Chapter 3. Effective atomic numbers and electron densities for some scintillators and plasticizers

Chapter 3 Effective atomic numbers and electron densities for some scintillators and plasticizers

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 85 In section 3.1 of this chapter the materials and motivation for the present study are given. In sections 3.2 and 3.3, the analysis and discussion of results on effective atomic number and effective electron density for total and partial photon interaction processes, and effective atomic numbers for photon energy-absorption and photon interaction for scintillators and plasticizers are presented. Conclusions are given in section 3.4. 3.1. Materials and motivation Organic scintillators Organic scintillators are aromatic hydrocarbon compounds which contain benzene ring structures interlinked in various ways. Their luminescence typically decays within a few nanoseconds. Some organic scintillators are pure crystals. The most common types are anthracene (C 14 H 10, decay time 30 ns), stilbene (C 14 H 12, few ns decay time), and naphthalene (C 10 H 8, few nanosecond decay time). They are very durable, but their response is anisotropic (which spoils energy resolution when the source is not collimated), and they cannot be easily machined, nor can they be grown in large sizes; hence they are not very often used. Anthracene has the highest light output of all organic scintillators and is therefore chosen as a reference: the light outputs of other scintillators are sometimes expressed as a percent of anthracene light. Organic liquids These are liquid solutions of one or more organic scintillators in an organic solvent. The typical solutes are fluors such as p-terphenyl (C 18 H 14 ), 2-(4-Biphenyl)-5-phenyl- 1,3,4-oxadiazole (PBD,C 20 H 14 N 2 O), 2-(4-tert-Butylphenol)-5-(4-biphenylyl)-1,3,4- oxadiazole (butyl PBD, C 24 H 22 N 2 O), 2,5-Diphenylamine (PPO, C 15 H 11 NO), and wavelength shifter such as 1,4-bis(5-phenyloxazol-2-yl) benzene (POPOP, C 24 H 16 N 2 O). The most widely used solvents are toluene, xylene, benzene, phenylcyclohexane,

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 86 triethylbenzene, and decalin. Liquid scintillators are easily loaded with other additives such as wavelength shifters to match the spectral sensitivity range of a particular PMT, or Boron to increase the neutron detection efficiency of the scintillation counter itself. For many liquids, dissolved oxygen can act as a quenching agent and lead to reduced light output, hence the necessity to seal the solution in an oxygen-free, air-tight enclosure. Plasticizers Plasticizers and super plasticizer are chemical admixtures that can be added to concrete mixtures to meliorate workability. Unless the mix is "starved" of water, the strength of concrete is inversely proportional to the amount of water added. In order to produce stronger concrete, less water is added which makes the concrete mixture less workable and difficult to mix, necessitating the use of plasticizers as a water reducers. Plasticizers are also often used when pozzolanic ash is added to concrete to improve the strength. This method of mix proportioning is especially popular when producing high strength concrete and fibre-reinforced concrete. Energetic material pyrotechnic compositions, especially solid rocket propellants and smokeless powders for guns, often employ plasticizers to improve physical properties of the propellant binder or of the overall propellant, to provide a secondary fuel, and ideally, to improve specific energy yield of the propellant. Energetic plasticizers reduce the required mass of propellant, enabling a rocket vehicle to carry more payloads or reach higher velocity. However, safety or cost considerations may demand that non-energetic plasticizers be used, even in rocket propellants. Diethyl phthalate () can cause damage to the nervous system as well as to the reproductive organs in males and females [1]. The Butanetriol trinitrate (), Triethylene glycol dinitrate (), Trimethylolethane trinitrate (), Diethylene glycol dinitrate () are having applications in solid propellants and also used as an

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 87 energetic plasticizer in explosives. The plasticizers have wide applications in explosives, propellants and biological field. Following the suggestions of Hine [2], several investigators have made extensive Z eff (or Z PI, eff ) studies in variety of composite materials like alloys, polymers, semiconductors, superconductors, thermoluminescent compounds, etc [Chapter 2, Section 2.2.2]. Such a study has also been made for tissues and their equivalent materials for photon interaction [Chapter 2, Section 2.2.2]. The selected organic compounds have wide applications in solid propellants and also used as an energetic plasticizer in explosives. The plasticizers have wide applications in explosives, propellants and biological field. Plastics, such as polyvinyl toluene, can be doped with anthracene to produce plastic scintillators that is approximately water-equivalent for use in radiation therapy dosimetry. It is also used in wood preservatives, insecticides, and coating materials. The attenuation of gamma and X- ray has motivated lots of researcher to figure out the attenuation coefficients, effective atomic number and electron density. Several investigators have [3 7] carried out broad investigation on Z PI, eff in a variety of composite materials like alloys, polymers, thermoluminescent and dosimetric compounds, semiconductors, superconductors, tissues, and equivalent materials for photon interaction. Corresponding studies for Z PEA,eff appear to be limited [8-10]. In the literature, there are no reports on the study of Z PI, eff, Ne,eff, Z PEA,eff and Kerma of selected organic scintillators. All the above facts prompted us to undertake a rigorous and exhaustive calculation of the Z eff and N e, eff for total and partial photon interaction processes over an extended energy range 1 kev 100 GeV. In the present work, the Z PEA,eff has been calculated for organic scintillators and plasticizers in the energy region of 1 kev to 20 MeV using the μ en /ρ values from the compilation of Hubbell and Seltzer [11] and also calculated Z PI, eff for total photon interaction with

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 88 coherent scattering by using WinXCom program [12-13]. The Kerma relative to air has also been computed and reported in the present work. TABLE 3.1: Molecular formulae of the organic scintillators and plasticizers studied in the present work. S.N is the sample number. <Z> are the mean atomic number calculated from the molecular formula. S.N Organic Scintillators <Z> 1. Anthracene (C 14 H 10 ) 3.91 2. Stilbene (C 14 H 12 ) 3.69 3. Naphthalene (C 10 H 8 ) 3.77 4. p-terphenyl (C 18 H 14 ) 3.81 5. PPO (C 15 H 11 NO) 4.14 6. Butyl PBD (C 24 H 22 N 2 O) 3.83 7. PBD (C 20 H 14 N 2 O) 4.21 Plasticizers 1. (C 4 H 8 O 7 N 2 ) 4.85 2. (C 6 H 12 O 8 N 2 ) 4.50 3. (C 4 H 7 O 9 N 3 ) 5.39 4. (C 5 H 9 O 9 N 3 ) 7 5. (C 12 H 14 O 4 ) 3.93 6. (C 16 H 22 O 4 ) 3.57

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 89 3.2. Analysis and discussion of results on effective atomic numbers and electron densities of scintillators and plasticizers for total and partial photon interaction processes In this section, the effective atomic number, Z eff, and effective electron density, N e, eff, of scintillators and plasticizers, listed in table 3.1, have been calculated for total and partial photon interaction processes in the wide energy range from 1 kev to 100 GeV using WinXCom [12, 13]. The notion of Z eff is given a new meaning, in the present work, by using a modern database of photon interaction cross-sections [11 13]. The values of these parameters have been found to change with energy and composition of the scintillators and plasticizers. The variations of Z eff and N e, eff with energy are shown graphically for all types photon interaction processes. The variations of photon mass attenuation coefficients with energy are shown graphically only for total photon interaction. The XMuDat program [14] provides a single-valued effective atomic number and an effective electron density, which also have been calculated in the present work. The detailed procedures for the calculations of all these parameters are explained in Section 2.1 of Chapter 2. 3.2.1. The effective atomic number and effective electron density for total and partial photon interaction processes The results on the variations of Z eff and N e, eff with photon energy are shown graphically in figures 3.1 3.4 for total and partial photon interaction processes. The present results clearly confirm the comment by Hine [2] that, Z eff of a multielement material varies with energy. In the following paragraphs, the energy dependence of Z eff and N e, eff for total and individual photon interaction processes are discussed. 3.2.1a. Total photon interaction (with coherent scattering) The variation of Z eff with photon energy for total photon interaction is shown in figures 3.1 and 3.2. The figures show the dominance of different interaction processes in different energy regions. The three energy ranges discussed for Z eff. The behavior of all scintillators

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 90 and plasticizers is almost identical. From figures it is clear that, the effective atomic numbers for photon interaction varies with energy. The values of Z PEA, eff and Z PI, eff with energy depends upon relative proportion and the range of atomic numbers of the elements of which organic compounds are composed off. In low energy region, photoelectric interaction is dominant. From 3 8 kev onwards, there is sharp decrease in Z eff with energy up to 150 kev, showing that contribution of scattering processes increases which decreases Z eff. From 150 kev to 3 MeV, Z eff is almost independent of energy. This may be due to the dominance of incoherent scattering in this region. From 3 MeV to 100 MeV, there is regular increase in Z eff with photon energy. This characteristic is due to sharing of incoherent scattering and pair production. It is observed that the variation in Z eff also depends upon relative proportion and the range of atomic numbers of the elements of which plasticizers is composed off. In low energy region, E < 0.01 MeV, photoelectric interaction is dominant and Z eff varies as in case of photoelectric interaction process. For a given organic compounds, the maximum value of Z eff is found in this low-energy range. From 3 8 kev onwards, there is a sharp decrease in Z eff with energy up to 150 kev, showing that contribution of scattering processes increases which decreases Z eff. Sastry and Jayanand [15] confirmed this by reporting that Z eff of a composite material is greater for photoelectric interaction than for any other processes. At intermediate energies, between about 0.03 MeV and 3 MeV, Z eff is almost independent of energy. This is due to the dominance of incoherent scattering. For a given organic compound, the minimum value of Z eff is found in this intermediate energy range. This minimum value of Z eff is very close to the mean atomic number of the scintillators and plasticizers, <Z> (table 3.1). From 3 MeV to 400 MeV, there is regular increase in Z eff with photon energy. This behavior is due to mixed contribution of incoherent scattering

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 91 and pair production. Above 400 MeV, Z eff remains almost constant. This is due to the dominance of pair production in the high-energy region. It is observed that the variation in Z eff also depends upon the relative proportion and the range of atomic numbers of the elements of which the organic compounds is composed. The, TEDGN,, and contain more number of elements when compared with and. Therefore the change of effective atomic number with energy is less for compounds which consists of nitrogen. In low energy region, electron density is more for all plasticizers, it s because of the photoelectric interaction is dominant. From 1 8 kev the electron density is almost constant then onwards, there is sharp decrease in N e,eff with energy up to 150 kev, showing that contribution of scattering processes increases which decreases N e,eff. From 150 kev to 3 MeV, N e,eff is almost independent of energy. This may be due to the dominance of incoherent scattering in this region. The N e,eff increases with energy from 3 MeV to 100 MeV it confirms the dominance of pair production in this region. The present theoretical results are in line with the result of Mudahar et al. [16] Bhandal and Singh [17-19]. They have reported effective atomic numbers for different alloys [16], biological samples [17], cements [18] and multielement materials [19] over a wide range of energy region 10 3 to 10 5 MeV. They reported that Z eff changes with energy and composition of the material. 3.2.1b. Photoelectric absorption The variation of Z eff with photon energy for photoelectric absorption is shown in figures 3.1 and 3.2, which indicates that Z eff is almost independent of photon energy for all the scintillators and plasticizers. From figure it is clear that the effective atomic number increases gradually up to 30 kev and then onwards remains constant with increase in

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 92 energy. This is due to the fact that these consist of elements, which are almost same in number and are within a close atomic-number range. 3.2.1c. Incoherent scattering The variation of Z eff with photon energy for incoherent scattering is shown in figures 3.1 and 3.2, which indicates that Z eff increases sharply with increase in energy in the region 1 400 kev. Beyond 400 kev, Z eff is independent of photon energy for all scintillators and plasticizers. Most of the elements in an organic compounds have a value of Z/A of about 0.5 whereas hydrogen has a value of 1.0, which affects Compton scattering. The Compton scattering cross-section is proportional to the atomic number, and in this special case, Z eff equals the mean atomic number of the material. Consider for example. The constant value of Z eff based on Compton scattering is 3.93. The same value (= 3.93) is also found for Z eff based on the total photon interaction, at say 1 MeV, where Compton scattering is totally dominating. Moreover, the value 3.93 is in perfect agreement with the value of the mean atomic number, <Z>, calculated from the molecular formula of (table 3.1). The present theoretical results are similar to the theoretical results of Mudahar et al. [16] who have reported a similar type of variation of Z eff for alloys, and to the experimental findings of Parthasaradhi [20] who has reported that the Z eff due to Compton scattering is constant in the energy range from 100 to 662 kev for some alloys. Khayyoom and Parthasaradhi [21] have also studied Z eff of some alloys and their experimental result suggests that Z eff for incoherent scattering is independent of photon energy from 20 to 800 kev. In the present study, Z eff is independent of photon energy only above 400 kev, but depends on photon energy below 400 kev.

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 93 3.2.1d. Coherent scattering The variation of Z eff with photon energy for coherent scattering is shown in figures 3.1 and 3.2. Figures show that Z eff increases with increase in energy from 1 kev to 200 kev for all scintillators and plasticizers. From here onwards Z eff remains constant with increase in energy, i.e. Z eff is independent of energy. The present theoretical results are similar to the experimental findings of Parthasaradhi [20] who has reported that Z eff for coherent scattering is constant in the energy range 100 662 kev for some alloys. 3.2.1e. Pair production in nuclear and electron field The variation of Z eff with photon energy for pair production in Coulomb field of the nucleus is given in figures 3.1 and 3.2, which shows that Z eff slightly decreases with increase in photon energy from 1.25 to 200 MeV and then it is almost independent of energy. It is due to the fact that pair production in nuclear field is Z 2 dependent. The present theoretical results are consistent with the experimental results of Rao and Parthasaradhi [22] and Rama Rao et al. [23]. Figures 3.1 and 3.2 also show the variation of Z eff with photon energy for pair production in the Coulomb field of electron, also called triplet production. From figure it is clear that Z eff is independent of photon energy from 3 kev 30 MeV. From 30 MeV, Z eff decreases with increase of photon energy up to 30 GeV and it is then independent of energy thereafter for all scintillators and plasticizers. The variations of N e, eff of all the scintillators and plasticizers for partial and total interaction processes with photon energy are similar to those of Z eff, since there is proportionality between the two parameters according to equation (2.25). These variations can be explained similar to Z eff and are shown in figures 3.3 and 3.4.

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 94 8.0 7.5 7.0 6.5 6.0 5.5 Total photon interaction (Coherent) 1 2 3 4 5 6 7 6.8 6.6 6.4 6.2 6.0 Coherent Z PI, eff 4.5 4.0 3.5 3.0 2.5 2.0 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 Z PI, eff 5.8 5.6 5.4 5.2 4.8 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 1 2 3 4 5 6 7 7.4 7.3 7.2 7.1 7.0 6.9 Photoelectric 1 2 3 4 5 6 7 3.6 3.4 3.2 1 2 3 4 5 6 7 Pair production (electric) Z PI, eff 6.8 6.7 6.6 6.5 Z PI, eff 3.0 2.8 6.4 6.3 2.6 6.2 6.1 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 2.4 10 1 10 2 10 3 10 4 10 5 Z PI, eff 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 Incoherent 1 2 3 4 5 6 7 Z PI, eff 6.0 Pair production (nuclear) 5.8 5.6 5.4 5.2 4.8 1 2 3 4 5 6 7 1.6 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 4.6 10 0 10 1 10 2 10 3 10 4 10 5 FIG. 3.1 Variation of effective atomic number, Z eff, of scintillators (samples as for table 3.1) for total photon interaction (with coherent) and partial photon interaction processes.

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 95 8.0 7.5 7.0 6.5 Total Photon Interaction (Coherent) 7.4 7.2 7.0 6.8 Coherent 6.0 6.6 Z eff 5.5 4.5 4.0 3.5 Z eff 6.4 6.2 6.0 5.8 10-3 10-2 10-1 10 0 10 1 10 2 10-3 10-2 10-1 10 0 10 1 10 2 7.8 7.7 7.6 Photoelectric 5.4 5.2 Pair Production(electronic) Z eff 7.5 7.4 7.3 7.2 7.1 7.0 6.9 6.8 6.7 10-3 10-2 10-1 10 0 10 1 10 2 Z eff 4.8 4.6 4.4 4.2 4.0 3.8 3.6 3.4 10 1 10 2 Z eff 5.6 5.4 5.2 4.8 4.6 4.4 4.2 4.0 3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 Incoherent 10-3 10-2 10-1 10 0 10 1 10 2 Z eff 7.0 6.8 6.6 6.4 6.2 6.0 5.8 5.6 Pair Production (nuclear) 10 0 10 1 10 2 FIG.3.2: Variation of effective atomic number, Z eff, of plasticizers for total photon interaction (with coherent) and partial photon interaction processes.

Electron Density(N el ) Electron Density(N el ) Electron Density(N el ) Electron Density (N el ) Electron Density(N el ) Electron Density(N el ) Studies on Z eff and N e,eff of some organic scintillators and plasticizers 96 8.0x10 23 Total photon interaction (Coherent) 7.5x10 23 7.0x10 23 6.5x10 23 6.0x10 23 5.5x10 23 x10 23 4.5x10 23 4.0x10 23 3.5x10 23 3.0x10 23 2.5x10 23 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 1 2 3 4 5 6 7 7.6x10 23 Coherent 7.4x10 23 7.2x10 23 7.0x10 23 6.8x10 23 6.6x10 23 6.4x10 23 6.2x10 23 6.0x10 23 5.8x10 23 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 1 2 3 4 5 6 7 7.8x10 23 6.2x10 23 Pair production (nuclear) 7.6x10 23 7.4x10 23 6.0x10 23 7.2x10 23 7.0x10 23 6.8x10 23 6.6x10 23 6.4x10 23 Photoelectric 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 1 2 3 4 5 6 7 5.8x10 23 5.6x10 23 5.4x10 23 5.2x10 23 10 0 10 1 10 2 10 3 10 4 10 5 1 2 3 4 5 6 7 4.0x10 23 3.5x10 23 Pair production (electic) 3.8x10 23 3.6x10 23 3.4x10 23 3.2x10 23 3.0x10 23 2.8x10 23 2.6x10 23 Incoherent 1 2 3 4 5 6 7 3.4x10 23 3.4x10 23 3.3x10 23 3.3x10 23 3.2x10 23 3.2x10 23 3.1x10 23 3.1x10 23 1 2 3 4 5 6 7 2.4x10 23 3.0x10 23 2.2x10 23 10-3 10-2 10-1 10 0 10 1 10 2 10 3 10 4 10 5 3.0x10 23 10 1 10 2 10 3 10 4 10 5 FIG. 3.3: Variation of effective electron density of scintillators for total and partial photon interaction processes. Notations as for Table 3.1

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 97 N el 6.4x10 23 6.2x10 23 Total Photon Interaction (Coherent) 6.0x10 23 5.8x10 23 5.6x10 23 5.4x10 23 5.2x10 23 x10 23 4.8x10 23 4.6x10 23 4.4x10 23 4.2x10 23 4.0x10 23 3.8x10 23 3.6x10 23 3.4x10 23 3.2x10 23 3.0x10 23 10-3 10-2 10-1 10 0 10 1 10 2 N el 5.8x10 23 Coherent 5.6x10 23 5.4x10 23 5.2x10 23 x10 23 4.8x10 23 4.6x10 23 4.4x10 23 4.2x10 23 4.0x10 23 10-3 10-2 10-1 10 0 10 1 10 2 6.3x10 23 3.3x10 23 Pair Paroduction (electronic) 6.0x10 23 5.7x10 23 Photoelectric 3.2x10 23 3.2x10 23 3.2x10 23 5.4x10 23 3.2x10 23 N el 5.1x10 23 N el 3.2x10 23 3.1x10 23 4.8x10 23 3.1x10 23 4.5x10 23 3.1x10 23 4.2x10 23 10-3 10-2 10-1 10 0 10 1 10 2 3.1x10 23 10 1 10 2 3.4x10 23 Incoherent 5.2x10 23 N el 3.2x10 23 3.0x10 23 2.8x10 23 2.6x10 23 N el x10 23 4.8x10 23 4.6x10 23 4.4x10 23 Pair Production (nuclear) 2.4x10 23 4.2x10 23 2.2x10 23 10-3 10-2 10-1 10 0 10 1 10 2 4.0x10 23 10 0 10 1 10 2 FIG. 3.4: Variation of effective electron density of plasticizers for total and partial photon interaction processes.

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 98 3.2.2. Comparison of calculated Z eff and N e, eff values for total photon interaction For a given material, the XMuDat program [10] calculates two single-valued parameters, namely the effective atomic number, Z eff, XMuDat, and the electron density, N e, XMuDat. Thus, Z eff, XMuDat and N e, XMuDat values predicted by XMuDat program are energy-independent. In table 3.2 these single-valued parameters are compared, for scintillators and plasticizers, with (Z eff ) max, (Z eff ) min, (N e, eff ) max and (N e, eff ) min, i.e. the maximum and minimum values of the effective atomic number and the effective electron density obtained in the present calculations using WinXCom in the energy range from 1 kev to 100 GeV. It can be seen in table 3.2 that, for each organic compounds, Z eff, XMuDat is close to (Z eff ) max, whereas N e, XMuDat is in perfect agreement with (N e, eff ) min. Therefore it follows that, as discussed in Section 2.1.3 of Chapter 2, XMuDat calculates Z eff, XMuDat by assuming that photoelectric absorption is the main interaction process [equation (2.30)], and N e, XMuDat by assuming that Compton scattering is dominating interaction process [equation (2.31)]. TABLE 3.2: Comparison between effective numbers (dimensionless) and electron densities (in units of 10 23 electrons/g) calculated by XMuDat program, and the corresponding maximum and minimum values calculated in the present work using WinXCom in the energy range 1 kev to 100 GeV. Numbers are as for table 3.1. S.N Z eff, XMuDat (Z eff ) min (Z eff ) max N e, XMuDat (N e, eff ) min (N e, eff ) max Scintillators 1. 5.81 3.92 5.99 3.17 3.18 4.86 2. 5.78 3.69 5.99 3.21 3.21 5.21 3. 5.79 3.78 5.99 3.19 3.20 7 4. 5.80 3.81 5.99 3.19 3.19 2 5. 6.11 4.14 6.33 3.16 3.16 4.82 6. 6.02 3.84 6.26 3.19 3.19 5.21 7. 6.11 4.22 6.30 3.15 3.15 4.71

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 99 Plasticizers S.N Z eff, XMuDat (Z eff ) min (Z eff ) max N e, XMuDat (N e, eff ) min (N e, eff ) max 1. 7.29 4.86 7.53 3.13 3.13 4.85 2. 7.17 4.50 7.46 3.16 3.16 5.24 3. 7.39 5.39 7.58 3.10 3.10 4.35 4. 7.31 8 7.52 3.12 3.12 4.62 5. 6.54 3.93 6.88 3.20 3.20 5.59 6. 6.36 3.57 6.73 3.25 3.25 6.12 3.3. Analysis and discussion of results on the energy dependence of the effective atomic numbers of essential scintillators and plasticizers for photon energyabsorption and for photon interaction In this section, the results on effective atomic numbers for photon energy-absorption, Z PEA, eff, and for photon interaction, Z PI, eff, are presented for essential scintillators and plasticizers for the photon-energy range from 1 kev to 20 MeV. The procedure of calculating Z PEA, eff, Z PI, eff and the ratio Z R, eff is described in Section 2.1.1 of Chapter 2. The variations of the effective atomic numbers Z PEA, eff and Z PI, eff with energy are shown graphically. The Z PEA, eff and Z PI, eff values have been found to change with energy and composition of the essential scintillators and plasticizers. The energy behavior of Z PEA, eff and Z PI, eff is the same for all scintillators and plasticizers. In table 3.3, Z PEA, eff and Z PI, eff are provided for the energy range 1 kev 20 MeV, since photons of energy 5 1500 kev have found immense applications in radiation biology especially during diagnostics and therapy [24]. The reasons for using Z PEA, eff rather than the commonly used Z PI, eff in medical radiation dosimetry for the calculation of absorbed dose in radiation therapy are also discussed. It is seen that variation in en / is large below 40 kev and negligible between 0.04 10 MeV and further there is again significant variation above 10 MeV. These variations are interpreted as due to (i) photoelectric absorption which varies as Z 4 5,

Effective atomic number Effective atomic number ratio Effective atomic number Effective atomic number ratio Effective atomic number Effective atomic number ratio Effective atomic number Effective atomic number ratio Effective atomic number Effective atomic number ratio Effective atomic number Effective atomic number ratio Studies on Z eff and N e,eff of some organic scintillators and plasticizers 100 6.0 5.5 Anthracene Z PI,eff Z PEA,eff Z R 0.85 0.80 0.75 6.0 5.5 p-terphenyl Z PI,eff Z PEA,eff Z R 0.85 0.80 0.75 0.70 0.70 4.5 0.65 0.60 4.5 0.65 0.60 4.0 0.55 4.0 0.55 0.50 3.5 10-3 10-2 10-1 10 0 10 1 0.50 3.5 10-3 10-2 10-1 10 0 10 1 6.0 5.5 Stilbene Z PI,eff Z PEA,eff Z R 0.85 0.80 0.75 6.5 6.0 PPO Z PI,eff Z PEA,eff Z R 0.90 0.85 0.80 0.70 0.65 5.5 0.75 0.70 4.5 4.0 0.60 0.55 4.5 0.65 0.60 3.5 10-3 10-2 10-1 10 0 10 1 0.50 4.0 10-3 10-2 10-1 10 0 10 1 0.55 6.0 Naphthalene Z PI,eff Z PEA,eff 0.85 0.80 6.5 6.0 ButylPBD Z PI,eff Z PEA,eff 0.90 0.85 5.5 Z R 0.75 0.70 0.65 5.5 Z R 0.80 0.75 0.70 4.5 4.0 3.5 10-3 10-2 10-1 10 0 10 1 0.60 0.55 0.50 4.5 4.0 3.5 10-3 10-2 10-1 10 0 10 1 FIG. 3.5: Variation of effective atomic number for photon energy-absorption, Z PEA, eff, effective atomic number for photon interaction, Z PI, eff, and effective atomic number ratio, Z R, eff, with photon energy for some scintillators(sample #1-6). 0.65 0.60 0.55 0.50

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 101 8.0 7.5 7.0 6.5 6.0 Z PI,eff 5.5 4.5 4.0 3.5 10-3 10-2 10-1 10 0 10 1 8.0 7.5 7.0 6.5 Z PEA,eff 6.0 5.5 4.5 4.0 3.5 10-3 10-2 10-1 10 0 10 1 FIG. 3.6: Variation of effective atomic number for photon energy-absorption, Z PEA, eff, effective atomic number for photon interaction, Z PI, eff, with photon energy for plasticizers.

Kerma Effective atomic number ratio Studies on Z eff and N e,eff of some organic scintillators and plasticizers 102 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 10-3 10-2 10-1 10 0 10 1 FIG. 3.7: Variation of effective atomic number ratio with photon energy for plasticizers 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 10-3 10-2 10-1 10 0 10 1 FIG. 3.8: Variation of Kerma with photon energy for plasticizers.

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 103 TABLE 3.3: Effective atomic numbers for photon energy-absorption, Z PEA, eff, for photon interaction, Z PI, eff, and effective atomic number ratio, Z R, eff, of some scintillators and plasticizers. Energy Anthracene Stilbene PPO PBD (MeV) Z PEA Z PI Z R Z PEA Z PI Z R Z PEA Z PI Z R Z PEA Z PI Z R 0.0010 5.99 5.99 0.83 5.99 5.99 0.83 6.30 6.30 0.87 6.28 6.28 0.87 0.0020 6.00 5.99 0.83 6.00 5.99 0.83 6.32 6.32 0.87 6.30 6.30 0.87 0.0030 6.00 5.99 0.83 6.00 5.99 0.83 6.34 6.33 0.87 6.31 6.30 0.87 0.0040 6.00 5.98 0.80 6.00 5.97 0.80 6.34 6.32 0.84 6.32 6.30 0.84 0.0050 6.00 5.96 0.80 6.00 5.95 0.80 6.35 6.31 0.84 6.32 6.29 0.84 0.0060 6.00 5.93 0.80 6.00 5.92 0.80 6.35 6.29 0.84 6.33 6.27 0.84 0.0080 6.00 5.85 0.79 5.99 5.82 0.79 6.36 6.22 0.84 6.33 6.20 0.84 0.0100 5.99 5.72 0.79 5.99 5.67 0.79 6.36 6.11 0.84 6.33 6.09 0.84 0.0150 5.97 5.28 0.79 5.96 5.16 0.79 6.34 5.68 0.84 6.31 5.69 0.84 0.0200 5.89 4.84 0.77 5.87 4.67 0.77 6.28 5.22 0.82 6.26 5.26 0.83 0.0300 5.54 4.33 0.72 5.46 4.12 0.71 5.96 4.64 0.78 5.95 4.70 0.82 0.0400 0 4.13 0.65 4.85 3.91 0.63 5.42 4.40 0.71 5.44 4.46 0.78 0.0500 4.56 4.04 0.60 4.36 3.82 0.57 4.93 4.29 0.65 4.97 4.36 0.72 0.0600 4.28 4.00 0.57 4.07 3.77 0.54 4.61 4.24 0.61 4.66 4.31 0.66 0.0800 4.05 3.96 0.54 3.83 3.73 0.51 4.32 4.19 0.58 4.38 4.26 0.62 0.1000 3.98 3.94 0.54 3.75 3.72 0.51 4.22 4.17 0.57 4.29 4.25 0.59 0.1500 3.93 3.93 0.54 3.71 3.70 0.51 4.16 4.16 0.57 4.23 4.23 0.59 0.2000 3.92 3.92 0.54 3.70 3.70 0.51 4.15 4.15 0.57 4.22 4.22 0.58 0.3000 3.92 3.92 0.54 3.69 3.70 0.51 4.14 4.15 0.57 4.22 4.22 0.58 0.4000 3.92 3.92 0.54 3.69 3.69 0.51 4.14 4.15 0.57 4.22 4.22 0.58 0.5000 3.92 3.92 0.54 3.69 3.69 0.51 4.14 4.14 0.57 4.22 4.22 0.58 0.6000 3.92 3.92 0.54 3.69 3.69 0.51 4.14 4.14 0.57 4.22 4.22 0.58 0.8000 3.92 3.92 0.54 3.69 3.69 0.51 4.14 4.14 0.57 4.22 4.22 0.58 1.0000 3.91 3.92 0.54 3.69 3.69 0.51 4.14 4.14 0.57 4.21 4.22 0.58 1.5000 3.91 3.92 0.54 3.69 3.69 0.51 4.14 4.15 0.57 4.21 4.22 0.58 2.0000 3.92 3.92 0.54 3.70 3.70 0.51 4.15 4.15 0.57 4.22 4.22 0.58 3.0000 3.94 3.94 0.54 3.72 3.72 0.51 4.17 4.17 0.57 4.24 4.24 0.58 4.0000 3.97 3.97 0.55 3.75 3.74 0.52 4.20 4.20 0.58 4.27 4.27 0.59 000 4.00 3.99 0.55 3.78 3.77 0.52 4.23 4.22 0.58 4.30 4.30 0.58 6.0000 4.03 4.02 0.56 3.81 3.80 0.53 4.26 4.25 0.59 4.34 4.33 0.59 8.0000 4.09 4.08 0.57 3.87 3.86 0.53 4.33 4.31 0.60 4.40 4.38 0.60 10.0000 4.15 4.13 0.57 3.93 3.91 0.54 4.39 4.37 0.60 4.46 4.44 0.61 1000 4.28 4.25 0.59 4.07 4.04 0.56 4.53 4.50 0.62 4.59 4.57 0.61 20.0000 4.37 4.35 0.59 4.17 4.14 0.57 4.63 4.60 0.63 4.69 4.67 0.63 TABLE 3.3 Continued

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 104 Energy (MeV) Z PEA Z PI Z R Z PEA Z PI Z R Z PEA Z PI Z R Z PEA Z PI Z R 0.00100 7.66 7.48 1.06 7.41 7.41 1.02 7.71 7.54 1.06 6.99 6.81 0.96 0.00200 7.52 7.52 1.04 7.45 7.44 1.03 7.56 7.56 1.04 6.86 6.86 0.95 0.00300 7.53 7.53 1.04 7.46 7.46 1.03 7.58 7.57 1.04 6.89 6.88 0.95 0.00400 7.54 7.53 1.00 7.47 7.46 0.99 7.58 7.58 1.01 6.90 6.88 0.92 0.00500 7.55 7.52 1.00 7.48 7.45 0.99 7.59 7.57 1.01 6.91 6.87 0.92 0.00600 7.55 7.51 1.00 7.49 7.43 0.99 7.59 7.56 1.01 6.92 6.85 0.92 0.00800 7.56 7.46 1.00 7.49 7.37 0.99 7.60 7.53 1.01 6.93 6.76 0.92 0.01000 7.56 7.38 1.00 7.49 7.27 0.99 7.60 7.47 1.01 6.93 6.62 0.92 0.01500 7.55 7.03 1.00 7.48 6.84 0.99 7.60 7.21 1.00 6.92 6.07 0.92 0.02000 7.51 6.56 0.98 7.43 6.3 0.97 7.57 6.86 0.99 6.85 5.46 0.90 0.03000 7.28 5.77 0.95 7.15 5.44 0.93 7.41 6.22 0.97 6.45 4.65 0.84 0.04000 6.80 5.36 0.89 6.58 0 0.86 7.05 5.85 0.92 5.75 4.30 0.75 0.05000 6.23 5.15 0.82 5.93 4.79 0.78 6.60 5.67 0.87 8 4.15 0.67 0.06000 5.76 5 0.76 5.42 4.69 0.72 6.21 5.57 0.82 4.63 4.07 0.61 0.08000 5.24 4.95 0.70 4.88 4.59 0.65 5.74 5.48 0.77 4.20 4.00 0.56 0.10000 4 4.91 0.68 4.68 4.56 0.63 5.56 5.45 0.75 4.05 3.97 0.55 0.15000 4.90 4.88 0.67 4.54 4.52 0.62 5.43 5.41 0.74 3.96 3.95 0.54 0.20000 4.87 4.87 0.67 4.52 4.51 0.62 5.41 5.40 0.74 3.95 3.94 0.54 0.30000 4.86 4.86 0.67 4.50 4.51 0.62 5.39 5.40 0.75 3.93 3.94 0.54 0.40000 4.86 4.86 0.67 4.50 4.50 0.62 5.39 5.39 0.74 3.93 3.94 0.54 0.50000 4.86 4.86 0.67 4.50 4.50 0.62 5.39 5.39 0.74 3.93 3.94 0.54 0.60000 4.86 4.86 0.67 4.50 4.50 0.62 5.39 5.39 0.74 3.93 3.93 0.54 0.80000 4.86 4.86 0.67 4.50 4.50 0.62 5.39 5.39 0.75 3.93 3.93 0.54 1.00000 4.85 4.86 0.67 4.49 4.50 0.62 5.39 5.39 0.74 3.93 3.93 0.54 1.50000 4.85 4.86 0.67 4.49 4.50 0.62 5.39 5.39 0.74 3.93 3.94 0.54 2.00000 4.86 4.87 0.67 4.50 4.51 0.62 5.40 5.40 0.75 3.94 3.94 0.54 3.00000 4.90 4.90 0.67 4.54 4.54 0.62 5.43 5.43 0.75 3.97 3.97 0.54 4.00000 4.94 4.94 0.68 4.58 4.58 0.63 5.47 5.46 0.75 4.00 4.00 0.55 0000 4.99 4.98 0.68 4.63 4.62 0.63 5.51 5.50 0.75 4.04 4.03 0.55 6.00000 3 2 0.69 4.68 4.66 0.65 5.55 5.54 0.77 4.08 4.07 0.56 8.00000 5.13 5.10 0.71 4.77 4.75 0.66 5.64 5.62 0.78 4.16 4.14 0.57 10.00000 5.22 5.18 0.72 4.87 4.83 0.67 5.72 5.69 0.79 4.24 4.21 0.58 10000 5.40 5.36 0.74 6 2 0.69 5.88 5.85 0.81 4.41 4.37 0.60 20.00000 5.54 5.50 0.76 5.20 5.16 0.71 6.00 5.97 0.82 4.53 4.50 0.62 (ii) less but significantly due to coherent scattering which varies as Z 2 3 and (iii) linear Z- dependence of incoherent scattering (intermediate energies) and Z 2 -dependence of pair production (high-energy region > 5 MeV).

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 105 Figure 3.5 and 3.6 shows that, the variation of Z PI, eff and Z PEA, eff with energy is almost similar for all essential scintillators and plasticizers. The Z PI, eff, Z PEA, eff and ratio Z R, eff steadily increase up to 3 10 kev and then they steadily decrease up to 60 150 kev after which they almost remain constant up to 1.25 2 MeV. From 2 MeV, the values increase with increase in energy up to 20 MeV. The variation of Z PEA, eff with energy may be attributed to the relative domination of the partial processes, viz. photoelectric absorption, coherent scattering, incoherent scattering and pair production. At low energies, photoelectric absorption is dominant and hence Z PEA, eff for the energy-absorption is mainly described by Z PEA, eff for this partial process. Similarly, at higher energies Compton scattering and pair production process will be more important than photoelectric absorption and this will affect Z PEA, eff for photon energy-absorption. Hence, at low energies where photoelectric absorption dominates, Z PEA, eff value is more, and at higher energies where the scattering and pair production process dominates, the Z PEA, eff value is less. Almost, the same behavior is seen for Z R, eff as a function of energy. The present theoretical results are similar to the theoretical results of Shivaramu et al. [9], Shivaramu [25], and Shivaramu and Ramprasath [8]. They have reported similar types of variation of Z PI, eff and Z PEA, eff for substances of dosimetric interest, human organs and tissues, and thermoluminescent dosimetric compounds. For Anthracene, Stilbene, Naphthalene and Terphenyl the Z PEA,eff is observed to be almost constant in the energy range 1 kev- 10 kev and decreases rapidly from 15 kev to 200 kev then after it remains constant up to 2 MeV and then again increases steadily up to 20 MeV. For PPO, Butyl PBD and PBD the Z PEA,eff increases slowly from 1 kev to 8 kev and then decreases rapidly up to 150 kev after that it remains constant up to 2 MeV. Above 3 MeV, the value increases with increase in energy up to 20 MeV.

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 106 The variation of Z PEA,eff with energy confirms the dominance of different processes, that is photoelectric absorption, compton scattering, pair production (Nuclear field and electric field). It is observed that the variation in Z PEA,eff also depends upon relative proportion and the range of atomic numbers of the elements of which scintillators is composed. The PPO, Butyl PBD and PBD consisting of (C, H, O and N) more elements compared to Anthracene, Stilbene, Naphthalene and Terphenyl (CH) because of which the change of effective atomic number for photon energy absorption with energy is more. The energy dependence of K a is plotted in Fig. 3.8. The variation of Kerma with energy is almost same for all organic scintillators. The Kerma value decreases for all scintillators from 1 kev to 20 kev then increases sharply up to 200 kev. From 300 kev to 2 MeV it remains constant and then gradual decreases up to 20 MeV. The significant differences exist among Z PEA,eff and Z PI,eff in the energy range 6-100 kev for all organic scintillators. The maximum difference is observed at 30 kev for all the scintillators studied. A maximum difference of 21%, 25.5%, 23.4%, 23%, 22%, 25% and 21% is observed for Anthracene, Stilbene, Naphthalene, Terphenyl, PPO, Butyl PBD and PBD respectively. The substantial change occurs between Z PEA,eff and Z PI,eff which represents the absorbed dose, it is preferable to use Z PEA,eff instead of Z PI,eff in medical radiation dosimetry for the calculation of absorbed dose in radiation therapy. 3.4. Conclusions 1) The effective atomic numbers and the effective electron densities of scintillators and plasticizers have been calculated for total and partial photon interaction process in the wide energy region from 1 kev to 100 GeV using the WinXCom program and a comprehensive and consistent set of formulas derived from first principles, which are valid for all types of materials and for all photon energies greater than 1 kev.

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 107 2) The maximum values of Z eff and N e, eff are found in the low-energy range, where photoelectric absorption is the main interaction process. The minimum values of Z eff and N e, eff are found at intermediate energies, where Compton scattering is dominant. In this case, Z eff is equal to the mean atomic number of the scintillators and plasticizers calculated from its chemical formula. 3) The variation of effective atomic number with energy for total photon interaction shows the dominance of different interaction processes in different energy regions. From1 to 8 kev Z eff is almost constant for all plasticizers then onwards, there is sharp decrease in Z eff with energy up to 150 kev, showing that contribution of scattering processes increases which decreases Z eff. From 150 kev to 3 MeV, Z eff is almost independent of energy. This may be due to the dominance of incoherent scattering in this region. From 3 MeV to 100 MeV, there is regular increase in Z eff with photon energy. This characteristic is due to sharing of incoherent scattering and pair production. 4) The Z eff and N e, eff values calculated in the present work are compared with the values obtained from other available methods and the single-values provided by the XMuDat program. Generally a good agreement is observed among the present values and the other values. However, the single values of the effective atomic number and the electron density provided by the XMuDat program are found to be unrelated. The users of XMuDat should be aware that, it calculates Z eff, XMuDat and N e, XMuDat based on two different assumptions, i.e. Z eff, XMuDat and N e, XMuDat have been calculated assuming that photoelectric absorption and Compton scattering are the main interaction process, respectively.

Studies on Z eff and N e,eff of some organic scintillators and plasticizers 108 5) The effective atomic numbers for photon energy-absorption, Z PEA, eff, for photon interaction, Z PI, eff, and the ratio, Z R, eff have been calculated for essential scintillators and plasticizers using the tabulated data of the mass energy-absorption and mass attenuation coefficient in the photon-energy range from 1 kev to 20 MeV. 6) The significant differences exist among Z PEA, eff and Z PI, eff in the energy range 6-100 kev for all organic scintillators. It has been shown that the substantial change occurs between Z PEA, eff and Z PI, eff for scintillators is insignificant (1%) at photon energies <6 kev and > 100 kev. The use of Z PEA, eff is important in dealing with the absorbed dose due to photons of range 6 100 kev. 7) The Kerma value decreases for all organic compounds from 1 kev to 20 kev then increases sharply up to 200 kev. From 300 kev to 2 MeV it remains constant and then gradual decreases up to 20 MeV. 8) It is expected that the new results on Z eff and N e,eff of selected plasticizers presented here will be useful in view of their importance in strengthening the concrete, which will help in the radiation shielding.

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