Applied Radiation and Isotopes 95 (2015) 208–213

Contents lists available at ScienceDirect

Applied Radiation and Isotopes journal homepage: www.elsevier.com/locate/apradiso

Analysis of the factors that affect photon counts in Compton scattering Guang Luo n, Guangyu Xiao College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 400047, PR China

H I G H L I G H T S

   

Compton scattering experiments of some alloy series and powder mixture series are explored. The influence of electron density is researched in terms of atom and lattice constants. The influence of attenuation coefficient is discussed. The active degree of electrons is discussed detailedly based on DFT theory.

art ic l e i nf o

a b s t r a c t

Article history: Received 13 January 2014 Received in revised form 11 October 2014 Accepted 17 October 2014 Available online 30 October 2014

Compton scattering has been applied in a variety of fields. The factors that affect Compton scattering have been studied extensively in the literature. However, the factors that affect the measured photon counts in Compton scattering are rarely considered. In this paper, we make a detailed discussion on those factors. First, Compton scattering experiments of some alloy series and powder mixture series are explored. Second, the electron density is researched in terms of atom and lattice constants. Third, the factor of attenuation coefficient is discussed. And then, the active degree of electrons is discussed based on the DFT theory. Lastly, the conclusions are made, that the factors affecting Compton scattering photon counts include mainly electron number density, attenuation coefficient and active degree of electrons. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Compton scattering Electronic structure Electron number density Attenuation factor

1. Introduction Compton scattering (Compton, 1923) refers to an interaction of an X- or gamma ray (i.e., a photon) with an electron of a scatterer, in which the wavelength of that ray will become longer because the X- or gamma ray will undergo partial energy loss. Based on the conservation of energy and momentum, one can write the formula for the frequency and wavelength of a Compton-scattered photon (Venugopal and Bhagdikar, 2013; Williams, 1977). For a certain number of incident photons, the scattered-photon counts in a certain direction at a scattering angle of θ are related to the Compton scattering frequency in a unit volume. As stated in Ref. Sharaf (2001), the scattered-photon counts are proportional to the number of electrons per unit volume of the scatterer, i.e., the scattered-photon counts are proportional to the electron density 



ΔN dσ ðθ Þ ¼ ϕ0 f 1 f 2 dΩ ΔV

KN

Sðq; ZÞ ρe Z

ð1Þ

where ϕ0 is the photon flux of the incident beam, Z is the atomic n

Corresponding author. E-mail address: [email protected] (G. Luo).

http://dx.doi.org/10.1016/j.apradiso.2014.10.015 0969-8043/& 2014 Elsevier Ltd. All rights reserved.

number, ρe is the electron density, f 1 is the attenuation factor of the incident beam, f 2 is the attenuation factor of the scattered beam, ΔN is the scattered-photon counts, ΔV is the volume of the scatterer, ðdσ ðθÞ=dΩÞKN is the Klein–Nishina differential cross section (Klein and Nishina, 1929) at the scattering angle, and Sðq; ZÞ is the incoherent atomic scattering function that accounts for the effects of the electron binding energy; here, q is the momentum transfer of the photon, the value of which can be considered to be Z for sufficiently large θ (Hubbell et al., 1975; Hubbell and Øverbø, 1979). Based on the description provided by Eq. (1), Compton scattering has been applied in a variety of fields; its applications lie chiefly in industry, for non-destructive evaluation, and in medical imaging, for measurements of the density and structure of scatterers (body structures) (Harding and Harding, 2010; Masuji et al., 2010; Yadav et al., 2005; Vetter et al., 2011; McFarlane et al., 2000). The factors that affect Compton scattering have been studied extensively in the literature. However, the factors that affect the measured photon counts in Compton scattering are rarely considered. In this paper, these factors shall be explored. Based on multiple Compton-scattering experiments, the study group determined several such factors, including the electron number density, the attenuation coefficient and the active degree of electrons. The remainder of the paper is organized as follows. In Section 2, we

G. Luo, G. Xiao / Applied Radiation and Isotopes 95 (2015) 208–213

introduce the preparation of the samples, which included a series of samples of Fe–Cu alloys and their X-ray diffraction spectra as well as two series of samples of Fe–Cu and Fe–C powder mixtures. In Section 3, we present the Compton-scattering experiments performed on those samples. In Section 4, the factors affecting the Compton-scattered photon counts are discussed in detail by considering the relation between the scattered-photon counts per unit mass and the contents of the scatterer series (alloys and powder mixtures). Conclusions are presented in the final section.

209

For the Fe–C powder-mixture series, the fitted line for the scattering angle of 601 is described by the equation

ΔN=Δm ¼ 472:45 x þ 310:25

ð6Þ

and the corresponding equation for the scattering angle of 1201 is

ΔN=Δm ¼ 588:77 x þ 285:36

ð7Þ

When our present experimental results are compared with the preliminary results of our research, it is found that the observed linear relation between ΔN=Δm and x is consistent with the predictions of Refs. Luo et al. (2012) and Luo and Hu (2013). In the

2. Samples 2.1. Preparation of the series of Fe–Cu alloys First, Fe–Cu powder mixtures with Cu contents of 0%, 2%, 4%, 6%, 8%, and 10% were poured into six different corundum crucibles (to reduce the impurity content introduced during melting) and melted in a vacuum induction furnace. Then, the molten metal liquids were poured into six prepared molds for shaping and allowed to cool naturally in air. Finally, the surface oxide layer was removed from each ingot, and the ingots were processed into a series of standard alloy samples with dimensions of Φ15 mm  7 mm. 2.2. Preparation of the series of Fe–Cu and Fe–C powder mixtures The Cu mass contents of the Fe–Cu powder mixture series were 0%, 2%, 4%, 6%, 8% and 10%. The C mass contents of the Fe–C powder mixture series were also 0%, 2%, 4%, 6%, 8% and 10%. First, 12 cylindrical molds of 30 mm in diameter were prepared by quenching and tempering 40Cr steel. Then, the powder samples were poured into individual molds, placed one at a time into a WE-60 hydraulic pressure universal testing machine and pressed at a pressure of 3.5  10 MPa to form block cylindrical specimens of 10 mm in thickness.

Fig. 1. The relation between ΔN=Δm and Cu content x of Fe–Cu alloy series.

3. Compton-scattering experiments and results In the experiments, Compton-scattering devices with radiation sources of 137Cs, at an energy of 662 keV, were used. The photons were collimated before they reached the sample scatterer. Measurements of the scattered photons were conducted using a highresolution (less than 9% in the investigated energy range) NaI crystal detector, the voltage on which was set to a high value of 600 V. The collected photon events were recorded by a computer. The scattering angle θ was set to 601 and 1201. For each test, the scattered photons were collected for a duration of 600 s. The test was repeated twice for each sample. Our results are presented in Figs. 1–3, where the straight lines were fitted using the least-squares method and ΔN=Δm is the scattered photon counts per unit mass. From Figs. 1–3, for the Fe–Cu alloy series, the fitted line for the scattering angle of 601 is described by the equation

ΔN=Δm ¼ 0:27 x þ 207:51

Fig. 2. The relation between ΔN=Δm and Cu content x of Fe–Cu binary powder mixture series.

ð2Þ

and the corresponding equation for the scattering angle of 1201 is

ΔN=Δm ¼ 43:16 x þ 138:18

ð3Þ

For the Fe–Cu powder-mixture series, the fitted line for the scattering angle of 601 is described by the equation

ΔN=Δm ¼ 215:04 x þ 165:30

ð4Þ

and the corresponding equation for the scattering angle of 1201 is

ΔN=Δm ¼ 230:01 x þ 247:04

ð5Þ

Fig. 3. The relation between ΔN=Δm and C content x of Fe–C binary powder mixture series.

210

G. Luo, G. Xiao / Applied Radiation and Isotopes 95 (2015) 208–213

references cited above, for a Cu–Ni powder-mixture series, the fitted line for a scattering angle of 601 is described by the equation

ΔN=Δm ¼ 126:20 x þ 323:08

ð8Þ

and the corresponding equation for a scattering angle of 1201 is

ΔN=Δm ¼ 106:50 x þ 293:52

ð9Þ

For a Cu–Ni alloy series, the fitted line for a scattering angle of 601 is described by the equation

ΔN=Δm ¼ 10:96 x þ 188:07

ð10Þ

series (or a Cu atom is replaced by an Ni atom in a Cu–Ni powdermixture (or alloy) series), the change in the electron density of the Fe–C powder-mixture (or alloy) series will be much larger than that of the Fe–Cu powder-mixture (or alloy) series. Moreover, the change in the number of counts of Compton-scattered photons for the Fe–C powder-mixture series will also be greater than that for the Fe–Cu powder-mixture (or alloy) series (or that for the Cu–Ni powder-mixture (or alloy) series), which explains why the slope of the data presented in Fig. 3 is steeper than those of the other figures.

and the corresponding equation for a scattering angle of 1201 is

ΔN=Δm ¼ 10:43 x þ 123:12

ð11Þ

Furthermore, several differences are apparent upon careful analysis: (i) according to Fig. 1, for the Fe–Cu alloy series, the Compton-scattering photon counts per unit mass change very little with increasing Cu content; the values merely fluctuate within a narrow range. A comparison between the Fe–Cu alloy series and a Cu–Ni alloy series (McFarlane et al., 2000; Luo et al., 2012) reveals that the slopes of the two lines are different. (ii) According to Figs. 2 and 3, for the powder-mixture samples, the Compton-scattered photon counts per unit mass increase with increasing Cu content. It is worth noting that the slope of the line for the Fe–C powder-mixture series is steeper than that for the Fe–Cu powder-mixture series.

4. Analysis of the factors affecting the results It is meaningful to analyze the factors that can lead to differences among the investigated scatterers. It can be observed from Eq. (1) that the attenuation coefficients and electron densities of the scatterers vary with their contents, and these two parameters influence the photon counts measured in Compton scattering. As is evident from the experimental results, the slopes of the lines are significantly different between the alloy and powder-mixture series prepared with the same composition and contents. This finding indicates that the structure of the scatterer also affects the Compton-scattered photon counts. These factors affecting Compton scattering will be discussed in detail in the following.

4.1.2. Electron number density related to lattice constants Using an XRD-6000 X-ray diffractometer produced by the Shimadzu Corporation, the X-ray diffraction (XRD) energy spectra of the samples were measured. The measurement conditions were as follows: copper target, a tube voltage of 40 kV, a tube current of 20 mA, and a scan range of 40–1401 in continuous-scanning mode. The results are presented in Figs. 4 and 5. Fig. 4 presents the XRD spectra of the Cu–Ni alloy series. With increasing Ni content, the diffraction peaks shift toward higher angles θ; the positions of peaks in the same crystal plane range from the θ values of the diffraction peaks in Cu to those in Ni. In addition, the diffraction intensity of the same crystal plane is different for different samples, in some cases even approaching zero—for example, the 220 crystal plane of the Cu60Ni40 sample (where Cu60Ni40 indicates that the Cu content of the Cu–Ni alloy is 60%) and the 222 crystal plane of Cu40Ni60. This finding demonstrates that as the Ni content increases in the Cu–Ni alloy series, different orientations arise. Fig. 5 presents the XRD spectra of the Fe–Cu alloy series. With increasing Cu content, the X-ray diffraction spectra of samples become similar, and the position and intensity of the diffraction peak do not change significantly. The reason for this behavior is that the solubility of Cu in α-Fe is very small (the solid solution of Cu in α-Fe has already reached saturation), and as the Cu content is increased far beyond the limits of solubility, the structure of the α-Fe essentially does not change. In addition to the α-Fe diffraction line, there are a small number of Cu diffraction lines, which increase in intensity with increasing Cu content.

4.1. The electron number density 4.1.1. Electron number density related to atomic species According to Eq. (1), Compton-scattered photon counts are proportional to the electron number density of the scatterer, which can be written as

ρe ¼

ρZN 0

ð12Þ

A

where ρ is the mass density of the scattering body, N 0 is Avogadro's number, A is the atomic weight of the scattering body, and Z is the atomic number of the scattering body. Using Eq. (12), one can easily determine the electron number densities of C, Fe, Ni and Cu; these values are presented in Table 1. It can be observed from Table 1 that if an Fe atom is replaced by a C atom in the Fe–C powder-mixture series and an Fe atom is replaced by a Cu atom in the Fe–Cu powder-mixture (or alloy)

Fig. 4. The spectrums of Cu–Ni alloy with XRD (Note: Cu denotes the pure copper, Cu80Ni20 denotes Cu–Ni alloy which contain 80% Cu and 20% Ni, and so on).

Table 1 The electron number density and attenuation coefficient of C, Fe, Ni and Cu. Element 23

3

Electron number density (  10 /cm ) Attenuation coefficient (  10  2 cm2/g) (Saloman and Hubbell, 1986; Saloman et al., 1988)

C

Fe

Ni

Cu

6.803 8.047

22.028 7.472

25.504 7.654

24.449 7.319

G. Luo, G. Xiao / Applied Radiation and Isotopes 95 (2015) 208–213

Based on the X-ray diffraction data, our group calculated the lattice constants of the two alloy series via extrapolation; the results are presented in Figs. 6 and 7, where the α-Fe lattice constant of 2.8662 Å was obtained from Ref. Abrahamson and Lopata (1966). As is evident from these two figures, the lattice constant increases with increasing Cu content in the Cu–Ni alloy series. This finding indicates that the unit-cell volume increases with increasing Cu content, and the electron number density simultaneously decreases gradually. However, in the Fe–Cu alloy series, the lattice constant does not change substantially with an increase in the Cu content. The small differences in the lattice constants in the Fe–Cu alloy series are comparable to the experimental error, indicating that the unit-cell volume does not change substantially with increasing Cu content in the Fe–Cu alloy series, and consequently, the electron number density also does not change significantly. The results obtained in the Compton-scattering experiments performed on the Cu–Ni and Fe–Cu alloy series can be summarized as follows: as the Cu content increases in the Cu–Ni alloy series, the lattice constant increases, and the unit-cell volume also increases, leading to a reduction in the electron density. Therefore, the Compton-scattered photon counts decrease with increasing Cu content in the Cu–Ni alloy series. However, in the Fe–Cu alloy series, the lattice constant does not substantially change with an increase in the Cu content. Therefore, the Compton-scattered photon counts do not substantially change with increasing Cu content in the Fe–Cu alloy series. These observations characterize the influence of the electron density on the number of Comptonscattered photon counts.

4.2. Attenuation coefficient According to Eq. (1), the number of Compton-scattered photons is proportional to f1 and f2 (where f1 is the attenuation factor of the incident beam and f2 is the attenuation factor of the scattered beam), and the attenuation coefficient of the scatterer is related to the energy of the incident light. The attenuation coefficients for the case in which the energy of the incident photons is 662 keV are presented in Table 1. In this table, with the exception of C, there is no striking difference among the attenuation coefficients of the elements of interest. Therefore, if an Fe atom is replaced by a C atom in the Fe–C powder mixture series, the same conclusion as that presented in Section 4.1 can be deduced, i.e., the change in the

Fig. 6. The lattice constant in Cu–Ni alloy series.

Fig. 5. The spectrums of Fe–Cu alloy with XRD (Note: Fe denotes the pure iron (α-Fe), Fe98Cu2 denotes Fe–Cu alloy which contain 98% Fe and 2% Cu, and so on).

Fe

211

Fig. 7. The lattice constant in Fe–Cu alloy series.

Cu(1)Fe(1) Fig. 8. The structure of Fe–Cu alloy after optimization.

Cu

212

G. Luo, G. Xiao / Applied Radiation and Isotopes 95 (2015) 208–213

number of Compton-scattered photons for the Fe–C powdermixture series will be greater than that for the Fe–Cu powdermixture (or alloy) series (or that for a Cu–Ni powder-mixture (or alloy) series), which explains why the slope of the data presented in Fig. 5 is steeper than those of the other figures. 4.3. Electronic structure It is well known that the cross section for Compton scattering represents the probability of Compton scattering and that this cross section can be affected by bound electrons in the Comptonscattering system (East and Lewis, 1969; Bergstrom et al., 1993; Ribberfors, 1975). The probability of scattering has a direct influence on the number of Compton-scattered photons. Therefore, the bound/unbound status of the electrons is also a very important factor in Compton scattering, and to discuss bound electrons means to discuss the electronic structure of the scattering body. Upon the comparison of the slope observed for the Fe–Cu powder-mixture series with that for the Fe–Cu alloy series, it is evident that these slopes are significantly different. The electronic structure of the scatterer plays an important role in determining this difference. To analyze its influence, the detailed electronic structure of each scattering body was calculated using the density functional theory (DFT) method, which begins by directly solving the basic quantum mechanics equations associated with the atomic configuration. DFT is a computational quantum mechanical method that is used in physics, chemistry and materials science to investigate the electronic structures of many-body systems, particularly atoms, molecules, and condensed phases. Because it does not rely on any empirical parameters, it offers high accuracy and predictive power. It is among the most popular and versatile Table 2 Fe, Cu(1)Fe(1), Cu atomic populations. Species

Ion

s

p

d

f

Total

Charge(e)

Fe Fe Fe Cu Cu Cu Cu Cu

1 2 1 1 1 2 3 4

0.64 0.64 0.41 0.88 0.52 0.52 0.52 0.52

0.67 0.67 0.45 0.93 0.78 0.78 0.78 0.78

6.69 6.69 6.74 9.59 9.71 9.71 9.71 9.71

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

8.00 8.00 7.61 11.39 11.00 11.00 11.00 11.00

0.00 0.00 0.39  0.39 0.00 0.00 0.00 0.00

methods available in condensed-matter physics, computational physics, and computational chemistry (Segall and Lindan, 2002; Burke et al., 2005; Kohn and Sham, 1965). (i) Optimized geometric structure: Through optimization, the relative electronic-structure parameters for an alloy can be calculated easily, although the structure of the Fe–Cu alloy series is very complex. The solid solubility of an Fe–Cu alloy is finite and very low for both Cu in Fe and Fe in Cu. The structure of the alloy consists predominantly of an α-Fe phase with a body-centered cubic structure and a Cu phase with a face-centered cubic structure when the Cu content of the Fe–Cu alloy is 0%, 2%, 4%, 6%, 8% or 10% at room temperature (Luo and Hu, 2013). To investigate the electronic structures of Fe–Cu alloys while accounting for the available computational capacity, it was assumed that at higher Cu contents, Cu atoms replaced Fe atoms in the body-centered cubic structure, similar to the structure depicted in Fig. 8. The optimized structure for the Fe–Cu alloys is depicted in Fig. 8; this structure was used to calculate the electronic structures of the Fe–Cu alloys. (ii) Electronic structure and density of states (DOS): Table 2 presents the electron populations of the Fe–Cu alloy series. The calculated results indicate that the electrons of the Fe atom transition from the 4s orbital to the 3d and 4p orbitals, whereas the electrons of the Cu atom transition from the 3d and 4s orbitals to the 4p orbital, i.e., the electrons transition toward the 3d and 4p orbitals (the outer orbitals). This indicates that the electrons become freer. Based on the atomic populations summarized in Table 2, an increase in the Fe content of the metal or alloy will increase the active degree of electrons in the system. Figs. 9 and 10 present the DOSs of Cu, Cu(1)Fe(1) and Fe, where the dotted line represents the Fermi surface. It can be observed from these figures that as the Fe content increases in Cu, Fe–Cu alloy and Fe, the DOSs of the s, p and d orbitals of Fe move to the right of the Fermi surface. This observation indicates that the number of free electrons is reduced with increasing Cu content. The same conclusion can also be reached by considering the sum of the DOSs of the s, p and d orbitals in Cu, Fe–Cu alloy and Fe. (iii) Discussion: Through the analysis of the electronic structure of Fe–Cu alloys, we conclude that with increasing Cu content, the active degree of the valence electrons in an Fe–Cu alloy

Fig. 9. (a) The DOSs of the p orbital in Cu, Fe and Fe–Cu alloy. (b) The DOSs the of s orbital in Cu, Fe and Fe–Cu alloy.

G. Luo, G. Xiao / Applied Radiation and Isotopes 95 (2015) 208–213

213

Fig. 10. (a) The DOSs of the d orbital in Cu, Fe and Fe–Cu alloy. (b) The sum of the DOSs of the s, p, d orbital in Cu, Fe and Fe–Cu alloy.

decreases. This freedom is related to the probability of Compton scattering. The more weakly the electrons are bound, the more probable it is that Compton scattering will occur. Therefore, it is predicted that for a given incident photon flux, as the freedom of the electrons in the scatterer decreases, Compton scattering will become less likely to occur, and the scattered-photon counts received by the detector will decrease. 5. Conclusions Based on the authors' preliminary work, this paper presents a further study of the relation between the number of scattered photons per unit mass of the scatterer and the contents of certain alloy and powder-mixture scatterers. This relation was found to be linear. Furthermore, the slope of this linear relation is different for different series of scatterers. Several factors, including electron density, attenuation coefficient and the active degree of electrons in the scatterer, are responsible for these differences. These factors play different roles in the Compton scattering for different types of scatterers. For an Fe–C powder-mixture series, the attenuation coefficient was the primary factor affecting the scattering, whereas for Fe–Cu and Cu–Ni powdermixture series, both the attenuation coefficient and the electron density played significant roles. For an Fe–Cu alloy series, the electron density and the active degree of electrons played significant roles. In addition to the factors discussed above, multiple scattering is also a very important factor. However, because of the limitations of the experimental conditions in our studies, it was not possible to investigate multiple Compton scattering. In future work, the experimental conditions will be improved to allow for such investigations.

Acknowledgments The authors are grateful for the financial support of the Innovation Team of Chongqing Universities of Chongqing Municipal Education Commission, Chongqing, China (Grant no. 201031); the Natural Science Foundation Project of CQ CSTC (Grant no. cstc2012jjA50018); the Basic Research of Chongqing Municipal Education Commission (Grant no. KJ120631); and the Students' Innovative Entrepreneurship Training Program of Chongqing Normal University (Grant no. 201210637036). The authors are also grateful for the support of the Optical Engineering Key Laboratory of Chongqing City.

References Abrahamson, E.P., Lopata, S.L., 1966. The lattice parameters and solubility limits of alpha-iron as affected by some binary transition-element additions. Ref. Trans. Metall. Soc. AIME 236, 76–87. Bergstrom Jr., P.M., Surić, T., Pisk, K., et al., 1993. Compton scattering of photons from bound electrons: full relativistic independent-particle-approximation calculations. Phys. Rev. A 48, 1134–1162. Burke, K., Werschnik, J., Gross, E.K.U., 2005. Time-dependent density functional theory: past, present, and future. J. Chem. Phys. 123 (6), 062206. Compton, A.H., 1923. A quantum theory of the scattering of X-rays by light elements. Phys. Rev. 21, 483–502. East, L.V., Lewis, E.R., 1969. Compton scattering by bound electrons. Physica 11 (44), 595–613. Harding, G., Harding, E., 2010. Compton scatter imaging: a tool for historical exploration. Appl. Radiat. Isot. 68, 993–1005. Hubbell, J.H., Øverbø, I., 1979. Relativistic atomic form factors and photon coherent scattering cross-sections. J. Phys. Chem. Ref. Data 8, 69. Hubbell, J.H., Veigele, W.J., Briggs, E.A., et al., 1975. Atomic form factors, incoherent scattering functions, and photon scattering cross sections. J. Phys. Chem. Ref. Data 4 (3), 471. Klein, O., Nishina, Y., 1929. Tber die streuung von strahlung durch freie elektronen nach der neuen relativistischen quantendynamik von Dirac. Z. Phys. 52, 853. Kohn, W., Sham, L.J., 1965. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 (4), A1133. Luo, G., Hu, X.Q., 2013. Studies on Compton scattering of the Fe–C, Fe–Cu and Ni–Cu binary powder mixtures. Appl. Radiat. Isot. 79, 114–117. Luo, G., Hu, X.Q., Xiao, G.Y., et al., 2012. Influence of electronic structure on Compton scattering through comparing Cu–Ni alloys with Cu–Ni powder mixtures. Acta Metall. Sin. (Engl. Lett.) 2 (25), 55–64. Masuji, R., Watanaben, K., Yamazaki, A., et al., 2010. A study on electron density imaging using the Compton scattered X-ray CT technique. Nucl. Instrum. Methods A 09, 106–110. McFarlane, N.J.B., Bull, C.R., Tillett, R.D., et al., 2000. The potential for Compton scattered X-rays in food inspection: the effect of multiple scatter and sample inhomogeneity. J. Agric. Eng. Res. 75, 265–274. Ribberfors, Roland, 1975. Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states. Phys. Rev. B (Solid State) 15 (12), 2067–2074. Saloman, E.B., Hubbell, J.H., 1986. X-ray attenuation coefficients (total cross sections): comparison of the experimental data base with the recommended values of Henke and the theoretical values of Scofield for energies between 0.1–100 keV. Natl. Bur. Stand. Inf. Rep. 86, 3431. Saloman, E.B., Hubbell, J.H., Scofield, J.H., 1988. X-ray attenuation cross sections for energies 100 eV to 100 keV and elements Z ¼ 1 to Z ¼92. At. Data Nucl. Data Tables 38, 1. Segall, M.D., Lindan, P.J., 2002. First-principles simulation: ideas, illustrations and the CASTEP code. J. Phys.: Condens. Matter 14 (11), 2717. Sharaf, J.M., 2001. Practical aspects of Compton scatter densitometry. Appl. Radiat. Isot. 54, 801–809. Venugopal, V., Bhagdikar, P.S., 2013. de Broglie wavelength and frequency of the scattered electrons in Compton effect. Phys. Educ. 29 (1), 35 (03). Vetter, K., Chivers, D., Plimley, B., et al., 2011. First demonstration of electrontracking based Compton imaging in solid-state detectors. Nucl. Instrum. Methods A 652, 599–601. Williams, B, 1977. Compton Scattering. McGraw-Hill, New York p. P34. Yadav, J.S., Savitri, S., Malkar, J.P., 2005. Near room temperature X and gamma-ray spectroscopic detectors for future space experiments. Nucl. Instrum. Methods A 552, 399–408.

Analysis of the factors that affect photon counts in Compton scattering.

Compton scattering has been applied in a variety of fields. The factors that affect Compton scattering have been studied extensively in the literature...
1MB Sizes 2 Downloads 4 Views