Total Photon Attenuation Coefficient

When a photon travels through matter, it may interact through any of the three major ways discussed earlier. (For pair production, 1.022 MeV.) There are other interactions, but they are not mentioned here because they are not important in the detection of gammas. 

The total probability for interaction fi, called the total linear attenuation coefficient, is equal to the sum of the three probabilities  

There are tables that give /x for all the elements, for many photon energies.  

Most of the tables provide (jl in units of m /kg (or cm /g), because in these units the density of the material does not have to be specified. If fi is given in m /kg (or cm /g), it is called the total mass attenuation coefficient. The relationship between linear and mass coefficients is 

If a parallel beam of monoenergetic photons with intensity 7(0) strikes a target of thickness t (Fig. 4.24), the number of photons, I t), emerging without having interacted in the target is given by 

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Figure 4.23 shows the individual coefficients as well as the total mass attenuation coefficient for lead, as a function of photon energy. The total mass attenuation coefficient shows a minimum because as E increases, r decreases, k increases, and a does not change appreciably. However, the minimum of p, does not fall at the same energy for all elements. For lead, p, shows a minimum at .y 3.5 MeV for aluminum, the minimum is at 20 MeV and for Nal, the minimum is at 5 MeV. 

Answer Cs emits a 0.662-MeV gamma. The mass absorption coefficient for this photon in water is (App. D) 0.00327 m /kg. The total mass attenuation coefficient is 0.00862 m /kg. The energy deposited at a distance of 0.05 m from the source is (E =... 

Figure 12.31 Photon attenuation coefficients for germanium. The dashed line is the approximate total linear attenuation coefficient.

Fig. 5.9. Relative contributions of various photon interactions to the total attenuation coefficient for (a)...

The attenuation coefficient for a beam of gamma rays is related to the number of gamma rays removed from the beam, either by absorption or scattering. For the Compton effect, the absorption cross section is determined by the energy absorbed by the electron, which is the total collision energy minus the average scattered photon... 

Fig. 1(a). Mass attenuation coefficient of X-ray and 7-photons in water, aluminium, iron and lead [2], (Note the relatively small dependence on chemical structure except at low energies, due to the photoelectric effect and, at high energies, to pair production, (b) Total energy absorption due to photoelectric effect, Compton scattering and pair production [2],... 

Unlike heavy particles and electrons which lose their energy as a result of many collisions, y-rays are completely stopped in one or, at most, a few interactions. For thin absorbers the attenuation of y-rays follows relation (6.7), where is the number of photons m s The proportionality factor p is called the total) attenuation coefficient. When it has the dimension of m and the thickness x is expressed in meters, ii is referred to as the linear attenuation coefficient. The attenuation coefficient can be expressed in other ways ... 

The number of photons (the intensity) is reduced but their energy is generally unchanged. The term p is called the mass attenuation coefficient and has the dimension cm g . The product pi = pp is called the linear absorption coefficient and is expressed in cm . p(E) is sometimes also called the total cross section for X-ray absorption at energy E. 

The attenuation coefficient. The total cross section of interaction of a gamma radiation photon with an atom is equal to the sum of all three mentioned partial cross sections a = Oc+Of+o. Depending on the photon energy and the absorber material, one of the three partial cross sections... 

As already mentioned, the total attenuation coefficient is the sum of the attenuation coefficients for each interaction process (eqn [1]). The percentage contribution of each process to the total attenuation changes with photon energy and depends on the atomic number of a single element absorber or the so-called effective atomic number in case of complex materials. 

Here fi is they-ray linear attenuation coefficient, usually measured in cm units. It is a sum of the interaction terms described in O Chap. 6 in this Volume, hence it is also called total attenuation coefficient. Its inverse is called the mean free path, while the thickness reducing the photon beam by half is the half-thickness di/y, both are measured in cm. Frequently the mass attenuation coefficient pip is used, because it does not depend on the physical state of the material. Its dimension is cm /g if the density p is given in g/cm units. Another important quantity is the mass-energy absorption coefficient p Jp, measured in the same units, which characterizes the energy deposition by photons. AH these quantities, their units and usage have been defined by the International Commission on Radiation Units and Measurements (ICRU) in ICRU Report 33 (ICRU 1980), which has recently been superseded by two new ones (ICRU 1993c, 1998). 

This is the parameter plotted in Figure 2.2, comparing attenuation and absorption. The attenuation coefficient only expresses the probability that a gamma-ray of a particular energy will interact with the material in question. It takes no account of the fact that as a result of the interaction a photon at a different energy may emerge as a consequence of that interaction. The total absorption coefficient, niust, of course, take into account those incomplete interactions ... 

Attenuation by scattering or pair-production processes is not treated at all in the present Volume. Attenuation by ionization of inner shells is treated in the Section on Ionization Processes and X-Ray Production , pp. 217/20. Compilations of individual and total photon cross sections (attenuation coefficients) for the whole range of photon energies were cited in, e.g., Tungsten Suppl. Vol. A2, 1987, pp. 69/77. 

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