- Email: [email protected]
On the angular dependence of L X-ray intensity ratios for Au following photoionization
Radiation Physics and Chemistry 133 (2017) 28–30
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
On the angular dependence of L X-ray intensity ratios for Au following photoionization
MARK
⁎
Xing Wang , Zhongfeng Xu, Ying Zhang School of Science, Xi’an Jiaotong University, Xi’an 710049, China
A R T I C L E I N F O
A BS T RAC T
Keywords: X-ray Angular distribution Photoionization Anisotropy parameter
The typical L X-ray spectra for Au induced by 15.9 keV photons have been measured at emission angles ranging from 110° to 150° at intervals of 10°. The intensities of Lα, Lβ1, Lβ2 and Lγ1 X-rays are obtained and the angular dependence of L X-ray intensity ratios is determined experimentally. It is found that the Lβ1, Lβ2 and Lγ1 X-rays present isotropic emission, while the measured Lα X-rays show anisotropic distribution spatially. The unexpected isotropic emission of Lβ2 X-rays is explained with Coster-Kronig vacancy transfer process. Moreover, the anisotropy parameter for Lα X-ray emission is deduced.
1. Introduction The inner-shell ionization of atom has been widely investigated for several decades (Raza et al., 2013; Mei, 2012; Wang, 20142014; Zhou, 2013; Wang et al., 2015; Bambynek, 1972; Zhou et al., 2013; Wang, 2013). The de-excitation of vacancy could accompany with the process of radiation transition-giving rise to typical X-rays emission or nonradiation transition-giving rise to Auger electron emission (Bambynek, 1972). In recent years, the study of characteristic X-ray emission focuses on the multiple-ionization effect (Wang and Zhao, 2012; Horvat et al., 2008; Wang, 2012; Wang, 20142014) and the alignment of vacancy state produced in collision process (Han et al., 2009; Salem and Stöhlker, 2013). In addition, there is a well-known analytical application to determine the species of elements in materials with Particle Induced X-ray Emission (PIXE) in geological and chemical fields (Šmit, 2005; Romo-Kröger, 2010; Johansson et al., 1970; Li, 1992; Maenhaut and Dereu, 1980; J.L. Campbell, J.A. Cookson, PIXE analysis of thick targets. Anal. Thick Targets. 3, 1984, pp. 185–197.). Consequently, it becomes more and more important to study the angular dependence of characteristic X-ray emission by measuring the typical X-ray intensity in photoionization (Raza et al., 2013; Han et al., 2009). In theory, there are two contrary viewpoints that predict on the alignment for vacancy state produced in collision process. One view predicts that all vacancy states produced in impact ionization with total angular momentum J≥1/2 are unaligned and consequently the emitted X-rays (or Auger electrons) have isotropic emission and are unpolarized (Cooper and Zare, 1969); While the other view predicts that vacancies created in impact ionization with J > 1/2 are aligned and X⁎
ray (or Auger electron) emission following the vacancy degradation is anisotropic and polarized (Flügge et al., 1972). Furthermore, the differential intensity dI(θ) of the X-rays at emission angle θ is given by Berezhko and Kabachnik (Berezhko and Kabachnik, 1977).
dI (θ ) I = 0 [1 + βP2 (cosθ )]. dΩ 4π
(1)
1 (3cos (2θ ) + 1). 4
(2)
P2 (cosθ ) =
Here I0 is the total X-ray intensity integrated over 4π solid angle; dΩ is the solid angle subtended by the detector at the target; β is the anisotropy parameter of a particular X-ray line; P2(cosθ) is the secondorder Legendre polynomial. The anisotropy parameter β can be derived by the measurement of differential intensity dI(θ). A lot of experiments have been implemented to investigate the alignment of vacancy states in inner-shell by the measurement of angular distribution or polarization of the emitted X-rays (Raza et al., 2013; Han et al., 2009; Salem and Stöhlker, 2013; Özdemir, 2011; Kumar, 2010; Tartari, 2003; Gonzales et al., 2012). It is found that the degradation of vacancy states with J > 1/2 presents an anisotropic Xray emission (Raza et al., 2013; Han et al., 2009; Salem and Stöhlker, 2013; Özdemir, 2011); While some other researchers have observed that the X-ray emission exhibits isotropic pattern via the de-excitation of vacancy states with J > 1/2 (Kumar, 2010; Tartari, 2003; Gonzales et al., 2012). In this work, the typical L X-ray spectra for Au are measured at emission angles ranging from 110° to 150° with 15.9 keV X-ray impact. The angular dependence of L X-ray intensity ratios is reported. In
Corresponding author. E-mail address: [email protected] (X. Wang).
http://dx.doi.org/10.1016/j.radphyschem.2016.12.007 Received 27 May 2016; Received in revised form 16 December 2016; Accepted 18 December 2016 Available online 21 December 2016 0969-806X/ © 2016 Elsevier Ltd. All rights reserved.
Radiation Physics and Chemistry 133 (2017) 28–30
X. Wang et al.
Fig. 1. Detail geometry (left) and nuclear instrument system (right) of experimental setup. The emission angle θ is depicted here.
typical X-ray emission of Au target at incident energy of 15.9 keV. The geometry of experimental apparatus is shown in Fig. 1. The X-ray tube (Mini-X, AMPTEK Inc., USA), which works with 0.75 µm silver target, is utilized as the primary radiation source. The bremsstrahlung photons generated from X-ray tube are collimated by a Zr tube with inside diameter of 2 mm. The collimated photons bombard on a secondary Zr target. The spectrum of emitted characteristic K X-rays of Zr can be considered as a single and symmetric peak centered at 15.9 keV. According to both theories (Cooper and Zare, 1969; Flügge et al., 1972), the K X-ray emission should be isotropic and unpolarized (filling of vacancy in K1 shell, j=1/2). The energy of 15.9 keV is consistent with the calculation of the weighted average of Zr Kα and Kβ X-ray energies considering their intensity ratio (Thompson, 2001). The Au sample with a thickness of 77.2 mg cm−2 is irradiated by the collimated fluorescent X-rays produced from the secondary target. At last, an X-ray detector (Type: XR-100SDD; Specification: silicon drift detector; Company: Amptek in USA) is employed to record the characteristic X-rays emission from the target at emission angles ranging from 110° to 150°. The X-ray detector is movable and other parts are fixed in the arrangement. A resolution about 125 eV at 5.9 keV can be achieved by the detector with an active crystal size of 25 mm2. The count of incident X-rays per second and per unit area can be determined by mounting the detector at the position of sample.
Fig. 2. Typical L X-ray spectra for Au at emission angle θ=130°.
3. Results and discussion Fig. 2 presents the measured typical L X-ray spectra for Au target at emission angle of 130°. It can be seen that the peak positions for Lα1 (L3M5) and Lα2 (L3M4) X-rays are too close and cannot be distinguished. While the typical Lα (L3M4,5), Lβ1 (L2M4), Lβ2 (L3N5) and Lγ1 (L2N4) X-rays of Au are distinguished with multi-peak Gaussian fitting procedure. The emission of Lβ1 (L2M4) X-rays which originate from L2 (j=1/2) subshell are found to be isotropic. Therefore, it is feasible to investigate the angular dependence with the study of typical intensity ratios, I(Lα)/ I(Lβ1), I(Lβ2)/I(Lβ1) and I(Lγ1)/I(Lβ1). The experimental X-ray intensity ratios can be calculated by
Fig. 3. The intensity ratio of I(Lα)/I(Lβ1), I(Lβ2)/I(Lβ1) and I(Lγ1)/I(Lβ1) for Au. The fitting curve is also shown here. Table 1. Experimental L-subshell Coster-Kronig yields fij for Au taken from Ref. (Bambynek, 1972) . f12
f13
f23
0.083
0.644
0.132
N (L i ) ε (L j ) β (L j ) I (L i ) = I (L j ) N (L j ) ε (L i ) β (L i )
(3)
Here N(Li)/N(Lj) is the ratio of the counting rates under the Li (i=α and β2) and Lj (j=β1) peaks. ε (Lj)//ε (Li) is the ratio of the detection efficiency values for Lj and Li X-rays. The self-absorption correction factor β is derived for both Lj and Li separately by the formula (Yalçın et al., 2008).
addition, the anisotropy parameter β is obtained for Lα X-ray emission. 2. Experimental details
βi = The experiment has been carried out to measure the spectra of 29
1 − exp[−(μinc secθ1 + μemt secθ2 ) t ] (μinc secθ1 + μemt secθ2 ) t
(4)
Radiation Physics and Chemistry 133 (2017) 28–30
X. Wang et al.
Here μinc (cm2 g−1) and μemt (cm2 g−1) are the mass absorption coefficients for incident and emitted radiation (Storm and Israel, 1970); t is the mass thickness of target (g cm−2). θ1 and θ2 are the angles of incident photons and emitted X-rays with respect to the normal at the surface of the target (Yalçın et al., 2008). Considering that the counts of measured X-rays are more than 1000 for each peak for Lα, Lβ1, Lβ2 and Lγ1 X-rays, the statistical error is calculated to be 3% (1/(1000)1/2). Combining statistical error (3%) with errors estimated for background subtraction (3%), solid angle (6%) and fitting procedure (4%), the total experimental error of X-ray intensities is less than 11% in this work. The Lβ1 X-rays which originate from initial L2 (2p1/2, j=1/2) subshell are found to have isotropic emission. Simultaneously, the geometrical misalignment can be excluded with the result of isotropic emission of Lβ1 X-rays. The intensity ratios of I(Lα)/I(Lβ1), I(Lβ2)/I(Lβ1) and I(Lγ1)/I(Lβ1) are plotted and presented in Fig. 3. It can be seen that the intensity ratio, I(Lα)/I(Lβ1), shows anisotropic distribution; while the intensity ratios, I(Lβ2)/I(Lβ1) and I(Lγ1)/I(Lβ1), present isotropic distribution. According to Eqs. (Raza et al., 2013; Mei, 2012)., the anisotropy parameter β=0.264 can be deduced for Lα X-rays in this experiment. Lγ1 X-rays originating from L2 subshell (j=1/2) are supposed to have isotropic emission and this is verified in Fig. 3. Unexpectedly, the emission of Lβ2 X-rays originating from L3 subshell (j=3/2), which is supposed to be anisotropic, is found to be isotropic. The phenomena can be understood with the vacancy transfer process. Besides direct ionization in photoionization, the vacancy in L3 subshell can also be produced by vacancy transfer from K or L1,2,3 subshells. The vacancy production cross section for L3 subshell, σ3, can be given by:
σ3 = (σL1 + σK ηKL1)( f13 + f12 f23 ) + (σL2 + σKL2 ) f23 + (σL3 + σK ηKL3)
isotropic. The anisotropy parameter for Lα X-ray emission is deduced to be 0.264. The probability of vacancy production in L3-subshell, σ3, can be affected strongly by the unaligned vacancy states in L1 and L2 subshells. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant Nos. 11375138, 11405123, 11605147, U1532263), the Fundamental Research Funds for the Central Universities, China Postdoctoral Science Foundation funded project (Grant No. 2014M562386) and Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) (Grant No. 20130201110066). References Bambynek, W., et al., 1972. X-ray fluorescence yields, Auger, and Coster-Kronig transition probabilities. Rev. Mod. Phys. 44, 716–813. Berezhko, E.G., Kabachnik, N.M., 1977. Theoretical study of inner-shell alignment of atoms in electron impact ionization: angular distribution and polarization of x-rays and Auger electrons. J. Phys. B 10, 2467–2477. Campbell, J.L., Cookson, J.A., 1984. PIXE analysis of thick targets. 3, pp. 185–197. Cooper, J., Zare, N., 1969. Atomic collision processes. vol. xic. Gordon & Breach, New York, p. 317. Flügge, S., Mehlhorn, W., Schmidt, V., 1972. Angular distribution of Auger electrons following photoionization. Phys. Rev. Lett. 29, 7–9. Gonzales, D., Requena, S., Williams, S., 2012. Au L x-rays induced by photons from 241 Am: comparison of experiment results and the predictions of PENELOPE. Appl. Radiat. Isot. 70, 301–304. Han, I., Şahin, M., Demir, L., 2009. The polarization of X-rays and magnetic photoionization cross-sections for L3 sub-shell. Appl. Radiat. Isot. 67, 1027–1032. Horvat, V., Watson, R.L., Blackadar, J.M., 2008. Effects of multiple ionization on the spectra of L x rays excited in heavy-ion collisions. Phys. Rev. A 77, 032724. Johansson, T.B., Akselsson, R., Johansson, S.A.E., 1970. X-ray analysis: elemental trace analysis at the 10−12g level. Nucl. Instr. Methods 84, 141–143. Kumar, A., et al., 2010. L3-subshell alignment of Au and Bi in collisions with 12–55 MeV carbon ions. Phys. Rev. A 81, 062709. Li, C.K., et al., 1992. PIXE x rays: from Z=4 to Z=92. Rev. Sci. Instr. 63, 4843. Maenhaut, W., Dereu, L., et al., 1980. Particle-induced X-Ray-Emission (PIXE) analysis of biological-materials-precision, accuracy and application to cancer tissues. Nucl. Instr. Methods 168, 557–562. Mei, C., et al., 2012. X-ray emission induced by 1.2–3.6 MeV Kr13+ ions. Laser Part. Beams 30, 665–670. Özdemir, Y., et al., 2011. L-shell polarization and alignment of heavy elements induced by 59.54 keV photons. Appl. Radiat. Isot. 69, 991–995. Raza, H.S., Kim, H.J., Ha, J.M., Cho, S.O., 2013. Behavior of characteristic X-rays from a partial-transmission-type X-ray target. Appl. Radiat. Isot. 80, 67–72. Romo-Kröger, C.M., 2010. How the sensitivity in PIXE elemental analysis is affected by the type of particle, cross-sections, background radiation and other factors? Vacuum 84, 1250–1253. Salem, S., Stöhlker, Th, et al., 2013. Angular distribution of photons for the simultaneous excitation and ionization of He-like uranium ions in relativistic ion-atom collisions. Phys. Rev. A 88, 012701. Šmit, Ž., 2005. Recent developments of material analysis with PIXE. Nucl. Instr. Methods B 240, 258–264. Storm, L., Israel, H.I., 1970. Photon cross sections from 1 keV to 100 MeV for elements Z=1 to Z=100. At. Data Nucl. Data Tables 7, 565–681. Tartari, A., et al., 2003. On the angular dependence of L x-ray production cross sections following photoionization at an energy of 59.54 keV. J. Phys. B 36, 843–851. Thompson, A.C., 2001. et al. X-ray data booklet, second edition. Wang, X., et al., 2012. Multiple ionization effect of Ta induced by heavy ions. Acta Phys. Sin. 61, 193201. Wang, X., et al., 2013. K-shell ionization of Al induced by ions near the threshold energy. Phys. Scr. T156, 014029. Wang, X., et al., 2014. Angular distribution of L X-ray emission from tungsten following photoionzation. Radia. Phys. Chem. 103, 213–215. Wang, X., et al., 2014. Effects of multiple ionization on total L X-ray emission by proton impact. J. Phys: Conf. Ser. 488, 132035. Wang, X., Zhao, Y., et al., 2012. Multiple ionization effects in M X-ray emission induced by heavy ions. Phys. Lett. A 376, 1197–1200. Wang, X., Xu, Z., Zhang, L., 2015. L X-ray intensity ratios for high Z elements induced with X-ray tube. Radiat. Phys. Chem. 112, 121–124. Yalçın, P., Porikli, S., Kurucu, Y., Şahin, Y., 2008. Measurement of relative L X-ray intensity ratio following radioactive decay and photoionization. Phys. Lett. B 663, 186–190. Zhou, X., et al., 2013. K and L-shell X-ray production cross sections for 50–250 keV proton impact on elements with Z=26-30. Nucl. Instr. Meth. B 299, 61–67. Zhou, X., Zhao, Y., Cheng, R., et al., 2013. Study of Si K-shell X-ray emission induced by H+ and Ar11+ ions. Acta Phys. Sin. 62, 083201.
(5)
Here σK, σL1, σL2 and σL3 are the K shell and L subshell photoionization cross sections; ηKLi are the number of additional vacancies transferred to the Li subshell from the K shell through radiative ηKLi (R) and non-radiative ηKLi (A) transitions; fij are Coster-Kronig (CK) transitions probabilities from the Li to Lj subshell, which represent the transitions happened within the same principal quantum numbers (Bambynek, 1972). Considering that the K-shell electrons of Au cannot be ionized since the binding energies (~80 keV) are much higher than the energy of incident electrons (15.9 keV), the vacancy transfer from K-shell to L-shell is not possible to happen. Therefore, the contribution of vacancy transfer to L3 subshell is limited to L1 and L2 subshell. In this case, the probability to produce L3 subshell vacancy can be rewritten as:
σ3 = σL1 ( f13 + f12 f23 ) + σL2 f23 + σL3
(6)
The CK yields for Au are taken from Ref. (Bambynek, 1972). and shown in Table 1. It can be concluded from Eq. (6) and Table 1 that the probability for vacancy production in L3 subshell, σ3, is significantly affected by the unaligned vacancy states of L1 and L2 subshells (especially for vacancy transfer from L1 to L3 subshell). The alignment of vacancy state in L3 subshell with j > 1/2 will be distorted by CosterKronig process. The anisotropy emission of X-rays originating from the filling of vacancy state with j > 1/2 may be overwhelmed if the anisotropy parameter β is close to zero. Consequently, only the emission of Lα X-ray is found to be anisotropic. 4. Conclusion In this work, the typical X-ray emission spectra of Au-Lα, Lβ1, Lβ2 and Lγ1 are measured in photoionization with energy of 15.9 keV at emission angles ranging from 110° to 150°. The angular distribution of L X-ray intensity ratios, Lα/Lβ1, Lβ2/Lβ1 and Lγ1/Lβ1, has been derived to study the alignment behavior of vacancy states. It can be inferred from the experimental results that the emission of Lα X-rays is spatially anisotropic while the emissions of Lβ1, Lβ2 and Lγ1 X-rays are 30
Contents lists available at ScienceDirect
Radiation Physics and Chemistry journal homepage: www.elsevier.com/locate/radphyschem
On the angular dependence of L X-ray intensity ratios for Au following photoionization
MARK
⁎
Xing Wang , Zhongfeng Xu, Ying Zhang School of Science, Xi’an Jiaotong University, Xi’an 710049, China
A R T I C L E I N F O
A BS T RAC T
Keywords: X-ray Angular distribution Photoionization Anisotropy parameter
The typical L X-ray spectra for Au induced by 15.9 keV photons have been measured at emission angles ranging from 110° to 150° at intervals of 10°. The intensities of Lα, Lβ1, Lβ2 and Lγ1 X-rays are obtained and the angular dependence of L X-ray intensity ratios is determined experimentally. It is found that the Lβ1, Lβ2 and Lγ1 X-rays present isotropic emission, while the measured Lα X-rays show anisotropic distribution spatially. The unexpected isotropic emission of Lβ2 X-rays is explained with Coster-Kronig vacancy transfer process. Moreover, the anisotropy parameter for Lα X-ray emission is deduced.
1. Introduction The inner-shell ionization of atom has been widely investigated for several decades (Raza et al., 2013; Mei, 2012; Wang, 20142014; Zhou, 2013; Wang et al., 2015; Bambynek, 1972; Zhou et al., 2013; Wang, 2013). The de-excitation of vacancy could accompany with the process of radiation transition-giving rise to typical X-rays emission or nonradiation transition-giving rise to Auger electron emission (Bambynek, 1972). In recent years, the study of characteristic X-ray emission focuses on the multiple-ionization effect (Wang and Zhao, 2012; Horvat et al., 2008; Wang, 2012; Wang, 20142014) and the alignment of vacancy state produced in collision process (Han et al., 2009; Salem and Stöhlker, 2013). In addition, there is a well-known analytical application to determine the species of elements in materials with Particle Induced X-ray Emission (PIXE) in geological and chemical fields (Šmit, 2005; Romo-Kröger, 2010; Johansson et al., 1970; Li, 1992; Maenhaut and Dereu, 1980; J.L. Campbell, J.A. Cookson, PIXE analysis of thick targets. Anal. Thick Targets. 3, 1984, pp. 185–197.). Consequently, it becomes more and more important to study the angular dependence of characteristic X-ray emission by measuring the typical X-ray intensity in photoionization (Raza et al., 2013; Han et al., 2009). In theory, there are two contrary viewpoints that predict on the alignment for vacancy state produced in collision process. One view predicts that all vacancy states produced in impact ionization with total angular momentum J≥1/2 are unaligned and consequently the emitted X-rays (or Auger electrons) have isotropic emission and are unpolarized (Cooper and Zare, 1969); While the other view predicts that vacancies created in impact ionization with J > 1/2 are aligned and X⁎
ray (or Auger electron) emission following the vacancy degradation is anisotropic and polarized (Flügge et al., 1972). Furthermore, the differential intensity dI(θ) of the X-rays at emission angle θ is given by Berezhko and Kabachnik (Berezhko and Kabachnik, 1977).
dI (θ ) I = 0 [1 + βP2 (cosθ )]. dΩ 4π
(1)
1 (3cos (2θ ) + 1). 4
(2)
P2 (cosθ ) =
Here I0 is the total X-ray intensity integrated over 4π solid angle; dΩ is the solid angle subtended by the detector at the target; β is the anisotropy parameter of a particular X-ray line; P2(cosθ) is the secondorder Legendre polynomial. The anisotropy parameter β can be derived by the measurement of differential intensity dI(θ). A lot of experiments have been implemented to investigate the alignment of vacancy states in inner-shell by the measurement of angular distribution or polarization of the emitted X-rays (Raza et al., 2013; Han et al., 2009; Salem and Stöhlker, 2013; Özdemir, 2011; Kumar, 2010; Tartari, 2003; Gonzales et al., 2012). It is found that the degradation of vacancy states with J > 1/2 presents an anisotropic Xray emission (Raza et al., 2013; Han et al., 2009; Salem and Stöhlker, 2013; Özdemir, 2011); While some other researchers have observed that the X-ray emission exhibits isotropic pattern via the de-excitation of vacancy states with J > 1/2 (Kumar, 2010; Tartari, 2003; Gonzales et al., 2012). In this work, the typical L X-ray spectra for Au are measured at emission angles ranging from 110° to 150° with 15.9 keV X-ray impact. The angular dependence of L X-ray intensity ratios is reported. In
Corresponding author. E-mail address: [email protected] (X. Wang).
http://dx.doi.org/10.1016/j.radphyschem.2016.12.007 Received 27 May 2016; Received in revised form 16 December 2016; Accepted 18 December 2016 Available online 21 December 2016 0969-806X/ © 2016 Elsevier Ltd. All rights reserved.
Radiation Physics and Chemistry 133 (2017) 28–30
X. Wang et al.
Fig. 1. Detail geometry (left) and nuclear instrument system (right) of experimental setup. The emission angle θ is depicted here.
typical X-ray emission of Au target at incident energy of 15.9 keV. The geometry of experimental apparatus is shown in Fig. 1. The X-ray tube (Mini-X, AMPTEK Inc., USA), which works with 0.75 µm silver target, is utilized as the primary radiation source. The bremsstrahlung photons generated from X-ray tube are collimated by a Zr tube with inside diameter of 2 mm. The collimated photons bombard on a secondary Zr target. The spectrum of emitted characteristic K X-rays of Zr can be considered as a single and symmetric peak centered at 15.9 keV. According to both theories (Cooper and Zare, 1969; Flügge et al., 1972), the K X-ray emission should be isotropic and unpolarized (filling of vacancy in K1 shell, j=1/2). The energy of 15.9 keV is consistent with the calculation of the weighted average of Zr Kα and Kβ X-ray energies considering their intensity ratio (Thompson, 2001). The Au sample with a thickness of 77.2 mg cm−2 is irradiated by the collimated fluorescent X-rays produced from the secondary target. At last, an X-ray detector (Type: XR-100SDD; Specification: silicon drift detector; Company: Amptek in USA) is employed to record the characteristic X-rays emission from the target at emission angles ranging from 110° to 150°. The X-ray detector is movable and other parts are fixed in the arrangement. A resolution about 125 eV at 5.9 keV can be achieved by the detector with an active crystal size of 25 mm2. The count of incident X-rays per second and per unit area can be determined by mounting the detector at the position of sample.
Fig. 2. Typical L X-ray spectra for Au at emission angle θ=130°.
3. Results and discussion Fig. 2 presents the measured typical L X-ray spectra for Au target at emission angle of 130°. It can be seen that the peak positions for Lα1 (L3M5) and Lα2 (L3M4) X-rays are too close and cannot be distinguished. While the typical Lα (L3M4,5), Lβ1 (L2M4), Lβ2 (L3N5) and Lγ1 (L2N4) X-rays of Au are distinguished with multi-peak Gaussian fitting procedure. The emission of Lβ1 (L2M4) X-rays which originate from L2 (j=1/2) subshell are found to be isotropic. Therefore, it is feasible to investigate the angular dependence with the study of typical intensity ratios, I(Lα)/ I(Lβ1), I(Lβ2)/I(Lβ1) and I(Lγ1)/I(Lβ1). The experimental X-ray intensity ratios can be calculated by
Fig. 3. The intensity ratio of I(Lα)/I(Lβ1), I(Lβ2)/I(Lβ1) and I(Lγ1)/I(Lβ1) for Au. The fitting curve is also shown here. Table 1. Experimental L-subshell Coster-Kronig yields fij for Au taken from Ref. (Bambynek, 1972) . f12
f13
f23
0.083
0.644
0.132
N (L i ) ε (L j ) β (L j ) I (L i ) = I (L j ) N (L j ) ε (L i ) β (L i )
(3)
Here N(Li)/N(Lj) is the ratio of the counting rates under the Li (i=α and β2) and Lj (j=β1) peaks. ε (Lj)//ε (Li) is the ratio of the detection efficiency values for Lj and Li X-rays. The self-absorption correction factor β is derived for both Lj and Li separately by the formula (Yalçın et al., 2008).
addition, the anisotropy parameter β is obtained for Lα X-ray emission. 2. Experimental details
βi = The experiment has been carried out to measure the spectra of 29
1 − exp[−(μinc secθ1 + μemt secθ2 ) t ] (μinc secθ1 + μemt secθ2 ) t
(4)
Radiation Physics and Chemistry 133 (2017) 28–30
X. Wang et al.
Here μinc (cm2 g−1) and μemt (cm2 g−1) are the mass absorption coefficients for incident and emitted radiation (Storm and Israel, 1970); t is the mass thickness of target (g cm−2). θ1 and θ2 are the angles of incident photons and emitted X-rays with respect to the normal at the surface of the target (Yalçın et al., 2008). Considering that the counts of measured X-rays are more than 1000 for each peak for Lα, Lβ1, Lβ2 and Lγ1 X-rays, the statistical error is calculated to be 3% (1/(1000)1/2). Combining statistical error (3%) with errors estimated for background subtraction (3%), solid angle (6%) and fitting procedure (4%), the total experimental error of X-ray intensities is less than 11% in this work. The Lβ1 X-rays which originate from initial L2 (2p1/2, j=1/2) subshell are found to have isotropic emission. Simultaneously, the geometrical misalignment can be excluded with the result of isotropic emission of Lβ1 X-rays. The intensity ratios of I(Lα)/I(Lβ1), I(Lβ2)/I(Lβ1) and I(Lγ1)/I(Lβ1) are plotted and presented in Fig. 3. It can be seen that the intensity ratio, I(Lα)/I(Lβ1), shows anisotropic distribution; while the intensity ratios, I(Lβ2)/I(Lβ1) and I(Lγ1)/I(Lβ1), present isotropic distribution. According to Eqs. (Raza et al., 2013; Mei, 2012)., the anisotropy parameter β=0.264 can be deduced for Lα X-rays in this experiment. Lγ1 X-rays originating from L2 subshell (j=1/2) are supposed to have isotropic emission and this is verified in Fig. 3. Unexpectedly, the emission of Lβ2 X-rays originating from L3 subshell (j=3/2), which is supposed to be anisotropic, is found to be isotropic. The phenomena can be understood with the vacancy transfer process. Besides direct ionization in photoionization, the vacancy in L3 subshell can also be produced by vacancy transfer from K or L1,2,3 subshells. The vacancy production cross section for L3 subshell, σ3, can be given by:
σ3 = (σL1 + σK ηKL1)( f13 + f12 f23 ) + (σL2 + σKL2 ) f23 + (σL3 + σK ηKL3)
isotropic. The anisotropy parameter for Lα X-ray emission is deduced to be 0.264. The probability of vacancy production in L3-subshell, σ3, can be affected strongly by the unaligned vacancy states in L1 and L2 subshells. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant Nos. 11375138, 11405123, 11605147, U1532263), the Fundamental Research Funds for the Central Universities, China Postdoctoral Science Foundation funded project (Grant No. 2014M562386) and Specialized Research Fund for the Doctoral Program of Higher Education (SRFDP) (Grant No. 20130201110066). References Bambynek, W., et al., 1972. X-ray fluorescence yields, Auger, and Coster-Kronig transition probabilities. Rev. Mod. Phys. 44, 716–813. Berezhko, E.G., Kabachnik, N.M., 1977. Theoretical study of inner-shell alignment of atoms in electron impact ionization: angular distribution and polarization of x-rays and Auger electrons. J. Phys. B 10, 2467–2477. Campbell, J.L., Cookson, J.A., 1984. PIXE analysis of thick targets. 3, pp. 185–197. Cooper, J., Zare, N., 1969. Atomic collision processes. vol. xic. Gordon & Breach, New York, p. 317. Flügge, S., Mehlhorn, W., Schmidt, V., 1972. Angular distribution of Auger electrons following photoionization. Phys. Rev. Lett. 29, 7–9. Gonzales, D., Requena, S., Williams, S., 2012. Au L x-rays induced by photons from 241 Am: comparison of experiment results and the predictions of PENELOPE. Appl. Radiat. Isot. 70, 301–304. Han, I., Şahin, M., Demir, L., 2009. The polarization of X-rays and magnetic photoionization cross-sections for L3 sub-shell. Appl. Radiat. Isot. 67, 1027–1032. Horvat, V., Watson, R.L., Blackadar, J.M., 2008. Effects of multiple ionization on the spectra of L x rays excited in heavy-ion collisions. Phys. Rev. A 77, 032724. Johansson, T.B., Akselsson, R., Johansson, S.A.E., 1970. X-ray analysis: elemental trace analysis at the 10−12g level. Nucl. Instr. Methods 84, 141–143. Kumar, A., et al., 2010. L3-subshell alignment of Au and Bi in collisions with 12–55 MeV carbon ions. Phys. Rev. A 81, 062709. Li, C.K., et al., 1992. PIXE x rays: from Z=4 to Z=92. Rev. Sci. Instr. 63, 4843. Maenhaut, W., Dereu, L., et al., 1980. Particle-induced X-Ray-Emission (PIXE) analysis of biological-materials-precision, accuracy and application to cancer tissues. Nucl. Instr. Methods 168, 557–562. Mei, C., et al., 2012. X-ray emission induced by 1.2–3.6 MeV Kr13+ ions. Laser Part. Beams 30, 665–670. Özdemir, Y., et al., 2011. L-shell polarization and alignment of heavy elements induced by 59.54 keV photons. Appl. Radiat. Isot. 69, 991–995. Raza, H.S., Kim, H.J., Ha, J.M., Cho, S.O., 2013. Behavior of characteristic X-rays from a partial-transmission-type X-ray target. Appl. Radiat. Isot. 80, 67–72. Romo-Kröger, C.M., 2010. How the sensitivity in PIXE elemental analysis is affected by the type of particle, cross-sections, background radiation and other factors? Vacuum 84, 1250–1253. Salem, S., Stöhlker, Th, et al., 2013. Angular distribution of photons for the simultaneous excitation and ionization of He-like uranium ions in relativistic ion-atom collisions. Phys. Rev. A 88, 012701. Šmit, Ž., 2005. Recent developments of material analysis with PIXE. Nucl. Instr. Methods B 240, 258–264. Storm, L., Israel, H.I., 1970. Photon cross sections from 1 keV to 100 MeV for elements Z=1 to Z=100. At. Data Nucl. Data Tables 7, 565–681. Tartari, A., et al., 2003. On the angular dependence of L x-ray production cross sections following photoionization at an energy of 59.54 keV. J. Phys. B 36, 843–851. Thompson, A.C., 2001. et al. X-ray data booklet, second edition. Wang, X., et al., 2012. Multiple ionization effect of Ta induced by heavy ions. Acta Phys. Sin. 61, 193201. Wang, X., et al., 2013. K-shell ionization of Al induced by ions near the threshold energy. Phys. Scr. T156, 014029. Wang, X., et al., 2014. Angular distribution of L X-ray emission from tungsten following photoionzation. Radia. Phys. Chem. 103, 213–215. Wang, X., et al., 2014. Effects of multiple ionization on total L X-ray emission by proton impact. J. Phys: Conf. Ser. 488, 132035. Wang, X., Zhao, Y., et al., 2012. Multiple ionization effects in M X-ray emission induced by heavy ions. Phys. Lett. A 376, 1197–1200. Wang, X., Xu, Z., Zhang, L., 2015. L X-ray intensity ratios for high Z elements induced with X-ray tube. Radiat. Phys. Chem. 112, 121–124. Yalçın, P., Porikli, S., Kurucu, Y., Şahin, Y., 2008. Measurement of relative L X-ray intensity ratio following radioactive decay and photoionization. Phys. Lett. B 663, 186–190. Zhou, X., et al., 2013. K and L-shell X-ray production cross sections for 50–250 keV proton impact on elements with Z=26-30. Nucl. Instr. Meth. B 299, 61–67. Zhou, X., Zhao, Y., Cheng, R., et al., 2013. Study of Si K-shell X-ray emission induced by H+ and Ar11+ ions. Acta Phys. Sin. 62, 083201.
(5)
Here σK, σL1, σL2 and σL3 are the K shell and L subshell photoionization cross sections; ηKLi are the number of additional vacancies transferred to the Li subshell from the K shell through radiative ηKLi (R) and non-radiative ηKLi (A) transitions; fij are Coster-Kronig (CK) transitions probabilities from the Li to Lj subshell, which represent the transitions happened within the same principal quantum numbers (Bambynek, 1972). Considering that the K-shell electrons of Au cannot be ionized since the binding energies (~80 keV) are much higher than the energy of incident electrons (15.9 keV), the vacancy transfer from K-shell to L-shell is not possible to happen. Therefore, the contribution of vacancy transfer to L3 subshell is limited to L1 and L2 subshell. In this case, the probability to produce L3 subshell vacancy can be rewritten as:
σ3 = σL1 ( f13 + f12 f23 ) + σL2 f23 + σL3
(6)
The CK yields for Au are taken from Ref. (Bambynek, 1972). and shown in Table 1. It can be concluded from Eq. (6) and Table 1 that the probability for vacancy production in L3 subshell, σ3, is significantly affected by the unaligned vacancy states of L1 and L2 subshells (especially for vacancy transfer from L1 to L3 subshell). The alignment of vacancy state in L3 subshell with j > 1/2 will be distorted by CosterKronig process. The anisotropy emission of X-rays originating from the filling of vacancy state with j > 1/2 may be overwhelmed if the anisotropy parameter β is close to zero. Consequently, only the emission of Lα X-ray is found to be anisotropic. 4. Conclusion In this work, the typical X-ray emission spectra of Au-Lα, Lβ1, Lβ2 and Lγ1 are measured in photoionization with energy of 15.9 keV at emission angles ranging from 110° to 150°. The angular distribution of L X-ray intensity ratios, Lα/Lβ1, Lβ2/Lβ1 and Lγ1/Lβ1, has been derived to study the alignment behavior of vacancy states. It can be inferred from the experimental results that the emission of Lα X-rays is spatially anisotropic while the emissions of Lβ1, Lβ2 and Lγ1 X-rays are 30