Determination of gamma-ray parameters for polyethylene glycol of different molecular weights

Determination of gamma-ray parameters for polyethylene glycol of different molecular weights 1 2 corresp first-author Corresponding author: hamarnehibrahim@gmail.com Corresponding author: hamarnehibrahim@gmail.com hamarnehibrahim@gmail.com 2 3 4 2 Department of Physics, Faculty of Science, Al-Balqa Applied University, Al-Salt 19117, Jordan Department of Physics, Faculty of Science, Al-Balqa Applied University, Al-Salt 19117, Jordan Department of Physics, College of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia Department of Physics, College of Science, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia Nuclear Science Research Institute, King Abdulaziz City for Science and Technology (KACST), Riyadh 11442, Saudi Arabia Nuclear Science Research Institute, King Abdulaziz City for Science and Technology (KACST), Riyadh 11442, Saudi Arabia National Centre for Nuclear Technology (NCNT), King Abdulaziz City for Science and Technology (KACST), Riyadh 11442, Saudi Arabia National Centre for Nuclear Technology (NCNT), King Abdulaziz City for Science and Technology (KACST), Riyadh 11442, Saudi Arabia Mass attenuation coefficient ( μ m ) for polyethylene glycol (PEG) of different molecular weights are determined by using NaI(Tl) scintillator and WinXCOM mixture rule at gamma energies of 59.5, 302.9, 356.0, 661.7, 1173.2 and 1332.5 keV. The total atomic, molecular and electronic cross-sections, half-value layer, effective atomic and electron numbers, mass energy-absorption coefficients, and kermas relative to air, are calculated. The energy and compositional dependence of μ m values, and the related radiation absorption parameters, are evaluated and discussed. The experimental results agree well with the theoretical ones, within an uncertainty of 1% in the effective atomic number for all PEG samples at the designated energies. Polyethylene glycol Mass attenuation coefficient Effective atomic number Electron density Kerma relative to air. 1. Introduction 1 Polyethylene glycol (PEG), a polymer composed of the -CH 2 -CH 2 -O- repeating units, is one of the most widely synthetic and inexpensive materials that has medical, chemical, biological and industrial uses [ 1 1 - 4 4 1-4 ] . PEG of different molecular weights are commercially available and are well-known as non-toxic, non-immunogenic, amphiphatic and biocompatible polymers. PEG is utilized as a polymer-protein conjugate [ 5 5 ] and also known for its ability to mitigate protein adsorption and cell adhesion [ 1 1 ] . Thus, it has been successfully attached to biomedical implants, joint replacements and tissue substitutes [ 6 6 - 9 9 6-9 ] . Besides, it is effective for biochips and biosensors [ 10 10 ] , medical instruments and implants technology [ 11 11 ] . With its distinctive physical properties, PEG is chosen for this investigation because it may play an important role in developing radiation shielding and phantom technologies, medical and nuclear applications, and radiation dosimeters. Therefore, knowledge of PEG molecules' radiological parameters; such as mass attenuation and mass energy-absorption coefficients, interaction cross sections, effective atomic numbers, half-value layer and kerma, is vital for understanding their physical properties. In the same context, knowledge of gamma ray interaction with PRG is essential for radiation and nuclear physics and chemistry, radiation protection and dosimetry, and biomedical and technological fields [ 12 12 - 16 16 12-16 ] . A great number of authors reported the mass attenuation coefficients and related parameters for a variety of materials, including dosimeters, metals, polymers, biological and medical materials etc . [ 17 17 - 25 25 17-25 ] , but none of the work were dedicated to evaluating the gamma attenuation performance of PEG. Therefore, it is important to study the radiation protection capabilities of this particular polymer against gamma irradiation [ 26 26 ] . To achieve this, an investigation of the behavior and performance of PEG of different molecular weights against different gamma-rays has been carried out. PEG of molecular different weights provides a scope for various application. For example, PEG molecular weight (chain length) affects the long-term stability of biomedical applications and the biofouling performance of PEG [ 27 27 ] . The chain length of PEG is a crucial factor affecting its grafting density, the number of hydrogen bonds, and other properties of PEG [ 28 28 ] . On the other hand, PEG of low molecular weights was significantly effective as a hydrate inhibitor for designing drilling fluids [ 29 29 ] . It is thus of interest to identify the photon energy absorption parameters of PEG of various molecular weights. In this research, the mass attenuation coefficients ( μ m ) for five PEG products were measured at 59.5, 302.9, 356.0, 661.7, 1173.2 and 1332.5 keV by using NaI (Tl) scintillator, and were calculated by using mixture rule. Total atomic, molecular and electronic cross-sections ( σ a , σ m and σ e ), half-value layer ( HVL ), effective atomic and electron numbers ( Z eff and N eff ), mass energy-absorption coefficients and kermas relative to air for the PEG samples, were calculated. These radiation interaction data are not tabulated in the literatures but are widely used in the shielding and dosimetry calculations used for medical diagnostic, therapeutic procedures and radiation biophysics. Therefore, the results can hopefully facilitate the use of PEG in specific applications such as gamma-ray shielding effectiveness, phantom technology, and many others. 2. Experimental 1 PEG of molecular weights of 1000, 10000, 20000, 100000, and 200000 were obtained from Sigma Aldrich (Germany). The common name, molecular formula, molecular weight and mean atomic number of each PEG sample are given in Table 1 Table 1 . The mean atomic number was calculated as: < Z > = ∑ f i Z i , where Z i is the atomic number of the i th element, f i = n i / ∑n i = n i / n is the fractional abundance of the i th element with respect to the number of atoms in the compound, n i is the number of formula units of the i th constituent element in the compound, and n is the total number of atoms in the molecule. 1 1 CN 1 1 MF 1 1 MW (Daltons) 1 1 <Z> 1 1 PEG 1 000 1 1 C 44 H 90 O 23   1 1 987.17 1 1 3.4268 1 1 PEG 10 000 1 1 C 454 H 910 O 228   1 1 10 017.95 1 1 3.4284 1 1 PEG 20 000 1 1 C 908 H 1818 O 455   1 1 20 017.88 1 1 3.4285 1 1 PEG 100 000 1 1 C 4540 H 9082 O 2271   1 1 100 017.33 1 1 3.4286 1 1 PEG 200 000 1 1 C 9080 H 18162 O 4541   1 1 200 016.64 1 1 3.4286 Each PEG sample was compressed in hydraulic press to thin disk of Φ 1 cm×0.2 cm. The PEG samples were exposed to gamma-rays from four standard point sources (10 mCi) of 214 Am (59.5 keV), 133 Ba (302.9 and 356.0 keV), 137 Cs (661.7 keV), and 60 Co (1173.2 and 1332.5 keV). A Φ 2''×2'' NaI(Tl) scintillation detector (EG & G Ortec, USA) was used. The source-detector distance was 25 cm ( Fig. 1 Fig. 1 ), and the detector energy resolution was 8% at 662 keV. A gamma spectrum was collected with a 2048-channel MCA, in data-collection time of 3000 s to ensure good statistics. The gamma spectra were analyzed using the Maestro-ORTEC. Each sample was measured for three times, and the average value was taken for calculating the parameters. The gamma-ray absorption of PEG samples was evaluated by a narrow beam collimated by two lead collimators of a Φ 5 mm aperture [ 30 30 ] : one in front of the source and the other above the detector ( Fig. 1 Fig. 1 ). PEG samples in mass thicknesses of 0.21–0.47 g/cm 2 were positioned at 15 cm from the source. The μ m for different PEG samples and energies were calculated by Eq.(1) [ 31 31 ] : <math display="block" id="M1"><mrow><mi>I</mi><mo>=</mo><msub><mi>I</mi><mtext>0</mtext></msub><mtext> </mtext><msup><mi>e</mi><mrow><mo>−</mo><msub><mi>μ</mi><mtext>m</mtext></msub><mi>x</mi></mrow></msup><mo>,</mo></mrow></math> where I 0 and I denote the incoming and attenuated photon intensities, respectively; μ m (cm 2 /g)= μ ℓ / ρ , with μ ℓ (cm −1 ) being the linear attenuation coefficient; ρ (g/cm 3 ) is the mass density; and x (g/cm 2 ) is mass thickness of the sample. For a material composed of more than one element, μ m is calculated by WinXcom [ 32 32 ] based on the mixture rule [ 33 33 ] as: <math display="block" id="M2"><mrow><msub><mi>μ</mi><mtext>m</mtext></msub><mo>=</mo><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder><mrow><msub><mi>w</mi><mi>i</mi></msub><msub><mrow><mo stretchy="false">(</mo><msub><mi>μ</mi><mtext>m</mtext></msub><mo stretchy="false">)</mo></mrow><mi>i</mi></msub></mrow></mstyle><mo>,</mo></mrow></math> where ( μ m ) i is μ m of the i th element in the composite and w i = n i A i / ∑ n j A j is the proportion by weight of the i th element, where A i is the atomic weight of that element. The mixture rule gives the attenuation coefficients of any substance as the sum of the appropriately weighted contributions from the individual atoms. The WinXcom can generate cross sections or attenuation coefficients on a standard energy grid, spaced approximately logarithmically, on a grid specified by the user, or for a mix of both grids. This program provides total cross sections and attenuation coefficients as well as partial cross sections for incoherent and coherent scattering, photoelectric absorption, and pair production [ 34 34 ] . The maximum uncertainties (Δ μ m ) in μ coefficients were calculated by Eq.(3): <math display="block" id="M3"><mrow><mtext>Δ</mtext><msub><mi>μ</mi><mtext>m</mtext></msub><mo>=</mo><mfrac><mn>1</mn><mi>x</mi></mfrac><msqrt><mrow><msup><mrow><mo stretchy="false">(</mo><mfrac><mrow><mtext>Δ</mtext><msub><mi>I</mi><mn>0</mn></msub></mrow><mrow><msub><mi>I</mi><mn>0</mn></msub></mrow></mfrac><mo stretchy="false">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo stretchy="false">(</mo><mfrac><mrow><mtext>Δ</mtext><mi>I</mi></mrow><mi>I</mi></mfrac><mo stretchy="false">)</mo></mrow><mn>2</mn></msup><mo>+</mo><msup><mrow><mo stretchy="false">(</mo><mi>ln</mi><mfrac><mrow><msub><mi>I</mi><mn>0</mn></msub></mrow><mrow><msub><mi>I</mi><mn>0</mn></msub></mrow></mfrac><mo stretchy="false">)</mo></mrow><mn>2</mn></msup><mi/><msup><mrow><mo stretchy="false">(</mo><mfrac><mrow><mtext>Δ</mtext><mi>x</mi></mrow><mi>x</mi></mfrac><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></mrow></msqrt><mo>,</mo></mrow></math> where Δ I 0 , Δ I , and Δ x are the uncertainties in the intensities I 0 and I and the mass thickness x , respectively. For composite materials, the effective atomic number ( Z eff ) is used to describe the gamma-ray interaction processes [ 35 35 , 36 36 ] , calculated by [ 39 39 ] : <math display="block" id="M4"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub><mo>=</mo><msub><mi>σ</mi><mtext>a</mtext></msub><mo>/</mo><msub><mi>σ</mi><mtext>e</mtext></msub><mo>,</mo></mrow></math> where σ a is the atomic cross-section [ 37 37 ] and σ e is the total electronic cross-section [ 38 38 ] : <math display="block" id="M5"><mrow><msub><mi>σ</mi><mtext>a</mtext></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></mfrac><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder><mrow><msub><mi>f</mi><mi>i</mi></msub><mtext> </mtext><msub><mi>A</mi><mi>i</mi></msub><mtext> </mtext><msub><mrow><mo stretchy="false">(</mo><msub><mi>μ</mi><mtext>m</mtext></msub><mo stretchy="false">)</mo></mrow><mi>i</mi></msub></mrow></mstyle><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mtext>m</mtext></msub><mtext> </mtext><msub><mi>A</mi><mtext>r</mtext></msub></mrow><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></mfrac><mo>,</mo></mrow></math> <math display="block" id="M6"><mrow><msub><mi>σ</mi><mtext>e</mtext></msub><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></mfrac><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder><mrow><mfrac><mrow><msub><mi>f</mi><mi>i</mi></msub><mtext> </mtext><msub><mi>A</mi><mi>i</mi></msub><mtext> </mtext><msub><mrow><mo stretchy="false">(</mo><msub><mi>μ</mi><mtext>m</mtext></msub><mo stretchy="false">)</mo></mrow><mi>i</mi></msub></mrow><mrow><msub><mi>Z</mi><mi>i</mi></msub></mrow></mfrac></mrow></mstyle><mo>.</mo></mrow></math> The mass attenuation coefficient is used to calculate the total molecular cross section ( σ m ): <math display="block" id="M7"><mrow><msub><mi>σ</mi><mtext>m</mtext></msub><mo>=</mo><mfrac><mrow><msub><mi>μ</mi><mtext>m</mtext></msub><mtext> </mtext><mi>M</mi></mrow><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></mfrac><mo>=</mo><mi>n</mi><msub><mi>σ</mi><mtext>a</mtext></msub><mo>,</mo></mrow></math> where M = ∑ n i A i is the molecular weight of the compound. The effective electron number is calculated as: <math display="block" id="M8"><mrow><msub><mi>N</mi><mrow><mtext>eff</mtext></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow><mi>N</mi></mfrac><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub><mtext> </mtext><mstyle displaystyle="true"><munder><mo>∑</mo><mi>i</mi></munder><mrow><msub><mi>n</mi><mi>i</mi></msub></mrow></mstyle><mo>=</mo><mfrac><mrow><msub><mrow><mo stretchy="false">(</mo><msub><mi>μ</mi><mtext>m</mtext></msub><mo stretchy="false">)</mo></mrow><mrow><mtext>polymer</mtext></mrow></msub></mrow><mrow><msub><mi>σ</mi><mtext>e</mtext></msub></mrow></mfrac><mo>,</mo></mrow></math> where N A is the Avogadro's number and A r = ∑n i A i / ∑n i = M / n is the relative atomic mass of the compound. The half-value layer, the material width required to reduce the air kerma of an X- or γ -ray to half its value, is defined as: <math display="block" id="M9"><mrow><mi>H</mi><mi>V</mi><mi>L</mi><mo>=</mo><mtext> ln</mtext><mn>2</mn><mo>/</mo><msub><mi>μ</mi><mi mathvariant="script">l</mi></msub><mo>.</mo></mrow></math> Kerma (kinetic energy released per unit mass) in a material, is feasible to uncharged particles and photons, and is related to energy fluence and mass energy-absorption coefficient ( μ en / ρ ). Kerma of PEG material relative to air is calculated as: <math display="block" id="M10"><mrow><mi>K</mi><mi>e</mi><mi>r</mi><mi>m</mi><mi>a</mi><mo>=</mo><mo> </mo><msub><mrow><mrow><mo>(</mo><mrow><msub><mi>μ</mi><mrow><mtext>en</mtext></mrow></msub><mo>/</mo><mi>ρ</mi></mrow><mo>)</mo></mrow></mrow><mrow><mtext>PEG</mtext></mrow></msub><mo>/</mo><msub><mrow><mrow><mo>(</mo><mrow><msub><mi>μ</mi><mrow><mtext>en</mtext></mrow></msub><mo>/</mo><mi>ρ</mi></mrow><mo>)</mo></mrow></mrow><mrow><mtext>air</mtext></mrow></msub><mo>,</mo></mrow></math> where the ( μ en / ρ ) = ∑ w j ( μ en / ρ ) i for PEG or air [ 40 40 , 41 41 ] . For air, the ( μ en / ρ ) i coefficients are taken from Ref. [ 42 42 ]. 3. Results and discussions 1 The μ m values for PEG 100 000 measured and calculated at the selected photon energies are shown in Fig. 2 Fig. 2 , while the insert shows μ m values for the other PEG samples. Experimental uncertainty in μ m coefficient was estimated at ≤3%, being mainly due to uncertainty in measuring the mass density and thickness, and counting the incident and transmitted gamma intensities. The μ m depends evidently on the photon energy and the chemical composition of PEG. At low energy region, the μ m coefficient decreases sharply with increasing energy, as photoelectric absorption is the main interaction between gamma-rays and PEG, which is characterized by the importance of atomic binding. Compton scattering process at intermediate energies (302.9, 356.0 and 661.7 keV), and pair production process at high energies (1173.2 and 1332.5 keV), dominate over photoelectric absorption process. Thus, μ m coefficients show a less energy-dependent behavior and gradual decrease with increasing energy. Fig. 2 Fig. 2 and its insert, the measured μ m for almost all samples is slightly lower than the calculated values. However, they agree well with each other within the experimental uncertainty. The observed discrepancy between measured and calculated values of μ m may be ascribed to potential existence of trace amounts of impurities in the PEG materials. Other factors that may include possible deviation of the experimental setup from perfect-narrowness, causing systematic uncertainty in the measured values of μ m [ 43 43 ] . The σ a , σ m and σ e values versus photon energy is similar to that of μ m values, as shown in Fig. 3 Fig. 3 for sample PEG 200,000. The behavior of σ a , σ m and σ e values for all PEG samples is nearly identical. The μ m values, measured and calculated, were used to calculate the effective atomic number ( Z eff ) and the electron density ( N eff ) for PEG samples. The Z eff and N eff for PEG 200 000 are listed in Table 2 Table 2 . The percentage differences between the calculation and experimental results are below 1% for the PEG samples (and for other PEG samples) at the designated energies. From Table 2 Table 2 , the Z eff values of PEG lie within the range of the atomic numbers of its constitute elements (1 < Z eff < 8), which is consistent with others findings for low Z constituents' materials [ 44 44 ] . 1 1 E (keV) 2 1 Measured 2 1 Calculated 1 1 Percentage difference in Z eff % 1 1   1 1 Z eff   1 1 N eff   1 1 Z eff   1 1 N eff   1 1   1 1 59.5 1 1 3.567 ± 0.091 1 1 3.413 ± 0.087 1 1 3.580 1 1 3.426 1 1 0.363 1 1 302.9 1 1 3.426 ± 0.092 1 1 3.278 ± 0.088 1 1 3.434 1 1 3.285 1 1 0.233 1 1 356.0 1 1 3.414 ± 0.089 1 1 3.266 ± 0.085 1 1 3.432 1 1 3.284 1 1 0.524 1 1 661.7 1 1 3.411 ± 0.093 1 1 3.264 ± 0.089 1 1 3.430 1 1 3.283 1 1 0.554 1 1 1137.2 1 1 3.400 ± 0.090 1 1 3.254 ± 0.086 1 1 3.429 1 1 3.282 1 1 0.846 1 1 1332.5 1 1 3.411 ± 0.091 1 1 3.264 ± 0.087 1 1 3.430 1 1 3.283 1 1 0.554 The Z eff and N eff versus photon energy for sample PEG 20 000 are shown in Fig. 4 Fig. 4 , and the insert in Fig.4(a) Fig.4(a) shows the Z eff versus for the other PEG samples. The behavior of Z eff and N eff with energy for all PEG samples is almost the same and the measurement and calculation results agree well with each other. These confirm that the effective atomic number depends on the energy and interaction processes involved [ 41 41 ] . Although Z eff has its highest value at lower energy region where photoelectric effect is dominant [ 16 16 ] , it can be observed from Fig. 4(a) Fig. 4(a) that Z eff values for PEG samples do not vary appreciably over the considered energy range. This observation agrees with the results in Ref. [ 38 38 ] that the effective atomic number tends to remain constant with increasing photon energy in materials containing carbon, hydrogen and oxygen. Also, from the inset in Fig. 4(b) Fig. 4(b) , N eff increases linearly with Z eff for the PEG samples. The energy dependence of the HVL values for all PEG samples are given in Table 3 Table 3 . The HVL increases with energy. All PEG samples showed similar behavior indicating that PEG with various molecular weights are equivalent in attenuating gamma radiation as their HVL values are almost the same. 1 1 PEG 2 1 59.5 keV 2 1 302.9 keV 2 1 356.0 keV 2 1 661.7 keV 2 1 1173.2 keV 2 1 1332.5 keV 1 1   1 1 Mea. 1 1 Cal. 1 1 Mea. 1 1 Cal. 1 1 Mea. 1 1 Cal. 1 1 Mea. 1 1 Cal. 1 1 Mea. 1 1 Cal. 1 1 Mea. 1 1 Cal. 1 1 1 000 1 1 2.967±0.078 1 1 2.955 1 1 4.992±0.128 1 1 4.980 1 1 5.325±0.135 1 1 5.299 1 1 6.898±0.175 1 1 6.860 1 1 9.082±0.230 1 1 9.011 1 1 9.667±0.245 1 1 9.611 1 1 10 000 1 1 2.968±0.075 1 1 2.958 1 1 4.993±0.125 1 1 4.984 1 1 5.326±0.138 1 1 5.299 1 1 6.899±0.178 1 1 6.860 1 1 9.086±0.232 1 1 9.011 1 1 9.671±0.246 1 1 9.627 1 1 20 000 1 1 2.969±0.076 1 1 2.958 1 1 4.994±0.127 1 1 4.984 1 1 5.327±0.137 1 1 5.299 1 1 6.900±0.179 1 1 6.860 1 1 9.086±0.231 1 1 9.011 1 1 9.672±0.245 1 1 9.627 1 1 100 000 1 1 2.969±0.075 1 1 2.958 1 1 4.994±0.128 1 1 4.984 1 1 5.328±0.139 1 1 5.299 1 1 6.901±0.172 1 1 6.860 1 1 9.086±0.233 1 1 9.011 1 1 9.672±0.244 1 1 9.627 1 1 200 000 1 1 2.969±0.076 1 1 2.958 1 1 4.994±0.129 1 1 4.984 1 1 5.328±0.135 1 1 5.299 1 1 6.901±0.177 1 1 6.860 1 1 9.086±0.230 1 1 9.011 1 1 9.672±0.243 1 1 9.627 The variation of theoretical μ en /ρ coefficient and kerma relative to air versus photon energy are given in Table 4 Table 4 for all PEG samples. Regarding the values of μ en /ρ coefficient and kerma relative to air, two distinct energy regions can be observed in Table 4 Table 4 . A strong energy dependence in the low energy region, at which the main interaction mechanism is photoelectric effect, and a less energy dependence in the higher energy regions, at which Compton scattering and pair production processes are the predominant interaction mechanisms. 1 1 PEG 2 1 59.5 keV 2 1 302.9 keV 2 1 356.0 keV 2 1 661.7 keV 2 1 1173.2 keV 2 1 1332.5 keV 1 1   1 1 μ en   1 1 Kerma 1 1 μ en   1 1 Kerma 1 1 μ en   1 1 Kerma 1 1 μ en   1 1 Kerma 1 1 μ en   1 1 Kerma 1 1 μ en   1 1 Kerma 1 1 1 000 1 1 0.0260 1 1 0.8553 1 1 0.0313 1 1 1.0919 1 1 0.0317 1 1 1.0922 1 1 0.0320 1 1 1.0923 1 1 0.0296 1 1 1.0915 1 1 0.0287 1 1 1.0923 1 1 10 000 1 1 0.0295 1 1 0.8521 1 1 0.0313 1 1 1.0916 1 1 0.0317 1 1 1.0919 1 1 0.0320 1 1 1.0920 1 1 0.0296 1 1 1.0912 1 1 0.0287 1 1 1.0919 1 1 20 000 1 1 0.0295 1 1 0.8519 1 1 0.0313 1 1 1.0915 1 1 0.0317 1 1 1.0918 1 1 0.0320 1 1 1.0920 1 1 0.0296 1 1 1.0912 1 1 0.0287 1 1 1.0919 1 1 100 000 1 1 0.0295 1 1 0.8517 1 1 0.0313 1 1 1.0915 1 1 0.0317 1 1 1.0918 1 1 0.0320 1 1 1.0920 1 1 0.0296 1 1 1.0912 1 1 0.0287 1 1 1.0919 1 1 200 000 1 1 0.0295 1 1 0.8517 1 1 0.0313 1 1 1.0915 1 1 0.0317 1 1 1.0918 1 1 0.0320 1 1 1.0920 1 1 0.0296 1 1 1.0912 1 1 0.0287 1 1 1.0919 4. Conclusion 1 The mass attenuation ( μ m ) and mass energy-absorption ( μ en /ρ ) coefficients, total atomic and electronic cross-sections ( σ a and σ e ), half-value layer ( HVL ), effective atomic ( Z eff ) and electron ( N eff ) numbers, and kermas relative to air for PEG in molecular weights of 1 000−200 000, have been investigated at 59.5, 302.9, 356.0, 661.7, 1173.2 and 1332.5 keV. The experiment and calculation results agree well with each other. The photon energy and compositional dependence of the values of μ m , σ a , and σ e are remarkable in the low energy range due to the predominant photoelectric absorption mechanism. Z eff and N eff behave with photon energy in a similar manner for all PEG samples and therefore they were linearly related. HVL values increase with photon energy. The energy dependence of μ en /ρ coefficients and kermas relative to air show two distinct energy regions in which they behave quite differently. 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Authors also thank all members of the Nuclear Science Research Institute at the King Abdulaziz City for Science and Technology in Riyadh, Saudi Arabia for providing the facilities to conduct the experiments. 10.1007/s41365-017-0311-y 2016-10-27 2017-02-13 2017-02-13 2017-10-25 2017-11-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2017 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-017-0311-y http://dx.doi.org/10.1007/s41365-017-0311-y . 2017 Nuclear Science and Techniques 11 28