Annals of Nuclear Energy 35 (2008) 2414–2416

Contents lists available at ScienceDirect

Annals of Nuclear Energy

journal homepage: www.elsevier .com/ locate/anucene

Technical Note

Effect of finite sample dimensions and total scatter acceptance angleon the gamma ray buildup factor

Sukhpal Singh a,*, Ashok Kumar b, Charanjeet Singh a, Kulwant Singh Thind c, Gurmel S. Mudahar a

a Department of Physics, Punjabi University, Patiala, Indiab College of Engineering, Punjabi University Neighbourhood Campus, Rampura Phul, Indiac Department of Physics, Guru Nanak Dev University, Amritsar, India

a r t i c l e i n f o

Article history:Received 6 April 2008Received in revised form 20 August 2008Accepted 21 August 2008Available online 5 October 2008

0306-4549/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.anucene.2008.08.008

* Corresponding author.E-mail address: sukhpal_78@rediffmail.com (S. Sin

a b s t r a c t

The simultaneous variation of gamma ray buildup factors with absorber thickness (up to 6.5 mfp) andtotal scatter acceptance angle (which is the sum of incidence and exit beam divergence) in the mediaof high volume flyash concrete and water was studied experimentally using a point isotropic 137Cs source.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

The gamma radiations interact with matter mainly via threeprocesses namely photoelectric effect, Compton scattering and pairproduction in the energy range of 10 keV to 10 MeV. Photoelectriceffect and pair production results the complete removal of photonwhich interacts with matter but Compton scattering reduces theenergy of the photons and also change its direction resulting abuildup of photons and hence an increase in photon fluence ratewill occur.

For narrow beam geometry used to measure the gamma rayattenuation coefficients of material it is assumed that no scatteredphoton can reach the detector. The intensity of the uncollidedtransmitted beam is given by Lambert law:

I ¼ Ioe�lx ð1Þ

where Io and I are the incident and transmitted intensities of gam-ma rays, x is the thickness of the target medium and l representsthe linear attenuation coefficient. Eq. (1) gives us the intensity oftransmitted flux of only uncollided photons. For this the thicknessof the absorber should be small ideally the incident photon shouldinteract once with the absorbing material and after interaction itshould not reach the detector. With the increase of the thickness,the probability of multiple scattering increases. Also if the exposedarea of the detector to the transmitted radiations increases thechance of reaching the scattered photons to the detector increases.Therefore as the thickness of the absorbing materials or the totalacceptance angle which is the sum of incidence and exit beamdivergence (Fig. 1) or both, i.e. thickness and total acceptance angleincreases simultaneously, there is always some finite probabilitythat the scattered part of the beam may reach the detector and

ll rights reserved.

gh).

thereby get counted as a part of the uncollided beam. Thereforeto correct the Lambert law for such a situation a correction param-eter is required. The modified Lambert law becomes:

I ¼ BIoe�lx ð2Þ

where ‘B’ is the buildup factor. Buildup factor is a multiplicative fac-tor used to obtain the corrected response to the uncollided photonsby including the contribution of scattered photons.

White (1950) introduced the concept of buildup factor; he ob-tained experimentally the buildup factor at 1.25 MeV gamma rayenergy for water up to 16 mfp. The importance of buildup factorin attenuation studies was further recognized by Fano (1953).Miyasaka and Tsuruo (1966) measured the buildup factor in leadup to 6 mfp using point isotropic source of 137Cs and 60Co. Thebuildup factor in iron was measured by Furuta et al. (1966) using60Co and Tamura and Tsuruo (1967) using 137Cs. Osonov et al.(1968) obtained experimentally the buildup factor data for waterup to 5 mfp using a point isotropic 137Cs source. Bishop et al.(1976) obtained experimentally the data for buildup factors in leadand iron using plane isotropic 16N source. Ahmed et al. (1983) mea-sured experimentally the buildup factor in magnetite and sylhetsand concrete using point isotropic 60Co source. Sidhu et al.(2000) studied experimentally the effect of collimator size and ab-sorber thickness on the gamma ray buildup factor for extendedmedia of soil and water up to 5 mfp using point isotropic 137Cssource. El-Hosiny and El-Faramawy (2000) studied the buildup fac-tor as a function of absorber thickness in hydrated Portland ce-ment–lead pastes using 137Cs gamma ray source. Singh et al.(2004) measured the buildup factors in the extended media ofbakelite and perspex under different collimation conditions usinga point isotropic 137Cs source.

Generally, concrete has been used as radiation shielding mate-rial because of its low price and good shielding performance.Cement is one of the most cost and energy intensive components

Table 1Size of the collimators and corresponding value of total scatter acceptance angle

Diameter ofcollimator C1

(mm)

Diameter ofcollimator C2(mm)

Diameter ofcollimator C3

(mm)

Total scatteracceptance angle(�)

4 6 9 3.576 9 16 5.489 16 20 8.3416 20 28 12.4920 28 45 16.98

Source Sample Detector

in out

sc

Collimator Collimator

θ θ

θ

Fig. 1. Ray-diagram representation of incident beam divergence and scatteredradiations reaching the detector (Midgley, 2006).

S. Singh et al. / Annals of Nuclear Energy 35 (2008) 2414–2416 2415

of concrete. The manufacturing of cement creates huge amountsof CO2 as a by-product which poses a serious threat to theenvironment. Fly ash, is a non-combusted by-product of coal-firedpower plants, can be substituted for large portions of Portland ce-ment, significantly improving concrete’s environmental character-istics. Fly ash, consisting mostly of silica, alumina, and iron, formsa compound similar to portland cement when mixed with limeand water. The cement can be replaced with the flyash even with-out lowering its mechanical properties moreover it creates astronger, more durable product and reduces concrete’s environ-mental impact considerably. In the present experiment, an at-tempt has been made to study the buildup factor for extendedmedia of high volume flyash concrete and water as a function ofabsorber thickness (mfp) and total scatter acceptance angle.

2. Experimental details

The schematic diagram of the experimental arrangement usedfor the present measurements is shown in Fig. 2. A radioactivepoint source of isotope 137Cs (5 mCi) obtained from Bhaba AtomicResearch Centre, Mumbai, India was enclosed in a lead containerwith one face aperture 0.5 cm, placed behind the source collimator.A gamma ray spectrometer containing an assembly of NaI(Tl)detector (4.5 cm diameter and 5.1 cm thickness), photomultipliertube (KL9656), pre-amplifier (HA 502 B), linear amplifier (PA521) and power supply (HV 216 D) and computerized 2K MCAplug-in-card was used to measure the transmitted gamma raybeam intensities. The position of source and the detector was fixed.The thickness of the absorber was increased from 8 to 56 cm in thesteps of 8 cm. Seven cubical blocks of high volume flyash concrete

Amplifier MCA

Pre-Amp

Lead collimators

C1 C2 C3

Lead Container Absorber

Source 5cm 60 cm NaI(Tl) Detector

70 cm

H.V

Fig. 2. Experimental set-up.

each having thickness 8 cm were used. The density of each block offlyash concrete was 1.56 g/cm3. The Perspex container havingdimension 7.5 cm � 8 cm � 57.25 cm with internal divisions of8 cm each, was used to hold the water sample. The thickness ofPerspex sheet used for container preparation was 0.25 cm. Threecollimators namely source collimator (C1), absorber collimator(C2) and detector collimator (C3) has been used. The width of eachcollimator was 1.5 cm. To vary the beam divergence and total angleof acceptance the diameter of source collimator (C1), absorber col-limator (C2) and detector collimator (C3) was varied. The values ofthese apertures and correspondingly the values of beam diver-gence and total angle of acceptance were given in Table 1. Thetransmitted beam intensity was measured by increasing the thick-ness of the absorber in steps at a particular value of total scatteracceptance angle. The same experimental procedure was repeatedfor different values of total scatter acceptance angle.

To avoid scattered radiation from reaching the detector, thedetector was surrounded with lead. Each spectrum was recordedfor sufficient long time to reduce the statistical error less than1%. Background spectra were recorded for the same time and sub-tracted from each spectrum. The magnitude of the background sig-nal in the region under the full energy peak was of the order of 4%of the peak area.

3. Calculations

The incident (Io) and transmitted (Imeasured) intensities of pho-tons were recorded for various sample thickness and different val-ues of total scatter acceptance angle using the above discussedexperimental details.

The value of transmitted intensity (Icalculated) for incident inten-sity (Io) was obtained using Eq. (1). by substituting the value of l(0.0859 cm�1 for water and 0.1159 cm�1 for high volume flyashconcrete at 662 keV gamma ray energy) for various sample thick-

1 2 3 4 5 6 71.00

1.02

1.04

1.06

1.08

1.10

High Volume Flyash Concrete Total scatter acceptance angle

16.9 8o

12.49o

8.34o

5.48o

3.57o

----

- Bui

ldup

Fac

tor

----

->

---- Absorber thickness (mfp)---->

Fig. 3. Variation of buildup factor with absorber thickness for different values ofscatter acceptance angle in high volume flyash concrete.

1 2 3 4 51.00

1.02

1.04

1.06

1.08

1.10

1.12Water

16.98o

12.49o

8.34o

5.48o

3.57o

Total scatter acceptance angle

----

- Bui

ldup

Fac

tor

----

-->

----- Absorber thickness ------>

Fig. 4. Variation of buildup factor with absorber thickness for different values ofscatter acceptance angle in water.

2416 S. Singh et al. / Annals of Nuclear Energy 35 (2008) 2414–2416

ness and different values of total scatter acceptance angle. It is ob-served that the value of Imeasured is always greater than Icalculated.The buildup factor:

B ¼ Imeasured

Icalculated: ð3Þ

4. Results and discussion

Figs. 3 and 4 show the values of buildup factors for high volumeflyash (HVFA) concrete and water at various absorber thicknesses(mfp) and for different values of total scatter acceptance angle,respectively.

The value of the buildup factor remains close to unity up to ahigh volume flyash concrete thickness of 4.5 mfp for total scatteracceptance angle of 3.57o. Similarly, for water this value of the

thickness comes to be 4 mfp. For small value of the angular widthof the beam, the probability of scattered photons reaching thedetector is very small. Hence the contribution of multiply scatteredphotons to the uncollided beam remains negligible even at largeabsorber thickness resulting buildup factor close to one. Thesefindings are in line with the results of Midgley (2006).

Further, it is seen that the value of buildup factor increases withthe increase in the absorber thickness and total scatter acceptanceangle. This is obvious as more and more numbers of multiple scat-tered photons are produced with the increase in absorber thicknessand simultaneously the exposure of the detector to the transmittedradiation increases, the probability of multiply scattered photonsreaching the detector also increases. These results are in line withthe previous findings of Singh et al. (2004).

References

Ahmed, F.U., Rehman, M.A., Husain, S.R., Rehman, M.M., 1983. An evaluation of twoaggregates for use in a concrete reactor shield. Nucl. Sci. Engng. 85, 427.

Bishop, G.B., Smitton, C., Packwood, A., 1976. Benchmark data for the penetration of6 MeV gamma photons through steel and lead. Ann. Nucl. Energy 3, 65.

El-Hosiny, F.I., El-Faramawy, N.A., 2000. Shielding of gamma radiation by hydratedPortland cement–lead pastes. Radiat. Meas. 32, 93.

Fano, U., 1953. Gamma-ray attenuation Part II – analysis of penetration. Nucleonics11, 55.

Furuta, Y., Tsuruo, A., Miyaaska, S., 1966. Dose buildup factors of plane parallelbarriers for60Co plane monodirectional source. Nucl. Sci. Engng. 25, 85.

Midgley, S., 2006. Angular width of a narrow beam for X-ray linear attenuationcoefficient measurements. Radiat. Phys. Chem. 75, 945.

Miyasaka, S., Tsuruo, A., 1966. Dose buildup factors of multi-layer slabs for pointisotropic source. J. Nucl. Sci. Technol. 3, 393.

Osonov, D.P., Panova, V.P., Radzievskii, G.B., 1968. Measurements of dose buildupfactors for low-energy point isotropic gamma sources in water. Atom. Energy24, 452.

Sidhu, G.S., Singh, K., Singh, P.S., Mudahar, G.S., 2000. Effect of absorber thicknessand beam divergence on gamma-ray buildup factor. Ind. J. Phys. 74A, 505.

Singh, C., Sidhu, G.S., Kumar, A., Singh, P.S., Mudahar, G.S., 2004. Simultaneous effectof collimator size and absorber thickness on the gamma ray buildup factor. Ind.J. Pure Appl. Phys. 42, 475.

Tamura, K., Tsuruo, S., 1967. Dose buildup factors of plane parallel barriers for 137Csplane monodirectional source. Nucl. Sci. Engng. 28, 144.

White, G.R., 1950. The penetration and diffusion of 60Co gamma-rays in water usingspherical geometry. Phys. Rev. 80, 154.