Experimental response function of a 3 in×3 in NaI(Tl) detector by inverse matrix method and effective atomic number of composite materials by gamma backscattering technique

Applied Radiation and Isotopes 111 (2016) 56–65

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Experimental response function of a 3 in
3 in NaI(Tl) detector by inverse matrix method and effective atomic number of composite materials by gamma backscattering technique K.U. Kiran a,n, K. Ravindraswami b, K.M. Eshwarappa a, H.M. Somashekarappa c a

Government Science College, Hassan 573201, Karnataka, India St Aloysius College (Autonomous), Mangalore 575001, Karnataka, India c University Science Instrumentation Centre (USIC), Mangalore University, Mangalagangothri 574199 (D K), Karnataka, India b

H I G H L I G H T S

 Response function of a widely used 32
32 NaI(Tl) detector is obtained using inverse matrix method.  Saturation thicknesses of carbon, aluminium, iron, copper, granite and Portland cement are obtained.  Effective atomic numbers of granite and Portland cement are obtained by experimental, Monte-Carlo simulation method and through empirical method.

art ic l e i nf o

a b s t r a c t

Article history: Received 9 November 2014 Received in revised form 11 February 2016 Accepted 12 February 2016 Available online 23 February 2016

Response function of a widely used 3 in
3 in NaI(Tl) detector is constructed to correct the observed pulse height distribution. A 10
10 inverse matrix is constructed using 7 mono-energetic gamma sources (57Co, 203Hg, 133Ba, 22Na, 137Cs, 54Mn and 65Zn) which are evenly spaced in energy scale to unscramble the observed pulse height distribution. Bin widths (E )1/2 of 0.01 (MeV)1/2 are used to construct the matrix. Backscattered photons for an angle of 110° are obtained from a well-collimated 0.2146 GBq (5.8 mCi) 137Cs gamma source for carbon, aluminium, iron, copper, granite and Portland cement. For each observed spectrum, single scattered spectrum is constructed analytically using detector parameters like FWHM, photo-peak efficiency and peak counts. Response corrected multiple scattered photons are extracted from the observed pulse height distribution by dividing the spectrum into a 10
1 matrix. Saturation thicknesses of carbon, aluminium, iron, copper, granite and Portland cement are found out. Variation of multiple scattered photons as a function of target thickness are simulated using MCNP code. A relationship between experimental and simulated saturation thicknesses of carbon, aluminium, iron and copper is obtained as a function of atomic number. Using this relation, effective atomic numbers of granite and Portland cement are obtained from interpolation method. Effective atomic numbers of granite and Portland cement are also obtained by theoretical equation using their elemental composition and comparing with the experimental and simulated results. & 2016 Elsevier Ltd. All rights reserved.

Keywords: Response function Bin contents Inverse matrix Granite Monte Carlo simulation

1. Introduction Among the wide variety of gamma detectors, the NaI(Tl) detector is one of the widely used detector systems because of its low cost and high efficiency. Because of its light weight, several researchers across the world have used NaI(Tl) detectors for in situ measurements in forest, underwater, road transport inspection and measurements of

n

Corresponding author. E-mail addresses: [email protected], [email protected], [email protected] (K.U. Kiran). http://dx.doi.org/10.1016/j.apradiso.2016.02.006 0969-8043/& 2016 Elsevier Ltd. All rights reserved.

building materials, soil and mineral (Plamboeck et al., 2006; Golosov et al., 2009; Vrba and Fojtik, 2014; Vlachos and Tsabaris, 2005; Kwang et al., 2008; Kovler et al., 2013; Bezuidenhout, 2013; Povinec et al., 1996; Jaquiel et al., 2010). The main purpose of a detector system is to reproduce faithfully a spectrum that is associated with the process by which gamma rays interact with the material. But in reality, there is a certain probability of photons of higher energies get registered in the lower side of the energy spectrum due to the partial absorption of photons or secondary emission of electrons (Hubbell, 1958; Hubbell and Scofield, 1958). If necessary corrections are not done to this observed spectra, incorrect data might be obtained from the spectral

K.U. Kiran et al. / Applied Radiation and Isotopes 111 (2016) 56–65

analysis (Sabharwal et al., 2008). Hence to obtain true spectra, and thereby to obtain more accurate physical data from the observed pulse height distribution, unfolding of the spectrum has to be carried out. Several scientific papers to obtain the response function of NaI detectors by Monte Carlo simulation methods are reported (Yi and Hah, 2012; Vitorelli et al., 2005; Shi et al., 2002; Rasolonjatovo et al., 2003; Puzovi and Aniin, 1998; Jorge and Scot, 2009). In their simulation, the effect of materials surrounding the detector and the attenuation of photons in the entrance window were not taken into account. Moreover in their study, infinitesimally narrow beam is used to impinge the center of the detector face, wherein, in reality the beam is always of finite size (Sabharwal et al., 2008). The realistic geometry and source descriptions can be made in MCNP. The realistic pulse highest distribution could be obtained by incorporating the details of the geometry in the simulation. The experimental response function of a 4 in
4 in NaI detector is obtained by inverse matrix method (Hubbell, 1958; Hubbell and Scofield, 1958). As the intrinsic properties like photo-peak efficiency, intrinsic efficiency, FWHM, etc., vary for different crystal sizes of the detectors (Crouthamel et al., 1970; Heath, 1964), this method is used to find the response function of a 2 in
2 in NaI detector using a maximum of five mono-energetic gamma sources viz., 279 keV, 320 keV, 511 keV, 662 keV and 834 keV (Singh et al., 2006, 2008; Saddi et al., 2008; Sabharwal et al., 2008; Singh et al., 2009; Sharma et al., 2010, 2011). Literature survey shows that no data exists to obtain the true photon spectrum from the observed pulse height distribution for a 3 in
3 in NaI(Tl) detector by inverse matrix method. Further, in order to have response function for accurate measurements of the 3 in
3 in NaI (Tl) detector system, the present work uses seven mono-energetic gamma sources of energies 123 keV, 279 keV, 360 keV, 511 keV, 662 keV, 835 keV and 1115 keV which are evenly distributed in the energy scale. A 10
10 inverse matrix is constructed using energy bins ranging from (E )1/2 = 0.01 to (E )1/2 = 1 (MeV)1/2. One of the major advantages of non-destructive evaluation of materials using gamma back-scattering technique is that it requires access to only one side of the material under study. This method is very useful in situations where there is a restriction to access of both sides of the material under study. In Compton backscattering experiments, photons interacting with thick samples suffer multiple scattering and absorption. Hence in addition to single scattered photons, multiple scattered photons of lower energy also get registered by the gamma detector. The work of Paramesh et al. (1983) shows that, in thick samples, scattered photons registered by the detector containing both single and multiple scattered counts can be separated by analytically estimating single scattered spectrum and subtracting it from the composite (that contains both single and multiple scattered

57

photons) spectrum. It was found that for a material, multiple scattered photons increases for an increase in target thickness and then becomes almost a constant. The thickness at which the multiple scattered photons become almost a constant is termed as “saturation thickness”. Their work established a co-relation between saturation thickness and atomic number by showing that elements with higher atomic numbers have lower saturation thickness. This correlation between the saturation thickness of multiple scattered photons and atomic number was successfully used to assign “effective atomic number” to certain composite materials (Singh et al., 2007, 2008, 2009; Ravindraswami et al., 2013, 2014). This is a very useful tool to know the information about attenuation and shielding of a particular material. With response correction, the present work uses this method to assign effective atomic numbers to granite and Portland cement using gamma back-scattering method.

2. Response function of the detector 2.1. Experimental set-up The experimental set-up to obtain the response function of the 3 in
3 in fully integrated MCA NaI(Tl) detector is shown in Fig. 1. The detector crystal is covered with an aluminium window of 0.8 mm thick and optically coupled to photo-multiplier tube. To avoid the contribution due to background radiations the detector is shielded by cylindrical lead shielding of 200 mm length, 35 mm thickness and internal diameter of 90 mm. The inner side of the shielding is covered with 3 mm thick aluminium sheet to absorb the lead K X-rays emitted by lead shielding. The front face of the detector was covered with a cylindrical lead shielding of 160 mm diameter, 50 mm thickness and 8 mm collimator. In order to minimize scattering from the floor and the walls of the room, the entire experimental arrangement was placed at the center of the room at a height of 340 mm on a sturdy wooden platform. Seven mono-energetic gamma sources, viz., 57Co, 203Hg, 133Ba, 22Na, 137Cs, 54 Mn and 65Zn of the order of kBqs (μCi) strengths procured from Board of Radiation and Isotope Technology (BRIT), Department of Atomic Energy, Government of India, Mumbai, India, are used to obtain energies 123, 279, 360, 511, 662, 835 and 1115 keV respectively. The sources are of disc type with a dimension of 25 mm in diameter and 5 mm thick, with an active portion of 6 mm in diameter. The source which is fixed to one side of an extended polystyrene with a dimension 100 mm
100 mm
30 mm and a density of 14
10  3 g/cm3 (weight¼5.1 g) is kept at a distance of 200 mm to the front face of the detector. The height of the goniometer was adjusted to align with the line of axis of the center of

Fig. 1. Experimental set-up for response function.

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Fig. 3. Normalized pulse height distributions. Fig. 2. Pulse height distribution obtained from 511 keV source.

the source and center of the detector assembly. 2.2. Methods of measurements Pulse height distributions for each of the gamma sources were obtained for a dead time corrected acquisition time of 86,400 s. A typical pulse height distribution obtained from a 511 keV source is shown in Fig. 2. Background noise in the absence of the source is subtracted. Because of different activities and half-lives of gamma sources, normalization of the pulse height distributions are done by equating the area under the photo-peaks to their respective crystal (intrinsic) efficiency values (Crouthamel et al., 1970) using the equation

ϵi (E ) = 1 − e−μ (E) t

(1)

The attenuation co-efficient value μ (E ) for energy E and crystal thickness t is obtained from the XCOM photon cross sections database (Berger et al., 2010). The normalized pulse height distributions is shown in Fig. 3. The photo-peaks of each of the normalized curves of energies E are omitted and the theoretical Compton edges (VC1 ¼40 keV, VC2 ¼146 keV, VC3 ¼211 keV, VC4 ¼341 keV, VC5 ¼ 478 keV, VC6 ¼639 keV and VC7 ¼ 907 keV) are marked [Fig. 4] whose values for energies Es are obtained using the relation

VC =

2E 2 m 0 c 2 + 2E

Fig. 4. Photo-peaks omitted curves with the theoretical Compton edge VC marked to the respective curves.

(2)

where m0 is the rest mass of the electron and c is the velocity of light in vacuum. Fig. 5 is obtained by normalizing the energy scale of Fig. 4 to VC. As the width at half maximum of the photo-peak almost varies 1

1

as E 2 , the plot of photo-peaks varies linearly in the E 2 rather than the E scale (Hubbell and Scofield, 1958; Hubbell, 1958). Hence 1

instead of plotting the distribution as a function of E, E 2 is chosen. Each distribution of Fig. 5 is divided into energy bins of constant 1

width in terms of E 2 . The areas under each energy bins are integrated and a graph of top of the energy of the bin contents as a 1

function of E 2 is plotted and is shown in Fig. 6. The cross-cuts of the top of the energy of the respective bins are marked by vertical drop lines. In the next step, the curves of Fig. 6 are interpolated to

Fig. 5. Energy scale normalized to V /VC .

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59

Fig. 8. Photo-peak efficiency of the 3 in
3 in NaI (Tl) detector. Fig. 6. Bin contents versus V /VC . Cross cuts of V /VC are shown by vertical lines.

accurate value of photo-peak efficiency, corrections are made for the iodine escape peak (Peter, 1954), air absorption between the source and the detector (Allison, 1958) and 0.8 mm thick aluminium window that covers the crystal of the detector (Hubbell, 1977). The solid curve in Fig. 8 shows the photo-peak efficiency of the detector system. The experimentally obtained photo-peak efficiency values for the present seven sources are also shown in the figure and are in good agreement with the solid curve. The corrected photo-peak efficiency values are then added to the principal diagonal of the matrix. By doing so, the summation of each elements j of ith row of the matrix R is made equal to the intrinsic efficiency ϵi (E ). The resulting 10
10 matrix R shown in Table 1 is the response function of the detector that converts the spectra N (E) into the expected measured distributions S (E′) by matrix multiplication N

Sj =

∑ Ni Rij

(3)

i=1

Here Sj and Ni are obtained from S (E′) and N(E) in the same way that is followed to obtain the elements of the matrix Rij. Fig. 7. Interpolated bin content curves for different incident photon energies.

2.4. Formation of inverse matrix

(0.1)1/2

obtain 10 different curves from energy bins to (1.0)1/2 (MeV)1/2 for the energy range 0.01–1 MeV to obtain a graph of counts versus energy for different values of Fig. 7.

1 (E′) 2

and is shown in

Even though it is possible to obtain the response function of the detector using matrix R, the inverse matrix R  1 is a better option for two reasons: one, obtaining response function of the detector Table 1

2.3. Formation of the matrix In order to form a triangular matrix, the curves of different 1

values of (E′)2 [Fig. 7] are further divided into energy bins each of 1

width (E )2 . The bin contents are written in the form of a triangular matrix R with the elements as Rij. The indices i and j refer to the incident energy E and pulse height of each energy bin E′. The sum of each row is equated to [ϵi (E ) − ϵi (E )ϵp (E )]. The second term is the product of intrinsic (crystal) efficiency ϵi (E ) and photo-fraction (peak to total ratio) ϵp (E ) and is called as photo-peak efficiency. Photo-peak efficiency values for the detector is obtained by the method reported by Sandhu et al. (1999). The intrinsic efficiency value is calculated for the desired energy and crystal thickness (t), using Eq. (1). The interpolated peak-to-total ratio values are obtained from the work Heath (Heath, 1964). In order to have a more

Response matrix, R, of the detector. (E )1/2 , (E′)1/2 values refer to tops of energy bins. Each row corresponds to a pulse-height distribution due to a line-source of energy E − ΔE/2 normalized to the efficiency of the crystal. Each element of the matrix should be multiplied by 10  4.

(E )1/2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(E′)1/2 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

10,000 8 5 3 0 0 0 0 0 0

9855 573 187 37 35 24 15 11 9

8593 185 179 192 165 129 110 99

8156 759 560 417 318 284 261

7079 952 669 530 438 368

5942 972 699 577 505

5125 898 717 598

4521 780 642

3966 625

3563

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is tedious and two, cumulation error is more (Hubbell, 1958) while using matrix R. The inverse matrix R  1 is as shown in Table 2.

2.5. Response correction for the measured pulse height distribution S (E′) The pulse height distributions S (E′) whose response has to be corrected are divided into the energy bins of the same widths that were used to construct the matrix. This results in a row matrix (with bin contents as elements Sj) of order 1
10. These values are multiplied to the elements of R  1 to form Ni as follows: N

Ni =

∑ Sj Rij−1

(4)

j=1

The response function of the detector (photons per unit energy internal) is obtained from Ni as follows:

N (E ) =

Ni Ei − Ei − 1

(5)

Fig. 9(b) shows the response corrected histogram spectrum of the pulse height distribution of 662 keV spectrum [Fig. 9(a)] for 76 mm
76 mm NaI(Tl) detector. Photons that have undergone partial absorption and secondary electrons that are registered in the lower side of the energy spectrum is now shifted towards the photo-peak region.

3. Effective atomic number 3.1. Experimental set-up of gamma backscattering experiment The experimental set-up of gamma backscattering experiment is shown in Fig. 10. Gamma photons of 662 keV are obtained by using 137Cs source of strength 0.2146 GBq (5.8 mCi) procured from Board of Radiation and Isotope Technology (BRIT), Mumbai, India. The 137Cs source is in the form of a capsule sealed in an aluminium tube of 20 mm diameter and 115 mm length. The active portion of the source is 10 mm in diameter and 6 mm in length. To minimize the background effects of radiation, the active portion of source is shielded using a cylindrical lead ring of 50 mm thickness and a diameter of 160 mm. The source shielding and collimation are achieved by using cylindrical lead rings of 50 mm thickness. In addition to this, 4 cylindrical lead rings (120 mm diameter and 50 mm thickness) were specially prepared to enclose the source, both from back and front sides. The angle between the center of the axis of the source and the detector is maintained at 110°.

Fig. 9. A typical response corrected spectrum for

137

Cs pulse height distribution.

3.2. Theory In the present set-up, the scattered photons from the target are measured by the detector located at an angle of 110°. The scattered spectrum consists of both single and multiple scattered counts. The multiple scattered counts are obtained from the measured spectrum by reconstructing single scattered spectrum. By referring to Fig. 11, let I0 be the incident gamma photons having an energy E0 from the 137Cs source to the target of thickness x0. During scattering, the energy of gamma photons reduces to E within the target dx at a distance x and scattering angle θ. The energy of backscattered photon is given by the Compton relation:

E=

E0 E0 (1 − cos θ ) 1+ m 0 c2

(6)

where m0 is the rest mass of the electron and c is the velocity of light in vacuum. The Klein–Nishina cross section at an angle θ is given by the relation

⎡ ⎤ ⎡ ⎤ ⎤2 ⎡ ⎢ dσ (E, θ ) ⎥ = ⎢ r0 E ⎥ ⎢ E + E0 − sin2 θ ⎥ E ⎢⎣ dΩ ⎥⎦ ⎣ 2 E0 ⎦ ⎢⎣ E0 ⎥⎦

(7)

where r0 is the classical electron radius. The number of photons n (E, x ) reaching the detector situated at D is given by the relation:

Table 2 Inverted response matrix, R−1. Each element of the matrix should be multiplied by 10  4.

(E )1/2

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

(E′)1/2 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

10,000 8 6 3 0 0 0 0 0 0

10,147  676  217  12  16 4 5 10 10

11,638  265  266  308  259  184  147  129

12,261  1315  946  647  434  392  374

14,127  2664  1416  1025  773  581

16,830  3192  1970  1483  1234

19,511  3875  2766  2093

22,119  4349  3222

25,217  4424

28,066

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61

Fig. 10. Experimental set-up of gamma back-scattering experiment.

(intrinsic) efficiency of the detector (Crouthamel et al., 1970). As the gamma photon penetrates deeper in the target, the scattering angle θ1 with respect to different points in the target also increases. The energy E0 varies, contributing NaI (Tl) output of Gaussian form

Y (E ) = Y0 e

Fig. 11. Scattering process diagram.

⎡ dσ ⎤ n (E, x) = I0 ϕ dxne e−μ1x ⎢ ⎥ e−μ2 r dΩ1 ⎣ dΩ ⎦θ

(8)

1

where

ϕ is the cross-section of the incident beam, ne is the dσ

−

2.77 ×(E − E0 ) 2 (FWHM ) 2

where Y0 is the normalization constant. The area under the Gaussian peak can be represented as A = 1.064 × Y0 × (FWHM ). The behavior of change in full width at half maximum (FWHM) as a function of source energies for the present detector was measured experimentally for eight different gamma sources viz., 241 Am, 57Co, 203Hg, 133Ba, 22Na, 137Cs, 65Zn and 54Mn. The value of FWHM for the desired backscattering energy E can be obtained by the best fitted curve of Fig. 12. The number of photons of the Gaussian distribution Y(E) for each energy E can be calculated by using the number of counts at peak position (Y0) and FWHM of the detector. The total number of photons at desired energy is obtained by numerically integrating Y (E). This results in an analytically estimated single scattered spectrum as registered by the detector. Normalization at the maximum peak results in the contribution of single scattered photons. Total intensity of the single scattered photons is then obtained by dividing normalized peak area by photo-fraction. In order to obtain multiple scattered photons, the analytically

number of electrons per unit volume in the medium, [ dΩ ]θ1 is the

Klein–Nishina cross-section at an angle θ1, dΩ1 is the solid angle subtended by the detector collimator at D, r ¼AB. For a given atomic number Z, the total attenuation co-efficients μ1 and μ2 for energies E0 and E respectively are obtained from the XCOM photon cross sections database (Berger et al., 2010). The relation between x and θ1 is given by

x = R 0 × tan (θ1 − θ )

(9)

Integrating n (E, x ) from 0 to x0 we obtain the total number of single scattered photons as follows:

n (E ) =

1 x0

∫0

x0

n (E, x) dx

(10)

The area of Gaussian distribution registered by the scintillation detector for n(E) is given by the relation

A = n (E )ϵp (E )ϵi (E )

(11)

where ϵp (E ) ¼peak to total ratio at the energy E, ϵi (E ) = crystal

(12)

Fig. 12. Variation of FWHM as a function of source energy.

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Fig. 13. Response corrected back-scattered spectrum.

reconstructed single scattered distribution is subtracted from the experimental noise-subtracted-response-corrected spectrum (Paramesh et al., 1983; Singh et al., 2009; Kiran et al., 2014). 3.3. Experimental method of measurements Measurement of gamma backscattered spectrum as a function of target thickness is carried out for a backscattering angle of 110°. A typical spectrum for copper target of 40 mm thickness is shown in Fig. 13. Backscattered spectrum for the sample is acquired for a duration of 4000 s [Fig. 13(a)]. Background spectrum is also recorded for same duration [Fig. 13(b)]. Noise subtracted spectrum that contains both single and multiple scattered photons is shown in Fig. 13(c). The spectrum of single scattered photons is analytically reconstructed and is shown in Fig. 13(d). The response corrected spectrum is represented by histogram [Fig. 13(e)]. Subtraction of single scattered photons from the response corrected spectrum results in multiple scattered photons only. This procedure is repeated for all the thicknesses of copper samples and different materials. A plot of multiple scattered photons versus target thickness for carbon, aluminium, iron, copper, granite and cement is shown in Fig. 14. Thickness at which the multiple scattered photons almost become a constant is noted for each material as saturation thickness and the values are tabulated in column 2 of Table 3. A graph of experimentally obtained saturation thickness versus atomic number is plotted for carbon, aluminium, iron and copper and is shown in Fig. 17. The best fitted curve of Fig. 17 shows an exponential decay relationship between the saturation thickness and atomic number of the elements which are in agreement with the earlier similar works (Paramesh et al., 1983; Singh et al., 2008; Ravindraswami et al., 2013; Singh et al., 1998). From this graph, effective atomic numbers of granite and Portland cement are assigned by interpolating the experimentally obtained values of saturation thicknesses and are tabulated in column 2 of Table 5. 3.4. Simulation In order to validate the experimentally obtained values of saturation thicknesses, the entire experimental set-up was simulated using MCNP code and the plot is shown in Fig. 15. Schematic diagram of geometry used in MCNP simulation is shown in Fig. 16. MCNP4A (Briesmeister, 1993) radiation transport code is adopted to obtain the saturation thicknesses of various materials. To

produce reliable confidence intervals, as many as 1.5
106 histories were run. F1 tally is used to estimate the number of photons crossing front surface of the detector. The results of the simulation per starting source photon are normalized . The plots of normalized backscattered photons per incident photon versus target thickness for carbon, aluminium, iron, copper, granite and Portland cement are shown in Fig. 14. Relative error of MCNP estimation was found to be within 5–6%. The size of the data points in the graphs represent the statistical error. The best fitted dotted curves show that multiple scattered intensity increases with the increase in target thickness and attains saturation. The saturation thicknesses of various materials obtained through simulation are tabulated in column 3 of Table 3. A graph of saturation thickness obtained from MCNP simulation versus atomic number is plotted for carbon, aluminium, iron and copper and is shown in Fig. 17. The best fitted curve of Fig. 17 also shows an exponential decay relationship between the saturation thickness and the atomic number of the elements. This behavior supports the present experimental work. From this graph, effective atomic numbers of granite and Portland cement are assigned by interpolating the values of saturation thicknesses which are obtained through simulation method and are tabulated in column 3 of Table 5. 3.5. Empirical method The effective atomic number of a composite material can also be obtained by simple power law of the form Taylor et al. (2012)

Zeff =

m

Σfi Zim

(13)

wherein the relative electron fraction of the ith element Zi is given by fi, where Σfi ¼ 1. Mayneord used the value of exponent m in the above relation as 2.94 (Khan, 1994). Hence the above equation can be written as

Zeff =

2.94

f1 Z12.94 + f2 Z22.94 + ⋯fn Z n2.94

(14)

Elemental analysis of granite and cement samples were carried out using X-ray fluorescence (XRF) facility at Centre for Earth Science Studies (CESS), Akkulam, Thiruvananthapuram, India. Bruker model S4 Pioneer sequential wavelength dispersive X-ray spectrometer is used for this analysis. Their elemental compositions along with their respective electron fractions are presented in Table 4. The Zeff of granite and Portland cement are obtained by substituting the elemental composition in Eq. (14) and are tabulated in column 4 of Table 5.

4. Conclusions The experimental response function of a 3 in
3 in NaI(Tl) detector obtained by inverse matrix method is very useful to unscramble the observed pulse height distribution. The response corrected spectra show that some photons of higher energies that are registered in the lower side of the energy scale, due to partial absorption and secondary emission of electrons, can be estimated and corrected to obtain a better physical data and hence lead to better interpretation. The present work is of obtaining the response function of the 3 in
3 in NaI(Tl) detector by inverse matrix method for an experimentally observed spectrum. Such a work has not yet been reported and this is the first work of this type. It will be a very useful data base for researchers to unscramble the observed pulse height distribution. Similar work reported by Berger and Seltzer (1972) compares the theoretically calculated response functions for a 3 in
3 in detector with that of experimentally response uncorrected measured spectrum. The

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63

Fig. 14. Multiple scattered photons as a function of target thickness for various materials.

empirical method of finding the response function of the 3 in
3 in by Hie (1978) has the limitation of obtaining the response function for energies less than 280 keV whereas the present work can be used to obtain the response function for gamma sources having energy less than 1000 keV. Gamma backscattering technique, which is a non-destructive method of evaluation of materials, is successfully used to assign ‘effective atomic numbers’ to granite and Portland cement. The experimental, simulated and empirically obtained values of effective atomic numbers of granite and Portland cement agree well

with each other. In spite of the fact that the composition of granite is different in different regions, an attempt is made to compare the present value of effective atomic number of granite with the reported results. The present work shows that the saturation thickness of elements versus atomic number is of exponential decay in nature and support earlier reported works (Paramesh et al., 1983; Singh et al., 1998, 2008; Ravindraswami et al., 2013). The saturation thickness and effective atomic number values of granite and Portland cement show that Portland cement is a better choice, in case, if it is considered for using in nuclear shielding.

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Acknowledgments Authors are grateful to University Grants Commission (UGC), Government of India, for providing financial assistance in the form of Major Research project. K.U. Kiran is also grateful to UGC for Table 3 Saturation thicknesses of different materials. Element/material

Carbon Aluminium Iron Copper Granite Portland cement

Saturation thickness (mm) Experimental

MCNP

135 80 34 27 77 69

140 85 35 21 88 69 Fig. 17. A plot of saturation thickness versus atomic number Z.

Table 4 Elemental composition of granite and Portland cement. Element

Al Ca Fe K Mg Mn Na O P S Si Ti F Fig. 15. MCNP plot of the experimental set-up.

Fig. 16. Schematic diagram of geometry used in MCNP simulation.

Percentage composition Granite

Portland cement

8.04 2.76 2.71 2.31 1.11 0.05 3.19 48.15 0.18 0.02 31.08 0.24 –

3.11 39.44 2.93 0.84 2.31 – 0.54 37.04 0.05 1.86 10.74 – 0.28

K.U. Kiran et al. / Applied Radiation and Isotopes 111 (2016) 56–65

Table 5 An inter-comparison of effective atomic number of composite materials. Composite material

Effective atomic number Experimental MCNP

Empirical Literature

Granite

13.5 ( 7 0.29)

13.1

Portland cement

15.1 ( 7 0.32)

12.7 ( 7 0.24) 16.1 ( 7 0.28)

16.3

10.13 (Gill et al., 1998) 14.8 (Singh and Singh, 2011)

awarding him a fellowship under its Faculty Development Programme. The work was carried out at the Center for Application of Radioisotopes and Radiation Technology (CARRT), Mangalore University, Karnataka, India. Authors are thankful to Dr Krishnaveni S., Department of Physics, University of Mysore, for her help in conducting the experiments.

References Allison, J.W., 1958. Gamma radiation absorption coefficients of air in the energy range 0.01 to 100 MeV. J. Appl. Phys. 29, 1175–1178. Berger, M., Seltzer, S., 1972. Response functions for sodium iodide scintillation detectors. Nucl. Instrum. Methods 104 (2), 317–332. Berger, M.J., Hubbell, J.H., Seltzer, S.M., Chang, J., Coursey, J.S., Sukumar, R., Zucker, D.S., Olsen, K., 2010. XCOM: Photon Cross Section Database, Technical Report 3597, National Institute of Standards and Technology, Gaithersburg, MD. Bezuidenhout, J., 2013. Measuring naturally occurring uranium in soil and minerals by analysing the 352 keV gamma-ray peak of 214Pb using a NaI(Tl)-detector. Appl. Radiat. Isot. 80, 1–6. Briesmeister, J.F., 1993. MCNP a General Purpose Monte Carlo N-Particle Transport Code, Version 4A, Technical Report LA-12625, Los Alamos National Laboratory report. Crouthamel, C.E., Adams, F., Dams, R., 1970. Applied Gamma-ray Spectrometry. Pergamon Press, Oxford. Gill, H., Kaur, G., Singh, K., Kumar, V., Singh, J., 1998. Study of effective atomic numbers in some glasses and rocks. Radiat. Phys. Chem. 51 (46), 671–672. Golosov, V.N., Walling, D.E., Kvasnikova, E.V., Stukin, E.D., Nikolaev, A.N., Panin, A.V., 2000. Application of a field-portable scintillation detector for studying the distribution of 137Cs inventories in a small basin in Central Russia. J. Environ. Radioact. 48, 79–94. Heath, H.L., 1964. Scintillation Spectrometry: Gamma-Ray Spectrum Catalogue. U.S. Atomic Energy Commission. Hie, S., 1978. A method for synthesizing response functions of nai detectors to gamma rays. Nucl. Instrum. Methods 155 (3), 475–483. Hubbell, J., 1958. Response of a large sodium iodide detector to high energy X rays. Rev. Sci. Instrum. 29, 65–68. Hubbell, J.H., 1977. Photon mass attenuation and mass energy-absorption coefficients for H, C, N, O, Ar, and seven mixtures from 0.1 keV to 20 MeV. Radiat. Res. 70, 58–81. Hubbell, J.H., Scofield, N.E., 1958. Unscrambling of Gamma-ray scintillation spectrometer pulse-height distributions. IRE Trans. Prof. Group Nucl. Scii. NS-5, 156–158. Jaquiel, S.F., Carlos, R.A., Avacir, C.A., 2010. Applicability of an X-ray and gamma-ray portable spectrometer for activity measurement of environmental soil samples. Radiat. Meas. 45, 801–805. Jorge, E.F., Scot, V., 2009. Simulation of the detector response function with the code {MCSHAPE}. Radiat. Phys. Chem. 78, 882–887. Khan, F.M., 1994. The Physics of Radiation Therapy. Lippincott Williams & Wilkins, New York. Kiran, K.U., Ravindraswami, K., Eshwarappa, K.M., Somashekarappa, H.M., 2014. An investigation of energy dependence on saturation thickness for 59.54, 123, 279, 360, 511, 662, 1115 and 1250 keV gamma photons in carbon and aluminium. Radiat. Phys. Chem. 97 (0), 107–112. Kovler, K., Prilutskiy, Z., Antropov, S., Antropova, N., Bozhko, V., Alfassi, Z.B., Lavi, N., 2013. Can scintillation detectors with low spectral resolution accurately determine radionuclides content of building material? Appl. Radiat. Isot. 77, 76–83. Kwang, H.K., In, S.J., Sung-Woo, K., Ho-Sik, Y., 2008. Optimum design of detector structure for road transport inspection. Nucl. Instrum. Methods Phys. Res. Sect. A: Accelerat. Spectromet. Detect. Assoc. Equip. 591, 59–62. Paramesh, L., Venkataramaiah, P., Gopala, K., Sanjeeviah, H., 1983. Z-dependence of saturation depth for multiple backscattering of 662 keV photons from thick

65

samples. Nucl. Instrum. Methods Phys. Res. 206, 327–330. Peter, A., 1954. Intensity corrections for iodine X-rays escaping from sodium iodide scintillation crystals. Rev. Sci. Instrum. 25 391–391. Plamboeck, A.H., Nylen, T., Agren, G., 2006. Comparative estimations of 137C distribution in a boreal forest in northern Sweden using a traditional sampling approach and a portable NaI detector. J. Environ. Radioact. 90, 100–109. Povinec, P.P., Osvath, I., Baxter, M.S., 1996. Underwater gamma-spectrometry with HPGe and NaI(Tl) detectors. Appl. Radiat. Isot. 47, 1127–1133. Puzovi, J.M., Aniin, I.V., 1998. User-friendly Monte-Carlo program for the generation of gamma-ray spectral responses in complex source-detector arrangements. Nucl. Instrum. Methods Phys. Res. Sect. A: Accelerat. Spectromet. Detect. Assoc. Equip. 414, 279–282. Rasolonjatovo, A.H.D., Nakamura, T., Nakao, N., Nunomiya, T., 2003. Response functions to photons and to muons of a 12.7 cm diam. by 12.7 cm long NaI(Tl) detector. Nucl. Instrum. Methods Phys. Res. Sect. A: Accelerat. Spectromet. Detect. Assoc. Equip. 498, 328–333. Ravindraswami, K., Kiran, K.U., Eshwarappa, K.M., Somashekarappa, H.M., 2013. Experimental observations of Z-dependence of saturation thickness of 662 keV gamma rays in metals and glasses. Indian J. Phys. 87 (11), 1141–1147. Ravindraswami, K., Kiran, K.U., Eshwarappa, K.M., Somashekarappa, H.M., 2014. Non destructive evaluation of selected polymers by multiple scattering of 662 keV gamma rays. J. Radioanal. Nucl. Chem. 300 (3), 997–1003. Sabharwal, A.D., Singh, M., Singh, B., Sandhu, B.S., 2008. Response function of NaI (Tl) detectors and multiple backscattering of gamma rays in aluminium. Appl. Radiat. Isot. 66, 1467–1473. Saddi, M.B., Singh, B., Sandhu, B.S., 2008. Measurement of collision integral crosssections of double-photon Compton effect using a single gamma ray detector: a response matrix approach. Nucl. Instrum. Methods Phys. Res. Sect. B: Beam Interact. Mater. Atoms 266 (14), 3309–3318. Sandhu, B.S., Dewan, R., Singh, B., Ghumman, B.S., 1999. Measurement of twophoton Compton cross sections. Phys. Rev. A 60, 4600–4605. Sharma, A., Sandhu, B.S., Singh, B., 2010. Incoherent scattering of gamma photons for non-destructive tomographic inspection of pipeline. Appl. Radiat. Isot. 68 (12), 2181–2188. Sharma, A., Singh, K., Singh, B., Sandhu, B.S., 2011. Experimental response function of NaI(Tl) scintillation detector for gamma photons and tomographic measurements for defect detection. Nucl. Instrum. Methods Phys. Res. Sect. B: Beam Interact. Mater. Atoms 269 (3), 247–256. Shi, H.-X., Chen, B.-X., Li, T.-Z., Yun, D., 2002. Precise Monte Carlo simulation of gamma-ray response functions for an NaI(Tl) detector. Appl. Radiat. Isot. 57, 517–524. Singh, T., Singh, S.S., 2011. Experimental investigation of the multiple scatter peak of gamma rays in Portland cement in the energy range 279–1332 keV. Phys. Scr. 84, 065804. Singh, G., Singh, M., Singh, B., Sandhu, B.S., 1998. Experimental observation of Z-dependence of saturation depth of 0.662 MeV multiply scattered gamma rays. Nucl. Instrum. Methods Phys. Res. B 251, 73–78. Singh, M., Singh, G., Singh, B., Sandhu, B.S., 2006. Energy and intensity distributions of multiple compton scattering of 0.279-, 0.662-, and 1.12- γ rays. Phys. Rev. A 74, 042714. Singh, M.P., Sandhu, B.S., Singh, B., 2007. Measurement of effective atomic number of composite materials using scattering of γ-rays. Nucl. Instrum. Methods Phys. Res. Sect. A: Accelerat. Spectromet. Detect. Assoc. Equip. 580 (1), 50–53, Proceedings of the 10 th International Symposium on Radiation Physics {ISRP} 10. Singh, M., Singh, B., Sandhu, B.S., 2008. Energy and intensity distributions of 279 keV multiply scattered photons in bronze an inverse response matrix approach. Pramana 70 (1), 61–73. Singh, G., Singh, M., Sandhu, B.S., Singh, B., 2008. Experimental investigations of multiple scattering of 662 keV gamma photons in elements and binary alloys. Appl. Radiat. Isot. 66 (8), 1151–1159. Singh, M., Singh, B., Sandhu, B.S., 2009. Investigations of multiple scattering of 320 keV γ rays: a new technique for assigning effective atomic number to composite material. Phys. Scr. 79 (3), 035101. Taylor, M.L., Smith, R.L., Dossing, F., Franich, R.D., 2012. Robust calculation of effective atomic numbers: the auto-Zeff software. Med. Phys. 39, 1769–1778. Vitorelli, J.C., Silva, A.X., Crispim, V.R., da Fonseca, E.S., Pereira, W.W., 2005. Monte carlo simulation of response function for a NaI(Tl) detector for gamma rays from 241Am/Be source. Appl. Radiat. Isot. 62, 619–622. Vlachos, D.S., Tsabaris, C., 2005. Response function calculation of an underwater gamma ray NaITl spectrometer. Nucl. Instrum. Methods Phys. Res. Sect. A: Accelerat. Spectromet. Detect. Assoc. Equip. 539, 414–420. Vrba, T., Fojtik, P., 2014. The design of a NaI(Tl) crystal in a system optimised for high-throughput and emergency measurement of iodine 131 in the human thyroid. Radiat. Phys. Chem. 104 (0), 385–388 1st International Conference on Dosimetry and its Applications. Yi, C.-Y., Hah, S.-H., 2012. Monte Carlo calculation of response functions to gammaray point sources for a spherical NaI(Tl) detector. Appl. Radiat. Isot. 70, 2133–2136, Proceedings of the 18th International Conference on Radionuclide Metrology and its Applications.