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Experimental determination of L subshell fluorescence yields of Ba, La and Pr using synchrotron radiation
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 243 (2006) 34–37 www.elsevier.com/locate/nimb
Experimental determination of L subshell fluorescence yields of Ba, La and Pr using synchrotron radiation N.M. Badiger a, Edgardo V. Bonzi b
b,*
a Department of Physics, Karnatak University, Dharwad 580 003, Karnataka, India ´ Facultad de Matematica, Astronomı´a y Fı´sica, Universidad Nacional de Co´rdoba, Ciudad Universitaria, 5010 Co´rdoba, Argentina
Received 9 June 2005; received in revised form 8 August 2005 Available online 21 September 2005
Abstract L subshell fluorescence yields x1, x2 and x3 have been measured for Ba, La and Pr elemental targets. The characteristic L X-ray photons, induced in the targets by synchrotron radiation, were measured with a Si(Li) detector coupled to multichannel analyzer. Measured L subshell fluorescence yields have been compared with theoretical values, compilation data and other experimental data. 2005 Elsevier B.V. All rights reserved. PACS: 32.50.+d; 32.80.Fb; 32.80.Hd; 33.50.j Keywords: L shells fluorescence; L fluorescence yield; Synchrotron radiations; Photon induced X-ray
1. Introduction Study of X-ray fluorescence has been a subject of experimental as well as theoretical interest in recent years [1] in view of their applications for non-destructive elemental analysis in medical physics, environmental science and industry. Precise values of these parameters are needed to check atomic physics theory and the existing models used in predicting theoretical fluorescence parameters. A vacancy produced by the primary radiation in the inner shell of an atom is filled by the radiative and nonradiative transitions. In the case of radiative transition, the inner shell vacancy is filled by the electrons from the higher shells by emitting X-ray photons. The Auger and Coster–Kronig transitions are the non-radiative transitions. In Auger transitions, because of the mutual repulsion of two electrons in higher shells, the vacancy can shift from one shell to another shell, whereas in the Coster–Kronig transition, the vacancy is transferred from tightly bound
*
Corresponding author. Tel.: +54 351 4334050; fax: +54 351 4334054. E-mail address: [email protected] (E.V. Bonzi).
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.08.125
subshell to less tightly bound subshells of the same shell. K shell fluorescence yields have been predicted accurately as the radiative and Auger transition probabilities are known accurately [1]. However, study of L shell fluorescence yields is interesting because the vacancies produced by the primary photons in the subshells may be redistributed among the higher subshells through Coster–Krong transitions. Campbell [2] has recently presented a critical review on L subshell fluorescence yields x1, x2 and x3 and Coster–Kronig transitions fij. Some researchers have calculated L subshell fluorescence yields using different models [3–5]. Krause [3] has carried out a semi-empirical compilation of atomic Li subshell X-ray fluorescence yields xi (i = 1, 2, 3), Auger transition yields ai and Coster–Kronig transition yields fij for the elements with Z = 12–110. Chen et al. [4] tabulated values of xi for elements with 18 6 Z 6 100 based on the relativistic Dirac–Hartree–Slater (DHS) model. Puri et al. [5] presented theoretical values of xi subshell fluorescence yields calculated using radiative emission rates of Scofield [6] and non-radiative emission rates computed by Chen et al. [7]. L subshell fluorescence yields have been measured by inducing L X-rays in the target by electron beam, proton
N.M. Badiger, E.V. Bonzi / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 34–37
beam, synchrotron radiation as well as gamma rays from radioactive isotopes. Xu [8] has measured the L shell fluorescence yields x1, x2 and x3 for the elements with atomic number Z = 73–83 by exciting the L X-ray photons with a 50 keV electron beam. Xu and Xu [9] have measured the L1 and L2 subshell fluorescence yields for the elements La, Nd, Dy, Yb and Lu by inducing L X-ray photons with a 2 MeV proton beam. By employing synchrotron photoionization method, which can selectively ionize the particular subshell, Werner and Jitschin [10] measured L1 and L2 fluorescence yields for high Z elements in the range 72 6 Z 6 82. Ka and La coincidence method, known to be powerful technique, has been adopted by several researchers to measure L2 and L3 fluorescence yields of the high Z elements [11,12]. L subshell fluorescence yields for the elements with Z = 55–92 have been measured by several investigators by employing radio-active isotopes [13–17]. From survey of literature, we understand that only a few researchers have measured L subshell fluorescence yields for Ba, La and Pr. It is interesting to note that all the researchers have used gamma rays from radio-isotope to excite the characteristic L X-ray in the targets. With the best of our knowledge, there are no L subshell fluorescence data on Ba, La and Pr using synchrotron radiation. In view of this, we have measured L subshell fluorescence yields for the elements Ba, La and Pr by keeping the detector at 90 and inducing the L X-ray with synchrotron radiation from LNLS, Campinas, Brazil. Measured values have been compared with theoretical values based on DHS wave functions, the compilation data and others experimental values. 2. Experimental details
35
Table 1 Notations for L X-ray according to Siegbahn and IUPAC Peak no.
Siegbahn
IUPACa
1 2 3b 4 5 6
Ll La1 and La2(La) Lb1 and Lb4 Lb2 Lc1 Lc2 and Lc3
L3–M1 L3–M4,5 L2–M4 and L1–M2 L3–N5 L2–N4 L1–N2,3
a b
IUPAC: International Union of Pure and Applied Chemistry. Not used in the present work.
obtained using the model proposed by Jaklevic and Giauque [19]. We recorded L X-ray spectrum for Ba, La and Pr targets in such way that the net counts under each main peak was more than 105 counts and the net counts under the peak Ll and (Lc2 + Lc3) were more than 104. From the typical L spectrum we noticed that there were six peaks and from analysis we found that these peaks were corresponding to Ll, (La1 + La2), (Lb1 + Lb4), Lb2, Lc1 and (Lc2 + Lc3); the transitions for these notations are given in Table 1. All six peaks were fitted to the Gaussian distribution functions to ascertain the net area under each peak. 3. Data analysis In order to obtain the L shell fluorescence yields x1, x2 and x3, we used the following expressions: From peak 6 reLc2 þc3 ðE0 Þ x1 ¼ ph . rL1 ðE0 ÞðF 1c2 þ F 1c3 Þ
ð1Þ
From peak 5
The experiment was carried out at the National Synchrotron Light Laboratory (LNLS), Campinas, Brazil using fluorescence beam line [18]. The polychromatic beam produced by 3.7 GeV electrons in the storage ring was monochromatised using Si(1 1 1) channel cut double crystal monochromator. The monochromator could tune the beam energies between 3 and 14 keV and the energy resolution was 3–4 · 104 in between 7 and 10 keV. To measure the intensity of the incident beam, the ionization chamber was placed before the target chamber. The targets were mounted in the target chamber at 45 to the incident beam. A Si(Li) detector was placed at 90 to the incident beam so as to observe minimum background in the measured L spectrum; it is well-known that the synchrotron radiation is linearly polarized and produces negligible scattering at 90. A 7 keV synchrotron radiation was used to excite the characteristic L X-ray photons in the pure elemental targets of Ba, La and Pr. The thickness of all three targets were 0.0127 cm. The L X-ray photons were detected with a Si(Li) detector coupled to multichannel analyzer through the electronic modules. The detector was 5 mm diameter with 5 mm thick detecting material and had 0.0024 mm beryllium window. The energy resolution of the detector was 165 eV at 5.9 keV. The efficiency of the detector was
reLc1 ðE0 Þ i . x2 ¼ h ph rph ðE Þf þ r ðE Þ F 0 12 0 2c1 L1 L2
ð2Þ
From peak 1 reLb2 ðE0 Þ i x3 ¼ h . ph ph rph L1 ðE 0 Þ½f13 þ f12 f23 þ rL2 ðE0 Þf23 þ rL3 ðE0 Þ ðF 3a1 þ F 3a2 Þ ð3Þ From peak 2 reLa ðE0 Þ i . x3 ¼ h ph ph rph ðE Þ ½ f þ f f þ r ðE Þf þ r ðE Þ ðF þ F Þ 0 13 12 23 0 23 0 3a 3a L1 L2 L3 1 2 ð4Þ From peak 4 reLb2 ðE0 Þ i x3 ¼ h ; ph ph rph L1 ðE 0 Þ½f13 þ f12 f23 þ rL2 ðE0 Þf23 þ rL3 ðE0 Þ F 3b2 ð5Þ
reLs ðs
where ¼ l; c1 ; c2 þ c3 ; b2 and aÞ is the experimental L X-ray production cross section, rph Li (i = 1, 2 and 3) is the theoretical L subshell photoionization cross section, fr (r = 12, 13 and 23) is the Coster–Kronig transition yield and F is the fractional X-ray emission rate.
36
N.M. Badiger, E.V. Bonzi / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 34–37
The experimental L subshell fluorescence cross sections were determined by measuring net counts under the peaks of L3–M1, (L3–M5 + L3–M4), L3–L5, L2–N4 and (L1–N2 + L1–N3). The experimental cross section is given by reLi ðE0 Þ ¼
Ii ; I 0 G eðELi Þ T ðE0 ; ELi Þ
ð6Þ
where Ii is the net counts under the peak i, I0 is the intensity of the incident photons at energy E0, G is the geometrical factor, e(ELi ) is the efficiency of the Si(Li) detector at energy ELi and T(E0, ELi ) is the self-attenuation factor for the incident and emitted X-rays. The self-attenuation factor is given by lðE0 Þ lðELi Þ T ðE0 ; ELi Þ ¼ 1 exp 1 þ qt sinðh1 Þ sinðh2 Þ 1 lðE0 Þ lðELi Þ þ ; ð7Þ sinðh1 Þ sinðh2 Þ where l(E0) and l(ELi ) are the total mass absorption coefficients of the target at incident energy E0 and emitted L X-ray energy ELi respectively. h1 and h2 are the angles of incident and emitted X-ray photons and they were equal to 45 in present setup. The factor I0Ge(ELi ), the effective incident photon flux, can be determined very accurately by measuring the K X-ray photons from the targets because K shell fluorescence cross sections and yields are known accurately. For I0Ge(ELi ) determination, the targets are selected in such a way that their K X-ray energies are in the region of L X-ray of the targets used for L subshell fluorescence studies. The I0Ge(ELi ) was obtained from the equation I 0 GeðEKi Þ ¼
I Ki ; rKi ðE0 Þ C i T ðE0 ; EKi Þ
ð8Þ
where I Ki is the measured K X-ray intensity, Ci is the weight concentration of the element of interest in the sample and aKi is the K X-ray fluorescence cross section at energy E0. The aKi is given by
tained in the present set-up by measuring Ka and Kb X-ray photons from the three targets Cl(NaCl), Ca(CaHPO4, 2H2O) and Ti (Ti foil) by exciting targets with 7 keV synchrotron beam. We observed six peaks in the L spectrum of each target used in the present study. These peaks were analyzed by fitting the Gaussian distribution function to each peak. From the analysis we found that the six peaks correspond to L3– M1, (L3–M5 + L3–M4), (L2–M4 + L1–M2), L3–L5, L2–N4 and (L1–N2 + L1–N3); the notations for these transitions are given in Table 1. To obtain the net area under each peak three methods were adopted. In the first method, the area under the selected peak was determined by sharing the width of the Gaussian function of the selected peak with the other four peaks in the given spectrum. In the second method, the area of the selected peak was determined by unsharing the Gaussian parameters of the selected peak with the other peaks. In third method, the area of the selected peak was determined by locking the Gaussian parameters of the two neighboring peaks and unsharing parameters of the selected peak. We noticed that in all three methods the change in net counts was not small. In this way we estimated counts under each peak of the characteristic L X-ray photons using average of three values. For estimation of experimental fluorescence cross section we used Eq. (6). From these fluorescence cross sections, L subshell fluorescence yields x1, x2 and x3 have been evaluated using Eqs. (1)–(5), by taking theoretical L shell photoionization cross sections from Scofield [21], the Coster–Kronig transitions rate from Puri et al. [5] and the fractional X-ray emission rates from Scofield [6]. And the total mass absorption coefficients used in Eq. (7) were taken from Hubbell and Seltzer [22]. In the case of x3 we have taken weighted average values because these values were obtained from three peaks. Our experimental values of x1, x2 and x3 for Ba, La and Pr targets along with theoretical values based on the Dirac– Hartree–Slater (DHS) wave function, compilation data and others experimental values are given in Tables 2–4. The theoretical values (DHS) are taken from Chen et al. [4] and compilation data from Krause [3].
rKi ðE0 Þ ¼ rph Ki ðE 0 Þ xK F Ki ; where rph Ki ðE0 Þ is the K shell photoionization cross section at energy E0, xk is the K shell fluorescence yield and F Ki is the fractional X-ray emission ratios for Ki X-rays. The F Ki for Ka and Kb are given by 1 F Ka ¼ 1 þ ðI Kb =I Ka Þ ;
1 F Kb ¼ 1 þ ðI Ka =I Kb Þ ;
where IKb/IKa is the intensity ratio for Kb and Ka. The energy dependence of I0Ge(ELi ) was known from the previous experiment [20]. Therefore we used the same energy dependence as our experimental arrangement is the same as that used in previous studies. However, in the present study, we needed the scale factor to consider the intensity of the beam current. This scale factor was ob-
Table 2 Comparison of x1 fluorescence yield of the present work with theoretical and other experimental values Element
Present work
DHS [4]
Krause [3]
Others work
Ref.
Ba
0.036 ± 0.004
0.053
0.052
0.037 ± 0.003 0.050 ± 0.005
[17] [18]
La
0.058 ± 0.007
0.057
0.055
0.064 ± 0.008 0.068 ± 0.005 0.055 ± 0.006
[9] [17] [18]
Pr
0.065 ± 0.006
0.065
0.061
0.060 ± 0.002 0.064 ± 0.007
[17] [18]
N.M. Badiger, E.V. Bonzi / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 34–37 Table 3 Comparison of x2 fluorescence yield of the present work with theoretical and other experimental values Element
Present work
DHS [4]
Krause [3]
Others work
Ref.
Ba
0.082 ± 0.005
0.103
0.096
0.112 ± 0.008 0.096 ± 0.010
[16] [17]
La
0.124 ± 0.008
0.111
0.103
0.110 ± 0.011 0.075 ± 0.006 0.097 ± 0.011
[9] [16] [17]
Pr
0.155 ± 0.009
0.128
0.117
0.119 ± 0.003 0.116 ± 0.013
[16] [17]
37
5. Conclusion The L subshell fluorescence yields x1, x2 and x3 have been measured for pure elemental Ba, La and Pr targets by inducing the characteristic L X-ray with a synchrotron radiation beam at 7 keV. The L X-ray photons were measured with high energy resolution Si(Li) detector. We have compared our measured values with theoretical values and semiempirical compilation data. From comparison we notice that some values agree with theory and some values differ from theory by 10–30%. Acknowledgements
Table 4 Comparison of x3 fluorescence yield of the present work with theoretical and other experimental values Element
Present work
DHS [4]
Krause [3]
Others work
Ref.
Ba
0.063 ± 0.003
0.104
0.097
0.077 ± 0.006 0.097 ± 0.006
[16] [17]
La
0.106 ± 0.005
0.112
0.104
0.093 ± 0.007 0.101 ± 0.007
[16] [17]
Pr
0.127 ± 0.006
0.126
0.118
0.107 ± 0.008 0.114 ± 0.007
[16] [17]
4. Results and discussion We have measured the L subshell fluorescence yields of the elements Ba, La and Pr by exciting the L X-rays with the synchrotron radiation. Measured values along with theoretical values and compilation data are presented in Tables 2–4. The experimental values xi have been evaluated by measuring the L X-ray production cross section of L3–M1, L3–M4 + L3–M5, L2–M4 + L1–M2, L3–N5, L2– N4 and L1–N2 + L1–N3 and by using theoretical L subshell photoionization cross sections, the Coster–Kronig transition yields and the fractional L X-ray emission rates. The net counts under each of the peaks Lc1, La and Lb2 had an error due to statistical fluctuation less than 1%. The total error in the measured L subshell fluorescence yields (x1, x2, x3) arises due to peak area evaluation, IoGe factor, the target thickness measurement and absorption correction. The errors given in the tables were estimated using the propagation of errors based on classical rules. From Table 2, we notice that x1 value for Ba is less than DHS [4] and Krause [3] value by 30%, but agree with experimental value obtained by Kaya and Ertugrul [16]. Our x1 value of La and Pr agree well with DHS prediction. From Table 3, we see that our x2 value for Ba is less than Krause prediction about 14%, for La is more than DHS value by about 10% and for Pr is more than DHS by about 20%. From Table 4, we find that x3 value for Ba is less than Krause value by 30%, for La agree with Krause value and for Pr agree with DHS.
This work was carried out under grants provided by SeCyT UNC (Argentina). Research was partially supported by LNLS – National Synchrotron Light Laboratory, Brazil. One of us (NMB) would like to thank TWAS– UNESCO–CONICET for the award of a research associateship to carry out this experiment. The authors are grateful to Dr. R.T. Mainardi for providing the set of measured samples. References [1] J.H. Hubbell, P.N. Trehan, N. Singh, B. Chand, D. Mehta, M.L. Garg, R.R. Garg, S. Singh, S. Puri, J. Phys. Chem. Ref. Data 23 (1994) 339. [2] J.L. Campbell, At. Data Nucl. Data Tables 85 (2003) 291. [3] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [4] M.H. Chen, B. Crasemann, H. Mark, Phys. Rev. A 24 (1981) 177. [5] S. Puri, D. Mehta, B. Chand, N. Nirmal, P.N. Trehan, X-ray Spectrom. 22 (1993) 358. [6] J.H. Scofield, At. Data Nucl. Data Tables 14 (1974) 121. [7] M.H. Chen, B. Crasemann, H. Mark, At. Data Nucl. Data Tables 24 (1979) 13. [8] J.Q. Xu, Phys. Rev. A 24 (1991) 177. [9] J.Q. Xu, X.J. Xu, Phys. Rev. A 49 (1994) 2191. [10] U. Werner, W. Jitschin, Phys. Rev. A 38 (1988) 4009. [11] P.L. McGhee, J.L. Campbell, J. Phys. B: At. Mol. Phys. 21 (1988) 2295. [12] J.L. Campell, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 3219. [13] S. Singh, D. Mehta, R.R. Garg, S. Kumar, M.L. Garg, N. Singh, P.C. Mangal, J.H. Hubbell, P.N. Trehan, Nucl. Instr. and Meth. B 51 (1990) 5. [14] E. Oz, Y. Ozdemir, N. Ekinci, M. Ertugrul, Y. Sahin, H. Erdogan, Spectrochim. Acta B 55 (2000) 1869. [15] R. Durak, Y. Ozdemir, J. Anal. At. Spectrom. 16 (2001) 1167. [16] A. Kaya, M. Ertugrul, J. Electron. Spectrosc. Related Phen. 130 (2003) 111. [17] Y. Ozdemir, R. Durak, J Quant. Spectrosc. Radiat. Transfer 77 (2003) 95. [18] C.A. Perez, M. Ratke, M.J. Sanchez, H. Tolentino, R.T. Neuenshwander, B. Brag, M. Rubio, M.I.S. Bueno, I.M. Raimundo, J.J.R. Rohwedder, X-ray Spectrom. 28 (1998) 320. [19] J.M. Jaklevic, R.D. GiauqueHandbook of X-ray Spectrometry, Vol. 14, Marcel Dekker, Inc., 1992, p. 160. [20] E.V. Bonzi, R.A. Barrea, X-ray Spectrom. 34 (2005) 253. [21] J.H. Scofield, Lawrence Livermore National Report No. UCRL 51326 (1973) 1. [22] J.H. Hubbell, S.M. Seltzer, NISTIR 5632 (1995).
Nuclear Instruments and Methods in Physics Research B 243 (2006) 34–37 www.elsevier.com/locate/nimb
Experimental determination of L subshell fluorescence yields of Ba, La and Pr using synchrotron radiation N.M. Badiger a, Edgardo V. Bonzi b
b,*
a Department of Physics, Karnatak University, Dharwad 580 003, Karnataka, India ´ Facultad de Matematica, Astronomı´a y Fı´sica, Universidad Nacional de Co´rdoba, Ciudad Universitaria, 5010 Co´rdoba, Argentina
Received 9 June 2005; received in revised form 8 August 2005 Available online 21 September 2005
Abstract L subshell fluorescence yields x1, x2 and x3 have been measured for Ba, La and Pr elemental targets. The characteristic L X-ray photons, induced in the targets by synchrotron radiation, were measured with a Si(Li) detector coupled to multichannel analyzer. Measured L subshell fluorescence yields have been compared with theoretical values, compilation data and other experimental data. 2005 Elsevier B.V. All rights reserved. PACS: 32.50.+d; 32.80.Fb; 32.80.Hd; 33.50.j Keywords: L shells fluorescence; L fluorescence yield; Synchrotron radiations; Photon induced X-ray
1. Introduction Study of X-ray fluorescence has been a subject of experimental as well as theoretical interest in recent years [1] in view of their applications for non-destructive elemental analysis in medical physics, environmental science and industry. Precise values of these parameters are needed to check atomic physics theory and the existing models used in predicting theoretical fluorescence parameters. A vacancy produced by the primary radiation in the inner shell of an atom is filled by the radiative and nonradiative transitions. In the case of radiative transition, the inner shell vacancy is filled by the electrons from the higher shells by emitting X-ray photons. The Auger and Coster–Kronig transitions are the non-radiative transitions. In Auger transitions, because of the mutual repulsion of two electrons in higher shells, the vacancy can shift from one shell to another shell, whereas in the Coster–Kronig transition, the vacancy is transferred from tightly bound
*
Corresponding author. Tel.: +54 351 4334050; fax: +54 351 4334054. E-mail address: [email protected] (E.V. Bonzi).
0168-583X/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2005.08.125
subshell to less tightly bound subshells of the same shell. K shell fluorescence yields have been predicted accurately as the radiative and Auger transition probabilities are known accurately [1]. However, study of L shell fluorescence yields is interesting because the vacancies produced by the primary photons in the subshells may be redistributed among the higher subshells through Coster–Krong transitions. Campbell [2] has recently presented a critical review on L subshell fluorescence yields x1, x2 and x3 and Coster–Kronig transitions fij. Some researchers have calculated L subshell fluorescence yields using different models [3–5]. Krause [3] has carried out a semi-empirical compilation of atomic Li subshell X-ray fluorescence yields xi (i = 1, 2, 3), Auger transition yields ai and Coster–Kronig transition yields fij for the elements with Z = 12–110. Chen et al. [4] tabulated values of xi for elements with 18 6 Z 6 100 based on the relativistic Dirac–Hartree–Slater (DHS) model. Puri et al. [5] presented theoretical values of xi subshell fluorescence yields calculated using radiative emission rates of Scofield [6] and non-radiative emission rates computed by Chen et al. [7]. L subshell fluorescence yields have been measured by inducing L X-rays in the target by electron beam, proton
N.M. Badiger, E.V. Bonzi / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 34–37
beam, synchrotron radiation as well as gamma rays from radioactive isotopes. Xu [8] has measured the L shell fluorescence yields x1, x2 and x3 for the elements with atomic number Z = 73–83 by exciting the L X-ray photons with a 50 keV electron beam. Xu and Xu [9] have measured the L1 and L2 subshell fluorescence yields for the elements La, Nd, Dy, Yb and Lu by inducing L X-ray photons with a 2 MeV proton beam. By employing synchrotron photoionization method, which can selectively ionize the particular subshell, Werner and Jitschin [10] measured L1 and L2 fluorescence yields for high Z elements in the range 72 6 Z 6 82. Ka and La coincidence method, known to be powerful technique, has been adopted by several researchers to measure L2 and L3 fluorescence yields of the high Z elements [11,12]. L subshell fluorescence yields for the elements with Z = 55–92 have been measured by several investigators by employing radio-active isotopes [13–17]. From survey of literature, we understand that only a few researchers have measured L subshell fluorescence yields for Ba, La and Pr. It is interesting to note that all the researchers have used gamma rays from radio-isotope to excite the characteristic L X-ray in the targets. With the best of our knowledge, there are no L subshell fluorescence data on Ba, La and Pr using synchrotron radiation. In view of this, we have measured L subshell fluorescence yields for the elements Ba, La and Pr by keeping the detector at 90 and inducing the L X-ray with synchrotron radiation from LNLS, Campinas, Brazil. Measured values have been compared with theoretical values based on DHS wave functions, the compilation data and others experimental values. 2. Experimental details
35
Table 1 Notations for L X-ray according to Siegbahn and IUPAC Peak no.
Siegbahn
IUPACa
1 2 3b 4 5 6
Ll La1 and La2(La) Lb1 and Lb4 Lb2 Lc1 Lc2 and Lc3
L3–M1 L3–M4,5 L2–M4 and L1–M2 L3–N5 L2–N4 L1–N2,3
a b
IUPAC: International Union of Pure and Applied Chemistry. Not used in the present work.
obtained using the model proposed by Jaklevic and Giauque [19]. We recorded L X-ray spectrum for Ba, La and Pr targets in such way that the net counts under each main peak was more than 105 counts and the net counts under the peak Ll and (Lc2 + Lc3) were more than 104. From the typical L spectrum we noticed that there were six peaks and from analysis we found that these peaks were corresponding to Ll, (La1 + La2), (Lb1 + Lb4), Lb2, Lc1 and (Lc2 + Lc3); the transitions for these notations are given in Table 1. All six peaks were fitted to the Gaussian distribution functions to ascertain the net area under each peak. 3. Data analysis In order to obtain the L shell fluorescence yields x1, x2 and x3, we used the following expressions: From peak 6 reLc2 þc3 ðE0 Þ x1 ¼ ph . rL1 ðE0 ÞðF 1c2 þ F 1c3 Þ
ð1Þ
From peak 5
The experiment was carried out at the National Synchrotron Light Laboratory (LNLS), Campinas, Brazil using fluorescence beam line [18]. The polychromatic beam produced by 3.7 GeV electrons in the storage ring was monochromatised using Si(1 1 1) channel cut double crystal monochromator. The monochromator could tune the beam energies between 3 and 14 keV and the energy resolution was 3–4 · 104 in between 7 and 10 keV. To measure the intensity of the incident beam, the ionization chamber was placed before the target chamber. The targets were mounted in the target chamber at 45 to the incident beam. A Si(Li) detector was placed at 90 to the incident beam so as to observe minimum background in the measured L spectrum; it is well-known that the synchrotron radiation is linearly polarized and produces negligible scattering at 90. A 7 keV synchrotron radiation was used to excite the characteristic L X-ray photons in the pure elemental targets of Ba, La and Pr. The thickness of all three targets were 0.0127 cm. The L X-ray photons were detected with a Si(Li) detector coupled to multichannel analyzer through the electronic modules. The detector was 5 mm diameter with 5 mm thick detecting material and had 0.0024 mm beryllium window. The energy resolution of the detector was 165 eV at 5.9 keV. The efficiency of the detector was
reLc1 ðE0 Þ i . x2 ¼ h ph rph ðE Þf þ r ðE Þ F 0 12 0 2c1 L1 L2
ð2Þ
From peak 1 reLb2 ðE0 Þ i x3 ¼ h . ph ph rph L1 ðE 0 Þ½f13 þ f12 f23 þ rL2 ðE0 Þf23 þ rL3 ðE0 Þ ðF 3a1 þ F 3a2 Þ ð3Þ From peak 2 reLa ðE0 Þ i . x3 ¼ h ph ph rph ðE Þ ½ f þ f f þ r ðE Þf þ r ðE Þ ðF þ F Þ 0 13 12 23 0 23 0 3a 3a L1 L2 L3 1 2 ð4Þ From peak 4 reLb2 ðE0 Þ i x3 ¼ h ; ph ph rph L1 ðE 0 Þ½f13 þ f12 f23 þ rL2 ðE0 Þf23 þ rL3 ðE0 Þ F 3b2 ð5Þ
reLs ðs
where ¼ l; c1 ; c2 þ c3 ; b2 and aÞ is the experimental L X-ray production cross section, rph Li (i = 1, 2 and 3) is the theoretical L subshell photoionization cross section, fr (r = 12, 13 and 23) is the Coster–Kronig transition yield and F is the fractional X-ray emission rate.
36
N.M. Badiger, E.V. Bonzi / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 34–37
The experimental L subshell fluorescence cross sections were determined by measuring net counts under the peaks of L3–M1, (L3–M5 + L3–M4), L3–L5, L2–N4 and (L1–N2 + L1–N3). The experimental cross section is given by reLi ðE0 Þ ¼
Ii ; I 0 G eðELi Þ T ðE0 ; ELi Þ
ð6Þ
where Ii is the net counts under the peak i, I0 is the intensity of the incident photons at energy E0, G is the geometrical factor, e(ELi ) is the efficiency of the Si(Li) detector at energy ELi and T(E0, ELi ) is the self-attenuation factor for the incident and emitted X-rays. The self-attenuation factor is given by lðE0 Þ lðELi Þ T ðE0 ; ELi Þ ¼ 1 exp 1 þ qt sinðh1 Þ sinðh2 Þ 1 lðE0 Þ lðELi Þ þ ; ð7Þ sinðh1 Þ sinðh2 Þ where l(E0) and l(ELi ) are the total mass absorption coefficients of the target at incident energy E0 and emitted L X-ray energy ELi respectively. h1 and h2 are the angles of incident and emitted X-ray photons and they were equal to 45 in present setup. The factor I0Ge(ELi ), the effective incident photon flux, can be determined very accurately by measuring the K X-ray photons from the targets because K shell fluorescence cross sections and yields are known accurately. For I0Ge(ELi ) determination, the targets are selected in such a way that their K X-ray energies are in the region of L X-ray of the targets used for L subshell fluorescence studies. The I0Ge(ELi ) was obtained from the equation I 0 GeðEKi Þ ¼
I Ki ; rKi ðE0 Þ C i T ðE0 ; EKi Þ
ð8Þ
where I Ki is the measured K X-ray intensity, Ci is the weight concentration of the element of interest in the sample and aKi is the K X-ray fluorescence cross section at energy E0. The aKi is given by
tained in the present set-up by measuring Ka and Kb X-ray photons from the three targets Cl(NaCl), Ca(CaHPO4, 2H2O) and Ti (Ti foil) by exciting targets with 7 keV synchrotron beam. We observed six peaks in the L spectrum of each target used in the present study. These peaks were analyzed by fitting the Gaussian distribution function to each peak. From the analysis we found that the six peaks correspond to L3– M1, (L3–M5 + L3–M4), (L2–M4 + L1–M2), L3–L5, L2–N4 and (L1–N2 + L1–N3); the notations for these transitions are given in Table 1. To obtain the net area under each peak three methods were adopted. In the first method, the area under the selected peak was determined by sharing the width of the Gaussian function of the selected peak with the other four peaks in the given spectrum. In the second method, the area of the selected peak was determined by unsharing the Gaussian parameters of the selected peak with the other peaks. In third method, the area of the selected peak was determined by locking the Gaussian parameters of the two neighboring peaks and unsharing parameters of the selected peak. We noticed that in all three methods the change in net counts was not small. In this way we estimated counts under each peak of the characteristic L X-ray photons using average of three values. For estimation of experimental fluorescence cross section we used Eq. (6). From these fluorescence cross sections, L subshell fluorescence yields x1, x2 and x3 have been evaluated using Eqs. (1)–(5), by taking theoretical L shell photoionization cross sections from Scofield [21], the Coster–Kronig transitions rate from Puri et al. [5] and the fractional X-ray emission rates from Scofield [6]. And the total mass absorption coefficients used in Eq. (7) were taken from Hubbell and Seltzer [22]. In the case of x3 we have taken weighted average values because these values were obtained from three peaks. Our experimental values of x1, x2 and x3 for Ba, La and Pr targets along with theoretical values based on the Dirac– Hartree–Slater (DHS) wave function, compilation data and others experimental values are given in Tables 2–4. The theoretical values (DHS) are taken from Chen et al. [4] and compilation data from Krause [3].
rKi ðE0 Þ ¼ rph Ki ðE 0 Þ xK F Ki ; where rph Ki ðE0 Þ is the K shell photoionization cross section at energy E0, xk is the K shell fluorescence yield and F Ki is the fractional X-ray emission ratios for Ki X-rays. The F Ki for Ka and Kb are given by 1 F Ka ¼ 1 þ ðI Kb =I Ka Þ ;
1 F Kb ¼ 1 þ ðI Ka =I Kb Þ ;
where IKb/IKa is the intensity ratio for Kb and Ka. The energy dependence of I0Ge(ELi ) was known from the previous experiment [20]. Therefore we used the same energy dependence as our experimental arrangement is the same as that used in previous studies. However, in the present study, we needed the scale factor to consider the intensity of the beam current. This scale factor was ob-
Table 2 Comparison of x1 fluorescence yield of the present work with theoretical and other experimental values Element
Present work
DHS [4]
Krause [3]
Others work
Ref.
Ba
0.036 ± 0.004
0.053
0.052
0.037 ± 0.003 0.050 ± 0.005
[17] [18]
La
0.058 ± 0.007
0.057
0.055
0.064 ± 0.008 0.068 ± 0.005 0.055 ± 0.006
[9] [17] [18]
Pr
0.065 ± 0.006
0.065
0.061
0.060 ± 0.002 0.064 ± 0.007
[17] [18]
N.M. Badiger, E.V. Bonzi / Nucl. Instr. and Meth. in Phys. Res. B 243 (2006) 34–37 Table 3 Comparison of x2 fluorescence yield of the present work with theoretical and other experimental values Element
Present work
DHS [4]
Krause [3]
Others work
Ref.
Ba
0.082 ± 0.005
0.103
0.096
0.112 ± 0.008 0.096 ± 0.010
[16] [17]
La
0.124 ± 0.008
0.111
0.103
0.110 ± 0.011 0.075 ± 0.006 0.097 ± 0.011
[9] [16] [17]
Pr
0.155 ± 0.009
0.128
0.117
0.119 ± 0.003 0.116 ± 0.013
[16] [17]
37
5. Conclusion The L subshell fluorescence yields x1, x2 and x3 have been measured for pure elemental Ba, La and Pr targets by inducing the characteristic L X-ray with a synchrotron radiation beam at 7 keV. The L X-ray photons were measured with high energy resolution Si(Li) detector. We have compared our measured values with theoretical values and semiempirical compilation data. From comparison we notice that some values agree with theory and some values differ from theory by 10–30%. Acknowledgements
Table 4 Comparison of x3 fluorescence yield of the present work with theoretical and other experimental values Element
Present work
DHS [4]
Krause [3]
Others work
Ref.
Ba
0.063 ± 0.003
0.104
0.097
0.077 ± 0.006 0.097 ± 0.006
[16] [17]
La
0.106 ± 0.005
0.112
0.104
0.093 ± 0.007 0.101 ± 0.007
[16] [17]
Pr
0.127 ± 0.006
0.126
0.118
0.107 ± 0.008 0.114 ± 0.007
[16] [17]
4. Results and discussion We have measured the L subshell fluorescence yields of the elements Ba, La and Pr by exciting the L X-rays with the synchrotron radiation. Measured values along with theoretical values and compilation data are presented in Tables 2–4. The experimental values xi have been evaluated by measuring the L X-ray production cross section of L3–M1, L3–M4 + L3–M5, L2–M4 + L1–M2, L3–N5, L2– N4 and L1–N2 + L1–N3 and by using theoretical L subshell photoionization cross sections, the Coster–Kronig transition yields and the fractional L X-ray emission rates. The net counts under each of the peaks Lc1, La and Lb2 had an error due to statistical fluctuation less than 1%. The total error in the measured L subshell fluorescence yields (x1, x2, x3) arises due to peak area evaluation, IoGe factor, the target thickness measurement and absorption correction. The errors given in the tables were estimated using the propagation of errors based on classical rules. From Table 2, we notice that x1 value for Ba is less than DHS [4] and Krause [3] value by 30%, but agree with experimental value obtained by Kaya and Ertugrul [16]. Our x1 value of La and Pr agree well with DHS prediction. From Table 3, we see that our x2 value for Ba is less than Krause prediction about 14%, for La is more than DHS value by about 10% and for Pr is more than DHS by about 20%. From Table 4, we find that x3 value for Ba is less than Krause value by 30%, for La agree with Krause value and for Pr agree with DHS.
This work was carried out under grants provided by SeCyT UNC (Argentina). Research was partially supported by LNLS – National Synchrotron Light Laboratory, Brazil. One of us (NMB) would like to thank TWAS– UNESCO–CONICET for the award of a research associateship to carry out this experiment. The authors are grateful to Dr. R.T. Mainardi for providing the set of measured samples. References [1] J.H. Hubbell, P.N. Trehan, N. Singh, B. Chand, D. Mehta, M.L. Garg, R.R. Garg, S. Singh, S. Puri, J. Phys. Chem. Ref. Data 23 (1994) 339. [2] J.L. Campbell, At. Data Nucl. Data Tables 85 (2003) 291. [3] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [4] M.H. Chen, B. Crasemann, H. Mark, Phys. Rev. A 24 (1981) 177. [5] S. Puri, D. Mehta, B. Chand, N. Nirmal, P.N. Trehan, X-ray Spectrom. 22 (1993) 358. [6] J.H. Scofield, At. Data Nucl. Data Tables 14 (1974) 121. [7] M.H. Chen, B. Crasemann, H. Mark, At. Data Nucl. Data Tables 24 (1979) 13. [8] J.Q. Xu, Phys. Rev. A 24 (1991) 177. [9] J.Q. Xu, X.J. Xu, Phys. Rev. A 49 (1994) 2191. [10] U. Werner, W. Jitschin, Phys. Rev. A 38 (1988) 4009. [11] P.L. McGhee, J.L. Campbell, J. Phys. B: At. Mol. Phys. 21 (1988) 2295. [12] J.L. Campell, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 3219. [13] S. Singh, D. Mehta, R.R. Garg, S. Kumar, M.L. Garg, N. Singh, P.C. Mangal, J.H. Hubbell, P.N. Trehan, Nucl. Instr. and Meth. B 51 (1990) 5. [14] E. Oz, Y. Ozdemir, N. Ekinci, M. Ertugrul, Y. Sahin, H. Erdogan, Spectrochim. Acta B 55 (2000) 1869. [15] R. Durak, Y. Ozdemir, J. Anal. At. Spectrom. 16 (2001) 1167. [16] A. Kaya, M. Ertugrul, J. Electron. Spectrosc. Related Phen. 130 (2003) 111. [17] Y. Ozdemir, R. Durak, J Quant. Spectrosc. Radiat. Transfer 77 (2003) 95. [18] C.A. Perez, M. Ratke, M.J. Sanchez, H. Tolentino, R.T. Neuenshwander, B. Brag, M. Rubio, M.I.S. Bueno, I.M. Raimundo, J.J.R. Rohwedder, X-ray Spectrom. 28 (1998) 320. [19] J.M. Jaklevic, R.D. GiauqueHandbook of X-ray Spectrometry, Vol. 14, Marcel Dekker, Inc., 1992, p. 160. [20] E.V. Bonzi, R.A. Barrea, X-ray Spectrom. 34 (2005) 253. [21] J.H. Scofield, Lawrence Livermore National Report No. UCRL 51326 (1973) 1. [22] J.H. Hubbell, S.M. Seltzer, NISTIR 5632 (1995).