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28 G Nelson and D Reilly,Fig 2 1 The fundamental law of. gamma ray attenua 10 1,lion The transmitted,gamma ray intensity I is. a function of gamma ray,energy absorber com,position and absorber. 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. 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. 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. 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. 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. 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, 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. 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 The electron binding energy is not lost but. appeiys as characteristic x rays emitted in coincidence with the photoelectron In most. cases these x rays are absorbed in the detector in coincidence with the photoelectron. and the resulting output pulse is proportional to the total energy of the incident gamma. ray For low energy gamma rays in very small detectors a sufficient number of K. x rays can escape from the detector to cause escape peaks in the observed spectrunx. the peaks appear below the full energy peak by an amount equal to the energy of the. Figure 2 5 shows the photoelectric mass attenuation coefficient of lead The in. teraction probability increases rapidly as energy decreases but then becomes much. Gamma Ray Interactions with Matter 33, smaller at a gamma ray energy just below the binding energy of the K electron This. discontinuity is called the K edge below this energy the gamma ray does not have suf. ticient energy to dislodge a K electron Below the K edge the interaction probability. increases again until the energy drops below the binding energies of the L eleetronw. these discontinuities are called the L1 LZI and LII1 edges The presence of these. absorption edges is important for densitometry and x ray fluorescence measurements. see Chapters 9 and 10,z 10 1 0 10,PHOTON ENERGY MeV. Fig 2 5 Photoelectric mass attenuation coefficient of. 2 3 2 Compton Scattering, Compton scattering is the process whereby a gamma ray interacts with a free or. weakly bound electron E and transfers part of its energy to the electron see. Figure 2 6 Conservation of energy and momentum allows only a partial energy trans. fer when the electron is not bound tightly enough for the atom to absorb recoil energy. This interaction involves the outer least tightly bound electrons in the scattering atom. The electron becomes a free electron with kinetic energy equal to the difference of the. energy lost by the gamma ray and the electron binding energy Because the electron. 34 G Nelson and D Reilly,Fig 2 6 A schematic representation of Copton. scattering, binding energy is very small compared to the gamma ray energy the kinetic energy.
of the electron is very nearly equal to the energy lost by the gamma ray. E E7 E 2 8,where E energy of scattered electron,energy of incident gamma ray. E energy of scattered gamma ray, IWOparticles leave the interaction site the freed electron and the scattered gamma. ray The directions of the electron and the scattered gamma ray depend on the amount. of energy transferred to the electron during the interaction Equation 2 9 gives the. energy of the scattered gamma ray wd Figure 2 7 shows the energy of the scattered. electron as a function of scattering angle and incident gamma ray energy. E moc2 1 cos moc2 E 2 9,where moc2 rest energy of electron 511 keV. angle between incident and scattered gamma rays see Figure 2 6. This energy is minimum for a head on collision where the gamma ray is scattered. 180 and the electron moves forward in the direction of the incident gamma ray For. this case the energy of the scattered gamma ray is given by Equation 2 10 and the. energy of the scattered electron is given by Equation 2 11. E min moc2 2 moc2 E,moc2 2 256 keV if E moc2 2 2 lo. E max E 1 moc2 2E,s E moc2 2 E 256 keV if E moc2 2 2 11.
Gamma Ray Interactions with Matter 35,o 0 1 0 2 0 3. 0 4 0 5 0 8,ENERGY MeV,0 7 0 8 0 9 1 0, Fig 2 7 Energy of Compton scattered electrons as a function of scat. teringangle andincident gamma ray energy E The, sharp discontinuity corresponds tothemaximum energy that. can be transferred in a single scattering, For very small angle scatterings NOO the energy of the scattered gamma ray is. only slightly less than the energy of the incident gamma ray and the scattered electron. takes very little energy away from the interaction l eenerg ygiventothe scattered. electron ranges from near zero to the maximum given by Equation 2 11. When a Compton scattering occurs in a detector the scattered electron is usually. stopped in the detection medium and the detector produces an output pulse that is. proportional to the energy lost by the incident gamma ray Compton scattering in a. detector produces a spectrum of output pulses from zero up to the maximum energy. given by Equation 2 11 It is difficult to relate the Compton scattering spectrum to. the energy of the incident gamma ray Figure 2 8 shows the measured gamma ray. spectrum from a monoenergetic gamma ray source 137Cs The full energy peak at. 662 keV is formed by interactions where the gamma ray loses all of its energy in. the detector either by a single photoelectric absorption or by a series of Cornpton. scattering followed by photoelectric absorption The spectrum of events below the. full energy peak is formed by Compton scattering where the gamma ray loses only. part of its energy in the detector The step near 470 keV corresponds to the maximum. energy that can be transferred to an electron by a 662 keV gamma ray in a single. Compton scattering This step is called a Compton edge the energy of the Compton. edge is given by Equation 2 11 and plotted in Figure 2 9 The small peak at 188 keV. in Figure 2 8 is called a backscatter peak The backscatter peak is formed when the. 36 G Nelson and D Reilly, gamma ray undergoes a large angle scattering N 180 in the material surrounding the.
detector and then is absorbed in the detector The energy of the backscatter peak is. given by Equation 2 10 which shows that the maximum energy is 256 keV The sum. of the energy of the backscatter peak and the Compton edge equals the energy of the. incident gamma ray Both features are the result of large angle Compton scattering of. the incident gamma ray The event contributes to the backscatter peak when only the. 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