Buildup factor

Consider a point isotropic monoenergetic gamma source at a distance r from a detector, as shown in Fig. 4.25, with a shield of thickness t between source and detector. The total gamma beam hitting the detector consists of two components. 

The unscattered beam ( ) consists of those photons that go through the shield without any interaction. If the source strength is 5( y/s), the intensity of the unscattered beam or the unscattered photon flux is given by the simple 

The scattered beam consists of scattered incident photons and others generated through interactions in the shield (e.g.. X-rays and annihilation gammas). The calculation of the scattered beam is not trivial, and there is no simple expression like Eq. 4.62 representing it. 

Obviously, for the calculation of the correct energy deposition by gammas, either for the determination of heating rate in a certain material or the dose rate to individuals, the total flux should be used. Experience has shown that rather than calculating the total flux using Eq. 4.67, there are advantages to writing the total flux in the form 

How will B be determined Equation 4.69 will be used, of course, but that means one has to determine the scattered flux. Then where is the advantage of using B The advantage comes from the fact that B values for a relatively small number of cases can be computed and tabulated and then, by interpolation, one can obtain the total flux using Eq. 4.68 for several other problems. In other words, the use of the buildup factor proceeds in two steps. 

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Tabulated buildup factors depend on the type of primary radiation, the energy, E, of the primary radiation, the charge, Z, atomic number, A, and thickness of the shielding material. 

For example, a 1 MeV point isotropic source of gamma-radiation has a buildup factor ol 2.1 when penetrating a mean-free thickness of water. If the build-up factor is ignored, equation 8.3-11 is exp(-l) = 0.36. Hence, 36% of the radiation passes through the shield. But when the buildup factor is included, 2.1 0.36 = 76% of the radiation penetrates the shield. 

E-5 rad. I was surprised by this result. It is low because of attenuation in the air. A more accurate result would include a buildup factor but still the dose would not be significant. The finite width of the cloud would increase the dose somewhat. 

Buildup Factor—The ratio of the radiation intensity, including both primary and scattered radiation, to the intensity of the primary (unscattered) radiation. 

The third correction factor, which is the ratio of the adsorbed dose buildup factors in the sample and the dosimeter, is usually ignored, but is shown in this paper to be very important. The absorbed dose buildup factor is defined in this paper analogous to the dose buildup factor, a notation used when the unit roentgen was still the unit of radiation dose. This paper shows the magnitude of this third correction factor, which is caused by differences in gamma-ray attenuation coefficients and softening of the gamma-ray spectrum. As an illustrative example, the dose in different dosimeters is calculated as a function of the distance from a point isotropic cobalt-60 source in water. 

Definition of Absorbed Dose Buildup Factor. In the analysis of the dose variation, the concept of dose buildup factor is useful. The usual definition of dose buildup factor (3, 5,7) limits its use to dose in an air dosimeter. The present definition of absorbed dose measured in rads, by which dose in any material or in any dosimeter is defined (6) makes the previous definition of dose buildup factor too restrictive. We will, therefore, replace the dose buildup factor by defining the absorbed dose buildup factor B(r) for a given dosimeter in a given medium as the ratio of the actual absorbed dose in the dosimeter to the absorbed dose that would be measured in the dosimeter if there was no scattered radiation. The value of Equation 7 was, therefore, divided by the absorbed dose... 

The absorbed dose buildup factor B(r) in Equation 8 is the ratio of the actual dose in the dosimeter at a point P, r cm. from a point isotropic 60Co source imbedded in large water container, to the dose that would be measured at the same point if there were no scattered radiation. In this equation I0 is the energy emitted by the source Zs is the scattered radiation flux at P m is the total absorption coefficient of water (0.0632... 

Cu, and Ce. The corresponding buildup factors calculated according to Equation 8 are listed in Table II. 

Table II. Dose Buildup Factors in Elements at Different Distances in Water from a Point Isotropic G0Co...

Element Buildup Factors at fit r— Element Buildup Factors at m r —... 

Figure 2. Absorbed dose buildup factors at distances r in water corresponding to r == 1 r = 2 and, r = 4 from a point isotropic 60Co...

Table III. Dose Buildup Factors in Compounds at Different...

The Buildup Factor of a Chemical Compound or Mixture. The absorbed dose buildup factor B(r) of a compound consisting of the elements Xi, X2, X3,. . . with the buildup factors Bl9 B2, B3,. . . and mass... 

Figure 3. Absorbed dose buildup factors in different dosimeters relative to that of water as a function of the distance r in cm. from a point isotropic 60Co source embedded in a large water container...

Dose as a Function of the Distance from the 60Co Sources. From Equations 7 and 8 we derive Equation 13 for the dose d in a dosimeter with an absorbed dose buildup factor B, r cm. from a point isotropic 60Co source in water. 

Table V. The Absorbed Dose Buildup Factors and the Dose in...

Let us assume that we want to measure the G-value, number of molecular changes per 100 e.v., of Ce4+ — Ce3+ in a ceric-sulfate solution as a function of the concentration. We measure the dose in a Fricke dosimeter vial or ferrous-cupric dosimeter vial at the same place as the vial containing the ceric solution, and then, as is usual, we correct for the difference in the energy transfer coefficient at 1.25 Mev. and for the difference in density of the solutions. However, as shown in Equation 14 and in Table V and Figures 3 and 4, these corrections are entirely inadequate because of the large difference in buildup factors. For 0.4M ceric sulfate solution, the correction caused by the buildup factor is 72% at fit r = 1 122% at /At r = 2 and 155% at fit r = 4. 

If the dose is corrected for the difference in energy transfer coefficient at 1.25 Mev. and for the differences in density of the solutions but not for the differences in buildup factors the G-value, even if actually constant, would behave as if it increased with concentration. This may partly explain the great increase in the G-values with concentration of ceric sulfate observed in the past by some authors. For poly(vinyl chloride) the buildup factors differ also greatly from those of water as is seen in Table III. This difference in buildup factors may explain some of the difficulties encountered in its use in gamma-ray facilities. 

Buildup factor values are tabulated for many cases. 

In general, the buildup factor depends on the energy of the photon, on the mean free paths traveled by the photon in the shield, on the geometry of the source (parallel beam or point isotropic), and on the geometry of the attenuating medium (finite, infinite, slab, etc.). 

Quantities of interest and corresponding buildup factors are shown in Table 4.4 The mathematical formulas for the buildup factors are (assuming a monoen-ergetic, Eq, point isotropic source) as follows ... 

Energy deposited in medium Energy deposition buildup factor... 

Note that the only difference between energy and dose buildup factors is the type of gamma absorption coefficient used. For energy deposition, one uses the absorption coefficient for the medium in which energy deposition is calculated for dose calculations, one uses the absorption coefficient in tissue. 

Extensive calculations of buildup factors have been performed, and the results have been tabulated for several gamma energies, media, and distances. In addition, attempts have been made to derive empirical analytic equations. Two of the most useful formulas are as follows ... 

The constants a( ), b E), A E Uj( ), U2( ) have been determined by fitting the results of calculations to these analytic expressions. Appendix E provides some values for the Berger formula constants. The best equations for the gamma buildup factor representation are based on the so-called geometric progression (G-P) form. The G-P function has the form... 

Extensive tables of these constants are given in Ref. 31. The use of the buildup factor is shown in Ex. 4.19. More examples are provided in Chap. 16 in connection with dose-rate calculations. 

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