In the present work, different methods were used to determine the effective atomic numbers of some low-Z materials, namely, polyethylene (PE), polystyrene (PS), polypropylene (PP), Perspex (PX), polycarbonate (PC), nylon 6-6 (PA-6), plaster of Paris (POP), and TH/L2. These methods are the direct method, the interpolation method, Auto- software, and single value XMuDat computer program. Some of the results obtained were compared with experimental data wherever possible. It can be concluded from this work that the effective atomic numbers calculated with the direct, the interpolation and Auto- methods demonstrate a good agreement in Compton scattering and pair production energy regions. A large difference in the effective atomic numbers calculated by the direct and the interpolation methods of low-Z materials was also observed in photoelectric and pair production regions. It was determined that PE, PS, PX, and PA-6 were equivalent to adipose and muscle; POP was equivalent to cortical bone; TH/L2 was equivalent to thyroid tissue; PP was equivalent to yellow bone marrow and adipose tissues; PC was equivalent to spongiosa. 1. Introduction Simulation of radiation dose distribution in human organs and tissues is possible by tissue equivalent materials. ICRU report 44 [1] describes various types of tissue substitutes for human organs and tissues. Tissue substitutes are being used for phantom, medical applications, radiology, nuclear engineering, health physics, radiation physics, radiation dosimetry, radiation protection, and space research. The effective atomic number is photon interaction parameter which is used for dosimetric properties. The effective atomic numbers can be calculated using different methods such as the direct method, the interpolation method, Auto- software, and single value XMuDat computer program. Many researchers have made extensive effective atomic numbers studies on a variety of materials such as gaseous mixtures [2], dosimetric materials [3–5], alloys [6–9], semiconductors [10, 11], building materials [12], glasses [13, 14], soils [15, 16], amino acids [17], fatty acids [18], minerals [19], and biological samples [20, 21]. In this study, the effective atomic numbers for low-Z materials have been determined using the direct, the interpolation, Auto- , and XMuDat methods. The theoretical results were compared with experimental data wherever possible. This study should be useful for readily available effective atomic numbers of the low-Z materials for choice of appropriate computational method. 2. Calculation Methods Mass attenuation
References
[1]
International Commission on Radiation Units and Measurements ICRU, “Tissue substitutes in radiation dosimetry and measurement,” Tech. Rep. 44, ICRU, Betheda , Md, USA, 1989.
[2]
V. P. Singh and N. M. Badiger, “Effective atomic numbers, electron densities, and tissue equivalence of some gases and mixtures for dosimetry of radiation detectors,” Nuclear Technology & Radiation Protection, vol. 27, no. 2, pp. 117–124, 2012.
[3]
T. K. Kumar, S. Venkataratnam, and K. V. Reddy, “Effective atomic number studies in clay minerals for total photon interaction in the energy region 10 keV-10 MeV,” Radiation Physics and Chemistry, vol. 48, no. 6, pp. 707–710, 1996.
[4]
Shivaramu and V. Ramprasath, “Effective atomic numbers for photon energy absorption and energy dependence of some thermoluminescent dosimetric compounds,” Nuclear Instruments and Methods in Physics Research B, vol. 168, no. 3, pp. 294–304, 2000.
[5]
T. Kiran Kumar and K. Venkata Reddy, “Effective atomic numbers for materials of dosimetric interest,” Radiation Physics and Chemistry, vol. 50, no. 6, pp. 545–553, 1997.
[6]
I. Han, M. Aygun, L. Demir, and Y. Sahin, “Determination of effective atomic numbers for 3d transition metal alloys with a new semi-empirical approach,” Annals of Nuclear Energy, vol. 39, no. 1, pp. 56–61, 2012.
[7]
M. Kurudirek, M. Büyüky？ld？z, and Y. ？zdemir, “Effective atomic num ber study of various alloys for total photon interaction in the energy region of 1？keV–100？GeV,” Nuclear Instruments and Methods in Physics Research A, vol. 613, pp. 251–256, 2010.
[8]
V. R. K. Murty, “Effective atomic numbers for W/Cu alloy for total photon attenuation,” Radiation Physics and Chemistry, vol. 71, no. 3-4, pp. 667–669, 2004.
[9]
A. H. El-Kateb, R. A. M. Rizk, and A. M. Abdul-Kader, “Determination of atomic cross-sections and effective atomic numbers for some alloys,” Annals of Nuclear Energy, vol. 27, no. 14, pp. 1333–1343, 2000.
[10]
A. ？elik, U. ？evik, E. Bacaksiz, and N. ？elik, “Effective atomic numbers and electron densities of CuGaSe2 semiconductor in the energy range 6-511 keV,” X-Ray Spectrometry, vol. 37, no. 5, pp. 490–494, 2008.
[11]
O. ？？elli, “Measurement of efffective atomic numbers of holmium doped and undoped layered semiconductors via transmission method around the absorption edge,” Nuclear Instruments and Methods in Physics Research A, vol. 600, no. 3, pp. 635–639, 2009.
[12]
N. Damla, H. Baltas, A. Celik, E. Kiris, and U. Cevik, “Calculation of radiation attenuation coefficients, effective atomic numbers and electron densities for some building materials,” Radiation Protection Dosimetry, vol. 150, no. 4, Article ID ncr432, pp. 541–549, 2012.
[13]
J. Kaewkhao and P. Limsuwan, “Mass attenuation coefficients and effective atomic numbers in phosphate glass containing Bi2O3, PbO and BaO at 662 keV,” Nuclear Instruments and Methods in Physics Research A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 619, no. 1–3, pp. 295–297, 2010.
[14]
H. Gill, G. Kaur, K. Singh, V. Kumar, and J. Singh, “Study of effective atomic numbers in some glasses and rocks,” Radiation Physics and Chemistry, vol. 51, no. 4–6, pp. 671–672, 1998.
[15]
G. S. Mudahar and H. S. Sahota, “Effective atomic number studies in different soils for total photon interaction in the energy region 10-5000？keV,” Applied Radiation and Isotopes, vol. 39, no. 12, pp. 1251–1254, 1988.
[16]
N. Kucuk, Z. Tumsavas, and M. Cakir, “Determining photon energy absorption parameters for different soil samples,” Journal of Radiation Research, vol. 54, no. 3, pp. 578–586, 2013.
[17]
S. Gowda, S. Krishnaveni, and R. Gowda, “Studies on effective atomic numbers and electron densities in amino acids and sugars in the energy range 30–1333 keV,” Nuclear Instruments and Methods in Physics Research B: Beam Interactions with Materials and Atoms, vol. 239, no. 4, pp. 361–369, 2005.
[18]
S. R. Manohara, S. M. Hanagodimath, and L. Gerward, “Studies on effective atomic number, electron density and kerma for some fatty acids and carbohydrates,” Physics in Medicine and Biology, vol. 53, no. 20, pp. N377–386, 2008.
[19]
I. Han, L. Demir, and M. ？ahin, “Determination of mass attenuation coefficients, effective atomic and electron numbers for some natural minerals,” Radiation Physics and Chemistry, vol. 78, no. 9, pp. 760–764, 2009.
[20]
V. Manjunathaguru and 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,” Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 39, no. 18, article 025, pp. 3969–3981, 2006.
[21]
N. Ko？ and H. ？zyol, “Z-dependence of partial and total photon interactions in some biological samples,” Radiation Physics and Chemistry, vol. 59, no. 4, pp. 339–345, 2000.
[22]
M. J. Berger and J. H. Hubbell, XCOM: Photon Cross Sections Database, NBSIR, 1987.
[23]
L. Gerward, N. Guilbert, K. B. Jensen, and H. Levring, “WinXCom: a program for calculating X-ray attenuation coefficients,” Radiation Physics and Chemistry, vol. 71, no. 3-4, pp. 653–654, 2004.
[24]
M. E. Wieser, N. Holden, T. B. Coplen et al., “Atomic weights of the elements 2011 (IUPAC technical report),” Pure and Applied Chemistry, vol. 85, no. 5, pp. 1047–1078, 2013.
[25]
M. L. Taylor, R. L. Smith, F. Dossing, and R. D. Franich, “Robust calculation of effective atomic numbers: the auto-Zeff software,” Medical Physics, vol. 39, no. 4, pp. 1769–1778, 2012.
[26]
S. R. Manohara, S. M. Hanagodimath, K. S. Thind, and L. Gerward, “On the effective atomic number and electron density: a comprehensive set of formulas for all types of materials and energies above 1 keV,” Nuclear Instruments and Methods in Physics Research B: Beam Interactions with Materials and Atoms, vol. 266, no. 18, pp. 3906–3912, 2008.
[27]
R. Nowotny, “XMuDat: photon attenuation data on PC,” Tech. Rep. IAEA-NDS-195, International Atomic Energy Agency, Vienna, Austria, 1998, https://www-nds.iaea.org/publications/iaea-nds/iaea-nds-0195.htm.
[28]
D. F. Jackson and D. J. Hawkes, “X-ray attenuation coefficients of elements and mixtures,” Physics Reports, vol. 70, no. 3, pp. 169–233, 1981.
[29]
K. Parthasaradhi, A. Esposito, and M. Pelliccioni, “Photon attenuation coefficients in tissue equivalent compounds,” Applied Radiation and Isotopes, vol. 43, no. 12, pp. 1481–1484, 1992.
[30]
N. Kucuk, M. Cakir, and N. A. Isitman, “Mass attenuation coefficients, effective atomic numbers and effective electron densities for some polymers,” Radiation Protection Dosimetry, vol. 153, no. 1, pp. 127–134, 2013.
[31]
S. P. Kumar, V. Manjunathaguru, and T. K. Umesh, “Effective atomic numbers of some H-, C-, N- and O-based composite materials derived from differential incoherent scattering cross-sections,” Pramana, vol. 74, no. 4, pp. 555–562, 2010.
[32]
R. Vijayakumar, L. Rajasekaran, and N. Ramamurthy, “Effective atomic numbers for photon energy absorption of some low-Z substances of dosimetric interest,” Radiation Physics and Chemistry, vol. 62, no. 5-6, pp. 371–377, 2001.
[33]
A. H. El-Kateb and A. S. Abdul-Hamid, “Photon attenuation coefficient study of some materials containing hydrogen, carbon and oxygen,” Applied Radiation and Isotopes, vol. 42, no. 3, pp. 303–307, 1991.
