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Gamma-Ray Interactions with Matter

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Gamma-Ray Interactions with Matter 2 Gamma-Ray Interactions with Matter G. Nelson and D. ReWy 2.1 INTRODUCTION A knowledge of gamma-ray interactions is important to the nondestructive assayist in order to understand gamma-ray detection and attenuation. A gamma ray must interact with a detector in order to be “seen.” Although the major isotopes of uranium and plutonium emit gamma rays at fixed energies and rates, the gamma-ray intensity measured outside a sample is always attenuated because of gamma-ray interactions with the sample. This attenuation must be carefully considered when using gamma-ray NDA instruments. This chapter discusses the exponential attenuation of gamma rays in bulk mater- ials and describes the major gamma-ray interactions, gamma-ray shielding, filtering, and collimation. The treatment given here is necessarily brief. For a more detailed discussion, see Refs. 1 and 2. 2.2 EXPONENTIAL A~ATION Gamma rays were first identified in 1900 by Becquerel and VMard as a component of the radiation from uranium and radium that had much higher penetrability than alpha and beta particles. In 1909, Soddy and Russell found that gamma-ray attenuation followed an exponential law and that the ratio of the attenuation coefficient to the density of the attenuating material was nearly constant for all materials. 2.2.1 The Fundamental Law of Gamma-Ray Attenuation Figure 2.1 illustrates a simple attenuation experiment. When gamma radiation of intensity IO is incident on an absorber of thickness L, the emerging intensity (I) transmitted by the absorber is given by the exponential expression (2-i) 27 28 G. Nelson and D. Reilly ~, -+ Fig. 2.1 The fundamental law of pj gamma-ray attenua- 10 -. —1 lion. The transmitted gamma-ray intensity I is .—- a function of gamma-ray energy, absorber com- position, and absorber -H thickness. I = I. ~-I@ where pl is the attenuation coefficient (expressed in cm– 1). The ratio I/I. is called the gamma-ray transmission. Figure 2.2 illustrates exponential attenuation for three different gamma-ray energies and shows that the transmission increases with increasing gamma-ray energy and decreases with increasing absorber thickness. Mea- surements with different sources and absorbers show that the attenuation coefficient Ml depends on the gamma-ray energy and the atomic number (Z) and density (p) of the absorber. For example, lead has a high density and atomic number and transmits 1.000 \ 0.750 0.500 0.250 0 : 0 0.625 1.250 1.875 ) LEAD THICKNESS (cm) Fig. 2.2 Transmission of gamma rays through lead absorbers. _—-, —.—_-—. —— .— — Gamma-Ray Interactions with Matter 29 a much lower fraction of incident gamma radiation than does a similar thickness of aluminum or steel. The attenuation coefficient in Equation 2-1 is called the linear attenuation coefficient. Figure 2.3 shows the linear attenuation of solid sodium iodide, a common material used in gamma-ray detectors. Alpha and beta particles have a well-defined range or stopping distance; however, as Figure 2.2 shows, gamma rays do not have a unique range. The reciprocal of the attenuation coefficient 1/p/ has units of length and is often called the mean free path. The mean free’path is the average distance a gamma ray travels in the absorber before interacting; it is also the absorber thickness that produces a transmission of l/e, or 0.37. 103 , ,,, : 1!, , 1 E L @ 3 a g 10-1z d Photoelectric z Pair production 10-2 I 1!! 11,11 1 1 1 1 1111 1 ()-2 10-1 1.0 101 Photon Energy (MeV) Fig. 2.3 Linear attenuation coeflcient of NaI showing contributions from photoelectric absorption, Common scatterirw,.,. and ~air .production. 30 G. Nelson and D. Reilly 2.2.2 Mass Attenuation Coefficient The linear attenuation coefficient is the simplest absorption coefficient to measure experimentally, but it is not usually tabulated because of its dependence on the density of the absorbing material. For example, at a given energy, the linear attenuation coefficients of water, ice, and steam are all different, even though the same material is involved. Gamma rays interact primarily with atomic electrons; therefore, the attenuation coefficient must be proportional to the electron density P, which is proportional to the bulk density of the absorbing material. However, for a given material the ratio of the electron density to the bulk density is a constant, Z/A, independent of bulk density. The ratio Z/A is nearly constant for all except the heaviest elements and hydrogen. P= Zp/A (2-2) where P = electron density Z = atomic number p = mass density A = atomic mass. The ratio of the linear attenuation coefficient to the density (p//p) is called the mass attenuation coefficient p and has the dimensions of area per unit mass (cm2/g). The units of this coefficient hint that one may think of it as the effective cross-sectional area of electrons per unit mass of absorber. The mass attenuation coefficient can be written in terms of a reaction cross section, o(cm2): Noo /J=— (2-3) A where No is Avagadro’s number (6.02 x 1023) and A is the atomic weight of the absorber. The cross section is the probability of a gamma ray interacting with a single atom. Chapter 12 gives a more complete definition of the cross-section concept. Using the mass attenuation coefficient, Equation 2-1 can be rewritten as 1=10 e-~f’L = IOe-~ (2-4) where x = pL. The mass attenuation coefficient is independent of density for the example mentioned above, water, ice, and steam all have the same value of p. This coefficient is more commonly tabulated than the linear attenuation coefficient because it quantifies the gamma-ray interaction probability of an individual element. References 3 and 4 are widely used tabulations of the mass attenuation coefficients of the elements. Equation 2-5 is used to calculate the mass attenuation coefficient for compound materials: —. —— Gamma-Ray interactions with Matter 31 P = z Piwi (2-5) where .I.Li. = mass attenuation coefficient of ith element w~= weight fraction of ith element. The use of Equation 2-5 is illustrated below for solid uranium hexafluoride (UFG) at 200 keV: k = mass attenuation coefficient of U at 200 keV = 1.23 cm2/g Pf = mass attenuation coefficient of F at 200 keV = 0.123 cm2/g WU= weight fraction of U in UF6 = 0.68 Wf = weight fraction of F in UF6 = 0.32 P = density of solid UF6 = 5.1 ~cm3 P = 14bwu + I.Jfwf = 1.23 x 0.68 + 0.123 x 0.32= 0.88 cm2/g P1 =pp= 0~88 x 5.1 = 4.5 cm-l. 2.3 INTERACTION PROCESSES The gamma rays of interest to NDA applications fall in the range 10 to 2000 keV and interact with detectors and absorbers by three major processes: photoelectric absorption, Compton scattering, and pair production. In the photoelectric absorption process, the gamma ray loses all of its energy in one interaction. The probability for this process depends very strongly on gamma-ray energy E-y and atomic number Z. In Compton scattering, the gamma ray loses only part of its energy in one interaction. The probability for this process is weakly dependent on E and Z. The gamma ray can lose all of its energy in one pair-production interaction. However, this process is relatively unimportant for fissile material assay since it has a threshold above 1 MeV. Reference 3 is recommended for more detailed physical descriptions of the interaction processes. 2.3.1 Photoelectric Absorption A gamma ray may interact with a bound atomic, electron in such a way that it loses all of its energy and ceases to exist as a gamma ray (see Figure 2.4). Some of the gamma-ray energy is used to overcome the electron binding energy, and most of the remainder is transferred to the freed electron as kinetic energy. A very small amount of recoil energy remains with the atom to conserve momentum. This is called photoelectric absorption because it is the gamma-ray analog of the process discovered by Hertz in 1887 whereby photons of visible light liberate electrons from a metal surface. Photoelectric absorption is important for gamma-ray detection because the gamma ray gives up all its energy, and the resulting pulse falls in the full-energy peak. 32 G. Nelson and D. Reilly Atom gamma Ee - Fig. 2.4 A schenratic representation of the photo- h electric absorption process. Photoelectron The probability of photoelectric absorption depends on the gamma-ray energy, the electron binding energy, and the atomic number of the atom. The probability is greater the more tightly bound the electrow therefore, K electrons are most affected (over 80% of the interactions involve K electrons), provided the gamma-ray energy exceeds the K-electron binding energy. The probability is given approximately by Equation 2-6, which shows that the interaction is more important for heavy atoms like lead and uranium and low-energy gamma rays: T (x Z4/E3 (2-6) where ~ = photoelectric, mass attenuation coefficient. ‘Ilk proportionality is only approximate because the exponent of Z varies in the range 4.0 to 4.8. As the gamma-ray energy decreases, the probability of photoelectric ab- sorption increases rapidly (see Figure 2.3). Photoelectric absorption is the predominant interaction for low-energy gamma rays, x rays, and bremsstrahlung. The energy of the photoelectron E. released by the interaction is the difference between the gamma-ray energy ET and the electron binding energy E~: E.=~–E~. (2-7) In most detectors, the photoelectron is stopped quickly in the active volume of the detector, which emits a small output pulse whose amplitude is proportional to the energy deposited by the photoelectron.
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