sheet of thickness 2.0 mm? −µl x Answer N = N0 e N -µ x 3 -1 -3 so the fraction left is = e l = e-(1.0 × 10 m ) × (2.0 × 10 m) N0 € = e-2.0 = 0.135. An alternative way of expressing the exponential attenuation law is to replace the linear attenuation coefficient by its reciprocal: € 1 λ = µ l −x λ so that N(x) = N0e where λ is known as the attenuation length or mean free path. It is the average distance travelled by a photon before it is absorbed. The distance over which one half the initial beam is absorbed is called the half thickness x1/2. It €is related to the linear attenuation coefficient and the mean free path by ln(2) x1 = = ln(2)λ = 0.693λ 2 . ... (1.2) µ l Since photons interact with individual atoms, the probability that a photon will interact somewhere within a slab of matter depends on the total number of atoms ahead of it along its path. So the attenuation of radiation depends on the amount of material in the beam's path and not on how it is distributed. It is useful, therefore, to describe the attenuation process in a way that does not depend on the density of material, only on what kind of stuff it is. We can achieve that by defining the mass attenuation coefficient µm which is related to the linear attenuation coefficient by µ l = µ mρ ... (1.3) where ρ is the density of the material. This means that the mass attenuation coefficient is the same for ice, liquid water and steam whereas the linear attenuation coefficients will differ greatly. The total attenuating effect of a slab of given type material can be described by quoting the mass attenuation coefficient, which is characteristic of the material's chemical composition and the photon energy, together with the material's density and its thickness. We now have yet another way of writing the attenuation law: -µl x -µm ρx N = N0e = N0e . The product ρx, the areal density (mass per area) of a thickness x of the attenuating material, is also called the density-thickness. It is often quoted instead of the geometrical thickness x. Although the SI unit of density-thickness€ is kg.m-2, the obsolete unit g.cm-2 is still used in the literature. Figure 1.2 Effect of density on attenuation Three samples of the same material present the same area to the incident radiation. The masses of all the samples are the same but the densities are different. The density-thickness is the same in each case, so the three slabs will attenuate a beam of monoenergetic photons by the same factor. If an absorber is made of a composite of materials the mass attenuation coefficient is readily calculated by adding together the products of the mass attenuation coefficient and the proportion (α) of the mass due to each element) for all the elements present in the material, i.e. µm [total] = Σ (α µm ) . ... (1.4) The exponential law will always describe the attenuation of the original radiation by matter. If the radiation is changed, degraded in energy (and not totally absorbed) or if secondary particles are produced then the effective attenuation is less so the radiation will penetrate more deeply into matter than is predicted by the exponential law alone. Indeed it is possible to get an increase in the number of particles with depth in the material. The process is called build-up and has to be taken into account when evaluating the effect of radiation shielding. Examples will be given after we examine the various interaction mechanisms that radiation has with matter. primary particles : 100 mm Attenuation length: secondary particles: 200 mm Number of 1000 particles 750 All particles 500 Primary particles 250 Secondary particles 0 0 100 200 300 Depth / mm Figure 1.3 Build-up of secondary particles -1 The primary particles are attenuated with µl = 0.010 mm .
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