Study on gamma-ray attenuation characteristics of some amino acids for ¹³³Ba, ¹³⁷Cs, and ⁶⁰Co sources

Study on gamma-ray attenuation characteristics of some amino acids for 133 Ba, 137 Cs, and 60 Co sources 1 corresp first-author Corresponding author, rzbagheri@aeoi.org.ir Corresponding author, rzbagheri@aeoi.org.ir rzbagheri@aeoi.org.ir https://orcid.org/0000-0002-4280-8636 2 3 Northwest Research Complex (Bonab), Radiation Applications Research School, Nuclear Science and Technology Research Institute, Tehran, Iran. Northwest Research Complex (Bonab), Radiation Applications Research School, Nuclear Science and Technology Research Institute, Tehran, Iran. Materials and Nuclear Fuel Research School, Nuclear Science and Technology Research Institute, Tehran, Iran Materials and Nuclear Fuel Research School, Nuclear Science and Technology Research Institute, Tehran, Iran Radiation Applications Research School, Nuclear Science and Technology Research Institute, Tehran, Iran. Radiation Applications Research School, Nuclear Science and Technology Research Institute, Tehran, Iran. Amino acids are the building blocks of proteins, which are the most abundant macromolecules in living cells. From the standpoint of the photon interaction cross sections of amino acids, the mass attenuation coefficients, half and tenth value layers, mean free path, effective atomic and electronic cross sections, effective atomic number, and effective electron density of fifteen essential amino acids have been determined for 133 Ba, 137 Cs, and 60 Co gamma ray sources. The MCNP-4C code and the XCOM program have been used to calculate these parameters. The results have been compared to the available experimental and theoretical data. The theoretical results agreed with the experimental data, with RD values of ≤±7%. In the energy region of 81 to 1332.5 keV, it was found that the µ m, σ a , and σ e values of the amino acids decreased as the photon energy increased, and the increasing density of amino acids had no steady effect on these quantities. Additionally, results demonstrated that the HVL, TVL and MFP values increased with the increase in photon energy. The µ m , σ a and Z eff values of aspartic acid were the highest among those of all amino acids, and they were the lowest for isoleucine. The Z eff value of each sample containing H, C, N, and O atoms was nearly constant in the studied energy region. The N eff values of the studied amino acids varied in the range of 3.14 × 10 23 – 3.44 × 10 23 electron/g. Furthermore, the N eff values were approximately independent of the amino acid type in this energy region. Amino acids Mass attenuation coefficient Effective electron density and atomic number MCNP-4C XCOM 1 Introduction 1 Proteins are vital molecules for every living organism. The DNA building blocks are made of proteins too. Amino acids are the building blocks of proteins [ 1 1 ], and there are 21 amino acids that are essential to the human body. Bearing in mind the vast application of X-ray and gamma ray scanners in medical diagnostic and therapeutic methods [ 2 2 ], the increasing usage of industrial radioactive sources, like 60 Co and 137 Cs, for applications, such as labelling amino acids for imaging various tumors [ 3 3 ], it is valuable to evaluate gamma-ray attenuation characteristics of amino acids for these radioactive sources. Photons of the 133 Ba radionuclide in the energy range of 80-400 keV were found to be suitable for medical and biological applications, whereas 137 Cs and 60 Co radioisotopes are increasingly used in radiation therapy, oncology, industry, biological studies, and radiation sterilization [ 4 4 ]. There have been many studies on the interactions and effects of radiation on amino acids. In radiation sterilization, it is important to know the effect of radiation on proteins, amino acids, and their content in foods. Garrison [ 5 5 ] studied the various radiation-induced effects on amino acids, peptides, and proteins leading to amino acid degradation and to the synthesis of higher molecular weight amino acid derivatives. The effects of the radiation process on total protein and amino acid composition of raw and processed pearl millet flour during storage were described by Mohamed et al. [ 6 6 ]. Pawar and Bichile [ 7 7 ] measured the mass attenuation coefficient, effective atomic number, and electron density of six amino acids in the energy range of 0.122–1.330 MeV using a well-collimated narrow beam good geometry set-up. One of the best biomarkers of life that can survive in harsh environments like other planets and in space are amino acids. Hence, the radiation-amino acid interactions have been investigated by many researchers due to the exposure of amino acids to radiation in outer space. Kminek and Bada [ 8 8 ] studied the effect of ionizing radiation on the preservation of amino acids on Mars based on measured radiolysis constants of amino acids and radiation dose estimates. Furthermore, Cataldo et al. [ 9 9 ] studied solid state radiolysis of amino acids with an astrochemical perspective, showing that the radiolysis rate constants of all the studied amino acids agreed with the radioracemization rate constant. Additionally, the formation of free radicals in solid state amino acids during exposure to radiation is a matter of concern in biological science and dosimetry. Foti et al. [ 10 10 ] investigated alanine amino acid decomposition induced by 200 keV helium and argon ion beams. A short description of produced radicals and an overview of the solid-state radiation chemistry of the simple amino acids were presented by Sagstuen et al. [ 11 11 ]. Furthermore, extensive theoretical and experimental studies of the radiation attenuation characteristics of various biological materials and organic compounds have been previously published. Mass attenuation coefficients of gamma-rays in 48 mixtures and compounds of dosimetric interest were theoretically tabulated by Hubbell and Seltzer [ 12 12 ] in the energy range 1 keV to 20 MeV. Ermis et al. [ 13 13 ] calculated the gamma-ray mass attenuation coefficients of different parts of the human body using various theoretical methods, like FLUKA, GEANT4 Monte Carlo methods, and the XCOM program. Medhat et al. [ 14 14 ] calculated gamma-ray attenuation coefficients of some biological materials (blood, bones, and muscle) using Geant 4 and MCNP simulation codes and compared the obtain results with those obtained using XCOM and experimental data. Here, the mass attenuation coefficients, effective atomic numbers, and electron densities of six amino acids were calculated based on the methods described by Elbashir et al. [ 15 15 ], using MCNP5 simulations and XCOM program in the energy range 0.122–1.330 MeV. The linear attenuation coefficient of the breast tissue was experimentally determined by Tomal et al. [ 16 16 ]. Mass and linear attenuation coefficients of gamma-rays for the glycine amino acid for 0.360, 0.662, 1.170, and 1.330 MeV photons were measured using Pawar and Mahajan [ 1 1 ]. Ahmadi et al. [ 17 17 ] obtained effective atomic numbers and electron densities of bacteriorhodopsin and its component amino acids in the energy range 1 keV–100 GeV using the WinXCom program. The attenuation parameters and energy absorption build-up factor of amine group materials in the energy range 122–1330 keV were experimentally calculated by Lokhande et al. [ 18 18 ] with the gamma ray count in the narrow beam geometry condition. More et al. [ 19 19 ] experimentally determined the photon attenuation coefficients of n-acetyl-L-tryptophan, n-acetyl-L-tyrosine, D-tryptophan, n-acetyl-L-glutamic acid, D-phenylalanine, and D-threonine amino acids for 57 Co, 133 Ba, 137 Cs, 22 Na, 54 Mn, and 60 Co radioisotopes. The effective atomic numbers and electron densities of eight essential amino acids were calculated by Manohara and Hanagodimath [ 20 20 ] for total and partial photon interactions in the wide energy range of 1–100 GeV using the WinXCOM program. Nair et al. [ 21 21 , 22 22 ], experimentally measured total attenuation cross sections of sixteen amino acids for 133 Ba, 137 Cs, and 60 Co gamma ray sources in a narrow beam good geometry set up. The effective atomic numbers and electron densities of the fifteen amino acids and eleven sugars were calculated by Gowda et al. [ 23 23 ] in the energy range 30–1333 keV using the measured total attenuation cross-section data reported by Nair et al. [ 21 21 , 22 22 ]. In this article, a piecewise interpolation method was used to find the effective atomic numbers and electron densities of the compounds. In addition, a semi-empirical formula was introduced using the logarithmic regression analysis of the XCOM data. Manjunathaguru and Umesh [ 24 24 ] calculated effective atomic numbers and electron densities of some biologically important compounds, like cholesterol, fatty acids, sugars, and some amino acids containing H, C, N and O atoms in the energy range 145–1330 keV, using a new matrix method and a semi-empirical relation for Z eff . Additionally, they derived a semi-empirical relation that can be used to determine the total attenuation cross sections of samples containing H, C, N, and O in the energy range 145–1332 keV based on the experimental total attenuation cross section values of several sugars, amino acids, and fatty acids. Here, fifteen amino acids, namely glycine, alanine, serine, valine, threonine, leucine, isoleucine, aspartic acid, lysine, glutamic acid, histidine, phenylalanine, arginine, tyrosine, and tryptophan were considered for gamma ray attenuation studies. The mass attenuation coefficients, half and tenth value layers, mean free path, effective atomic and electronic cross sections, effective atomic number, and effective electron density of these amino acids were calculated for 133 Ba (81, 276, 302.9, 356 and 383.9 keV), 137 Cs (661.6), and 60 Co (1173 and 1332.5 keV) gamma ray sources using the MCNP-4C code and XCOM program for the first time. We tabulated obtained quantities and interpreted simulated and calculated results in terms of numerical values. Additionally, we verified and validated the MCNP-4C code and XCOM program with the available experimental and theoretical data. For this, the experimentally measured total attenuation cross sections determined by Nair et al. [ 21 21 , 22 22 ], the semi-empirical formula described by Manjunathaguru and Umesh [ 24 24 ] for the total attenuation cross sections of samples containing H, C, N and O, the semi-empirical formula described by Gowda et al. [ 23 23 ] for the calculation of Z eff using a piecewise interpolation method, and finally the theoretical values obtained from the XAAMDI database (NIST physical reference data) and other experimental works were used. The MCNP code is a general-purpose Monte Carlo radiation transport code, which models the interaction of radiation with matter [ 25 25 ]. Besides, the theoretical values for mass attenuation coefficients of different elements, c ompounds, and mixtures over a wide photon energy range were tabulated by Hubbell and Seltzer [ 12 12 ]. Using these tables and the computerized program WinXCom or its predecessor, XCOM program, mass attenuation coefficients were calculated at energies 1 keV to 100 GeV [ 26 26 , 27 27 ]. 2 Materials and methods 1 2.1 Simulation 2 Cylindrical geometry was used for modeling amino acid samples. According to experimental conditions [ 21 21 , 22 22 ], a cylinder of Φ 1 cm and different thicknesses was defined for each amino acid sample. The thicknesses of the samples have not been mentioned in previous experimental studies [ 21 21 , 22 22 ], and it has only been noted that the thickness of the samples was chosen such that a µt < 0.4 criterion was satisfied at each energy to minimize the effects of multiple scattering. Thus, the thickness was set to achieve the average value for each sample ( µt was considered about 0.2). It should be noted that the thickness of the samples affects the shielding data analysis. When thick samples are used, these cause the incident photons to be scattered. These photons can reach the detector and render an overestimation of the transmitted intensity, resulting in an underestimation of the measured attenuation coefficients. The attenuation coefficients were measured in narrow beam transmission geometry using sources, such as planar, collimated, and monoenergetic beams that emit gamma rays perpendicular to the front face of samples. A disk source of Φ 1 cm and parallel to the surface of the samples was defined in a data card of MCNP code with ERG, PAR, POS, and DIR commands for energy, type of particle, position, and direction, respectively. The chemical formulas, elemental compositions, densities, and molecular weights of amino acids used in the material card of MCNP code are presented in Table 1 Table 1 . 1 2 Amino acid 1 2 Chemical formula 1 2 Molecular weight (g mol -1 ) 1 2 Density (g cm -3 ) 4 1 Element 1 1 H 1 1 C 1 1 N 1 1 O 1 1 Glycine 1 1 C 2 H 5 NO 2 1 1 75.07 1 1 1.595 1 1 0.0671 1 1 0.3200 1 1 0.1866 1 1 0.4263 1 1 Alanine 1 1 C 3 H 7 NO 2 1 1 89.09 1 1 1.420 1 1 0.0792 1 1 0.4044 1 1 0.1572 1 1 0.3592 1 1 Serine 1 1 C 3 H 7 NO 3 1 1 105.09 1 1 1.600 1 1 0.0671 1 1 0.3429 1 1 0.1333 1 1 0.4567 1 1 Valine 1 1 C 5 H 11 NO 2 1 1 117.15 1 1 1.230 1 1 0.0946 1 1 0.5126 1 1 0.1196 1 1 0.2732 1 1 Threonine 1 1 C 4 H 9 NO 3 1 1 119.12 1 1 1.307 1 1 0.0762 1 1 0.4033 1 1 0.1176 1 1 0.4029 1 1 Leucine 1 1 C 6 H 13 NO 2 1 1 131.17 1 1 1.035 1 1 0.0999 1 1 0.5494 1 1 0.1068 1 1 0.2439 1 1 Isoleucine 1 1 C 6 H 13 NO 2 1 1 131.17 1 1 1.035 1 1 0.0999 1 1 0.5494 1 1 0.1068 1 1 0.2439 1 1 Aspartic acid 1 1 C 4 H 7 NO 4 1 1 133.10 1 1 1.514 1 1 0.0530 1 1 0.3609 1 1 0.1052 1 1 0.4808 1 1 Lysine 1 1 C 6 H 14 N 2 O 2 1 1 146.19 1 1 1.125 1 1 0.0965 1 1 0.4930 1 1 0.1916 1 1 0.2189 1 1 Glutamic acid 1 1 C 5 H 9 NO 4 1 1 147.13 1 1 1.538 1 1 0.0617 1 1 0.4082 1 1 0.0952 1 1 0.4350 1 1 Histidine 1 1 C 6 H 9 N 3 O 2 1 1 155.15 1 1 1.423 1 1 0.0585 1 1 0.4645 1 1 0.2708 1 1 0.2062 1 1 Phenyl alanine 1 1 C 9 H 11 NO 2 1 1 165.19 1 1 1.201 1 1 0.0671 1 1 0.6544 1 1 0.0848 1 1 0.1937 1 1 Arginine 1 1 C 6 H 14 N 4 O 2 1 1 174.20 1 1 1.460 1 1 0.0810 1 1 0.4137 1 1 0.3216 1 1 0.1837 1 1 Tyrosine 1 1 C 9 H 11 NO 3 1 1 181.19 1 1 1.340 1 1 0.0612 1 1 0.5966 1 1 0.0773 1 1 0.2649 1 1 Tryptophan 1 1 C 11 H 12 N 2 O 2 1 1 204.23 1 1 1.340 1 1 0.0592 1 1 0.6469 1 1 0.1372 1 1 0.1567 A small cylinder of Φ 5 cm × 6 cm was considered as the detector volume (an ORTEC HPGe detector model 23210 with Φ 52.5 mm × 58.1 mm cylinder crystal was used in experiment). A Φ 19 cm × 6 cm lead cylinder with a Φ 1 cm × 6 cm hole was used as the detector shield and set behind a Φ 1 cm lead collimator. Additionally, a Φ 15 cm × 7 cm lead cylinder with a Φ 0.6 cm × 7 cm hole was inserted between the samples and detector collimator. The geometry of the system is shown in Fig. 1 Fig. 1 , according to the experimental condition. Tally F4 was used to obtain MCNP-4C simulated data. It calculates the average flux in a cell (detector volume) for only one incident gamma photon. The simulations were performed with 100,000 histories. All simulated results were reported with a ≤0.5% error. 2.2 Theory 2 Linear and mass attenuation coefficients of samples ( µ and µ m ) were derived using the transmission factors for various thicknesses of samples, using Lambert’s law, which is described as follows [ 28 28 ]: <math display="block" id="M1"><mrow><mi>I</mi><mo>=</mo><msub><mi>I</mi><mn>0</mn></msub><msup><mi>e</mi><mrow><mo>−</mo><mi>μ</mi><mi>t</mi></mrow></msup><mo>,</mo></mrow></math> where I 0 and I denote the intensities of photons incoming and outgoing through the attenuator, t is sample thickness, and μ denotes the linear attenuation coefficient. The mass attenuation coefficients were calculated by dividing the linear attenuation coefficient of each amino acid by its density. On the contrary, the mass attenuation coefficients of glass samples were calculated using XCOM program data using Eq. (2), in which w i and µ m ,i (obtained directly from the XCOM program) are the fractional weight and mass attenuation coefficient of the i th element in the sample, respectively [ 29 29 ]: <math display="block" id="M2"><mrow><msub><mo>µ</mo><mtext>m</mtext></msub><munderover><mstyle mathsize="140%" displaystyle="true"><mrow><mo>=</mo><mo>∑</mo></mrow></mstyle><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>w</mi><mi>i</mi></msub><mo>×</mo><msub><mtext>µ</mtext><mrow><mtext>m</mtext><mo>,</mo><mi>i</mi></mrow></msub><mo>.</mo></mrow></math> Additionally, the HVL and TVL quantities are defined as the extent of attenuator thickness, which reduce photon intensity to half and tenth of its initial value, respectively. These quantities can be calculated using the following relations [ 4 4 ]: <math display="block" id="M3"><mrow><mtext>HVL=</mtext><mfrac><mrow><mtext>ln</mtext><mn>2</mn></mrow><mtext>µ</mtext></mfrac><mo>,</mo></mrow></math> <math display="block" id="M4"><mrow><mtext>TVL=</mtext><mfrac><mrow><mtext>ln</mtext><mn>10</mn></mrow><mtext>µ</mtext></mfrac><mo>.</mo></mrow></math> The interactions of gamma rays can also be analyzed using their mean free path, which is defined as the average distance traveled by the rays in the absorber before an interaction takes place [ 4 4 ]. The mean free path can be obtained as follows: <math display="block" id="M5"><mrow><mtext>MFP</mtext><mo>=</mo><mfrac><mn>1</mn><mo>µ</mo></mfrac></mrow></math> The total molecular cross sections ( σ t ) of amino acids are calculated using the simulated and theoretical values of µ m using the following relationship [ 23 23 ]: <math display="block" id="M6"><mrow><msub><mi>σ</mi><mtext>t</mtext></msub><mo>=</mo><mfrac><mrow><msub><mtext>µ</mtext><mtext>m</mtext></msub><mi>M</mi></mrow><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></mfrac></mrow></math> where M is the molecular weight of materials and N A is Avogadro’s number. The experimental values of the total molecular cross sections for amino acids were directly derived from Nair et al. [ 21 21 , 22 22 ]. Additionally, the effective atomic and electronic cross sections ( σ a and σ e ) were calculated from the following mixture equations using the XCOM program and obtained total molecular cross sections [ 30 30 - 32 32 30-32 ]: <math display="block" id="M7"><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><mo>∑</mo><msub><mi>f</mi><mi>i</mi></msub><msub><mi>A</mi><mi>i</mi></msub><msub><mo>µ</mo><mrow><mtext>m</mtext><mo>.</mo><mi>i</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>σ</mi><mtext>t</mtext></msub></mrow><mrow><msub><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>i</mi></msub><msub><mi>n</mi><mi>i</mi></msub></mrow></mfrac><mo>,</mo></mrow></math> <math display="block" id="M8"><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><mo>∑</mo><mfrac><mrow><msub><mi>f</mi><mi>i</mi></msub><msub><mi>A</mi><mi>i</mi></msub><msub><mo>µ</mo><mrow><mtext>m</mtext><mo>.</mo><mi>i</mi></mrow></msub></mrow><mrow><msub><mi>Z</mi><mi>i</mi></msub></mrow></mfrac><mo>,</mo></mrow></math> where f i denotes the fractional abundance of the i th element with respect to the number of atoms, such that f 1 + f 2 + f 3 +…+ f i = 1, and Z i and A i are the atomic number and atomic weight of the i th element, respectively. Additionally, n i is the atomic number of i th element in the material. Finally, the effective atomic number ( Z eff ) and effective electron density ( N eff ) of samples are calculated using µ m , σ a and, σ e values and the following formulas [ 33 33 ]: <math display="block" id="M9"><mrow><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>σ</mi><mtext>a</mtext></msub></mrow><mrow><msub><mi>σ</mi><mtext>e</mtext></msub></mrow></mfrac><mo>,</mo></mrow></math> <math display="block" id="M10"><mrow><msub><mi>N</mi><mrow><mtext>eff</mtext></mrow></msub><mo>=</mo><mo> </mo><mfrac><mrow><msub><mi>N</mi><mtext>A</mtext></msub><msub><mi>Z</mi><mrow><mtext>eff</mtext></mrow></msub></mrow><mrow><mo>∑</mo><msub><mi>f</mi><mi>i</mi></msub><msub><mi>A</mi><mi>i</mi></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><msub><mo>µ</mo><mtext>m</mtext></msub></mrow><mrow><msub><mtext>σ</mtext><mtext>e</mtext></msub></mrow></mfrac><mo>.</mo></mrow></math> 3 Results and discussion 1 3.1 Mass attenuation coefficients HVL, TVL, and MFP of amino acids 2 The simulated and calculated values of mass attenuation coefficients ( µ m ) compared to experimental data [ 21 21 , 22 22 ] are given in Table 2 Table 2 for the studied gamma ray energies. A: MCNP-4C, B: XCOM, and C: experimental values [ 21 21 , 22 22 ] 1 3 Amino acid 1 3 Density (g cm -3 ) 12 1 Energy (keV) 12 1 Energy (keV) 3 1 81 3 1 276 3 1 302.9 3 1 356 3 1 383.9 3 1 661.6 3 1 1173 3 1 1332.5 1 1 A 1 1 B 1 1 C 1 1 A 1 1 B 1 1 C 1 1 A 1 1 B 1 1 C 1 1 A 1 1 B 1 1 C 1 1 A 1 1 B 1 1 C 1 1 A 1 1 B 1 1 C 1 1 A 1 1 B 1 1 C 1 1 A 1 1 B 1 1 C 1 1 Leucine 1 1 1.035 1 1 0.181 1 1 0.177 1 1 0.175 1 1 0.123 1 1 0.121 1 1 0.117 1 1 0.119 1 1 0.117 1 1 0.114 1 1 0.112 1 1 0.110 1 1 0.110 1 1 0.109 1 1 0.107 1 1 0.106 1 1 0.087 1 1 0.085 1 1 0.084 1 1 0.067 1 1 0.065 1 1 0.065 1 1 0.062 1 1 0.060 1 1 0.061 1 1 Isoleucine 1 1 1.035 1 1 0.181 1 1 0.177 1 1 0.174 1 1 0.123 1 1 0.121 1 1 0.117 1 1 0.119 1 1 0.117 1 1 0.111 1 1 0.112 1 1 0.110 1 1 0.108 1 1 0.109 1 1 0.107 1 1 0.107 1 1 0.087 1 1 0.085 1 1 0.082 1 1 0.067 1 1 0.065 1 1 0.064 1 1 0.062 1 1 0.060 1 1 0.061 1 1 Lysine 1 1 1.125 1 1 0.180 1 1 0.177 1 1 0.174 1 1 0.123 1 1 0.121 1 1 0.123 1 1 0.119 1 1 0.116 1 1 0.115 1 1 0.112 1 1 0.110 1 1 0.107 1 1 0.108 1 1 0.106 1 1 0.103 1 1 0.086 1 1 0.085 1 1 0.082 1 1 0.066 1 1 0.064 1 1 0.064 1 1 0.062 1 1 0.060 1 1 0.061 1 1 Phenyl alanine 1 1 1.201 1 1 0.176 1 1 0.172 1 1 0.174 1 1 0.119 1 1 0.117 1 1 0.115 1 1 0.115 1 1 0.113 1 1 0.112 1 1 0.109 1 1 0.107 1 1 0.105 1 1 0.106 1 1 0.104 1 1 0.102 1 1 0.084 1 1 0.082 1 1 0.082 1 1 0.065 1 1 0.063 1 1 0.064 1 1 0.060 1 1 0.059 1 1 0.061 1 1 Valine 1 1 1.230 1 1 0.181 1 1 0.177 1 1 0.174 1 1 0.122 1 1 0.120 1 1 0.118 1 1 0.118 1 1 0.116 1 1 0.112 1 1 0.112 1 1 0.109 1 1 0.106 1 1 0.108 1 1 0.106 1 1 0.102 1 1 0.086 1 1 0.084 1 1 0.083 1 1 0.066 1 1 0.064 1 1 0.064 1 1 0.062 1 1 0.060 1 1 0.060 1 1 Threonine 1 1 1.307 1 1 0.179 1 1 0.175 1 1 0.174 1 1 0.120 1 1 0.118 1 1 0.115 1 1 0.117 1 1 0.114 1 1 0.111 1 1 0.110 1 1 0.108 1 1 0.105 1 1 0.106 1 1 0.104 1 1 0.105 1 1 0.085 1 1 0.083 1 1 0.082 1 1 0.065 1 1 0.063 1 1 0.064 1 1 0.061 1 1 0.059 1 1 0.060 1 1 Tyrosine 1 1 1.340 1 1 0.176 1 1 0.172 1 1 0.174 1 1 0.119 1 1 0.117 1 1 0.115 1 1 0.115 1 1 0.113 1 1 0.111 1 1 0.108 1 1 0.106 1 1 0.106 1 1 0.105 1 1 0.103 1 1 0.102 1 1 0.084 1 1 0.082 1 1 0.082 1 1 0.064 1 1 0.062 1 1 0.063 1 1 0.060 1 1 0.058 1 1 0.060 1 1 Tryptophan 1 1 1.340 1 1 0.174 1 1 0.171 1 1 0.171 1 1 0.119 1 1 0.116 1 1 0.115 1 1 0.115 1 1 0.113 1 1 0.111 1 1 0.109 1 1 0.106 1 1 0.105 1 1 0.105 1 1 0.103 1 1 0.102 1 1 0.083 1 1 0.082 1 1 0.082 1 1 0.064 1 1 0.062 1 1 0.063 1 1 0.060 1 1 0.058 1 1 0.059 1 1 Alanine 1 1 1.420 1 1 0.179 1 1 0.175 1 1 0.174 1 1 0.121 1 1 0.119 1 1 0.119 1 1 0.117 1 1 0.115 1 1 0.114 1 1 0.110 1 1 0.108 1 1 0.107 1 1 0.106 1 1 0.105 1 1 0.102 1 1 0.085 1 1 0.083 1 1 0.083 1 1 0.065 1 1 0.063 1 1 0.064 1 1 0.061 1 1 0.059 1 1 0.060 1 1 Histidine 1 1 1.423 1 1 0.176 1 1 0.171 1 1 0.174 1 1 0.119 1 1 0.116 1 1 0.115 1 1 0.115 1 1 0.113 1 1 0.111 1 1 0.108 1 1 0.106 1 1 0.105 1 1 0.105 1 1 0.103 1 1 0.102 1 1 0.083 1 1 0.082 1 1 0.082 1 1 0.064 1 1 0.062 1 1 0.064 1 1 0.060 1 1 0.058 1 1 0.059 1 1 Arginine 1 1 1.460 1 1 0.179 1 1 0.175 1 1 0.174 1 1 0.121 1 1 0.119 1 1 0.115 1 1 0.117 1 1 0.115 1 1 0.114 1 1 0.110 1 1 0.108 1 1 0.105 1 1 0.107 1 1 0.105 1 1 0.102 1 1 0.085 1 1 0.083 1 1 0.082 1 1 0.065 1 1 0.064 1 1 0.064 1 1 0.061 1 1 0.059 1 1 0.061 1 1 Aspartic acid 1 1 1.514 1 1 0.176 1 1 0.172 1 1 0.174 1 1 0.118 1 1 0.116 1 1 0.115 1 1 0.115 1 1 0.112 1 1 0.111 1 1 0.107 1 1 0.105 1 1 0.105 1 1 0.104 1 1 0.102 1 1 0.102 1 1 0.083 1 1 0.081 1 1 0.082 1 1 0.064 1 1 0.062 1 1 0.064 1 1 0.060 1 1 0.058 1 1 0.059 1 1 Glutamic acid 1 1 1.538 1 1 0.176 1 1 0.173 1 1 0.174 1 1 0.119 1 1 0.117 1 1 0.115 1 1 0.115 1 1 0.113 1 1 0.111 1 1 0.109 1 1 0.106 1 1 0.105 1 1 0.105 1 1 0.103 1 1 0.102 1 1 0.084 1 1 0.082 1 1 0.082 1 1 0.064 1 1 0.062 1 1 0.064 1 1 0.060 1 1 0.058 1 1 0.060 1 1 Glycine 1 1 1.595 1 1 0.179 1 1 0.174 1 1 0.174 1 1 0.120 1 1 0.117 1 1 0.115 1 1 0.117 1 1 0.113 1 1 0.112 1 1 0.110 1 1 0.107 1 1 0.105 1 1 0.106 1 1 0.104 1 1 0.103 1 1 0.085 1 1 0.082 1 1 0.082 1 1 0.065 1 1 0.063 1 1 0.063 1 1 0.061 1 1 0.059 1 1 0.059 1 1 Serine 1 1 1.600 1 1 0.178 1 1 0.174 1 1 0.174 1 1 0.120 1 1 0.117 1 1 0.115 1 1 0.116 1 1 0.113 1 1 0.111 1 1 0.109 1 1 0.107 1 1 0.105 1 1 0.106 1 1 0.104 1 1 0.102 1 1 0.084 1 1 0.082 1 1 0.082 1 1 0.064 1 1 0.063 1 1 0.064 1 1 0.061 1 1 0.059 1 1 0.060 The HVL, TVL, and MFP values were determined using Eqs. (3), (4), and (5), respectively. The dependencies of the HVL, TVL, and MFP of the amino acids on gamma ray energy are demonstrated in Fig. 2 Fig. 2 . As seen in Table 2 Table 2 , a good agreement was observed between experimental, simulated, and calculated values of µ m . The discrepancies are considered and acceptable. It should be noted that the reported experimental errors were to the extent of ±2% [ 21 21 , 22 22 ]. As illustrated in Fig. 2 Fig. 2 , the HVL, TVL, and MFP values of the amino acids increase with the increase in photon energy and decreased with the increase in the density of amino acids. Additionally, it is obvious from Fig. 2 Fig. 2 that isoleucine and serine, with the minimum and maximum amount of density, respectively, have the highest and lowest values of HVL, TVL, and MFP, respectively. 3.2 Effective atomic and electronic cross sections of amino acids 2 The MCNP-4C, XCOM, and experimental values of effective atomic cross sections of amino acids were calculated using Eqs. (6) and (7). Additionally, we calculated effective atomic cross sections of amino acids using the semi-empirical formula given by Manjunathaguru and Umesh [ 24 24 ] for the total attenuation cross sections of samples containing H, C, N, and O in the energy range of 145–1330 keV. This formula relates total attenuation cross section ( σ t ) to the molecular weight ( M ) and energy ( E ) as follows: <math display="block" id="M11"><mrow><msub><mi>σ</mi><mtext>t</mtext></msub><mo>=</mo><mtext> </mtext><mn>2.2</mn><mi>M</mi><mtext> </mtext><msup><mi>E</mi><mrow><mo>−</mo><mn>0.43</mn></mrow></msup><mo>.</mo></mrow></math> Table 3 Table 3 shows the simulated, calculated, and experimental values of effective atomic cross sections. A: MCNP-4C, B: XCOM, C: experimental [ 21 21 , 22 22 ], and D: Manjunathaguru and Umesh values [ 24 24 ] 1 3 Amino acid 16 1 Energy (keV) 16 1 Energy (keV) 4 1 81 4 1 276 4 1 302.9 4 1 356 4 1 383.9 4 1 661.6 4 1 1173 4 1 1332.5 1 1 A 1 1 B 1 1 C 1 1 D 1 1 A 1 1 B 1 1 C 1 1 D 1 1 A 1 1 B 1 1 C 1 1 D 1 1 A 1 1 B 1 1 C 1 1 D 1 1 A 1 1 B 1 1 C 1 1 D 1 1 A 1 1 B 1 1 C 1 1 D 1 1 A 1 1 B 1 1 C 1 1 D 1 1 A 1 1 B 1 1 C 1 1 D 1 1 Leucine 1 1 1.789 1 1 1.753 1 1 1.732 1 1 --- 1 1 1.217 1 1 1.196 1 1 1.155 1 1 1.170 1 1 1.178 1 1 1.156 1 1 1.132 1 1 1.124 1 1 1.113 1 1 1.087 1 1 1.089 1 1 1.049 1 1 1.078 1 1 1.055 1 1 1.051 1 1 1.015 1 1 0.857 1 1 0.840 1 1 0.830 1 1 0.804 1 1 0.659 1 1 0.639 1 1 0.640 1 1 0.628 1 1 0.617 1 1 0.599 1 1 0.600 1 1 0.595 1 1 Isoleucine 1 1 1.789 1 1 1.753 1 1 1.723 1 1 --- 1 1 1.217 1 1 1.196 1 1 1.155 1 1 1.170 1 1 1.178 1 1 1.156 1 1 1.103 1 1 1.124 1 1 1.113 1 1 1.087 1 1 1.073 1 1 1.049 1 1 1.078 1 1 1.055 1 1 1.060 1 1 1.015 1 1 0.857 1 1 0.840 1 1 0.814 1 1 0.804 1 1 0.659 1 1 0.639 1 1 0.634 1 1 0.628 1 1 0.617 1 1 0.599 1 1 0.599 1 1 0.595 1 1 Lysine 1 1 1.823 1 1 1.787 1 1 1.758 1 1 --- 1 1 1.241 1 1 1.219 1 1 1.247 1 1 1.195 1 1 1.201 1 1 1.177 1 1 1.167 1 1 1.149 1 1 1.131 1 1 1.107 1 1 1.079 1 1 1.072 1 1 1.093 1 1 1.075 1 1 1.044 1 1 1.037 1 1 0.872 1 1 0.855 1 1 0.829 1 1 0.821 1 1 0.672 1 1 0.651 1 1 0.648 1 1 0.642 1 1 0.628 1 1 0.610 1 1 0.613 1 1 0.607 1 1 Phenyl alanine 1 1 2.102 1 1 2.050 1 1 2.074 1 1 --- 1 1 1.425 1 1 1.399 1 1 1.371 1 1 1.410 1 1 1.377 1 1 1.351 1 1 1.330 1 1 1.354 1 1 1.299 1 1 1.271 1 1 1.257 1 1 1.263 1 1 1.262 1 1 1.234 1 1 1.222 1 1 1.223 1 1 1.004 1 1 0.981 1 1 0.978 1 1 0.968 1 1 0.769 1 1 0.748 1 1 0.763 1 1 0.757 1 1 0.720 1 1 0.700 1 1 0.722 1 1 0.716 1 1 Valine 1 1 1.854 1 1 1.808 1 1 1.779 1 1 --- 1 1 1.252 1 1 1.232 1 1 1.205 1 1 1.210 1 1 1.209 1 1 1.190 1 1 1.147 1 1 1.163 1 1 1.142 1 1 1.119 1 1 1.089 1 1 1.085 1 1 1.106 1 1 1.086 1 1 1.047 1 1 1.050 1 1 0.883 1 1 0.864 1 1 0.853 1 1 0.831 1 1 0.678 1 1 0.658 1 1 0.655 1 1 0.650 1 1 0.634 1 1 0.616 1 1 0.616 1 1 0.615 1 1 Threonine 1 1 2.083 1 1 2.033 1 1 2.024 1 1 --- 1 1 1.400 1 1 1.376 1 1 1.338 1 1 1.375 1 1 1.360 1 1 1.331 1 1 1.295 1 1 1.321 1 1 1.274 1 1 1.251 1 1 1.225 1 1 1.233 1 1 1.239 1 1 1.215 1 1 1.221 1 1 1.193 1 1 0.989 1 1 0.966 1 1 0.953 1 1 0.944 1 1 0.757 1 1 0.736 1 1 0.745 1 1 0.738 1 1 0.708 1 1 0.689 1 1 0.703 1 1 0.699 1 1 Tyrosine 1 1 2.207 1 1 2.150 1 1 2.183 1 1 --- 1 1 1.494 1 1 1.463 1 1 1.442 1 1 1.482 1 1 1.443 1 1 1.413 1 1 1.396 1 1 1.424 1 1 1.357 1 1 1.329 1 1 1.325 1 1 1.328 1 1 1.319 1 1 1.290 1 1 1.283 1 1 1.286 1 1 1.049 1 1 1.026 1 1 1.028 1 1 1.017 1 1 0.807 1 1 0.782 1 1 0.794 1 1 0.795 1 1 0.752 1 1 0.732 1 1 0.750 1 1 0.753 1 1 Tryptophan 1 1 2.185 1 1 2.143 1 1 2.148 1 1 --- 1 1 1.496 1 1 1.462 1 1 1.445 1 1 1.484 1 1 1.444 1 1 1.413 1 1 1.400 1 1 1.426 1 1 1.363 1 1 1.329 1 1 1.324 1 1 1.331 1 1 1.319 1 1 1.290 1 1 1.287 1 1 1.288 1 1 1.048 1 1 1.026 1 1 1.030 1 1 1.019 1 1 0.806 1 1 0.782 1 1 0.789 1 1 0.797 1 1 0.753 1 1 0.732 1 1 0.741 1 1 0.754 1 1 Alanine 1 1 2.036 1 1 1.991 1 1 1.977 1 1 --- 1 1 1.374 1 1 1.351 1 1 1.355 1 1 1.345 1 1 1.328 1 1 1.305 1 1 1.298 1 1 1.292 1 1 1.255 1 1 1.227 1 1 1.215 1 1 1.206 1 1 1.208 1 1 1.191 1 1 1.158 1 1 1.167 1 1 0.967 1 1 0.947 1 1 0.941 1 1 0.924 1 1 0.743 1 1 0.721 1 1 0.731 1 1 0.722 1 1 0.695 1 1 0.676 1 1 0.681 1 1 0.683 1 1 Histidine 1 1 2.264 1 1 2.205 1 1 2.242 1 1 --- 1 1 1.527 1 1 1.499 1 1 1.482 1 1 1.523 1 1 1.478 1 1 1.449 1 1 1.435 1 1 1.463 1 1 1.389 1 1 1.363 1 1 1.358 1 1 1.365 1 1 1.353 1 1 1.323 1 1 1.315 1 1 1.321 1 1 1.073 1 1 1.052 1 1 1.057 1 1 1.045 1 1 0.824 1 1 0.801 1 1 0.825 1 1 0.817 1 1 0.772 1 1 0.750 1 1 0.760 1 1 0.774 1 1 Arginine 1 1 1.993 1 1 1.941 1 1 1.936 1 1 --- 1 1 1.343 1 1 1.322 1 1 1.279 1 1 1.315 1 1 1.301 1 1 1.277 1 1 1.265 1 1 1.263 1 1 1.226 1 1 1.202 1 1 1.173 1 1 1.179 1 1 1.188 1 1 1.166 1 1 1.139 1 1 1.141 1 1 0.946 1 1 0.927 1 1 0.912 1 1 0.903 1 1 0.726 1 1 0.706 1 1 0.712 1 1 0.706 1 1 0.680 1 1 0.662 1 1 0.673 1 1 0.668 1 1 Aspartic acid 1 1 2.430 1 1 2.373 1 1 2.403 1 1 --- 1 1 1.637 1 1 1.601 1 1 1.588 1 1 1.633 1 1 1.584 1 1 1.547 1 1 1.538 1 1 1.569 1 1 1.481 1 1 1.455 1 1 1.456 1 1 1.463 1 1 1.438 1 1 1.412 1 1 1.413 1 1 1.417 1 1 1.145 1 1 1.122 1 1 1.131 1 1 1.121 1 1 0.881 1 1 0.855 1 1 0.878 1 1 0.876 1 1 0.827 1 1 0.801 1 1 0.816 1 1 0.830 1 1 Glutamic acid 1 1 2.263 1 1 2.221 1 1 2.237 1 1 --- 1 1 1.529 1 1 1.502 1 1 1.479 1 1 1.520 1 1 1.477 1 1 1.450 1 1 1.432 1 1 1.460 1 1 1.400 1 1 1.364 1 1 1.355 1 1 1.362 1 1 1.355 1 1 1.324 1 1 1.316 1 1 1.319 1 1 1.080 1 1 1.053 1 1 1.053 1 1 1.044 1 1 0.824 1 1 0.802 1 1 0.823 1 1 0.816 1 1 0.774 1 1 0.751 1 1 0.768 1 1 0.772 1 1 Glycine 1 1 2.237 1 1 2.165 1 1 2.170 1 1 --- 1 1 1.498 1 1 1.463 1 1 1.434 1 1 1.473 1 1 1.459 1 1 1.413 1 1 1.400 1 1 1.416 1 1 1.370 1 1 1.330 1 1 1.314 1 1 1.321 1 1 1.327 1 1 1.290 1 1 1.280 1 1 1.278 1 1 1.059 1 1 1.026 1 1 1.022 1 1 1.012 1 1 0.811 1 1 0.782 1 1 0.788 1 1 0.791 1 1 0.762 1 1 0.732 1 1 0.734 1 1 0.749 1 1 Serine 1 1 2.221 1 1 2.166 1 1 2.169 1 1 --- 1 1 1.494 1 1 1.463 1 1 1.434 1 1 1.473 1 1 1.441 1 1 1.413 1 1 1.389 1 1 1.415 1 1 1.363 1 1 1.330 1 1 1.314 1 1 1.321 1 1 1.316 1 1 1.290 1 1 1.276 1 1 1.278 1 1 1.047 1 1 1.026 1 1 1.022 1 1 1.012 1 1 0.803 1 1 0.782 1 1 0.798 1 1 0.791 1 1 0.755 1 1 0.732 1 1 0.754 1 1 0.749 The relative deviation (RD) differences between simulated and calculated results with the experimental data of effective atomic cross sections are plotted in Fig. 3 Fig. 3 for MCNP-4C code, XCOM program, and semi-empirical formula of Manjunathaguru and Umesh [ 24 24 ] using Eq. (9): <math display="block" id="M12"><mrow><mtext>RD = {Theoretical</mtext><mi>－</mi><mtext> Experimental} </mtext><mo>×</mo><mtext> 100 / Experimental</mtext></mrow></math> For all of the amino acids, the RD values ranged from –0.44% to 6.83%, –2.99% to 4.82%, and –4.17% to 2.81% for data obtained using MCNP-4C, XCOM, and the semi-empirical formula given by Manjunathaguru and Umesh [ 24 24 ], respectively (see Fig. 3 Fig. 3 ). The RD values were found to be ≤±7% for all amino acids. Additionally, it was found that the RD values were approximately independent of amino acid type, gamma ray energy, and the σ a calculation method. Additionally, a good agreement was observed between experimental and theoretical values of σ a . Tables 2 Tables 2 and 3 3 indicate that the µ m and σ a values of the amino acids decrease with the increase in the photon energy, while an increase in the density of amino acids does not monotonously increase these quantities. It is obvious from Tables 2 Tables 2 and 3 3 that aspartic acid and isoleucine have the greatest and lowest values of µ m and σ a , respectively. The XCOM results showed better agreement with the experimental data than the MCNP-4C results. The effective electronic cross section ( σ e ) values of amino acids were calculated using Eq. (8) and are listed in Table 4 Table 4 . 1 2 Amino acid 1 2 Density (g cm -3 ) 1 2 Molecular weight (g mol -1 ) 8 1 Energy (keV) 1 1 81 1 1 276 1 1 302.9 1 1 356 1 1 383.9 1 1 661.6 1 1 1173 1 1 1332.5 1 1 Leucine 1 1 1.035 1 1 131.17 1 1 0.5254 1 1 0.3649 1 1 0.3528 1 1 0.3319 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Isoleucine 1 1 1.035 1 1 131.17 1 1 0.5254 1 1 0.3649 1 1 0.3528 1 1 0.3319 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Lysine 1 1 1.125 1 1 146.19 1 1 0.5257 1 1 0.3649 1 1 0.3528 1 1 0.3319 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Phenyl alanine 1 1 1.201 1 1 165.19 1 1 0.5272 1 1 0.3651 1 1 0.3529 1 1 0.3319 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Valine 1 1 1.230 1 1 117.15 1 1 0.5260 1 1 0.3650 1 1 0.3528 1 1 0.3319 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Threonine 1 1 1.307 1 1 119.12 1 1 0.5284 1 1 0.3651 1 1 0.3529 1 1 0.3320 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Tyrosine 1 1 1.340 1 1 181.19 1 1 0.5284 1 1 0.3650 1 1 0.3529 1 1 0.3319 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Tryptophan 1 1 1.340 1 1 204.23 1 1 0.5278 1 1 0.3650 1 1 0.3529 1 1 0.3319 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Alanine 1 1 1.420 1 1 89.09 1 1 0.5279 1 1 0.3651 1 1 0.3529 1 1 0.3320 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Histidine 1 1 1.423 1 1 155.15 1 1 0.5290 1 1 0.3651 1 1 0.3530 1 1 0.3320 1 1 0.3224 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Arginine 1 1 1.460 1 1 174.20 1 1 0.5270 1 1 0.3650 1 1 0.3529 1 1 0.3319 1 1 0.3223 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Aspartic acid 1 1 1.514 1 1 133.10 1 1 0.5316 1 1 0.3652 1 1 0.3531 1 1 0.3321 1 1 0.3224 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Glutamic acid 1 1 1.538 1 1 147.13 1 1 0.5301 1 1 0.3652 1 1 0.3530 1 1 0.3320 1 1 0.3224 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Glycine 1 1 1.595 1 1 75.07 1 1 0.5298 1 1 0.3651 1 1 0.3530 1 1 0.3320 1 1 0.3224 1 1 0.2565 1 1 0.1954 1 1 0.1830 1 1 Serine 1 1 1.600 1 1 105.09 1 1 0.5299 1 1 0.3651 1 1 0.3530 1 1 0.3320 1 1 0.3224 1 1 0.2565 1 1 0.1954 1 1 0.1830 As shown in Table 4 Table 4 , the effective electronic cross section values of amino acids decreased with the increase in photon energy. Additionally, they were approximately independent of amino acid type, density, and molecular weight. 3.2 Effective atomic number and electron density of amino acids 2 The MCNP-4C, XCOM, and experimental [ 21 21 , 22 22 ] values of the effective atomic number (Z eff ) and effective electron density (N eff ) of amino acids are given in Tables 5 Tables 5 and 6 6 . A: MCNP-4C, B: XCOM, C: experimental [ 21 21 , 22 22 ], D: Gowda et al. method [ 23 23 ], E: matrix method, and F: semiempirical formula given by Manjunathaguru and Umesh [ 24 24 ] 1 3 Amino acid 12 1 Energy (keV) 12 1 Energy (keV) 12 1 Energy (keV) 12 1 Energy (keV) 6 1 81 6 1 276 6 1 302.9 6 1 356 6 1 383.9 6 1 661.6 6 1 1173 6 1 1332.5 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 Leucine 1 1 3.404 1 1 3.337 1 1 3.296 1 1 3.313 1 1 - 1 1 - 1 1 3.336 1 1 3.277 1 1 3.164 1 1 3.178 1 1 3.11 1 1 3.140 1 1 3.341 1 1 3.278 1 1 3.210 1 1 3.221 1 1 - 1 1 3.143 1 1 3.355 1 1 3.275 1 1 3.282 1 1 3.284 1 1 - 1 1 3.147 1 1 3.345 1 1 3.275 1 1 3.262 1 1 3.257 1 1 - 1 1 3.149 1 1 3.341 1 1 3.273 1 1 3.236 1 1 3.242 1 1 3.18 1 1 3.162 1 1 3.371 1 1 3.273 1 1 3.274 1 1 3.282 1 1 3.17 1 1 3.177 1 1 3.372 1 1 3.273 1 1 3.279 1 1 3.278 1 1 3.13 1 1 3.180 1 1 Isoleucine 1 1 3.404 1 1 3.337 1 1 3.279 1 1 3.296 1 1 - 1 1 - 1 1 3.336 1 1 3.277 1 1 3.164 1 1 3.178 1 1 - 1 1 3.140 1 1 3.341 1 1 3.278 1 1 3.127 1 1 3.139 1 1 - 1 1 3.143 1 1 3.355 1 1 3.275 1 1 3.232 1 1 3.236 1 1 - 1 1 3.147 1 1 3.345 1 1 3.275 1 1 3.288 1 1 3.285 1 1 - 1 1 3.149 1 1 3.341 1 1 3.273 1 1 3.172 1 1 3.189 1 1 - 1 1 3.162 1 1 3.371 1 1 3.273 1 1 3.244 1 1 3.251 1 1 - 1 1 3.177 1 1 3.372 1 1 3.273 1 1 3.274 1 1 3.273 1 1 - 1 1 3.180 1 1 Lysine 1 1 3.467 1 1 3.400 1 1 3.345 1 1 3.360 1 1 - 1 1 - 1 1 3.401 1 1 3.339 1 1 3.416 1 1 3.430 1 1 - 1 1 3.213 1 1 3.405 1 1 3.337 1 1 3.307 1 1 3.320 1 1 - 1 1 3.215 1 1 3.409 1 1 3.337 1 1 3.252 1 1 3.254 1 1 - 1 1 3.218 1 1 3.392 1 1 3.336 1 1 3.240 1 1 3.236 1 1 - 1 1 3.220 1 1 3.400 1 1 3.334 1 1 3.233 1 1 3.238 1 1 - 1 1 3.232 1 1 3.439 1 1 3.334 1 1 3.314 1 1 3.318 1 1 - 1 1 3.245 1 1 3.432 1 1 3.334 1 1 3.348 1 1 3.350 1 1 - 1 1 3.248 1 1 Phenyl alanine 1 1 3.986 1 1 3.888 1 1 3.934 1 1 3.933 1 1 - 1 1 - 1 1 3.903 1 1 3.832 1 1 3.756 1 1 3.769 1 1 3.80 1 1 3.828 1 1 3.902 1 1 3.829 1 1 3.770 1 1 3.782 1 1 - 1 1 3.828 1 1 3.914 1 1 3.830 1 1 3.785 1 1 3.789 1 1 - 1 1 3.828 1 1 3.916 1 1 3.829 1 1 3.791 1 1 3.786 1 1 - 1 1 3.827 1 1 3.915 1 1 3.827 1 1 3.814 1 1 3.819 1 1 3.86 1 1 3.825 1 1 3.939 1 1 3.827 1 1 3.906 1 1 3.915 1 1 3.83 1 1 3.824 1 1 3.933 1 1 3.826 1 1 3.944 1 1 3.947 1 1 3.84 1 1 3.823 1 1 Valine 1 1 3.525 1 1 3.437 1 1 3.382 1 1 3.398 1 1 - 1 1 - 1 1 3.431 1 1 3.375 1 1 3.302 1 1 3.315 1 1 3.23 1 1 3.254 1 1 3.427 1 1 3.372 1 1 3.251 1 1 3.263 1 1 - 1 1 3.256 1 1 3.440 1 1 3.371 1 1 3.281 1 1 3.284 1 1 - 1 1 3.260 1 1 3.432 1 1 3.370 1 1 3.250 1 1 3.245 1 1 - 1 1 3.261 1 1 3.442 1 1 3.369 1 1 3.324 1 1 3.331 1 1 3.30 1 1 3.272 1 1 3.471 1 1 3.369 1 1 3.352 1 1 3.359 1 1 3.27 1 1 3.284 1 1 3.463 1 1 3.369 1 1 3.366 1 1 3.366 1 1 3.24 1 1 3.287 1 1 Threonine 1 1 3.942 1 1 3.846 1 1 3.829 1 1 3.842 1 1 - 1 1 - 1 1 3.834 1 1 3.770 1 1 3.664 1 1 3.679 1 1 3.71 1 1 3.729 1 1 3.854 1 1 3.772 1 1 3.669 1 1 3.683 1 1 - 1 1 3.729 1 1 3.838 1 1 3.768 1 1 3.691 1 1 3.693 1 1 - 1 1 3.729 1 1 3.844 1 1 3.768 1 1 3.787 1 1 3.783 1 1 - 1 1 3.729 1 1 3.854 1 1 3.766 1 1 3.715 1 1 3.751 1 1 3.74 1 1 3.730 1 1 3.877 1 1 3.765 1 1 3.812 1 1 3.822 1 1 3.73 1 1 3.731 1 1 3.870 1 1 3.766 1 1 3.842 1 1 3.843 1 1 3.73 1 1 3.731 1 1 Tyrosine 1 1 4.177 1 1 4.069 1 1 4.132 1 1 4.129 1 1 - 1 1 - 1 1 4.092 1 1 4.008 1 1 3.950 1 1 3.964 1 1 - 1 1 4.037 1 1 4.089 1 1 4.004 1 1 3.956 1 1 3.969 1 1 - 1 1 4.036 1 1 4.087 1 1 4.003 1 1 3.992 1 1 3.994 1 1 - 1 1 4.034 1 1 4.093 1 1 4.002 1 1 3.982 1 1 3.975 1 1 - 1 1 4.033 1 1 4.091 1 1 4.001 1 1 4.008 1 1 4.014 1 1 - 1 1 4.026 1 1 4.130 1 1 4.001 1 1 4.063 1 1 4.074 1 1 - 1 1 4.018 1 1 4.110 1 1 4.001 1 1 4.099 1 1 4.101 1 1 - 1 1 4.017 1 1 Tryptophan 1 1 4.140 1 1 4.060 1 1 4.070 1 1 4.066 1 1 - 1 1 - 1 1 4.098 1 1 4.005 1 1 3.959 1 1 3.972 1 1 4.03 1 1 4.045 1 1 4.094 1 1 4.004 1 1 3.968 1 1 3.980 1 1 - 1 1 4.044 1 1 4.107 1 1 4.003 1 1 3.988 1 1 3.991 1 1 - 1 1 4.042 1 1 4.092 1 1 4.002 1 1 3.992 1 1 3.987 1 1 - 1 1 4.041 1 1 4.085 1 1 4.001 1 1 4.014 1 1 4.021 1 1 4.06 1 1 4.034 1 1 4.128 1 1 4.001 1 1 4.038 1 1 4.049 1 1 4.04 1 1 4.026 1 1 4.116 1 1 4.000 1 1 4.048 1 1 4.051 1 1 4.01 1 1 4.024 1 1 Alanine 1 1 3.856 1 1 3.772 1 1 3.745 1 1 3.757 1 1 - 1 1 - 1 1 3.763 1 1 3.700 1 1 3.711 1 1 3.725 1 1 3.62 1 1 3.642 1 1 3.763 1 1 3.699 1 1 3.680 1 1 3.691 1 1 - 1 1 3.643 1 1 3.781 1 1 3.695 1 1 3.661 1 1 3.663 1 1 - 1 1 3.643 1 1 3.747 1 1 3.696 1 1 3.592 1 1 3.588 1 1 - 1 1 3.644 1 1 3.769 1 1 3.693 1 1 3.668 1 1 3.674 1 1 3.66 1 1 3.646 1 1 3.802 1 1 3.693 1 1 3.741 1 1 3.750 1 1 3.63 1 1 3.649 1 1 3.796 1 1 3.693 1 1 3.721 1 1 3.722 1 1 3.63 1 1 3.650 1 1 Histidine 1 1 4.280 1 1 4.169 1 1 4.239 1 1 4.235 1 1 - 1 1 - 1 1 4.182 1 1 4.106 1 1 4.057 1 1 4.073 1 1 - 1 1 4.156 1 1 4.188 1 1 4.106 1 1 4.066 1 1 4.080 1 1 - 1 1 4.154 1 1 4.182 1 1 4.105 1 1 4.090 1 1 4.093 1 1 - 1 1 4.151 1 1 4.196 1 1 4.104 1 1 4.079 1 1 4.074 1 1 - 1 1 4.150 1 1 4.183 1 1 4.101 1 1 4.119 1 1 4.127 1 1 - 1 1 4.139 1 1 4.215 1 1 4.101 1 1 4.223 1 1 4.234 1 1 - 1 1 4.129 1 1 4.221 1 1 4.101 1 1 4.154 1 1 4.156 1 1 - 1 1 4.126 1 1 Arginine 1 1 3.783 1 1 3.684 1 1 3.673 1 1 3.683 1 1 - 1 1 - 1 1 3.680 1 1 3.621 1 1 3.505 1 1 3.537 1 1 - 1 1 3.555 1 1 3.687 1 1 3.620 1 1 3.586 1 1 3.598 1 1 - 1 1 3.556 1 1 3.693 1 1 3.620 1 1 3.534 1 1 3.537 1 1 - 1 1 3.558 1 1 3.687 1 1 3.617 1 1 3.535 1 1 3.530 1 1 - 1 1 3.558 1 1 3.689 1 1 3.616 1 1 3.554 1 1 3.561 1 1 - 1 1 3.563 1 1 3.718 1 1 3.616 1 1 3.644 1 1 3.652 1 1 - 1 1 3.568 1 1 3.715 1 1 3.616 1 1 3.679 1 1 3.679 1 1 - 1 1 3.569 1 1 Aspartic acid 1 1 4.570 1 1 4.464 1 1 4.520 1 1 4.525 1 1 - 1 1 - 1 1 4.481 1 1 4.383 1 1 4.348 1 1 4.363 1 1 4.43 1 1 4.476 1 1 4.487 1 1 4.382 1 1 4.355 1 1 4.371 1 1 - 1 1 4.473 1 1 4.461 1 1 4.380 1 1 4.385 1 1 4.388 1 1 - 1 1 4.468 1 1 4.460 1 1 4.379 1 1 4.381 1 1 4.377 1 1 - 1 1 4.465 1 1 4.465 1 1 4.376 1 1 4.410 1 1 4.415 1 1 4.46 1 1 4.446 1 1 4.509 1 1 4.376 1 1 4.492 1 1 4.502 1 1 4.45 1 1 4.426 1 1 4.519 1 1 4.376 1 1 4.461 1 1 4.463 1 1 4.45 1 1 4.422 1 1 Glutamic acid 1 1 4.269 1 1 4.189 1 1 4.220 1 1 4.226 1 1 - 1 1 - 1 1 4.186 1 1 4.113 1 1 4.050 1 1 4.065 1 1 4.11 1 1 4.148 1 1 4.185 1 1 4.109 1 1 4.056 1 1 4.071 1 1 - 1 1 4.146 1 1 4.217 1 1 4.109 1 1 4.080 1 1 4.084 1 1 - 1 1 4.143 1 1 4.203 1 1 4.108 1 1 4.082 1 1 4.077 1 1 - 1 1 4.142 1 1 4.210 1 1 4.106 1 1 4.104 1 1 4.111 1 1 4.14 1 1 4.132 1 1 4.219 1 1 4.106 1 1 4.211 1 1 4.224 1 1 4.14 1 1 4.121 1 1 4.228 1 1 4.106 1 1 4.199 1 1 4.199 1 1 4.12 1 1 4.119 1 1 Glycine 1 1 4.222 1 1 4.086 1 1 4.096 1 1 4.106 1 1 - 1 1 - 1 1 4.102 1 1 4.008 1 1 3.927 1 1 3.962 1 1 - 1 1 4.013 1 1 4.134 1 1 4.005 1 1 3.966 1 1 3.980 1 1 - 1 1 4.012 1 1 4.125 1 1 4.006 1 1 3.958 1 1 3.961 1 1 - 1 1 4.010 1 1 4.115 1 1 4.002 1 1 3.971 1 1 3.966 1 1 - 1 1 4.009 1 1 4.128 1 1 4.001 1 1 3.984 1 1 3.990 1 1 - 1 1 4.002 1 1 4.152 1 1 4.001 1 1 4.034 1 1 4.044 1 1 - 1 1 3.996 1 1 4.162 1 1 4.001 1 1 4.011 1 1 4.013 1 1 - 1 1 3.994 1 1 Serine 1 1 4.191 1 1 4.088 1 1 4.093 1 1 4.104 1 1 - 1 1 - 1 1 4.091 1 1 4.008 1 1 3.926 1 1 3.942 1 1 - 1 1 4.013 1 1 4.083 1 1 4.004 1 1 3.934 1 1 3.949 1 1 - 1 1 4.012 1 1 4.106 1 1 4.006 1 1 3.959 1 1 3.961 1 1 - 1 1 4.010 1 1 4.084 1 1 4.002 1 1 3.960 1 1 3.953 1 1 - 1 1 4.009 1 1 4.081 1 1 4.001 1 1 3.985 1 1 3.990 1 1 - 1 1 4.002 1 1 4.109 1 1 4.001 1 1 4.084 1 1 4.095 1 1 - 1 1 3.996 1 1 4.125 1 1 4.001 1 1 4.118 1 1 4.123 1 1 - 1 1 3.994 A: MCNP-4C, B: XCOM, C: experimental [ 21 21 , 22 22 ], D: Gowda et al. method [ 23 23 ], E: matrix method, and F: semiempirical formula given by Manjunathaguru and Umesh [ 24 24 ] 1 3 Amino acid 12 1 Energy (keV) 12 1 Energy (keV) 12 1 Energy (keV) 12 1 Energy (keV) 6 1 81 6 1 276 6 1 302.9 6 1 356 6 1 383.9 6 1 661.6 6 1 1173 6 1 1332.5 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 Leucine 1 1 0.344 1 1 0.337 1 1 0.333 1 1 0.335 1 1 - 1 1 - 1 1 0.337 1 1 0.331 1 1 0.320 1 1 0.321 1 1 0.314 1 1 0.317 1 1 0.337 1 1 0.331 1 1 0.324 1 1 0.325 1 1 - 1 1 0.317 1 1 0.339 1 1 0.331 1 1 0.331 1 1 0.332 1 1 - 1 1 0.318 1 1 0.338 1 1 0.331 1 1 0.330 1 1 0.329 1 1 - 1 1 0.318 1 1 0.337 1 1 0.331 1 1 0.327 1 1 0.327 1 1 0.321 1 1 0.319 1 1 0.341 1 1 0.331 1 1 0.331 1 1 0.331 1 1 0.320 1 1 0.321 1 1 0.341 1 1 0.331 1 1 0.331 1 1 0.331 1 1 0.316 1 1 0.321 1 1 Isoleucine 1 1 0.344 1 1 0.337 1 1 0.331 1 1 0.333 1 1 - 1 1 - 1 1 0.337 1 1 0.331 1 1 0.320 1 1 0.321 1 1 - 1 1 0.317 1 1 0.337 1 1 0.331 1 1 0.316 1 1 0.317 1 1 - 1 1 0.317 1 1 0.339 1 1 0.331 1 1 0.326 1 1 0.327 1 1 - 1 1 0.318 1 1 0.338 1 1 0.331 1 1 0.332 1 1 0.332 1 1 - 1 1 0.318 1 1 0.337 1 1 0.331 1 1 0.320 1 1 0.321 1 1 - 1 1 0.319 1 1 0.341 1 1 0.331 1 1 0.328 1 1 0.328 1 1 - 1 1 0.321 1 1 0.341 1 1 0.331 1 1 0.331 1 1 0.331 1 1 - 1 1 0.321 1 1 Lysine 1 1 0.343 1 1 0.336 1 1 0.331 1 1 0.332 1 1 - 1 1 - 1 1 0.336 1 1 0.330 1 1 0.338 1 1 0.339 1 1 - 1 1 0.318 1 1 0.337 1 1 0.330 1 1 0.327 1 1 0.328 1 1 - 1 1 0.318 1 1 0.337 1 1 0.330 1 1 0.321 1 1 0.322 1 1 - 1 1 0.318 1 1 0.335 1 1 0.330 1 1 0.320 1 1 0.320 1 1 - 1 1 0.318 1 1 0.336 1 1 0.330 1 1 0.320 1 1 0.320 1 1 - 1 1 0.320 1 1 0.340 1 1 0.330 1 1 0.328 1 1 0.328 1 1 - 1 1 0.321 1 1 0.339 1 1 0.330 1 1 0.331 1 1 0.331 1 1 - 1 1 0.321 1 1 Phenyl alanine 1 1 0.334 1 1 0.326 1 1 0.330 1 1 0.330 1 1 - 1 1 - 1 1 0.327 1 1 0.321 1 1 0.315 1 1 0.316 1 1 0.319 1 1 0.321 1 1 0.327 1 1 0.321 1 1 0.316 1 1 0.317 1 1 - 1 1 0.321 1 1 0.328 1 1 0.321 1 1 0.317 1 1 0.318 1 1 - 1 1 0.321 1 1 0.328 1 1 0.321 1 1 0.318 1 1 0.317 1 1 - 1 1 0.321 1 1 0.328 1 1 0.321 1 1 0.320 1 1 0.320 1 1 0.324 1 1 0.321 1 1 0.330 1 1 0.321 1 1 0.328 1 1 0.328 1 1 0.321 1 1 0.321 1 1 0.330 1 1 0.321 1 1 0.331 1 1 0.331 1 1 0.322 1 1 0.321 1 1 Valine 1 1 0.344 1 1 0.336 1 1 0.330 1 1 0.332 1 1 - 1 1 - 1 1 0.335 1 1 0.330 1 1 0.323 1 1 0.324 1 1 0.316 1 1 0.318 1 1 0.335 1 1 0.329 1 1 0.318 1 1 0.319 1 1 - 1 1 0.318 1 1 0.336 1 1 0.329 1 1 0.320 1 1 0.321 1 1 - 1 1 0.318 1 1 0.335 1 1 0.329 1 1 0.317 1 1 0.317 1 1 - 1 1 0.319 1 1 0.336 1 1 0.329 1 1 0.325 1 1 0.326 1 1 0.322 1 1 0.320 1 1 0.339 1 1 0.329 1 1 0.327 1 1 0.328 1 1 0.320 1 1 0.321 1 1 0.338 1 1 0.329 1 1 0.329 1 1 0.329 1 1 0.317 1 1 0.321 1 1 Threonine 1 1 0.339 1 1 0.331 1 1 0.329 1 1 0.331 1 1 - 1 1 - 1 1 0.330 1 1 0.324 1 1 0.315 1 1 0.316 1 1 0.319 1 1 0.321 1 1 0.331 1 1 0.324 1 1 0.315 1 1 0.317 1 1 - 1 1 0.321 1 1 0.330 1 1 0.324 1 1 0.317 1 1 0.318 1 1 - 1 1 0.321 1 1 0.330 1 1 0.324 1 1 0.325 1 1 0.325 1 1 - 1 1 0.321 1 1 0.331 1 1 0.324 1 1 0.319 1 1 0.320 1 1 0.322 1 1 0.321 1 1 0.333 1 1 0.324 1 1 0.328 1 1 0.329 1 1 0.321 1 1 0.321 1 1 0.333 1 1 0.324 1 1 0.330 1 1 0.330 1 1 0.321 1 1 0.321 1 1 Tyrosine 1 1 0.333 1 1 0.325 1 1 0.330 1 1 0.329 1 1 - 1 1 - 1 1 0.326 1 1 0.320 1 1 0.315 1 1 0.316 1 1 - 1 1 0.322 1 1 0.326 1 1 0.319 1 1 0.316 1 1 0.317 1 1 - 1 1 0.322 1 1 0.326 1 1 0.319 1 1 0.318 1 1 0.319 1 1 - 1 1 0.322 1 1 0.327 1 1 0.319 1 1 0.318 1 1 0.317 1 1 - 1 1 0.322 1 1 0.326 1 1 0.319 1 1 0.320 1 1 0.320 1 1 - 1 1 0.321 1 1 0.329 1 1 0.319 1 1 0.324 1 1 0.325 1 1 - 1 1 0.321 1 1 0.328 1 1 0.319 1 1 0.327 1 1 0.327 1 1 - 1 1 0.320 1 1 Tryptophan 1 1 0.330 1 1 0.323 1 1 0.324 1 1 0.326 1 1 - 1 1 - 1 1 0.326 1 1 0.319 1 1 0.315 1 1 0.316 1 1 0.321 1 1 0.322 1 1 0.326 1 1 0.319 1 1 0.316 1 1 0.317 1 1 - 1 1 0.322 1 1 0.327 1 1 0.319 1 1 0.318 1 1 0.318 1 1 - 1 1 0.322 1 1 0.326 1 1 0.319 1 1 0.318 1 1 0.318 1 1 - 1 1 0.322 1 1 0.325 1 1 0.319 1 1 0.320 1 1 0.320 1 1 0.323 1 1 0.321 1 1 0.329 1 1 0.319 1 1 0.322 1 1 0.322 1 1 0.322 1 1 0.321 1 1 0.328 1 1 0.319 1 1 0.322 1 1 0.323 1 1 0.319 1 1 0.320 1 1 Alanine 1 1 0.339 1 1 0.331 1 1 0.329 1 1 0.330 1 1 - 1 1 - 1 1 0.331 1 1 0.325 1 1 0.326 1 1 0.327 1 1 0.318 1 1 0.320 1 1 0.331 1 1 0.325 1 1 0.323 1 1 0.324 1 1 - 1 1 0.320 1 1 0.332 1 1 0.325 1 1 0.322 1 1 0.322 1 1 - 1 1 0.320 1 1 0.329 1 1 0.325 1 1 0.316 1 1 0.315 1 1 - 1 1 0.320 1 1 0.331 1 1 0.325 1 1 0.322 1 1 0.323 1 1 0.322 1 1 0.320 1 1 0.334 1 1 0.325 1 1 0.329 1 1 0.330 1 1 0.319 1 1 0.321 1 1 0.334 1 1 0.325 1 1 0.327 1 1 0.327 1 1 0.319 1 1 0.321 1 1 Histidine 1 1 0.332 1 1 0.324 1 1 0.329 1 1 0.329 1 1 - 1 1 - 1 1 0.325 1 1 0.319 1 1 0.315 1 1 0.316 1 1 - 1 1 0.323 1 1 0.325 1 1 0.319 1 1 0.316 1 1 0.317 1 1 - 1 1 0.322 1 1 0.325 1 1 0.319 1 1 0.318 1 1 0.318 1 1 - 1 1 0.322 1 1 0.326 1 1 0.319 1 1 0.317 1 1 0.316 1 1 - 1 1 0.322 1 1 0.325 1 1 0.318 1 1 0.320 1 1 0.320 1 1 - 1 1 0.321 1 1 0.327 1 1 0.318 1 1 0.328 1 1 0.329 1 1 - 1 1 0.321 1 1 0.328 1 1 0.318 1 1 0.322 1 1 0.323 1 1 - 1 1 0.320 1 1 Arginine 1 1 0.340 1 1 0.331 1 1 0.330 1 1 0.331 1 1 - 1 1 - 1 1 0.331 1 1 0.325 1 1 0.315 1 1 0.316 1 1 - 1 1 0.320 1 1 0.331 1 1 0.325 1 1 0.322 1 1 0.323 1 1 - 1 1 0.320 1 1 0.332 1 1 0.325 1 1 0.318 1 1 0.318 1 1 - 1 1 0.320 1 1 0.331 1 1 0.325 1 1 0.318 1 1 0.317 1 1 - 1 1 0.320 1 1 0.332 1 1 0.325 1 1 0.319 1 1 0.320 1 1 - 1 1 0.320 1 1 0.334 1 1 0.325 1 1 0.328 1 1 0.328 1 1 - 1 1 0.321 1 1 0.334 1 1 0.325 1 1 0.331 1 1 0.331 1 1 - 1 1 0.321 1 1 Aspartic acid 1 1 0.331 1 1 0.323 1 1 0.327 1 1 0.328 1 1 - 1 1 - 1 1 0.324 1 1 0.317 1 1 0.315 1 1 0.316 1 1 0.321 1 1 0.324 1 1 0.325 1 1 0.317 1 1 0.315 1 1 0.316 1 1 - 1 1 0.324 1 1 0.323 1 1 0.317 1 1 0.317 1 1 0.318 1 1 - 1 1 0.323 1 1 0.323 1 1 0.317 1 1 0.317 1 1 0.317 1 1 - 1 1 0.323 1 1 0.323 1 1 0.317 1 1 0.319 1 1 0.320 1 1 0.323 1 1 0.322 1 1 0.326 1 1 0.317 1 1 0.325 1 1 0.326 1 1 0.322 1 1 0.320 1 1 0.327 1 1 0.317 1 1 0.323 1 1 0.323 1 1 0.322 1 1 0.320 1 1 Glutamic acid 1 1 0.332 1 1 0.326 1 1 0.328 1 1 0.329 1 1 - 1 1 - 1 1 0.326 1 1 0.320 1 1 0.315 1 1 0.316 1 1 0.320 1 1 0.323 1 1 0.325 1 1 0.320 1 1 0.315 1 1 0.317 1 1 - 1 1 0.322 1 1 0.328 1 1 0.320 1 1 0.317 1 1 0.318 1 1 - 1 1 0.322 1 1 0.327 1 1 0.320 1 1 0.317 1 1 0.317 1 1 - 1 1 0.322 1 1 0.327 1 1 0.319 1 1 0.319 1 1 0.320 1 1 0.322 1 1 0.321 1 1 0.328 1 1 0.319 1 1 0.327 1 1 0.329 1 1 0.322 1 1 0.321 1 1 0.329 1 1 0.319 1 1 0.327 1 1 0.327 1 1 0.320 1 1 0.320 1 1 Glycine 1 1 0.339 1 1 0.328 1 1 0.329 1 1 0.329 1 1 - 1 1 - 1 1 0.329 1 1 0.322 1 1 0.315 1 1 0.316 1 1 - 1 1 0.322 1 1 0.332 1 1 0.321 1 1 0.318 1 1 0.319 1 1 - 1 1 0.322 1 1 0.331 1 1 0.321 1 1 0.318 1 1 0.318 1 1 - 1 1 0.322 1 1 0.330 1 1 0.321 1 1 0.319 1 1 0.318 1 1 - 1 1 0.322 1 1 0.331 1 1 0.321 1 1 0.320 1 1 0.320 1 1 - 1 1 0.321 1 1 0.333 1 1 0.321 1 1 0.324 1 1 0.324 1 1 - 1 1 0.321 1 1 0.334 1 1 0.321 1 1 0.322 1 1 0.322 1 1 - 1 1 0.320 1 1 Serine 1 1 0.336 1 1 0.328 1 1 0.328 1 1 0.329 1 1 - 1 1 - 1 1 0.328 1 1 0.322 1 1 0.315 1 1 0.316 1 1 - 1 1 0.322 1 1 0.328 1 1 0.321 1 1 0.316 1 1 0.317 1 1 - 1 1 0.322 1 1 0.329 1 1 0.321 1 1 0.318 1 1 0.318 1 1 - 1 1 0.322 1 1 0.328 1 1 0.321 1 1 0.318 1 1 0.317 1 1 - 1 1 0.322 1 1 0.327 1 1 0.321 1 1 0.320 1 1 0.320 1 1 - 1 1 0.321 1 1 0.330 1 1 0.321 1 1 0.328 1 1 0.329 1 1 - 1 1 0.321 1 1 0.331 1 1 0.321 1 1 0.330 1 1 0.331 1 1 - 1 1 0.320 Additionally, the calculated effective atomic numbers and electron densities of some amino acids based on the formulae described by Manjunathaguru and Umesh [ 24 24 ] and Gowda et al. [ 23 23 ] are given in Tables 5 Tables 5 and 6 6 . Manjunathaguru and Umesh [ 24 24 ] calculated the effective atomic numbers and electron densities of some amino acids in the energy range of 145–1330 keV using two different methods: the new matrix method and the semi-empirical relation for Z eff . Additionally, Gowda et al. [ 23 23 ] obtained the semi-empirical formula for Z eff using a piecewise interpolation method. At any photon energy of interest, it can be seen that the Z eff values agree to within ±7% for all amino acid samples based on various methods. Table 5 Table 5 suggests that the effective atomic number values of each amino acid containing H, C, N, and O atoms is almost constant in the studied region of energy. Aspartic acid and isoleucine have the greatest and lowest values of Z eff , respectively. This is due to the higher ratio of oxygen element content (up to 50%) in aspartic acid and the greatest effective atomic cross section of this amino acid compared to those of other amino acids. Furthermore, the results shown in Table 6 Table 6 indicate that the effective electron density of studied amino acids varies in the range of 3.14 × 10 23 – 3.44 × 10 23 electron/g. In sum, it is evident from Table 6 Table 6 that N eff values are approximately identical and independent of the amino acid type in the studied energy regions. 3.3 Comparison with the XAAMDI database and other experimental data 2 The obtained values of mass attenuation coefficients for the amino acid alanine were compared with the theoretical values obtained from the XAAMDI (the X-ray Attenuation and Absorption for Materials of Dosimetric Interest) database using NIST (the National Institute of Standards and Technology) databases provided on the physical reference data web page to verify and validate theoretical (MCNP-4C and XCOM) and experimental results. The physical density of alanine was about 1.424 g cm -3 in this database. The µ m values of the alanine amino acid obtained by MCNP-4C code simulation, XCOM program calculation, experimental measurements [ 7 7 , 21 21 , 22 22 ], and XAAMDI database calculation are presented in Table 7 Table 7 for photon energies here. Additionally, the differences between theoretical and experimental results obtained from the XAAMDI database are given in Table 7 Table 7 . 1 1 Energy (keV) 1 1 81 1 1 276 1 1 302.9 1 1 356 1 1 383.9 1 1 661.6 1 1 1173 1 1 1332.5 1 1 XAAMDI 1 1 0.175 1 1 0.119 1 1 0.115 1 1 0.108 1 1 0.105 1 1 0.084 1 1 0.064 1 1 0.060 1 1 MCNP-4C 1 1 0.179 1 1 0.121 1 1 0.117 1 1 0.110 1 1 0.106 1 1 0.085 1 1 0.065 1 1 0.061 1 1 Difference (%) 1 1 2.21 1 1 1.13 1 1 1.70 1 1 1.81 1 1 1.12 1 1 1.57 1 1 2.61 1 1 2.50 1 1 XCOM 1 1 0.175 1 1 0.119 1 1 0.115 1 1 0.108 1 1 0.105 1 1 0.083 1 1 0.063 1 1 0.059 1 1 Difference (%) 1 1 0.00 1 1 0.00 1 1 0.00 1 1 0.00 1 1 0.00 1 1 -0.49 1 1 -0.32 1 1 -0.28 1 1 Nair et al. 1994, 1995 1 1 0.174 1 1 0.119 1 1 0.114 1 1 0.107 1 1 0.102 1 1 0.083 1 1 0.064 1 1 0.060 1 1 Difference (%) 1 1 -0.75 1 1 0.00 1 1 -0.56 1 1 -1.40 1 1 -3.06 1 1 -1.17 1 1 0.00 1 1 0.00 1 1 Pawar and Bichile, 2013 1 1 --- 1 1 --- 1 1 --- 1 1 0.107 1 1 --- 1 1 0.084 1 1 0.065 1 1 0.059 1 1 Difference (%) 1 1 --- 1 1 --- 1 1 --- 1 1 -1.40 1 1 --- 1 1 0.00 1 1 2.61 1 1 -0.28 As seen in Table 7 Table 7 , the MCNP-4C, XCOM, experimental, and XAAMDI data are in good agreement with each other. The differences were found to be less than ±3.1% for all methods. The maximum difference was observed –3.06% for the data reported by Nair et al. [ 21 21 , 22 22 ] at 383.9 keV photon energy. The other experimental data [ 7 7 ] showed good agreement with XAAMDI data with differences of ≤±2.7%. XCOM presented the most analogous values to the XAAMDI data, with nearly full accordance, because both of them were developed for radiological physics and dosimetry by NIST and are based on the same theoretical calculations. In addition, five experimental measurements [ 1 1 , 7 7 , 18 18 , 19 19 , 21 21 , 22 22 ] of mass attenuation coefficients for some amino acids along with MCNP-4C data are given in Table 8 Table 8 . A: MCNP-4C; B: Nair et al. [ 21 21 , 22 22 ], C: Pawar and Mahajan [ 1 1 ], D: Pawar and Bichile [ 7 7 ], E: More et al. [ 19 19 ], and F: Lokhonde et al. [ 18 18 ] values 1 3 Amino acid 12 1 Energy (keV) 12 1 Energy (keV) 6 1 356 6 1 661.6 6 1 1173 6 1 1332.5 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 A 1 1 B 1 1 C 1 1 D 1 1 E 1 1 F 1 1 Leucine 1 1 0.112 1 1 0.110 1 1 --- 1 1 0.107 1 1 --- 1 1 --- 1 1 0.087 1 1 0.084 1 1 --- 1 1 0.083 1 1 --- 1 1 --- 1 1 0.067 1 1 0.065 1 1 --- 1 1 0.065 1 1 --- 1 1 --- 1 1 0.062 1 1 0.061 1 1 --- 1 1 0.061 1 1 --- 1 1 --- 1 1 Phenyl alanine 1 1 0.109 1 1 0.105 1 1 --- 1 1 --- 1 1 0.109 1 1 --- 1 1 0.084 1 1 0.082 1 1 --- 1 1 --- 1 1 0.085 1 1 --- 1 1 0.065 1 1 0.064 1 1 --- 1 1 --- 1 1 0.064 1 1 --- 1 1 0.060 1 1 0.061 1 1 --- 1 1 --- 1 1 0.059 1 1 --- 1 1 Threonine 1 1 0.110 1 1 0.105 1 1 --- 1 1 --- 1 1 0.109 1 1 --- 1 1 0.085 1 1 0.082 1 1 --- 1 1 --- 1 1 0.086 1 1 --- 1 1 0.065 1 1 0.064 1 1 --- 1 1 --- 1 1 0.065 1 1 --- 1 1 0.061 1 1 0.060 1 1 --- 1 1 --- 1 1 0.060 1 1 --- 1 1 Tryptophan 1 1 0.109 1 1 0.105 1 1 --- 1 1 --- 1 1 0.106 1 1 --- 1 1 0.083 1 1 0.082 1 1 --- 1 1 --- 1 1 0.082 1 1 --- 1 1 0.064 1 1 0.063 1 1 --- 1 1 --- 1 1 0.062 1 1 --- 1 1 0.060 1 1 0.059 1 1 --- 1 1 --- 1 1 0.061 1 1 --- 1 1 Alanine 1 1 0.110 1 1 0.107 1 1 --- 1 1 0.107 1 1 --- 1 1 --- 1 1 0.085 1 1 0.083 1 1 --- 1 1 0.084 1 1 --- 1 1 --- 1 1 0.065 1 1 0.064 1 1 --- 1 1 0.065 1 1 --- 1 1 --- 1 1 0.061 1 1 0.060 1 1 --- 1 1 0.059 1 1 --- 1 1 --- 1 1 Arginine 1 1 0.110 1 1 0.105 1 1 --- 1 1 0.108 1 1 --- 1 1 0.105 1 1 0.085 1 1 0.082 1 1 --- 1 1 0.083 1 1 --- 1 1 0.091 1 1 0.065 1 1 0.064 1 1 --- 1 1 0.063 1 1 --- 1 1 0.067 1 1 0.061 1 1 0.061 1 1 --- 1 1 0.058 1 1 --- 1 1 0.053 1 1 Glutamic acid 1 1 0.109 1 1 0.105 1 1 --- 1 1 --- 1 1 --- 1 1 0.108 1 1 0.084 1 1 0.082 1 1 --- 1 1 --- 1 1 --- 1 1 0.099 1 1 0.064 1 1 0.064 1 1 --- 1 1 --- 1 1 --- 1 1 0.060 1 1 0.060 1 1 0.060 1 1 --- 1 1 --- 1 1 --- 1 1 0.058 1 1 Glycine 1 1 0.110 1 1 0.105 1 1 0.107 1 1 0.104 1 1 --- 1 1 --- 1 1 0.085 1 1 0.082 1 1 0.084 1 1 0.084 1 1 --- 1 1 --- 1 1 0.065 1 1 0.063 1 1 0.060 1 1 0.062 1 1 --- 1 1 --- 1 1 0.061 1 1 0.059 1 1 0.057 1 1 0.059 1 1 --- 1 1 --- It can be seen from Table 8 Table 8 that the experimental measurements are up to ±17.86% compared to each other. Except for the values reported by Lokhonde et al. [ 18 18 ] for a 661.6 keV photon energy, the differences of experimental results among each other and with MCNP-4C code data were less than ±8%. However, all the experimental measurements were in good agreement with MCNP-4C code data and the µ m values showed dependency on the photon energy (the µ m values decreased with an increase in photon energy). It should be noted that some observed differences in results could be because of the MCNP-4C code and the model itself, including the physical and mathematical models; uncertainties in the nuclear/atomic data; improper modeling of source energy and geometry; differences in experimental conditions like nuclear electronic set up and related errors; different physical conditions of the environment (pressure, humidity, and temperature); and different related errors in the measurement of physical quantities, like dimensions, densities, elemental composition of materials, and intensity of sources. 4 Conclusion 1 The µ m , σ a , σ e , Z eff , and N eff values for fifteen essential amino acids in the energy range of 81-1332.5 keV were simulated and calculated using the MCNP-4C code and the XCOM program and were compared to available experimental and theoretical data. This study revealed that MCNP-4C simulation and XCOM calculations provide reliable photon interaction parameters for various amino acids within ±7% RD values compared to the previous experimental data. The data calculated using the XCOM program showed better agreement with experimental data compared to MCNP-4C simulated results. It was found that the µ m , σ a , and σ e values decreased with the increase in photon energy, while the Z eff and N eff values were almost constant in the studied region of energy for each amino acid. The data presented in this study would probably be beneficial in radiation dosimetry, health physics, and other radiation applications in the energy regions of interest. References P.P. Pawar , C.S. Mahajan , Measurement of mass and linear attenuation coefficients of gamma-rays of glycine for 0.360, 0.662, 1.170 and 1.330 MeV photons , Sci. Res. Report 3 , 53 - 56 ( 2013 ). Measurement of mass and linear attenuation coefficients of gamma-rays of glycine for 0.360, 0.662, 1.170 and 1.330 MeV photons M. Donya , M. Radford , A. ElGuindy et al ., Radiation in medicine: Origins, risks and aspirations, Glob . Cardiol. Sci. Pract . 2014 , 57 ( 2014 ). https://doi.org/10.5339/gcsp.2014.57 https://doi.org/10.5339/gcsp.2014.57 Radiation in medicine: Origins, risks and aspirations, Glob C.F. Huang , J. McConathy , Fluorine-18 labeled amino acids for oncologic imaging with positron emission tomography, Curr . Top. Med. Chem . 13 , 871 - 891 ( 2013 ). https://doi.org/10.2174/1568026611313080002 https://doi.org/10.2174/1568026611313080002 Fluorine-18 labeled amino acids for oncologic imaging with positron emission tomography, Curr S. Sharifi , R. Bagheri , S.P. Shirmardi , Comparison of shielding properties for ordinary, barite, serpentine and steel-magnetite concretes using MCNP-4C code and available experimental results . Ann. Nucl. Energy 53 , 529 - 534 ( 2013 ). https://doi.org/10.1016/j.anucene.2012.09.015 https://doi.org/10.1016/j.anucene.2012.09.015 Comparison of shielding properties for ordinary, barite, serpentine and steel-magnetite concretes using MCNP-4C code and available experimental results W.M. Garrison , The radiation chemistry of amino acids, peptides and proteins in relation to the radiation sterilization of high-protein foods , Radiat. Eff. Defect S . 54 , 29 - 39 ( 1981 ). https://doi.org/10.1080/00337578108207124 https://doi.org/10.1080/00337578108207124 The radiation chemistry of amino acids, peptides and proteins in relation to the radiation sterilization of high-protein foods E.A. Mohamed , I.A.M. Ahmed , A. E.G.A. Yagoub et al ., Effects of radiation process on total protein and amino acids composition of raw and processed pearl millet flour during storage , Int. J. Food Sci. Tech . 45 , 906 - 912 ( 2010 ). https://doi.org/10.1111/j.1365-2621.2010.02228.x https://doi.org/10.1111/j.1365-2621.2010.02228.x Effects of radiation process on total protein and amino acids composition of raw and processed pearl millet flour during storage P.P. Pawar , G.K. Bichile , Studies on mass attenuation coefficient, effective atomic number and electron density of some amino acids in the energy range 0.122-1.330 MeV , Radiat. Phys. Chem . 92 , 22 - 27 ( 2013 ). https://doi.org/10.1016/j.radphyschem.2013.07.004 https://doi.org/10.1016/j.radphyschem.2013.07.004 Studies on mass attenuation coefficient, effective atomic number and electron density of some amino acids in the energy range 0.122-1.330 MeV G. Kminek , L.J. Bada , The effect of ionizing radiation on the preservation of amino acids on Mars, Earth Planet . Sci. Lett . 245 , 1 - 5 ( 2006 ). https://doi.org/10.1016/j.epsl.2006.03.008 https://doi.org/10.1016/j.epsl.2006.03.008 The effect of ionizing radiation on the preservation of amino acids on Mars, Earth Planet F. Cataldo , G. Angelini , S. Iglesias-Groth et al ., Solid state radiolysis of amino acids in an astrochemical perspective , Radiat. Phys. Chem . 80 , 57 - 65 ( 2011 ). https://doi.org/10.1016/j.radphyschem.2010.08.012 https://doi.org/10.1016/j.radphyschem.2010.08.012 Solid state radiolysis of amino acids in an astrochemical perspective A.M. Foti , F. Milano , L. Torrisi , Amino acid decomposition induced by keV ion irradiation , Nucl. Instr. Meth. Phys. Res. B 46 , 361 - 363 ( 1990 ). https://doi.org/10.1016/0168-583x(90)90730-i https://doi.org/10.1016/0168-583x(90)90730-i Amino acid decomposition induced by keV ion irradiation E. Sagstuen , A. Sanderud , E.O. Hole , The solid-state radiation chemistry of simple amino acids, revisited , Radiat. Res . 162 , 112 - 119 ( 2004 ). https://doi.org/10.1002/chin.200450256 https://doi.org/10.1002/chin.200450256 The solid-state radiation chemistry of simple amino acids, revisited J.H. Hubbell , S.M. Seltzer , Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z = 1-92 and 48 additional substances of dosimetric interest, NISTIR 5632 . National Institute of Standards and Technology , Gaithersburg ( 1995 ). https://doi.org/10.6028/nist.ir.5632 https://doi.org/10.6028/nist.ir.5632 Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z = 1-92 and 48 additional substances of dosimetric interest, NISTIR 5632 E.E. Ermis , F.B. Pilicer , E. Pilicer , et al ., A comprehensive study for mass attenuation coefficients of different parts of the human body through Monte Carlo methods , Nucl. Sci. Tech . 27 , 54 ( 2016 ). https://doi.org/10.1007/s41365-016-0053-2 https://doi.org/10.1007/s41365-016-0053-2 A comprehensive study for mass attenuation coefficients of different parts of the human body through Monte Carlo methods M.E. Medhat , S.P. Shirmardi , V.P. Singh , Comparison of Geant 4, MCNP simulation codes of studying attenuation of gamma rays through biological materials with XCOM and experimental data , J. Appl. Computat. Math . 3 ( 6 ), 1 - 5 ( 2014 ). https://doi.org/10.4172/2168-9679.1000179 https://doi.org/10.4172/2168-9679.1000179 Comparison of Geant 4, MCNP simulation codes of studying attenuation of gamma rays through biological materials with XCOM and experimental data B.O. Elbashir , M.G. Dong , M.I. Sayyed et al ., Comparison of Monte Carlo simulation of gamma ray attenuation coefficients of amino acids with XCOM program and experimental data , Results Phys . 9 , 6 - 11 ( 2018 ). https://doi.org/10.1016/j.rinp.2018.01.075 https://doi.org/10.1016/j.rinp.2018.01.075 Comparison of Monte Carlo simulation of gamma ray attenuation coefficients of amino acids with XCOM program and experimental data A. Tomal , I. Mazarro , E.M. Kakuno et al ., Experimental determination of linear attenuation coefficient of normal, benign and malignant breast tissues . Radiat. Meas . 45 , 1055 - 1059 ( 2010 ). https://doi.org/10.1016/j.radmeas.2010.08.008 https://doi.org/10.1016/j.radmeas.2010.08.008 Experimental determination of linear attenuation coefficient of normal, benign and malignant breast tissues M. Ahmadi , N. Lunscher , J.T.W. Yeow , Effective atomic numbers and electron densities of bacteriorhodopsin and its comprising amino acids in the energy range 1 keV-100 GeV , Nucl. Instr. Meth. Phys. Res. B 300 , 30 - 34 ( 2013 ). https://doi.org/10.1016/j.nimb.2013.01.002 https://doi.org/10.1016/j.nimb.2013.01.002 Effective atomic numbers and electron densities of bacteriorhodopsin and its comprising amino acids in the energy range 1 keV-100 GeV R.M. Lokhande , C.V. More , B.S. Surung et al ., Determination of attenuation parameters and energy absorption build-up factor of amine group materials , Radiat. Phys. Chem . 141 , 292 - 299 ( 2017 ). https://doi.org/10.1016/j.radphyschem.2017.08.004 https://doi.org/10.1016/j.radphyschem.2017.08.004 Determination of attenuation parameters and energy absorption build-up factor of amine group materials C.V. More , R.M. Lokhande , P.P. Pawar , Effective atomic number and electron density of amino acids within the energy range of 0.122-1.330 MeV , Radiat. Phys. Chem . 125 , 14 - 20 ( 2016 ). https://doi.org/10.1016/j.radphyschem.2016.02.024 https://doi.org/10.1016/j.radphyschem.2016.02.024 Effective atomic number and electron density of amino acids within the energy range of 0.122-1.330 MeV S.R. Manohara , S.M. Hanagodimath , Studies on effective atomic numbers and electron densities of essential amino acids in the energy range 1 keV-100 GeV . Nucl. Instr. Meth. Phys. Res. B 258 , 321 - 328 ( 2007 ). https://doi.org/10.1016/j.nimb.2007.02.101 https://doi.org/10.1016/j.nimb.2007.02.101 Studies on effective atomic numbers and electron densities of essential amino acids in the energy range 1 keV-100 GeV K.P.G. Nair , C. Gowda , J.S. Kumari et al ., Photon interaction cross sections for some amino acids in the range 30-385 keV , Radiat. Phys. Chem . 43 , 581 - 584 ( 1994 ). https://doi.org/10.1016/0969-806x(94)90171-6 https://doi.org/10.1016/0969-806x(94)90171-6 Photon interaction cross sections for some amino acids in the range 30-385 keV K.P.G. Nair , T.K. Umesh , R. Gowda , Total attenuation cross sections of several amino acids at 661.6, 1173 and 1332.5 keV , Radiat. Phys. Chem . 45 , 231 - 233 ( 1995 ). https://doi.org/10.1016/0969-806x(94)00065-4 https://doi.org/10.1016/0969-806x(94)00065-4 Total attenuation cross sections of several amino acids at 661.6, 1173 and 1332.5 keV S. Gowda , S. Krishnaveni , R. Gowda , Studies on effective atomic numbers and electron densities in amino acids and sugars in the energy range 30-1333 keV , Nucl. Instr. Meth. Phys. Res. B 239 , 361 - 369 ( 2005 ). https://doi.org/10.1016/j.nimb.2005.05.048 https://doi.org/10.1016/j.nimb.2005.05.048 Studies on effective atomic numbers and electron densities in amino acids and sugars in the energy range 30-1333 keV V. Manjunathaguru , T.K. Umesh , Effective atomic numbers and electron densities of some biologically important compounds containing H, C, N and O in the energy range 145-1330 keV , J. Phys. B: At. Mol. Opt. Phys . 39 , 3969 - 3981 ( 2006 ). https://doi.org/10.1088/0953-4075/39/18/025 https://doi.org/10.1088/0953-4075/39/18/025 Effective atomic numbers and electron densities of some biologically important compounds containing H, C, N and O in the energy range 145-1330 keV J.K. Shultis , R.E. Faw , An MCNP primer (Department of Mechanical and Nuclear Engineering , Kansas State University , Manhattan , 2011 ) Retrieved from http://krex.ksu.edu http://krex.ksu.edu An MCNP primer (Department of Mechanical and Nuclear Engineering M.J. Berger , J.H. Hubbell , XCOM: Photon Cross Sections Database . National Institute of Standards and Technology , Gaithersburg, MD 20899, USA. Web version 1.2 (1987-1999). https://doi.org/10.6028/nbs.ir.87-3597 https://doi.org/10.6028/nbs.ir.87-3597 XCOM: Photon Cross Sections Database L. Gerward , N. Guilbert , K.B. Jensen et al ., WinXCom: a program for calculating X ray attenuation coefficients . Radiat. Phys. Chem . 71 , 653 - 654 ( 2004 ). https://doi.org/10.1016/j.radphyschem.2004.04.040 https://doi.org/10.1016/j.radphyschem.2004.04.040 WinXCom: a program for calculating X ray attenuation coefficients M.I. Sayyed , H.O. Tekin , O. Kılıcoglu et al ., Shielding features of concrete types containing sepiolite mineral: Comprehensive study on experimental, XCOM and MCNPX results . Results Phys . 11 , 40 - 45 ( 2018 ). https://doi.org/10.1016/j.rinp.2018.08.029 https://doi.org/10.1016/j.rinp.2018.08.029 Shielding features of concrete types containing sepiolite mineral: Comprehensive study on experimental, XCOM and MCNPX results R. Bagheri , A.K. Moghaddam , A. Yousefi , Gamma-ray shielding study of light to heavyweight concretes using MCNP-4C code , Nucl. Sci. Tech . 28 , 15 ( 2017 ). https://doi.org/10.1007/s41365-016-0167-6 https://doi.org/10.1007/s41365-016-0167-6 Gamma-ray shielding study of light to heavyweight concretes using MCNP-4C code S.S. Obaid , D.K. Gaikwad , P.P. Pawar , Determination of gamma ray shielding parameters of rocks and concrete . Radiat. Phys. Chem . 144 , 356 - 360 ( 2018 ). https://doi.org/10.1016/j.radphyschem.2017.09.022 https://doi.org/10.1016/j.radphyschem.2017.09.022 Determination of gamma ray shielding parameters of rocks and concrete R. Bagheri , A.K. Moghaddam , H. Yousefnia , Gamma ray shielding study of barium-bismuth-borosilicate glasses as transparent shielding materials using MCNP-4C code, XCOM program, and available experimental data , Nucl. Eng. Technol . 49 , 216 - 223 ( 2017 ). https://doi.org/10.1016/j.net.2016.08.013 https://doi.org/10.1016/j.net.2016.08.013 Gamma ray shielding study of barium-bismuth-borosilicate glasses as transparent shielding materials using MCNP-4C code, XCOM program, and available experimental data R. Bagheri , A.K. Moghaddam , S.P. Shirmardi et al ., Determination of gamma-ray shielding properties for silicate glasses containing bi2O3, pbO, and baO , J. Non-Cryst. Solids 479 , 62 - 71 ( 2018 ). https://doi.org/10.1016/j.jnoncrysol.2017.10.006 https://doi.org/10.1016/j.jnoncrysol.2017.10.006 Determination of gamma-ray shielding properties for silicate glasses containing bi2O3, pbO, and baO S.S. Obaid , M.I. Sayyed , D.K. Gaikwad et al , Photon attenuation coefficients of different rock samples using MCNPX, Geant4 simulation codes and experimental results: a comparison study , Radiat. Eff. Defect S . 173 , 900 - 914 ( 2018 ). https://doi.org/10.1080/10420150.2018.1505890 https://doi.org/10.1080/10420150.2018.1505890 Photon attenuation coefficients of different rock samples using MCNPX, Geant4 simulation codes and experimental results: a comparison study 10.1007/s41365-020-0725-9 2019-09-21 2019-12-23 2019-12-25 2020-02-05 2020-02-01 2021-04-10 © 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. 2020 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/s41365-020-0725-9 http://dx.doi.org/10.1007/s41365-020-0725-9 . 2020 Nuclear Science and Techniques 2 31