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. 2025 Oct 23;15:37145. doi: 10.1038/s41598-025-21003-8

Experimental and simulation assessment of gamma-radiation shielding properties of the polyester polymer reinforced with WO3

Farzad Isazadeh 1, Akbar Abdi Saray 1,✉
PMCID: PMC12549913  PMID: 41131178

Abstract

In this study, the shielding features of six samples of the polyester (PE)/WO3 polymer composite against gamma rays (137Cs, 22Na, 60Co, and 133Ba sources) were evaluated via an experimental setup in the laboratory, using GEANT4 and MCNP Monte Carlo codes, as well as Phy-X/PSD and XCOM online programs. To study the structure of the composites, the X-ray diffraction (XRD) and scanning electron microscopy (SEM) analyses were conducted. Moreover, parameters such as the linear attenuation coefficient (LAC), mass attenuation coefficient (MAC), half-value layer (HVL), tenth-value layer (TVL), mean free path (MFP), effective atomic number (Zeff), and effective electron density (Neff) were calculated and compared for the six samples. The values of the MAC parameter for the six samples (W0, W1, W2, W3, W4, and W5) and for the experimental measurements are 0.0712 ± 0.003, 0.0714 ± 0.001, 0.0764 ± 0.002, 0.0791 ± 0.004, 0.0796 ± 0.006, and 0.0823 ± 0.003 cm2/g (662 keV), 0.0887 ± 0.002, 0.0889 ± 0.005, 0.0893 ± 0.007, 0.0902 ± 0.003, 0.0913 ± 0.008, and 0.0938 ± 0.002 cm2/g (511 keV),0.0577 ± 0.004, 0.0576 ± 0.006, 0.0568 ± 0.009, 0.0561 ± 0.002, 0.0560 ± 0.005, and 0.0551 ± 0.002 cm2/g (1.275 MeV),0.0615 ± 0.006, 0.0614 ± 0.008, 0.0605 ± 0.008, 0.0601 ± 0.002, 0.0596 ± 0.001, and 0.0593 ± 0.008 cm2/g (1.173 MeV),0.0581 ± 0.002, 0.0579 ± 0.003, 0.0572 ± 0.003, 0.0568 ± 0.003, 0.0565 ± 0.005, and 0.0560 ± 0.001 cm2/g (1.332 MeV), and 0.1012 ± 0.002, 0.1015 ± 0.001, 0.1035 ± 0.001, 0.1066 ± 0.005, 0.1099 ± 0.008, and 0.1201 ± 0.007 cm2/g (356 keV), respectively. According to the results, the W5 samples can be selected as the most effective shielding material among the samples. In addition, the experimental data and the simulated values obtained from the four mentioned programs were in good agreement, indicating that the Monte Carlo codes and online programs are reliable tools for studying nuclear reactions with high accuracy while also saving time and costs.

Keywords: Shielding, WO3, GEANT4, MCNP, Photon, Polyester

Subject terms: Physics, Nuclear physics

Introduction

Although the use of ionization radiation in different areas of science, such as medical centers, is increasing, protecting the environment and human life from radiation risks has been an essential issue for researchers1,2. Using high-density materials and substances containing elements with high atomic numbers has been a suitable solution for shielding purposes. Some alloys, such as W, Pb, and stainless-steel alloys, have been selected to be assessed for their shielding capacity against nuclear radiation3,4. In addition, some building materials such as concretes, cements, hematite, and paste cements have attracted attention for use as shield materials5–7. Due to properties such as high resistance, low cost, ease of synthesis and shaping, polymers and their composites have drawn increasing attention from researchers8. In a study by Yılmaz and Akman (2023), the protection properties of the unsaturated polyester resin with methyl ethyl ketone peroxide and cobalt octoate doped with the (Bi2(WO4)3) compound were investigated9. Doping high atomic number elements such as W, Pb, Fe, Zn, Ni, and Bi into polymers such as polyvinyl alcohol (PVA), polyvinyl chloride (PVC), polytetrafluoroethylene, polypropylene, polyester, polyvinyl alcohol, polyvinylpyrrolidone, polyethylene glycol, glycidyl methacrylate, polyethylene, and polystyrene has resulted in polymer composites with good shielding properties against nuclear radiations10–20. Moreover, in 2025, the shielding properties of several smart polymers (polyurethane, silicon carbide, polypropylene, polytetrafluoroethylene, polyvinylidene fluoride, and poly) against photons were studied by Ghuge et al.21. In addition, the protection features of the boron-based polymers against photons were assessed by Gu et al.22. In 2025, Hossein et al. examined the shielding parameters of the acrylic polymer/graphene composite against photons23. Moreover, the attenuation ability of tungsten and cadmium-reinforced polymeric materials against photons was studied by Aloraini et al.24. The shielding features of the glycidyl methacrylate polymer were examined by Kassim et al. (2025)17. Due to features such as easy synthesis, being flexible for shaping, and low cost, polymers and their composites have attracted more interest from researchers compared to other materials8. In this study, the shielding properties of six samples of the polyester (PE)/WO3 polymer composite against gamma ray sources of the 137Cs, 22Na, 60Co, and 133Ba are investigated in the laboratory using an experimental approach and simulation methods, including Monte Carlo codes (GEANT4 and MCNP codes) and online programs (Phy-X/PSD and XCOM). Furthermore, to study the structure of the composites, the X-ray diffraction (XRD) and scanning electron microscopy (SEM) tests were performed. Parameters, including linear attenuation coefficient (LAC), mass attenuation coefficient (MAC), half-value layer (HVL), tenth-value layer (TVL), mean free path (MFP), effective atomic number (Zeff), and effective electron density (Neff), were calculated for the six samples and compared to each other. Afterward, to assess the accuracy and validity of the work, the obtained experimental data and the calculated simulation values were compared.

Materials and methods

Sample Preparation

To prepare six composites of PE/WO3, 20 g of PE was poured into a beaker and mixed until bubbles disappeared. Then, a hardener equal to 10% of the PE weight (2 g) was added to the mixed liquid. According to Table 1, different amounts of WO3 (0%, 0.5%, 1.5%, 5%, 10%, and 15%) with an average particle size of 5 μm were added to the hardener and mixed PE. Afterwards, the PE/hardener/WO3 mixture was stirred by an electrical drill until the bubbles were eliminated. Finally, the mixture was left to dry at room temperature for three days before being used for shielding measurements. Figure 1 indicates the six prepared samples of the PE/WO3 polymer composite. Based on the added amount of WO3, the samples are named W0, W1, W2, W3, W4, and W5 corresponding to WO₃ percentages of 0%, 0.5%, 1.5%, 5%, 10%, and 15%, respectively.

Table 1.

Chemical and mole % details of the six prepared samples of PE/WO3 polymer composite.

Sample Sample
Code		 PE WO3 Density (g/cm3)
PE W0 100 - 1.380
0.5% WO 3 W1 99.5 0.5 1.386
1.5% WO 3 W2 98.5 1.5 1.397
5% WO 3 W3 95 5 1.438
10% WO 3 W4 90 10 1.501
15% WO 3 W5 85 15 1.570
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Fig. 1.

Fig. 1

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The prepared samples of the PE/WO3 polymer composite.

Moreover, according to Table 1, the density of the samples is evaluated to be 1.380, 1.386, 1.397, 1.438, 1.501, and 1.570 g/cm3 for the W0, W1, W2, W3, W4, and W5 samples, respectively. The densities are calculated using the following equation25:

graphic file with name 41598_2025_21003_Article_Equ1.gif 1

where ρco is the density of the composites in g/cm3, fpolyester and fwo3 are the mole% of the PE and WO3, and ρpolyester and ρwo3 are the densities of the PE and WO3 in g/cm3.

In addition, the weight percentages (W%) of the elements in the samples are given in Table 2. According to this table, although the W% of the W element rises with increasing the amount of WO3 in each sample, the weight percentages of the other elements decrease accordingly.

Table 2.

Weight% (W%) of the six prepared samples of PE/WO3 polymer composite.

Sample
Code		 C H W O
W0 62.5010 4.1961 - 33.3029
W1 62.1244 4.1708 0.4778 33.2270
W2 61.3734 4.1204 1.4306 33.0756
W3 58.7696 3.9455 4.7344 32.5505
W4 55.1132 3.7001 9.3731 31.8136
W5 51.5302 3.4595 13.9189 31.0914
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Experimental and simulation set-up

Figures 2 and 3 represent the experimental and simulation (GEANT4 and MCNP codes) setups for the radiation measurements of the PE/WO3 composite, respectively. According to Fig. 2, the photon sources of 137Cs (Eγ = 662 keV) with an activity of 10 mCi, 133Ba (Eγ = 356 keV, activity = 10 µCi), 22Na (Eγ1 = 511 keV and Eγ2 = 1.275 MeV, activity = 10 µCi), and 60Co (Eγ1 = 1.173 MeV and Eγ2 = 1.332 MeV, activity = 10 µCi) are located in the middle of an orange Pb shield with a thickness of 22 cm, at a distance of 11 cm from the sample (thickness = 0.7 cm, radius = 3 cm). The sample is 5 cm away from the cubic Pb collimator, which is placed between the NaI(Tl) scintillation detector (2.54 × 2.54 cm2) and the sample.

Fig. 2.

Fig. 2

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Experimental radiation measurements set-up.

Fig. 3.

Fig. 3

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Simulation radiation calculation set-up of the (a) MCNP and (b) GEANT4 Monte Carlo codes.

In addition, in this work, the MCNPX-2.6 version of the MCNP package was used for the radiation simulations. Similar to the GEANT4 toolkit, the MCNP nuclear code is a Monte Carlo code that uses random numbers. The users can observe the geometry of the sources, samples, and detectors in both 3D and 2D dimensions. Moreover, the MCNP code can support the interaction of charged and non-charged particles, including neutrons, photons, protons, deuterons, tritons, and alpha particles (with a wide range of energies) with various types of materials and elements26–29. In this study, the tally of F1 was used for the calculations. The experimental set-up of the present work, simulated using the MCNP code, is illustrated in Fig. 3 (a). The details of the setup are the same as the experimental one shown in Fig. 2.

In the present work, GEANT4-10.7, which is a version of the GEANT4 code, is employed to calculate the shielding features of the PE/WO3 composite against photons with an energy range of 0.010-15 MeV (including the 137Cs, 22Na, 60Co, and 133Ba sources). The GEANT4 toolkit is a Monte Carlo nuclear code that uses random numbers for its calculations. The most significant feature of the code is its flexibility in selecting the input (geometry, source details, physics lists, particle tracks, materials, and elements) and output (tallies and scores) keys and files, which allows the user to simulate photon interactions that are more similar to the experimental ones. Choosing the right physics lists is essential for ensuring the accuracy of the calculations30–32. In the present study, the G4EmPenelopePhysics and GammaNuclearPhysics lists (which contain G4PhotonuclearProcess, G4LowEGammaNuclearmodel, and G4CasvadeInterface processes) were applied for the simulation of the interactions of photons with PE/WO3 composites. Figure 3 (b) displays the GEANT4 shielding set-up with details similar to the experimental set-up.

Moreover, the Phy-X/PSD online program (available at “https://phy-x.net/PSD”) and XCOM (Photon Cross Sections Database) are utilized to further validate the experimental results and simulation calculations and compare them to each other. Although both programs allow the user to define the elements and their weight%, the Phy-X program does not provide the option of selecting the energy of the photons33,34.

XRD and SEM analyses

The XRD analysis

XRD and SEM analyses were used to study the structure of the PE/WO3 polymer composite. XRD is a technique that can assess the crystallographic structure, chemical composition, and physical properties of different compositions. A Cu target under a voltage of 40 kV and a current of 30 mA was applied for the XRD analysis of the PE/WO3 composites, with a scanning degree ranging from 2 to 80 (deg).

The SEM analysis

To examine the surface structure and composition of materials at a high magnification, the SEM analysis is used. The structure of the PE/WO3 polymer composites was studied using the SEM test with a voltage of 15 kV.

Shielding parameters

LAC (Linear Attenuation coefficient)

The LAC parameter is the number of attenuated photons per unit thickness, which is calculated using Eq. (2)35:

graphic file with name 41598_2025_21003_Article_Equ2.gif 2

where LAC is the linear attenuation coefficient (cm− 1), x is the thickness of the sample (cm), N0 is the primary number of photons, and N is the ultimate number of photons.

MAC (Mass Attenuation coefficient)

The interaction probability of photons in a unit of mass is known as the MAC parameter. The following equation is used to calculate the MAC parameter36:

graphic file with name 41598_2025_21003_Article_Equ3.gif 3

where MAC is the mass attenuation coefficient (cm2/g), and ρ is the density of the sample (g/cm3).

HVL (Half-value layer)

The HVL parameter is the thickness of the polymer in which the number of photons is decreased to half. The HVL of the samples (expressed in cm) can be computed using Eq. (4)37:

graphic file with name 41598_2025_21003_Article_Equ4.gif 4

TVL (Tenth-value layer)

TVL is the thickness of the polymer in which the number of photons is attenuated to one-tenth of the initial intensity. The TVL of the samples (expressed in cm) is calculated using the following equation38:

graphic file with name 41598_2025_21003_Article_Equ5.gif 5

MFP (Meant free path)

The thickness of the polymer through which a photon passes without having an interaction can be defined as MFP. It is calculated as the inverse of the LAC parameter as follows (expressed in cm)39:

graphic file with name 41598_2025_21003_Article_Equ6.gif 6

Zeff (Effective atomic number)

The Zeff of the samples is estimated using Eq. (7)40:

graphic file with name 41598_2025_21003_Article_Equ7.gif 7

Ai, ρ, and fi are the atomic mass, sample density, and molar fraction, respectively.

Neff (Effective electron density)

Equation (8) is used to compute the number of electrons per unit of mass, known as Neff (electron/g)41:

graphic file with name 41598_2025_21003_Article_Equ8.gif 8

Results and discussion

XRD analysis

To study the structure of the samples of the PE/WO3 polymer composite, the XRD analysis of the samples was conducted, and the results are illustrated in Fig. 4. The first curve from the bottom belongs to the W0 sample, which shows a significant peak around 200. A broad amorphous halo can be observed in the XRD spectrum of pure PE, which confirms the non-crystalline nature of the polymer. The W2, W3, and W5 curves belong to the W2, W3, and W5 samples, which exhibit five peaks around 230, 330, 420, 500, and 640. The observed peaks indicate that the samples containing WO3 particles have a crystalline nature. These peaks become sharper when the amount of WO3 in the samples rises.

Fig. 4.

Fig. 4

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XRD results of the PE/WO3 polymer composites.

SEM analysis

Figure 5 shows the SEM images of the W0, W2, and W4 samples of the PE/WO3 polymer composite on a 10-µm scale. According to this figure, a monotonous distribution of WO3 particles can be seen in the polymer matrix. The pure PE sample (W0), PE doped with 1.5% WO3 (W2), and PE doped with 10% WO3 (W4) are indicated in Fig. 5(a), 5(b), and 5(c), respectively. As shown in Fig. 5(b) and 5(c), the WO3 particles are successfully dispersed and interfaced with the polymer matrix. It is apparent that in the W2 and W4 samples, the WO3 particles are homogeneously mixed with the PE polymer.

Fig. 5.

Fig. 5

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SEM images of (a) W0, (b) W2, and (c) W4 samples.

Shielding parameter results

In Table 3, the simulated MAC values of the W0, W1, W2, W3, W4, and W5 samples of the PE/WO3 polymer composite against photons with an energy range of 0.010-15 MeV using the GEANT4, MCNP, Phy-X/PSD, and XCOM programs. According to the table, the MAC results of the Monte Carlo codes (GEANT4 and MCNP) and online program (Phy-X/PSD and XCOM) have good compatibility. For instance, in the energy of 0.03 MeV, the MAC values of the W5 sample are 3.3917 ± 0.043, 3.4184, 3.4255, and 3.4250 cm2/g for the GEANT4, MCNP, Phy-X/PSD, and XCOM programs respectively, which have about 1% difference. Moreover, for the whole energy range of 0.010-15 MeV with increasing the amount of WO3 in the samples, the MAC values gradually rise.

Table 3.

The simulated MAC values of the six samples of the PE/WO3 polymer composite.

Energy (keV) MAC (cm2/g)-W0
GEANT4 MCNP Phy-X XCOM
0.01 3.4398 ± 0.015 3.4689 - 3.4820
0.015 1.1368 ± 0.006 1.1247 1.1318 1.1320
0.02 0.5725 ± 0.006 0.5757 0.5799 0.5799
0.03 0.3006 ± 0.005 0.2950 0.3009 0.3009
0.04 0.2284 ± 0.001 0.2260 0.2304 0.2304
0.05 0.2008 ± 0.004 0.1977 0.2020 0.2020
0.06 0.1818 ± 0.006 0.1832 0.1868 0.1868
0.07 0.1722 ± 0.002 0.1730 - 0.1768
0.08 0.1662 ± 0.007 0.1666 0.1695 0.1695
0.09 0.1628 ± 0.003 0.1605 - 0.1636
0.1 0.1593 ± 0.003 0.1555 0.1586 0.1586
0.15 0.1369 ± 0.008 0.1378 0.1406 0.1406
0.2 0.1354 ± 0.004 0.1258 0.1282 0.1282
0.3 0.1108 ± 0.005 0.1095 0.1111 0.1111
0.356 0.1031 ± 0.001 0.1032 0.1041 0.1041
0.4 0.0960 ± 0.001 0.0979 0.0995 0.0995
0.5 0.0941 ± 0.002 0.0891 0.0908 0.0908
0.511 0.0909 ± 0.001 0.0893 0.0900 0.0900
0.6 0.0815 ± 0.003 0.0826 0.0839 0.0840
0.662 0.0795 ± 0.008 0.0796 0.0804 0.0804
0.7 0.0781 ± 0.004 0.0769 - 0.0784
0.8 0.0756 ± 0.008 0.0726 0.0737 0.0737
0.9 0.0711 ± 0.008 0.0685 - 0.0697
1 0.0679 ± 0.009 0.0651 0.0663 0.0663
1.173 0.0606 ± 0.009 0.0601 0.0612 0.0612
1.275 0.0593 ± 0.002 0.0575 0.0587 0.0587
1.332 0.0588 ± 0.001 0.0559 0.0573 0.0574
1.5 0.0544 ± 0.003 0.0529 0.0539 0.0540
2 0.0493 ± 0.004 0.0451 0.0463 0.0463
3 0.0380 ± 0.005 0.0359 0.0371 0.0372
4 0.0301 ± 0.005 0.0302 0.0318 0.0318
5 0.0250 ± 0.005 0.0260 0.0283 0.0283
6 0.0246 ± 0.008 0.0252 0.0258 0.0258
7 0.0217 ± 0.001 0.0235 - 0.0240
8 0.0209 ± 0.001 0.0220 0.0226 0.0226
9 0.0198 ± 0.003 0.0212 - 0.0215
10 0.0182 ± 0.003 0.0201 0.0206 0.0206
15 0.0173 ± 0.001 0.0153 0.0179 0.0179
Energy (keV) MAC (cm2/g)-W1
GEANT4 MCNP Phy-X XCOM
0.01 3.9336 ± 0.021 3.9116 - 3.9310
0.015 1.7905 ± 0.011 1.7808 1.7909 1.7910
0.02 0.8952 ± 0.005 0.8868 0.8915 0.8915
0.03 0.4132 ± 0.008 0.4040 0.4082 0.4082
0.04 0.2782 ± 0.005 0.2742 0.2803 0.2803
0.05 0.2297 ± 0.004 0.2249 0.2295 0.2295
0.06 0.2014 ± 0.009 0.1996 0.2036 0.2036
0.07 0.2147 ± 0.008 0.2242 - 0.2287
0.08 0.2063 ± 0.007 0.2028 0.2060 0.2060
0.09 0.1914 ± 0.006 0.1872 - 0.1905
0.1 0.1840 ± 0.008 0.1761 0.1791 0.1791
0.15 0.1432 ± 0.001 0.1448 0.1475 0.1475
0.2 0.1320 ± 0.005 0.1289 0.1314 0.1314
0.3 0.1138 ± 0.003 0.1104 0.1122 0.1122
0.356 0.1045 ± 0.004 0.1038 0.1048 0.1048
0.4 0.0944 ± 0.007 0.0983 0.0999 0.0999
0.5 0.0957 ± 0.007 0.0893 0.0910 0.0910
0.511 0.0910 ± 0.009 0.0895 0.0902 0.0902
0.6 0.0900 ± 0.003 0.0826 0.0841 0.0841
0.662 0.0799 ± 0.001 0.0797 0.0805 0.0805
0.7 0.0768 ± 0.004 0.0771 - 0.0785
0.8 0.0713 ± 0.005 0.0726 0.0737 0.0738
0.9 0.0674 ± 0.004 0.0684 - 0.0697
1 0.0686 ± 0.004 0.0650 0.0663 0.0663
1.173 0.0604 ± 0.007 0.0600 0.0612 0.0612
1.275 0.0589 ± 0.003 0.0575 0.0587 0.5865
1.332 0.0583 ± 0.008 0.0559 0.0573 0.0574
1.5 0.0559 ± 0.007 0.0528 0.0539 0.0539
2 0.0480 ± 0.006 0.0451 0.0463 0.0463
3 0.0366 ± 0.006 0.0359 0.0372 0.0372
4 0.0332 ± 0.007 0.0313 0.0318 0.0319
5 0.0279 ± 0.005 0.0275 0.0284 0.0284
6 0.0252 ± 0.003 0.0252 0.0259 0.0259
7 0.0231 ± 0.007 0.0235 - 0.0241
8 0.0206 ± 0.008 0.0222 0.0227 0.0227
9 0.0181 ± 0.009 0.0212 - 0.0216
10 0.0172 ± 0.002 0.0203 0.0207 0.0207
15 0.0171 ± 0.002 0.0176 0.0181 0.0181
Energy (keV) MAC (cm2/g)-W2
GEANT4 MCNP Phy-X XCOM
0.01 4.7789 ± 0.035 4.7904 - 4.8270
0.015 3.0713 ± 0.014 3.0924 3.1051 3.1050
0.02 1.5461 ± 0.009 1.5116 1.5128 1.5130
0.03 0.6235 ± 0.008 0.6163 0.6221 0.6221
0.04 0.3778 ± 0.008 0.3754 0.3798 0.3798
0.05 0.2798 ± 0.004 0.2778 0.2843 0.2843
0.06 0.2400 ± 0.005 0.2323 0.2372 0.2372
0.07 0.3411 ± 0.005 0.3252 - 0.3322
0.08 0.2745 ± 0.006 0.2740 0.2788 0.2788
0.09 0.2398 ± 0.003 0.2402 - 0.2441
0.1 0.2144 ± 0.004 0.2167 0.2198 0.2198
0.15 0.1573 ± 0.005 0.1589 0.1612 0.1612
0.2 0.1391 ± 0.005 0.1351 0.1376 0.1376
0.3 0.1155 ± 0.001 0.1120 0.1142 0.1142
0.356 0.1052 ± 0.002 0.1049 0.1060 0.1060
0.4 0.0987 ± 0.002 0.0992 0.1008 0.1008
0.5 0.0961 ± 0.005 0.0897 0.0915 0.0915
0.511 0.0913 ± 0.008 0.0898 0.0906 0.0906
0.6 0.0924 ± 0.006 0.0828 0.0843 0.0843
0.662 0.0800 ± 0.004 0.0798 0.0806 0.0806
0.7 0.0789 ± 0.007 0.0773 - 0.0786
0.8 0.0755 ± 0.007 0.0726 0.0738 0.0738
0.9 0.0734 ± 0.006 0.0685 - 0.0698
1 0.0693 ± 0.006 0.0649 0.0663 0.0663
1.173 0.0603 ± 0.006 0.0599 0.0612 0.0612
1.275 0.0578 ± 0.003 0.0574 0.0586 0.0586
1.332 0.0580 ± 0.004 0.0559 0.0573 0.0573
1.5 0.0565 ± 0.003 0.0528 0.0539 0.0539
2 0.0491 ± 0.003 0.0450 0.0463 0.0463
3 0.0371 ± 0.004 0.0359 0.0372 0.0372
4 0.0343 ± 0.005 0.0313 0.0319 0.0319
5 0.0299 ± 0.005 0.0276 0.0285 0.0285
6 0.0267 ± 0.009 0.0254 0.0261 0.0261
7 0.0232 ± 0.009 0.0237 - 0.0243
8 0.0226 ± 0.004 0.0224 0.0229 0.0229
9 0.0206 ± 0.005 0.0214 - 0.0218
10 0.0184 ± 0.005 0.0206 0.0210 0.0210
15 0.0184 ± 0.001 0.0179 0.0184 0.0184
Energy (keV) MAC (cm2/g)-W3
GEANT4 MCNP Phy-X XCOM
0.01 7.7808 ± 0.063 7.8426 - 7.9350
0.015 7.6439 ± 0.023 7.6180 7.6623 7.6620
0.02 3.6426 ± 0.012 3.6696 3.6674 3.6670
0.03 1.3667 ± 0.008 1.3585 1.3637 1.3640
0.04 0.7219 ± 0.009 0.7181 0.7249 0.7249
0.05 0.4683 ± 0.006 0.4679 0.4743 0.4743
0.06 0.3445 ± 0.005 0.3472 0.3538 0.3538
0.07 0.6797 ± 0.005 0.6793 - 0.6910
0.08 0.5380 ± 0.001 0.5269 0.5312 0.5312
0.09 0.4307 ± 0.002 0.4268 - 0.4299
0.1 0.3550 ± 0.002 0.3574 0.3611 0.3611
0.15 0.2086 ± 0.004 0.2061 0.2088 0.2088
0.2 0.1573 ± 0.003 0.1573 0.1592 0.1592
0.3 0.1172 ± 0.008 0.1186 0.1212 0.1212
0.356 0.1096 ± 0.007 0.1089 0.1103 0.1103
0.4 0.1028 ± 0.007 0.1021 0.1038 0.1038
0.5 0.0964 ± 0.005 0.0910 0.0930 0.0930
0.511 0.0918 ± 0.006 0.0910 0.0920 0.0920
0.6 0.0931 ± 0.002 0.0833 0.0851 0.0851
0.662 0.0808 ± 0.005 0.0804 0.0812 0.0812
0.7 0.0773 ± 0.008 0.0774 - 0.0790
0.8 0.0766 ± 0.007 0.0726 0.0740 0.0740
0.9 0.0725 ± 0.001 0.0685 - 0.0698
1 0.0678 ± 0.008 0.0646 0.0662 0.0662
1.173 0.0600 ± 0.003 0.0597 0.0611 0.0611
1.275 0.0576 ± 0.009 0.0572 0.0585 0.0585
1.332 0.0578 ± 0.009 0.0557 0.0571 0.0572
1.5 0.0564 ± 0.005 0.0527 0.0537 0.0537
2 0.0489 ± 0.004 0.0448 0.0462 0.0462
3 0.0368 ± 0.003 0.0358 0.0373 0.0373
4 0.0336 ± 0.004 0.0315 0.0322 0.0322
5 0.0299 ± 0.008 0.0281 0.0289 0.0289
6 0.0282 ± 0.006 0.0258 0.0266 0.0266
7 0.0254 ± 0.006 0.0241 - 0.0249
8 0.0256 ± 0.002 0.0230 0.0236 0.0236
9 0.0215 ± 0.003 0.0222 - 0.0226
10 0.0184 ± 0.001 0.0214 0.0218 0.0219
15 0.0199 ± 0.001 0.0192 0.0196 0.0196
Energy (keV) MAC (cm2/g)-W4
GEANT4 MCNP Phy-X XCOM
0.01 12.1589 ± 0.045 12.1183 - 12.3000
0.015 14.0218 ± 0.041 13.9528 14.0608 14.0600
0.02 6.6662 ± 0.036 6.6857 6.6925 6.6930
0.03 2.3804 ± 0.024 2.4016 2.4050 2.4050
0.04 1.2201 ± 0.010 1.2008 1.2095 1.2090
0.05 0.7315 ± 0.008 0.7306 0.7411 0.7411
0.06 0.5149 ± 0.009 0.5072 0.5174 0.5174
0.07 1.1841 ± 0.004 1.1752 - 1.1950
0.08 0.8818 ± 0.007 0.8811 0.8855 0.8855
0.09 0.6908 ± 0.007 0.6858 - 0.6909
0.1 0.5506 ± 0.008 0.5541 0.5595 0.5595
0.15 0.2740 ± 0.009 0.2710 0.2755 0.2755
0.2 0.1912 ± 0.004 0.1869 0.1896 0.1896
0.3 0.1303 ± 0.005 0.1280 0.1310 0.1310
0.356 0.1162 ± 0.006 0.1146 0.1163 0.1163
0.4 0.1037 ± 0.003 0.1054 0.1081 0.1081
0.5 0.1013 ± 0.007 0.0931 0.0951 0.0951
0.511 0.0939 ± 0.005 0.0927 0.0940 0.0940
0.6 0.0907 ± 0.006 0.0841 0.0862 0.0863
0.662 0.0816 ± 0.007 0.0809 0.0820 0.0819
0.7 0.0842 ± 0.005 0.0779 - 0.0796
0.8 0.0741 ± 0.006 0.0729 0.0743 0.0743
0.9 0.0717 ± 0.005 0.0684 - 0.0699
1 0.0656 ± 0.004 0.0646 0.0662 0.0662
1.173 0.0598 ± 0.004 0.0596 0.0609 0.0609
1.275 0.0574 ± 0.008 0.0570 0.0583 0.0583
1.332 0.0575 ± 0.009 0.0556 0.0569 0.0570
1.5 0.0576 ± 0.004 0.0523 0.0535 0.0535
2 0.0471 ± 0.004 0.0449 0.0461 0.0461
3 0.0372 ± 0.002 0.0365 0.0375 0.0375
4 0.0341 ± 0.003 0.0318 0.0326 0.0326
5 0.0291 ± 0.004 0.0287 0.0295 0.0295
6 0.0293 ± 0.008 0.0267 0.0273 0.0273
7 0.0257 ± 0.007 0.0250 - 0.0258
8 0.0254 ± 0.007 0.0238 0.0247 0.0247
9 0.0244 ± 0.002 0.0229 - 0.0238
10 0.0235 ± 0.001 0.0224 0.0231 0.0231
15 0.0228 ± 0.001 0.0210 0.0213 0.0213
Energy (keV) MAC (cm2/g)-W5
GEANT4 MCNP Phy-X XCOM
0.01 16.2966 ± 0.063 16.3238 - 16.5700
0.015 20.2277 ± 0.054 20.1905 20.3311 20.3300
0.02 9.6592 ± 0.067 9.6351 9.6571 9.6570
0.03 3.3917 ± 0.043 3.4184 3.4255 3.4250
0.04 1.6808 ± 0.013 1.6754 1.6843 1.6840
0.05 0.9967 ± 0.010 0.9901 1.0025 1.0030
0.06 0.6609 ± 0.003 0.6650 0.6777 0.6777
0.07 1.6737 ± 0.009 1.6636 - 1.6880
0.08 1.2263 ± 0.009 1.2286 1.2328 1.2330
0.09 0.9571 ± 0.008 0.9409 - 0.9466
0.1 0.7361 ± 0.004 0.7471 0.7540 0.7540
0.15 0.3427 ± 0.009 0.3372 0.3410 0.3410
0.2 0.2153 ± 0.003 0.2155 0.2194 0.2194
0.3 0.1436 ± 0.007 0.1377 0.1406 0.1406
0.356 0.1206 ± 0.005 0.1203 0.1222 0.1222
0.4 0.1087 ± 0.008 0.1093 0.1123 0.1123
0.5 0.0995 ± 0.006 0.0950 0.0972 0.0972
0.511 0.0940 ± 0.006 0.0944 0.0959 0.0959
0.6 0.0877 ± 0.007 0.0852 0.0874 0.0874
0.662 0.0825 ± 0.004 0.0815 0.0827 0.0827
0.7 0.0825 ± 0.003 0.0781 - 0.0802
0.8 0.0730 ± 0.007 0.0730 0.0746 0.0746
0.9 0.0713 ± 0.007 0.0685 - 0.0700
1 0.0633 ± 0.005 0.0646 0.0662 0.0662
1.173 0.0595 ± 0.006 0.0591 0.0607 0.0607
1.275 0.0571 ± 0.009 0.0568 0.0581 0.0581
1.332 0.0570 ± 0.001 0.0554 0.0567 0.0568
1.5 0.0562 ± 0.002 0.0522 0.0533 0.0533
2 0.0471 ± 0.006 0.0445 0.0460 0.0460
3 0.0363 ± 0.008 0.0352 0.0376 0.0376
4 0.0348 ± 0.008 0.0323 0.0330 0.0330
5 0.0298 ± 0.009 0.0292 0.0300 0.0301
6 0.0294 ± 0.004 0.0275 0.0281 0.0281
7 0.0261 ± 0.003 0.0259 - 0.0267
8 0.0258 ± 0.005 0.0248 0.0257 0.0257
9 0.0236 ± 0.002 0.0240 - 0.0249
10 0.0230 ± 0.001 0.0235 0.0243 0.0243
15 0.0233 ± 0.001 0.0223 0.0229 0.0229
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Figure 6 indicate the simulated MAC values of the PE/WO3 samples against photons with an energy range of 0.010-15 MeV via the GEANT4, MCNP, Phy-X/PSD, and XCOM programs. As can be seen from Fig. 6, although the MAC values decrease with increasing the energy of the photons for all mentioned codes, there is two peaks at the energies of 0.015 and 0.07 MeV for the W3, W4, and W5 samples. These peaks occurs when the energy of photons exceed the energy of the k-shell of the W element. In this case, the k-edge effect happens, the interaction between photons and W element rise, and the number absorbed photons increase. Therefore, the probability of Photoelectric absorption interaction increases and the two mentioned peaks occur. After the energy of 0.07 MeV, with increasing the energy of the photons, the values of MAC gently decrease. In addition, as Fig. 6 explains, with the amount of WO3 in the samples, the density of the samples increases and the values of MAC parameter rise. Therefore, the maximum values are belonged to the W5 sample.

Fig. 6.

Fig. 6

Open in a new tab

The simulated MAC values of the PE/WO3 samples.

Table 4 shows the experimental and simulation values of the MAC parameter for the six samples of the PE/WO3 composite against photons with the energies of 662 keV (137Cs source), 511 keV (22Na source), 1.275 MeV (22Na source), 1.173 MeV (60Co source), 1.332 MeV (60Co source), and 356 keV (133Ba source). It is noteworthy that at an energy of 661 keV and above, the Compton scattering predominates over photoelectric absorption. According to the table, the values for the W5 sample were reported to be 0.0823 ± 0.003, 0.0825 ± 0.004, 0.0815, 0.0827, and 0.0827 cm2/g (662 keV), 0.0938 ± 0.002, 0.0940 ± 0.006, 0.0944, 0.0959, and 0.0959 cm2/g (511 keV), 0.0551 ± 0.002, 0.0571 ± 0.009, 0.0548, 0.0581, and 0.0581 cm2/g (1.275 MeV), 0.0593 ± 0.008, 0.0595 ± 0.006, 0.0591, 0.0607, and 0.0607 cm2/g (1.173 MeV), 0.0560 ± 0.001, 0.0570 ± 0.001, 0.0554, 0.0567, and 0.0568 cm2/g (1.332 MeV), and 0.1201 ± 0.007, 0.1206 ± 0.005, 0.1203, 0.1222, and 0.1222 cm2/g (356 keV) based on the experimental measurements, GEANT4 toolkit, MCNP code, Phy-X/PSD software, and XCOM program, respectively. As observed in the table, the maximum MAC values belong to the W5 sample due to its higher density compared to the other samples. In the W5 sample, the WO3 content is higher than in the other samples, which results in an increased content of the high atomic number element W.

Table 4.

The MAC values of the six samples of the PE/WO3 polymer composite.

Sample Code MAC (cm2/g)-137Cs (Eγ = 662 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.0712 ± 0.003 0.0795 ± 0.008 0.0796 0.0804 0.0804
W1 0.0714 ± 0.001 0.0799 ± 0.001 0.0797 0.0805 0.0805
W2 0.0764 ± 0.002 0.0800 ± 0.004 0.0798 0.0806 0.0806
W3 0.0791 ± 0.004 0.0808 ± 0.005 0.0804 0.0812 0.0812
W4 0.0796 ± 0.006 0.0816 ± 0.007 0.0809 0.0820 0.0819
W5 0.0823 ± 0.003 0.0825 ± 0.004 0.0815 0.0827 0.0827
Sample Code MAC (cm2/g)-22Na (Eγ = 511 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.0887 ± 0.002 0.0909 ± 0.001 0.0893 0.0900 0.0900
W1 0.0889 ± 0.005 0.0910 ± 0.009 0.0895 0.0902 0.0902
W2 0.0893 ± 0.007 0.0913 ± 0.008 0.0898 0.0906 0.0906
W3 0.0902 ± 0.003 0.0918 ± 0.006 0.0910 0.0920 0.0920
W4 0.0913 ± 0.008 0.0939 ± 0.005 0.0927 0.0940 0.0940
W5 0.0938 ± 0.002 0.0940 ± 0.006 0.0944 0.0959 0.0959
Sample Code MAC (cm2/g)-22Na (Eγ = 1.275 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.0577 ± 0.004 0.0593 ± 0.002 0.0575 0.0587 0.0587
W1 0.0576 ± 0.006 0.0589 ± 0.003 0.0575 0.0587 0.0587
W2 0.0568 ± 0.009 0.0578 ± 0.003 0.0574 0.0586 0.0586
W3 0.0561 ± 0.002 0.0576 ± 0.009 0.0572 0.0585 0.0585
W4 0.0560 ± 0.005 0.0574 ± 0.008 0.0570 0.0583 0.0583
W5 0.0551 ± 0.002 0.0571 ± 0.009 0.0548 0.0581 0.0581
Sample Code MAC (cm2/g)-60Co (Eγ = 1.173 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.0615 ± 0.006 0.0606 ± 0.009 0.0601 0.0612 0.0612
W1 0.0614 ± 0.008 0.0604 ± 0.007 0.0600 0.0612 0.0612
W2 0.0605 ± 0.008 0.0603 ± 0.006 0.0599 0.0612 0.0612
W3 0.0601 ± 0.002 0.0600 ± 0.003 0.0597 0.0611 0.0611
W4 0.0596 ± 0.001 0.0598 ± 0.004 0.0596 0.0609 0.0609
W5 0.0593 ± 0.008 0.0595 ± 0.006 0.0591 0.0607 0.0607
Sample Code MAC (cm2/g)-60Co (Eγ = 1.332 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.0581 ± 0.002 0.0588 ± 0.001 0.0559 0.0573 0.0574
W1 0.0579 ± 0.003 0.0583 ± 0.008 0.0559 0.0573 0.0574
W2 0.0572 ± 0.003 0.0580 ± 0.004 0.0559 0.0573 0.0573
W3 0.0568 ± 0.003 0.0578 ± 0.009 0.0557 0.0571 0.0572
W4 0.0565 ± 0.005 0.0575 ± 0.009 0.0556 0.0569 0.0570
W5 0.0560 ± 0.001 0.0570 ± 0.001 0.0554 0.0567 0.0568
Sample Code MAC (cm2/g)-133Ba (Eγ = 356 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.1012 ± 0.002 0.1031 ± 0.001 0.1032 0.1041 0.1041
W1 0.1015 ± 0.001 0.1045 ± 0.004 0.1038 0.1048 0.1048
W2 0.1035 ± 0.001 0.1052 ± 0.002 0.1049 0.1060 0.1060
W3 0.1066 ± 0.005 0.1096 ± 0.007 0.1089 0.1103 0.1103
W4 0.1099 ± 0.008 0.1162 ± 0.006 0.1146 0.1163 0.1163
W5 0.1201 ± 0.007 0.1206 ± 0.005 0.1203 0.1222 0.1222
Open in a new tab

Due to containing the high atomic element W, in energy ranges lower than 662 keV, photon absorption is higher in the 0.7 cm thickness of the samples. In addition, the probability of the occurrence of photoelectric absorption and Compton scattering is higher in the X-ray energy range. For higher energy ranges (> 662 keV), the absorbance of photons in the samples of the PE/WO3 polymer composite decreases because of the increased strength of the photons.

Table 5 Presents the LAC values computed by experimental measurements and simulated calculations using GEANT4, MCNP, Phy-X, and XCOM programs. For the W4 sample, which contains 10% WO3, LAC values are obtained to be 0.1188 ± 0.011, 0.1225 ± 0.009, 0.1214, 0.1230, and 0.1298 cm− 1 (662 keV), 0.1370 ± 0.013, 0.1409 ± 0.007, 0.1391, 0.1411, and 0.1411 cm− 1 (511 keV), 0.0841 ± 0.009, 0.0875 ± 0.001, 0.0856, 0.0875, and 0.0875 cm− 1 (1.275 MeV), 0.0895 ± 0.005, 0.0907 ± 0.002, 0.0895, 0.0914, and 0.0914 cm− 1 (1.173 MeV), 0.0848 ± 0.001, 0.0907 ± 0.006, 0.0835, 0.0855, and 0.0856 cm− 1 (1.332 MeV), and 0.1650 ± 0.011, 0.1663 ± 0.002, 0.1720, 0.1745, and 0.1746 cm− 1 (356 keV) for the experimental evaluations and the mentioned programs, respectively, whereas the previous experimental values of MAC in the mentioned photon energies for the reinforced unsaturated polyester resin with chromium diboride (containing 10% B4C) are 0.1364 ± 0.003, 0.1561 ± 0.004, 0.0972 ± 0.003, 0.1020 ± 0.002, 0.0956 ± 0.002, and 0.1717 ± 0.004 cm− 1, reported by H. Oğul et al.42. According to the results, except for the values of the W0 and W1 samples, the experimental data and simulation values are in good agreement. Experimental errors (such as operator mistakes and detector noises) and simulation errors (experimental and simulation data are not completely identical) could be the reason for the differences between the experimental and simulation values.

Table 5.

The LAC values of the six samples of the PE/WO3 polymer composite.

Sample Code LAC (cm− 1)-137Cs (Eγ = 662 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.0982 ± 0.005 0.1097 ± 0.004 0.1099 0.1109 0.1110
W1 0.0989 ±0.009 0.1109 ± 0.007 0.1104 0.1115 0.1116
W2 0.1067 ± 0.010 0.1117 ± 0.015 0.1115 0.1126 0.1126
W3 0.1145 ± 0.008 0.1162 ± 0.011 0.1156 0.1167 0.1168
W4 0.1188 ± 0.011 0.1225 ± 0.009 0.1214 0.1230 0.1229
W5 0.1292 ± 0.014 0.1296 ± 0.003 0.1279 0.1298 0.1298
Sample Code LAC (cm− 1)-22Na (Eγ = 511 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.1224 ± 0.009 0.1255 ± 0.011 0.1232 0.1242 0.1242
W1 0.1232 ± 0.005 0.1257 ± 0.009 0.1240 0.1250 0.1250
W2 0.1248 ± 0.008 0.1262 ± 0.008 0.1255 0.1265 0.1266
W3 0.1297 ± 0.012 0.1320 ± 0.013 0.1309 0.1323 0.1323
W4 0.1370 ± 0.013 0.1409 ± 0.007 0.1391 0.1411 0.1411
W5 0.1473 ± 0.010 0.1476 ± 0.001 0.1482 0.1506 0.1506
Sample Code LAC (cm− 1)-22Na (Eγ = 1.275 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.0796 ± 0.005 0.0819 ± 0.002 0.0794 0.0810 0.0810
W1 0.0798 ± 0.002 0.0817 ± 0.003 0.0797 0.0813 0.0814
W2 0.0793 ± 0.006 0.0807 ± 0.003 0.0802 0.0819 0.0819
W3 0.0807 ± 0.008 0.0834 ± 0.001 0.0823 0.0841 0.0841
W4 0.0841 ± 0.009 0.0875 ± 0.001 0.0856 0.0875 0.0875
W5 0.0865 ± 0.004 0.0873 ± 0.001 0.0860 0.0912 0.0912
Sample Code LAC (cm− 1)-60Co (Eγ = 1.173 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.0849 ± 0.002 0.0828 ± 0.001 0.0829 0.0845 0.0845
W1 0.0851 ± 0.008 0.0804 ± 0.003 0.0832 0.0848 0.0848
W2 0.0845 ± 0.006 0.0836 ± 0.005 0.0837 0.0855 0.0855
W3 0.0864 ± 0.007 0.0872 ± 0.001 0.0858 0.0878 0.0879
W4 0.0895 ± 0.005 0.0907 ± 0.002 0.0895 0.0914 0.0914
W5 0.0931 ± 0.004 0.0938 ± 0.001 0.0928 0.0954 0.0953
Sample Code LAC (cm− 1)-60Co (Eγ = 1.332 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.0802 ± 0.002 0.0812 ± 0.001 0.0771 0.0791 0.0792
W1 0.0802 ± 0.009 0.0809 ± 0.001 0.0775 0.0795 0.0796
W2 0.0799 ± 0.006 0.0831 ± 0.002 0.0781 0.0800 0.0800
W3 0.0817 ± 0.007 0.0866 ± 0.004 0.0801 0.0822 0.0823
W4 0.0848 ± 0.001 0.0907 ± 0.006 0.0835 0.0855 0.0856
W5 0.0879 ± 0.004 0.0928 ± 0.003 0.0870 0.0891 0.0892
Sample Code LAC (cm− 1)-133Ba (Eγ = 356 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 0.1397 ± 0.010 0.1338 ± 0.005 0.1424 0.1437 0.1437
W1 0.1407 ± 0.009 0.1406 ± 0.008 0.1439 0.1452 0.1453
W2 0.1446 ± 0.015 0.1424 ± 0.003 0.1465 0.1481 0.1481
W3 0.1533 ± 0.018 0.1486 ± 0.002 0.1566 0.1586 0.1586
W4 0.1650 ± 0.011 0.1663 ± 0.002 0.1720 0.1745 0.1746
W5 0.1886 ± 0.008 0.1818 ± 0.006 0.1889 0.1918 0.1919
Open in a new tab

Moreover, the W5 sample contains a higher content of the high atomic number element W compared to the other samples. Therefore, the density of the W5 sample is higher than the other samples. Due to the higher W content in the W5 sample, Compton scattering occurs more frequently in this sample. Thus, the number of photons that are scattered or absorbed is higher.

The experimental measurements and simulation values of the HVL parameter for the six PE/WO3 polymer composite samples (W0, W1, W2, W3, W4, and W5) against gamma rays with an energy of 662 keV are provided in Table 6. According to this table, for the energy of 662 keV the experimental result of the W3 sample (6.0548 ± 0.071 cm) exhibits good agreement with the values obtained by GEANT4, MCNP, Phy-X, and XCOM programs (5.9651 ± 0.023, 5.9972, 5.9377, and 5.9362 cm, respectively), with a discrepancy of about 2%. The HVL values for W3 sample in the energies of 511 keV, 1.275 MeV, 1.173 MeV, 1.332 MeV, and 356 keV are (5.3439 ± 0.010, 5.2508 ± 0.015, 5.2969, 5.2395, and 5.2394 cm), (8.5922 ± 0.024, 8.3155 ± 0.010, 8.4270, 8.2434, and 8.2397 cm), (8.0203 ± 0.024, 7.9519 ± 0.026, 8.0741, 7.8934, and 7.8891 cm), (8.4863 ± 0.018, 8.0012 ± 0.032, 8.6539, 8.4364, and 8.4270 cm), and (4.5218 ± 0.018, 4.6651 ± 0.008, 4.4263, 4.3713, and 4.3701 cm) for the experimental approach and simulated methods (GEANT4, MCNP, Phy-X, and XCOM programs), respectively.

Table 6.

The HVL values of the six samples of the PE/WO3 polymer composite.

Sample Code HVL (cm)-137Cs (Eγ = 662 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 7.0555 ± 0.045 6.3196 ± 0.021 6.3073 6.2478 6.2473
W1 7.0074 ± 0.068 6.2507 ± 0.013 6.2750 6.2146 6.2125
W2 6.4969 ± 0.023 6.2056 ± 0.016 6.2135 6.1535 6.1559
W3 6.0548 ± 0.071 5.9651 ± 0.023 5.9972 5.9377 5.9362
W4 5.8341 ± 0.047 5.6562 ± 0.019 5.7064 5.6350 5.6385
W5 5.3625 ± 0.087 5.3485 ± 0.010 5.4162 5.3382 5.3385
Sample Code HVL (cm)-22Na (Eγ = 511 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 5.6627 ± 0.027 5.5230 ± 0.005 5.6246 5.5830 5.5809
W1 5.6255 ± 0.033 5.5126 ± 0.008 5.5878 5.5462 5.5444
W2 5.5562 ± 0.015 5.4921 ± 0.009 5.5253 5.4777 5.4765
W3 5.3439 ± 0.010 5.2508 ± 0.015 5.2969 5.2395 5.2394
W4 5.0579 ± 0.021 4.9187 ± 0.010 4.9816 4.9132 4.9127
W5 4.7068 ± 0.013 4.6946 ± 0.008 4.6769 4.6017 4.6037
Sample Code HVL (cm)-22Na (Eγ = 1.275 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 8.7050 ± 0.025 8.4661 ± 0.016 8.7353 8.5606 8.5567
W1 8.6824 ± 0.036 8.4855 ± 0.009 8.6975 8.5265 8.5197
W2 8.7354 ± 0.014 8.5842 ± 0.009 8.6440 8.4651 8.4670
W3 8.5922 ± 0.024 8.3155 ± 0.010 8.4270 8.2434 8.2397
W4 8.2463 ± 0.041 7.9219 ± 0.014 8.1016 7.9241 7.9209
W5 8.0126 ± 0.011 7.9428 ± 0.021 8.0565 7.6009 7.5989
Sample Code HVL (cm)-60Co (Eγ = 1.173 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 8.1672 ± 0.041 8.3692 ± 0.010 8.3574 8.2025 8.2072
W1 8.1451 ± 0.056 8.6217 ± 0.012 8.3351 8.1693 8.1717
W2 8.2011 ± 0.051 8.2883 ± 0.009 8.2833 8.1094 8.1073
W3 8.0203 ± 0.024 7.9519 ± 0.026 8.0741 7.8934 7.8891
W4 7.7482 ± 0.043 7.6417 ± 0.014 7.7482 7.5826 7.5828
W5 7.4451 ± 0.031 7.3864 ± 0.008 7.4703 7.2687 7.2734
Sample Code HVL (cm)-60Co (Eγ = 1.332 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 8.6451 ± 0.054 8.5389 ± 0.009 8.9853 8.7588 8.7505
W1 8.6374 ± 0.015 8.5709 ± 0.009 8.9464 8.7241 8.7127
W2 8.6743 ± 0.027 8.3417 ± 0.012 8.8760 8.6617 8.6591
W3 8.4863 ± 0.018 8.0012 ± 0.032 8.6539 8.4364 8.4270
W4 8.1733 ± 0.011 7.6445 ± 0.017 8.3056 8.1115 8.1016
W5 7.8838 ± 0.046 7.4695 ± 0.024 7.9692 7.7825 7.7728
Sample Code HVL (cm)-133Ba (Eγ = 356 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 4.9632 ± 0.016 5.1786 ± 0.011 4.8671 4.8233 4.8250
W1 4.9272 ± 0.022 4.9315 ± 0.009 4.8180 4.7741 4.7720
W2 4.7939 ± 0.014 4.8666 ± 0.016 4.7299 4.6813 4.6808
W3 4.5218 ± 0.018 4.6651 ± 0.008 4.4263 4.3713 4.3701
W4 4.2019 ± 0.035 4.1685 ± 0.004 4.0296 3.9713 3.9707
W5 3.6761 ± 0.053 3.8126 ± 0.007 3.6700 3.6137 3.6129
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Moreover, Fig. 7 compares the experimental data of the HVL parameter for the 137Cs, 22Na, 60Co, and 133Ba sources with the simulation values obtained by GEANT4, MCNP, Phy-X, and XCOM programs for the six samples of the PE/WO3 composite. As indicated in this figure, due to the fact that increasing the amount of WO3 in the samples results in a decrease in the HVL values, the highest HVL values belong to the W0 sample.

Fig. 7.

Fig. 7

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HVL values of the PE/WO3 samples.

Table 7; Fig. 8 demonstrate the TVL results obtained by experimental and simulation calculations for the W0, W1, W2, W3, W4, and W5 samples against photons with the energies of 662 keV (137Cs source), 511 keV (22Na source), 1.275 MeV (22Na source), 1.173 MeV (60Co source), 1.332 MeV (60Co source), and 356 keV (133Ba source). As shown in Table 7, the experimental TVL value of the W0 sample (23.4429 ± 0.132 cm) for the energy of 662 keV has a discrepancy of around 11% with the minimum simulated values of 20.9976 ± 0.078, 20.9569, 20.7546, and 20.7530 cm obtained from GEANT4, MCNP, Phy-X, and XCOM, respectively. There is a similar level of discrepancy between the experimental and simulation values of the W1 sample, which is due to experimental and simulation errors. For the other samples, the experimental and simulation values are in good agreement.

Table 7.

The TVL values of the six samples of the PE/WO3 polymer composite.

Sample Code TVL (cm)-137Cs (Eγ = 662 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 23.4429 ± 0.132 20.9976 ± 0.078 20.9569 20.7546 20.7530
W1 23.2831 ± 0.114 20.7688 ± 0.098 20.8496 20.6444 20.6375
W2 21.5870 ± 0.231 20.6189 ± 0.103 20.6451 20.4416 20.4496
W3 20.1178 ± 0.201 19.8200 ± 0.097 19.9265 19.7246 19.7197
W4 19.3845 ± 0.103 18.7936 ± 0.105 18.9601 18.7191 18.7306
W5 17.8175 ± 0.162 17.7711 ±0.089 17.9961 17.7331 17.7342
Sample Code TVL (cm)-22Na (Eγ = 511 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 18.8110 ± 0.058 18.3469 ± 0.012 18.6847 18.5463 18.5393
W1 18.6875 ± 0.075 18.3126 ± 0.023 18.5622 18.4240 18.4181
W2 18.4573 ± 0.066 18.2444 ± 0.009 18.3545 18.1964 18.1924
W3 17.7521 ± 0.015 17.4429 ± 0.005 17.5961 17.4051 17.4048
W4 16.8021 ± 0.044 16.3397 ± 0.008 16.5484 16.3213 16.3195
W5 15.6356 ± 0.065 15.5952 ± 0.011 15.5362 15.2866 15.2932
Sample Code TVL (cm)-22Na (Eγ = 1.275 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 28.9175 ± 0.125 28.1236 ± 0.028 29.0181 28.4376 28.4249
W1 28.8423 ± 0.203 28.1883 ± 0.033 28.8925 28.3243 28.3018
W2 29.0182 ± 0.146 28.5162 ± 0.015 28.7149 28.1206 28.1269
W3 28.5426 ± 0.171 27.6233 ± 0.052 27.9937 27.3841 27.3716
W4 27.3935 ± 0.102 26.3160 ± 0.009 26.9129 26.3232 26.3128
W5 26.6173 ± 0.095 26.3854 ± 0.021 26.7630 25.2497 25.2429
Sample Code TVL (cm)-60Co (Eγ = 1.173 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 27.1307 ± 0.118 27.8019 ± 0.055 27.7627 27.2481 27.2637
W1 27.0573 ± 0.101 28.6405 ± 0.024 27.6886 27.1377 27.1457
W2 27.2436 ± 0.159 27.5332 ± 0.011 27.5165 26.9389 26.9320
W3 26.6430 ± 0.201 26.4157 ± 0.051 26.8215 26.2213 26.2069
W4 25.7388 ± 0.177 25.3851 ± 0.048 25.7388 25.1889 25.1894
W5 24.7321 ± 0.202 24.5369 ± 0.023 24.8158 24.1461 24.1617
Sample Code TVL (cm)-60Co (Eγ = 1.332 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 28.7184 ± 0.144 28.3657 ± 0.009 29.8487 29.0960 29.0686
W1 28.6929 ± 0.213 28.4720 ± 0.013 29.7194 28.9807 28.9428
W2 28.8153 ± 0.163 27.7106 ± 0.008 29.4854 28.7737 28.7650
W3 28.1909 ± 0.099 26.5794 ± 0.022 28.7476 28.0250 27.9937
W4 27.1510 ± 0.181 25.3943 ± 0.011 27.5905 26.9457 26.9129
W5 26.1895 ± 0.128 24.8133 ± 0.010 26.4732 25.8530 25.8207
Sample Code TVL (cm)-133Ba (Eγ = 356 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 16.4875 ± 0.088 17.2030 ± 0.029 16.1680 16.0227 16.0282
W1 16.3677 ± 0.075 16.3821 ± 0.010 16.0050 15.8591 15.8523
W2 15.9250 ± 0.111 15.7106 ± 0.023 15.7124 15.5509 15.5494
W3 15.0210 ± 0.096 15.4971 ± 0.009 14.7038 14.5210 14.5171
W4 13.9585 ± 0.054 13.8476 ± 0.015 13.3860 13.1924 13.1903
W5 12.2116 ± 0.103 12.6651 ± 0.014 12.1913 12.0045 12.0018
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Fig. 8.

Fig. 8

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TVL values of the PE/WO3 samples.

Moreover, the good compatibility between the experimental and simulation values of TVL parameter is visible for other energies. For instance, the reported TVL values of W0 sample for the 511 keV, 1.275 MeV, 1.173 MeV, 1.332 MeV, and 356 keV are (18.8110 ± 0.058, 18.3469 ± 0.012, 18.6847, 18.5463, and 18.5393 cm), (28.9175 ± 0.125, 28.1236 ± 0.028, 29.0181, 28.4376, and 28.4249 cm), (27.1307 ± 0.118, 27.8019 ± 0.055, 27.7627, 27.2481, and 27.2637 cm), (28.7184 ± 0.144, 28.3657 ± 0.009, 29.8487, 29.0960, and 29.0686 cm), and (16.4875 ± 0.088, 17.2030 ± 0.029, 16.1680, 16.0227, and 16.0282 cm) for the experimental and simulated methods (using GEANT4, MCNP, Phy-X, and XCOM programs), respectively.

In addition, as observed in Fig. 8, TVL values rise with a decrease in the amount of WO3 in the samples. Therefore, W5 with the highest amount of WO3 (15%) had the lowest TVL values.

Table 8 exhibits the MFP values of the six samples of PE/WO3 polymer composite computed via experimental and simulation methods. The calculated MFP values for the W0 sample are 10.1811 ± 0.082, 9.1191 ± 0.032, 9.1015, 9.0136, and 9.0129 cm (662 keV), 8.1695 ± 0.023, 7.6979 ± 0.008, 8.1146, 8.0546, and 8.0515 cm (511 keV), 12.5587 ± 0.019, 12.2139 ± 0.008, 12.6024, 12.3503, and 12.3448 cm (1.275 MeV), 11.7827 ± 0.022, 12.0742 ± 0.009, 12.0572, 11.8337, and 11.8405 cm (1.173 MeV), 12.4722 ± 0.084, 12.3191 ± 0.023, 12.9631, 12.6362, and 12.6243 cm (1.332 MeV), and 7.1605 ± 0.012, 7.4712 ± 0.009, 7.0217, 6.9586, and 6.9610 cm (356 keV) for the experimental measurements, GEANT4 code, MCNP package, Phy-X/PSD program, and XCOM software, respectively. Except for the W0 and W1 samples, the experimental and simulation results show good compatibility with each other.

Table 8.

The MFP values of the six samples of the PE/WO3 polymer composite.

Sample Code MFP (cm)-137Cs (Eγ = 662 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 10.1811 ± 0.082 9.1191 ± 0.032 9.1015 9.0136 9.0129
W1 10.1117 ± 0.056 9.0198 ± 0.025 9.0549 8.9657 8.9627
W2 9.3751 ± 0.063 8.9547 ± 0.043 8.9661 8.8777 8.8811
W3 8.7371 ± 0.045 8.6077 ± 0.027 8.6540 8.5663 8.5642
W4 8.4186 ± 0.034 8.1620 ± 0.052 8.2343 8.1296 8.1346
W5 7.7381 ± 0.022 7.7179 ± 0.031 7.8156 7.7014 7.7018
Sample Code MFP (cm)-22Na (Eγ = 511 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 8.1695 ± 0.023 7.6979 ± 0.008 8.1146 8.0546 8.0515
W1 8.1159 ± 0.041 7.9531 ± 0.006 8.0615 8.0015 7.9989
W2 8.0159 ± 0.034 7.9234 ± 0.012 7.9713 7.9026 7.9009
W3 7.7096 ± 0.011 7.5754 ± 0.001 7.6419 7.5589 7.5588
W4 7.2971 ± 0.012 7.0962 ± 0.005 7.1869 7.0882 7.0875
W5 6.7904 ± 0.036 6.7729 ± 0.006 6.7473 6.6389 6.6417
Sample Code MFP (cm)-22Na (Eγ = 1.275 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 12.5587 ± 0.019 12.2139 ± 0.008 12.6024 12.3503 12.3448
W1 12.5261 ± 0.024 12.2420 ± 0.009 12.5478 12.3011 12.2913
W2 12.6025 ± 0.011 12.3844 ± 0.014 12.4707 12.2126 12.2154
W3 12.3959 ± 0.037 11.9967 ± 0.036 12.1575 11.8928 11.8874
W4 11.8968 ± 0.042 11.4289 ± 0.008 11.6881 11.4320 11.4275
W5 11.5598 ± 0.013 11.4590 ± 0.007 11.6230 10.9658 10.9629
Sample Code MFP (cm)-60Co (Eγ = 1.173 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 11.7827 ± 0.022 12.0742 ± 0.009 12.0572 11.8337 11.8405
W1 11.7508 ± 0.014 12.4384 ± 0.008 12.0250 11.7857 11.7892
W2 11.8317 ± 0.061 11.9575 ± 0.015 11.9502 11.6994 11.6964
W3 11.5709 ± 0.041 11.4722 ± 0.009 11.6484 11.3878 11.3815
W4 11.1782 ± 0.112 11.0246 ± 0.011 11.1782 10.9394 10.9396
W5 10.7410 ± 0.087 10.6563 ± 0.010 10.7774 10.4865 10.4933
Sample Code MFP (cm)-60Co (Eγ = 1.332 MeV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 12.4722 ± 0.084 12.3191 ± 0.023 12.9631 12.6362 12.6243
W1 12.4612 ± 0.021 12.3652 ± 0.009 12.9070 12.5862 12.5697
W2 12.5143 ± 0.094 12.0346 ± 0.014 12.8054 12.4963 12.4925
W3 12.2431 ± 0.035 11.5433 ± 0.008 12.4849 12.1711 12.1575
W4 11.7915 ± 0.044 11.0286 ± 0.009 11.9824 11.7024 11.6881
W5 11.3740 ± 0.015 10.7763 ± 0.013 11.4972 11.2278 11.2138
Sample Code MFP (cm)-133Ba (Eγ = 356 keV)
Experimental GEANT4 MCNP Phy-X XCOM
W0 7.1605 ± 0.012 7.4712 ± 0.009 7.0217 6.9586 6.9610
W1 7.1084 ± 0.034 7.1146 ± 0.004 6.9509 6.8875 6.8845
W2 6.9161 ± 0.010 7.0210 ± 0.008 6.8238 6.7537 6.7530
W3 6.5235 ± 0.041 6.7303 ± 0.010 6.3858 6.3064 6.3047
W4 6.0621 ± 0.033 6.0139 ± 0.007 5.8135 5.7294 5.7285
W5 5.3034 ± 0.015 5.5004 ± 0.009 5.2946 5.2135 5.2123
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A comparison of the experimental and simulation values of the MFP parameter is illustrated in Fig. 9. The MFP values decrease when the density and the amount of WO3 in the samples increase. Therefore, the highest values of the MFP parameter belong to the W0 sample with a density of 1.380 g/cm3.

Fig. 9.

Fig. 9

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MFP values of the PE/WO3 samples.

Table 9 demonstrates the Zeff and Neff values of the six samples of the PE/WO3 composite against gamma rays with energies of 662 keV, 511 keV, 1.275 MeV, 1.173 MeV, 1.332 MeV, and 356 keV.

Table 9.

The Zeff and Neff values of the six samples of the PE/WO3 polymer composite.

Sample Code 137Cs (Eγ = 662 keV)
Zeff Neff × 1023 (electron/g)
W0 4.5467 3.1346
W1 4.5740 3.1373
W2 4.6292 3.1426
W3 4.8298 3.1610
W4 5.1373 3.1862
W5 5.4724 3.2104
Sample Code 22Na (Eγ = 511 keV)
Zeff Neff × 1023 (electron/g)
W0 4.5475 3.1352
W1 4.5804 3.1417
W2 4.6468 3.1546
W3 4.8879 3.1990
W4 5.2570 3.2605
W5 5.6584 3.3195
Sample Code 22Na (Eγ = 1.275 MeV)
Zeff Neff × 1023 (electron/g)
W0 4.5466 3.1346
W1 4.5682 3.1333
W2 4.6119 3.1309
W3 4.7707 3.1223
W4 5.0145 3.1101
W5 5.2807 3.0979
Sample Code 60Co (Eγ = 1.173 MeV)
Zeff Neff × 1023 (electron/g)
W0 4.5462 3.1343
W1 4.5681 3.1333
W2 4.6124 3.1312
W3 4.7733 3.1240
W4 5.0202 3.1137
W5 5.2899 3.1034
Sample Code 60Co (Eγ = 1.332 MeV)
Zeff Neff × 1023 (electron/g)
W0 4.5468 3.1347
W1 4.5683 3.1334
W2 4.6118 3.1308
W3 4.7698 3.1217
W4 5.0124 3.1088
W5 5.2773 3.0960
Sample Code 133Ba (Eγ = 356 keV)
Zeff Neff × 1023 (electron/g)
W0 4.5488 3.1361
W1 4.5974 3.1534
W2 4.6956 3.1877
W3 5.0511 3.3058
W4 5.5930 3.4689
W5 6.1793 3.6251
Open in a new tab

As shown in this table, the Zeff values for the W0, W1, W2, W3, W4, and W5 samples for the energies of 662 keV, 511 keV, 1.275 MeV, 1.173 MeV, 1.332 MeV, and 356 keV are computed to be (4.5467, 4.574, 4.6292, 4.8298, 5.1373, and 5.4724), (4.5740, 4.5804, 4.6468, 4.8879, 5.257, and 5.6584), (4.6292, 4.5682, 4.6119, 4.7707, 5.0145, and 5.2807), (4.8298, 4.5681, 4.6124, 4.7733, 5.0202, and 5.2899), (5.1373, 4.5683, 4.6118, 4.7698, 5.0124, and 5.2773), and (5.4724, 4.5974, 4.6956, 5.0511, 5.593, and 6.1793), respectively.

In addition, the Neff values reported in this study for the mentioned samples and the energies of 662 keV, 511 keV, 1.275 MeV, 1.173 MeV, 1.332 MeV, and 356 keV are (3.1346 × 1023, 3.1373 × 1023, 3.1426 × 1023, 3.1610 × 1023, 3.1862 × 1023, and 3.2104 × 1023 (electron/g)), (3.1352 × 1023, 3.1417 × 1023, 3.1546 × 1023, 3.1990 × 1023, 3.2605 × 1023, and 3.3195 × 1023 (electron/g)), (3.1346 × 1023, 3.1333 × 1023, 3.1309 × 1023, 3.1223 × 1023, 3.1101 × 1023, and 3.0979 × 1023 (electron/g)), (3.1343 × 1023, 3.1333 × 1023, 3.1312 × 1023, 3.1240 × 1023, 3.1137 × 1023, and 3.1034 × 1023 (electron/g)), (3.1347 × 1023, 3.1334 × 1023, 3.1308 × 1023, 3.1217 × 1023, 3.1088 × 1023, and 3.0960 × 1023 (electron/g)), and (3.1361 × 1023, 3.1534 × 1023, 3.1877 × 1023, 3.3058 × 1023, 3.4689 × 1023, and 3.6251 × 1023 (electron/g)) respectively.

As indicated in Fig. 10, the values of the Zeff parameter increase with the rising amounts of WO3 in the PE/WO3 composite samples. Therefore, the W5 sample showed the maximum Zeff values (5.4724, 5.6584, 5.2807, 5.2899, 5.2773, and 6.1793 for the 662 keV, 511 keV, 1.275 MeV, 1.173 MeV, 1.332 MeV, and 356 keV energies, respectively) among the samples.

Fig. 10.

Fig. 10

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Zeff values of the PE/WO3 samples.

Figure 11 displays the Neff values of the W0, W1, W2, W3, W4, and W5 samples against gamma rays with the energies of 662 keV, 511 keV, 1.275 MeV, 1.173 MeV, 1.332 MeV, and 356 keV. Similar to the Zeff parameter, the Neff values decline with decreasing density of the samples. Therefore, the highest value of the Neff parameter (3.2104 × 1023, 3.3195 × 1023, 3.0979 × 1023, 3.1034 × 1023, 3.0960 × 1023, and 3.6251 × 1023 (electron/g)) belonged to the W5 sample.

Fig. 11.

Fig. 11

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Neff values of the PE/WO3 samples.

Conclusion

In the present work, shielding parameters, including LAC, MAC, HVL, TVL, MFP, Zeff, and Neff, for the W0, W1, W2, W3, W4, and W5 samples of the PE/WO3 polymer composite were calculated against photons with energies of 662 keV (137Cs), 511 keV (22Na), 1.275 MeV (22Na), 1.173 MeV (60Co), 1.332 MeV (60Co), and 356 keV (133Ba) using an experimental method in the laboratory, as well as GEANT4, MCNP, Phy-X/PSD, and XCOM programs. Furthermore, XRD and SEM analyses were used to assess the structure of the composite. The experimental values of the MAC parameter for the six samples were calculated to be 0.0712 ± 0.003, 0.0714 ± 0.001, 0.0764 ± 0.002, 0.0791 ± 0.004, 0.0796 ± 0.006, and 0.0823 ± 0.003 cm2/g (662 keV), 0.0887 ± 0.002, 0.0889 ± 0.005, 0.0893 ± 0.007, 0.0902 ± 0.003, 0.0913 ± 0.008, and 0.0938 ± 0.002 cm2/g (511 keV),0.0577 ± 0.004, 0.0576 ± 0.006, 0.0568 ± 0.009, 0.0561 ± 0.002, 0.0560 ± 0.005, and 0.0551 ± 0.002 cm2/g (1.275 MeV),0.0615 ± 0.006, 0.0614 ± 0.008, 0.0605 ± 0.008, 0.0601 ± 0.002, 0.0596 ± 0.001, and 0.0593 ± 0.008 cm2/g (1.173 MeV),0.0581 ± 0.002, 0.0579 ± 0.003, 0.0572 ± 0.003, 0.0568 ± 0.003, 0.0565 ± 0.005, and 0.0560 ± 0.001 cm2/g (1.332 MeV), and 0.1012 ± 0.002, 0.1015 ± 0.001, 0.1035 ± 0.001, 0.1066 ± 0.005, 0.1099 ± 0.008, and 0.1201 ± 0.007 cm2/g (356 keV), respectively. These results were in good agreement with the simulation values obtained by GEANT4 (0.0795 ± 0.008, 0.0799 ± 0.001, 0.0800 ± 0.004, 0.0808 ± 0.005, 0.0816 ± 0.007, and 0.0825 ± 0.004 cm2/g (662 keV), 0.0909 ± 0.001, 0.0910 ± 0.009, 0.0913 ± 0.008, 0.0918 ± 0.006, 0.0939 ± 0.005, and 0.0940 ± 0.006 cm2/g (511 keV), 0.0593 ± 0.002, 0.0589 ± 0.003, 0.0578 ± 0.003, 0.0576 ± 0.009, 0.0574 ± 0.008, and 0.0571 ± 0.009 cm2/g (1.275 MeV), 0.0606 ± 0.009, 0.0604 ± 0.007, 0.0603 ± 0.006, 0.0600 ± 0.003, 0.0598 ± 0.004, and 0.0595 ± 0.006 cm2/g (1.173 MeV), 0.0588 ± 0.001, 0.0583 ± 0.008, 0.0580 ± 0.004, 0.0578 ± 0.009, 0.0575 ± 0.009, and 0.0570 ± 0.001 cm2/g (1.332 MeV), and 0.1031 ± 0.001, 0.1045 ± 0.004, 0.1052 ± 0.002, 0.1096 ± 0.007, 0.1162 ± 0.006, and 0.1206 ± 0.005 cm2/g (356 keV)), MCNP (0.0796, 0.0797, 0.0798, 0.0804, 0.0809, and 0.0815 cm2/g (662 keV), 0.0893, 0.0895, 0.0898, 0.0910, 0.0927, and 0.0944 cm2/g (511 keV), 0.0575, 0.0575, 0.0574, 0.0572, 0.0570, and 0.0548 cm2/g (1.275 MeV), 0.0601, 0.0600, 0.0599, 0.0597, 0.0596, and 0.0591 cm2/g (1.173 MeV), 0.0559, 0.0559, 0.0559, 0.0557, 0.0556, and 0.0554 cm2/g (1.332 MeV), 0.1032, 0.1038, 0.1049, 0.1089, 0.1146, and 0.1203 and cm2/g (356 keV)), Phy-X (0.0804, 0.0805, 0.0806, 0.0812, 0.0820, and 0.0827 cm2/g (662 keV), 0.0900, 0.0902, 0.0906, 0.0920, 0.0940, and 0.0959cm2/g (511 keV), 0.0587, 0.0587, 0.0586, 0.0585, 0.0583, and 0.0581 cm2/g (1.275 MeV), 0.0612, 0.0612, 0.0612, 0.0611, 0.0609, and 0.0607 cm2/g (1.173 MeV), 0.0573, 0.0573, 0.0573, 0.0571, 0.0569, and 0.0567 cm2/g (1.332 MeV), and 0.1041, 0.1048, 0.1060, 0.1103, 0.1163, and 0.1222 cm2/g (356 keV)), and XCOM (0.0804, 0.0805, 0.0806, 0.0812, 0.0819, and 0.0827 cm2/g (662 keV), 0.0900, 0.0902, 0.0906, 0.0920, 0.0940, and 0.0959 cm2/g (511 keV), 0.0587, 0.0587, 0.0586, 0.0585, 0.0583, and 0.0581 cm2/g (1.275 MeV), 0.0612, 0.0612, 0.0612, 0.0611, 0.0609, and 0.0607 cm2/g (1.173 MeV), 0.0574, 0.0574, 0.0573, 0.0572, 0.0570, and 0.0568 cm2/g (1.332 MeV), and 0.1041, 0.1048, 0.1060, 0.1103, 0.1163, and 0.1222 cm2/g (356 keV)). Therefore, the W5 sample with the highest amount of WO3 and the maximum density of 1.570 g/cm3 had the highest MAC values, which makes it the most effective shielding material against photons with the energies of 662 keV (137Cs), 511 keV (22Na), 1.275 MeV (22Na), 1.173 MeV (60Co), 1.332 MeV (60Co), and 356 keV (133Ba) among the studied samples. As a result, the good compatibility between the experimental data and the simulation values indicates that GEANT4, MCNP, Phy-X/PSD, and XCOM programs are credible and effective tools for simulating nuclear reactions with high accuracy before experimental evaluation in the laboratory.

Acknowledgements

We would like to express our gratitude to the Head and staff of the Institute for considering our paper.

Author contributions

Akbar Abdi Saray: Supervision, Conceptualization, Methodology, Formal analysis, Writing - Review & EditingFarzad Isazadeh: Software, Conceptualization, Methodology, Writing - Review & Editing, Investigation and Calculation.

Funding

No funds, grants, or other support was received.

Data availability

All data generated or analyzed during this study were included in this article.

Declarations

Competing interests

The authors declare no competing interests.

Footnotes

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