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Measurement of relative L X-ray intensity ratio following radioactive decay and photoionization
Physics Letters B 663 (2008) 186–190
Contents lists available at ScienceDirect
Physics Letters B www.elsevier.com/locate/physletb
Measurement of relative L X-ray intensity ratio following radioactive decay and photoionization b P. Yalçın a,∗ , S. Porikli b , Y. Kurucu b , Y. Sahin ¸ a b
Department of Science Education, Faculty of Education, Erzincan University, 24030 Erzincan, Turkey Department of Physics, Faculty of Sciences, Atatürk University, 25240 Erzurum, Turkey
a r t i c l e
i n f o
Article history: Received 26 November 2007 Received in revised form 28 February 2008 Accepted 11 April 2008 Available online 16 April 2008 Editor: V. Metag Keywords: Intensity ratio following radioactive decay Intensity ratio by photoionization L X-ray intensity ratio Radioisotopes L X-rays
a b s t r a c t The measurements of the L X-ray intensity ratio I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) for elements Dy, Ho, Yb, W, Hg, Tl and Pb were experimentally determined both by photon excitation, in which 59.5 keV γ -rays from a filtered radioisotope 241 Am was used, and by the radioactive decay of 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi. L X-rays emitted by samples were counted by a Si(Li) detector with resolution 160 eV at 5.9 keV. Obtained values were compared with the calculated theoretical values. Theoretical values of the I ( L α / L β), I ( L α / L γ ), I ( L α / L ι), I ( L β/ L γ ) and I ( L ι/ L γ ) intensity ratios were calculated using theoretically tabulated values of subshell photoionization cross-section, fluorescence yield, fractional X-ray emission rates, Coster–Kronig transition probabilities. It was observed that present values agree with previous theoretical and other available experimental results. © 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental detail
The accurate determination of L-shell X-ray line intensities for elements is important because of their wide use in non-destructive trace fluorescence techniques, in geological and medical research, in basic studies of nuclear and atomic physics. It is also important for developing more reliable theoretical models describing fundamental inner-shell ionization processes. Several experiments regarding the X-ray intensity ratios for heavy elements were carried out [1–24]. Rao et al. studied L-subshell fluorescence yields and Coster–Kronig transition probabilities of Pb following electroncapture decay 207 Bi [25]. However, with this study the ratio of L X-ray intensity ratios obtained following the radioactive decay to those from photoionization was computed for the first time. Merely, K X-ray intensity ratios I ( K β)/ I ( K α ), I ( K α2 )/ I ( K α1 ) and I ( K β1 )/ I ( K α1 ) for some elements have been in comparison with measured following radioactive decay and photon excitation by Büyükkasap et al. [26] and Yalçın [27]. The purpose of this study is to compare the L X-ray intensity ratio I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) obtained both for elements Dy, Ho, Yb, W, Hg, Tl and Pb by radioactive decay of radioisotopes 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi, and photon excitation of 59.5 keV γ -rays with energy-dispersive X-ray deduction system.
As shown in Fig. 1, the lead shield prevented the detector from the direct exposure of radiation from the source and the environment. An iron lining on its inner side was used to reduce the Pb L X-rays. The aluminum lining was used to reduce the K X-rays from the iron. Photons by 59.5 keV γ -rays from a filtered radioisotope 241 Am (100 mCi) annular source was used for excitation of the samples. The purity of commercially obtained in powder form materials was higher than 99.5%. All of the samples were sieved using −325 + 400 mesh. The powder materials were pelletized into the size of 10 mm diameter and 2 mm thick for final use in the experiments. The geometry used for the results obtained by photon excitation is shown in Fig. 1(a) and the geometry used for the results obtained by the decay of radioactive isotope is shown in Fig. 1(b). The present X-ray intensity measurements were performed using a Si(Li) detector (Manufacturer: Canberra, Model: SL12160, Series No. 1290538) with an active area of 12 mm2 , a sensitive crystal depth of 3 mm and Be window of 0.025 mm thickness. Si(Li) detector was adopted using electronic system and was kept at the temperature of liquid nitrogen. The measured energy resolution of the detector system was 160 eV FWHM for the Mn K α line at 5.96 keV. The electronic set up was a standard one consisting of a stabilized detector voltage supply unit, FET preamplifier, a main amplifier, an analogue to digital converter and 1024-channel pulse height analyzer. To keep the counting error in minimum, X-ray spectra were accumulated in time intervals ranging from 6 to 12 h.
*
Corresponding author. Tel.: +90 446 2240089; fax: +90 446 2231901. E-mail address: [email protected] (P. Yalçın).
0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2008.04.021
P. Yalçın et al. / Physics Letters B 663 (2008) 186–190
187
Fig. 1. The experimental set-up.
given by I (L i ) I (L j )
=
N ( L i ) ε ( L j ) β( L j ) N ( L i ) ε ( L i ) β( L i )
(1)
,
where N ( L i )/ N ( L j ) represents the ratio of the counting rates under the L i (i = α , β and ι) and L j ( j = β, ι and γ ) peaks. ε ( L j )/ε ( L i ) is the ratio of the detector efficiency values for L j and L i Xrays, respectively. In this work, the photopeak efficiency of the Si(Li) semiconductor detector was determined by Yalçın et al. [29]. β( L j )/β( L i ) is the target self-absorption correction factors for both the incident and the emitted radiations. The self-absorption correction factor βi is calculated for both L j and L i separately by using the following expression,
βi =
Fig. 2. Typical L X-ray spectrum both for element Tl by radioactive decay of radioisotope 203 Pb, and photon excitation of 59.5 keV γ -rays.
Fig. 2 shows a typical L shell X-ray spectrum both for element Tl by radioactive decay of radioisotope 203 Pb, and photon excitation of 59.5 keV γ -rays with energy-dispersive X-ray deduction system. The present work was performed by positioning fluorescence X-rays reach in front of the detector (Fig. 1(b)). The radioisotope sources were housed at the center of a cylindrical shield of 1 cm diameter and 3.4 cm length. The cylindrical shield consists of a concentrically placed glass tube covered by Mylar film, located inside of a cylindrical aluminum and lead cap as is shown Fig. 1(b). The experiment was carried out using polyester coated radioisotopes of 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi provided by Amersham International Limited. The source activities were separately measured in equipment experimental in our laboratory and theoretical was calculated. The uncertainties in the activities of the sources used were 0.7% for 160 Tb; 1.5% for 160 Er; less than 0.1% for 173 Lu; 1.8% for 182 Re; 1.4% for 201 Tl; 2.4% for 203 Pb and less than 0.05% 207 Bi. The polyester coating sources, purity better then 99.8% and thickness ∼ 15 μg/cm2 absorb less than 1% for X-rays of energy above 2 keV. The net peak areas of the L X-rays of each target were determined after background subtraction, tailing and escape-peak corrections [28]. The experimental values of I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) X-ray intensity ratios are
1 − exp[−(μinc sec θ1 + μemt sec θ2 )t ]
(μinc sec θ1 + μemt sec θ2 )t
,
(2)
where μinc (cm2 g−1 ) and μemt (cm2 g−1 ) are the mass absorption coefficients for incident and emitted radiation [30], t is the mass thickness of the 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 sample. Relative intensities are associated with the radiative transition rates from different occupied atomic states, and accurate values for them may be used in testing theoretical models for atomic structure descriptions. L X-ray intensity ratios in the literature are given in Table 1. Theoretical values of I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) were calculated by using the relation
σL α = (σ1 + σ K n K L1 )( f 13 + f 12 f 23 ) + (σ2 + σ K n K L2 ) f 23 + (σ3 + σ K n K L3 ) w 3 f 3α , σLl = (σ1 + σ K n K L1 )( f 13 + f 12 f 23 )
σLβ
+ (σ2 + σ K n K L2 ) f 23 + (σ3 + σ K n K L3 ) w 3 f 3l , = (σ1 + σ K n K L1 ) w 1 F 1β + (σ2 + σ K n K L2 ) + (σ1 + σ K n K L1 ) f 12 w 2 F 2β + (σ1 + σ K n K L1 )( f 13 + f 12 f 23 ) + (σ2 + σ K n K L2 ) f 23 + (σ3 + σ K n K L3 ) w 3 f 3β ,
(3)
(4)
σL γ = (σ1 + σ K n K L1 ) w 1 F 1γ
+ (σ2 + σ K n K L2 ) + (σ1 + σ K n K L1 ) f 12 w 2 F 2γ ,
(5)
188
P. Yalçın et al. / Physics Letters B 663 (2008) 186–190
Table 1 Comparison of present and literature and theoretical values of I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) intensity ratios Radioactive isotope (decay mode) → daughter nucleus
L X-rays intensity ratios
Excitation modes Decay
Decay Photoionization
Litera.
Theo.
Photoionization
160
Tb (β − ) → Dy = 66
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
1.189 ± 0.087 8.217 ± 0.098 23.13 ± 0.130 6.591 ± 0.033 0.313 ± 0.019
1.272 ± 0.005 8.427 ± 0.012 23.32 ± 0.035 6.663 ± 0.031 0.348 ± 0.014
0.856 0.978 0.992 0.988 0.899
1.267a 8.452a 23.38b 6.672a 0.357a
1.263 8.412 23.39 6.656 0.351
160
Er (EC) → Ho = 67
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
1.105 ± 0.069 8.122 ± 0.026 23.16 ± 0.175 6.458 ± 0.098 0.293 ± 0.029
1.230 ± 0.016 8.259 ± 0.008 23.62 ± 0.055 6.645 ± 0.004 0.362 ± 0.006
0.898 0.986 0.989 0.972 0.805
1.205a 8.333a 23.39b 6.986a 0.366a
1.243 8.274 23.51 6.653 0.350
173
Lu (EC) → Yb = 70
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.686 ± 0.017 2.811 ± 0.021 22.10 ± 0.230 4.012 ± 0.044 0.119 ± 0.006
0.704 ± 0.008 2.971 ± 0.019 22.34 ± 0.110 4.128 ± 0.014 0.132 ± 0.011
0.974 0.980 0.989 0.982 0.902
0.690a 2.950a 22.28b 4.272a 0.132a
0.720 2.952 22.56 4.100 0.131
182
Re (EC + β + ) → W = 74
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.625 ± 0.014 3.082 ± 0.053 21.14 ± 0.005 4.677 ± 0.108 0.127 ± 0.011
0.653 ± 0.071 3.213 ± 0.070 21.27 ± 0.018 4.856 ± 0.013 0.156 ± 0.004
0.957 0.963 0.994 0.963 0.814
0.628a 2.781a 21.44b 4.030a 0.131a
0.653 3.198 21.13 4.892 0.150
201
Tl (EC) → Hg = 80
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.838 ± 0.106 4.624 ± 0.301 18.83 ± 0.120 4.930 ± 0.244 0.218 ± 0.015
0.924 ± 0.013 4.836 ± 0.015 19.11 ± 0.020 5.249 ± 0.066 0.261 ± 0.006
0.797 0.882 0.895 0.882 0.896
1.011a 5.597a 19.28b 5.500a 0.280a
0.950 4.866 19.07 5.117 0.248
203
Pb (EC) → Tl = 81
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.938 ± 0.019 4.303 ± 0.287 17.69 ± 0.350 5.004 ± 0.039 0.230 ± 0.011
0.973 ± 0.007 4.785 ± 0.046 18.43 ± 0.020 5.432 ± 0.175 0.266 ± 0.007
0.947 0.895 0.954 0.921 0.865
0.967a 5.514a 18.05b 5.702a 0.284a
0.959 4.876 18.39 5.082 0.252
207
Bi (EC + β + ) → Pb = 82
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.915 ± 0.023 4.164 ± 0.319 18.65 ± 0.140 4.480 ± 0.261 0.218 ± 0.017
0.941 ± 0.015 4.558 ± 0.122 18.74 ± 0.095 4.646 ± 0.178 0.243 ± 0.018
0.972 0.914 0.995 0.964 0.987
0.939a 5.063a 18.75b 5.387a 0.278a
0.960 4.802 18.93 5.001 0.253
a
Ref. [15].
b
Ref. [19].
where σ K and σ1 , σ2 and σ3 are the K shell and L subshell photoionization cross-section [31], w i (i = 1, 2 and 3) are L subshell fluorescence yields [32], f i j are Coster–Kronig transitions probabilities from the i to j subshell fluorescence yields [32]. F ny (F 3l , F 3α , F 3β , . . .) are the fractional X-ray emission rates [33], n K Li are the number of additional vacancies transferred to the L i subshell from the K shell through radiative n K Li ( R ) and nonradiative n K Li ( A ) transitions [34]. n K Li is given by n K Li = n K Li ( R ) + n K Li ( A ).
(6)
3. Results and discussion The measured relative intensities I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) both for elements daughter/product-nucleus Dy, Ho, Yb, W, Hg, Tl and Pb by radioactive decay of radioisotopes 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi, and those elements photon excitation of 59.5 keV γ -rays have been compared with theoretical L-shell intensity ratios in Table 1. The values of the intensity ratio for seven elements, determined experimentally using Eq. (1), are listed both for product elements by radioactive decay of radioisotopes and photon excitation of 59.5 keV γ -rays in Table 1. The theoretical values were calculated by using Eqs. (3)–(6).
In this Letter, the errors in the intensity ratios have been calculated using Eqs. (1) and (2). As a result, the overall error in the measured relative intensities are estimated to be about 7%; this error arises as a result of uncertainties in different parameters; namely, the statistical and other possible errors in the area of evaluation of the L X-ray peaks N ( L i , j ) (< 0.5–5%), errors in the self-absorption correction factor at incident and emitted photon energies β( Li , j ) (0.2–3%), errors in the parameters used to photopeak efficiency ε ( L i , j ) (< 0.3–5%), errors activities of the radioisotope sources used (about 0.05–3%). The present results support the theoretical and other experimental results that are presented in Table 1 and Fig. 3. However, the L X-ray intensity ratios for the elements by radioactive decay of radioisotopes are found to deviate from both experimental and theoretical values in literature. One of the reasons of the deviation may be recoiling of the decayed nucleus, consequently relevant decay parameters. That is, the shape of every shell electron cloud is changed by recoiling of the nucleus during the decay process [26,27]. Actually, the reason for the decrease in intensity ratio of radioactive decay is that every beta decay lead to a sudden change of the proton number of the nucleus, and therefore necessarily triggers a re-arrangement of the electron cloud, accompanied mostly also by the emission of electrons (“shake-off”). Additionally, when beta particles with energies ranging between hundreds of keV and a few MeV penetrate mat-
P. Yalçın et al. / Physics Letters B 663 (2008) 186–190
189
(a)
(b)
(c)
(d)
(e) Fig. 3. Comparison of decay of radioisotope, photon excitation and theoretical predictions of L X-ray intensity ratios ((a) I ( L α )/ I ( L β), (b) I ( L α )/ I ( L γ ), (c) I ( L α )/ I ( L ι), (d) I ( L β)/ I ( L γ ) and (e) I ( L ι)/ I ( L γ )).
ter, they strongly interact with the atomic electron cloud and with the atomic nucleus [35]. As a consequence the incident electrons lose energy by radiation and by collision with a relative probabil-
ity that depends on its kinetic energy and on the atomic number of the target atoms. Vacancies in the K , L, M, N, etc., shells are thus produced, which in turn yield the characteristic lines [36].
190
P. Yalçın et al. / Physics Letters B 663 (2008) 186–190
Consequently, the transmission probabilities change from transition between energy levels. To compare theoretical values and measured intensity ratios by radioactive decay of radioisotopes together with photon excitation, L X-ray intensity ratios were plotted as a function of atomic number in Figs. 3(a), (b), (c), (d) and (e). As shown in Table 1 and Figs. 3, L X-ray intensity ratios generally decrease together with increasing atomic number. 4. Conclusion The measurements of the L X-ray intensity ratio for elements Dy, Ho, Yb, W, Hg, Tl and Pb were experimentally determined both by photon excitation and by the radioactive decay of 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi. The values of the intensity ratio determined experimentally using Eq. (1), were listed both for product elements by radioactive decay of radioisotopes and photon excitation of 59.5 keV γ -rays in Table 1. The theoretical values were calculated by using Eqs. (3)–(6). L X-rays emitted by samples were counted by a Si(Li) detector. Although the present results of this study support the theoretical and other experimental results, the L X-ray intensity ratios for elements by radioactive decay of radioisotopes deviated significantly from both experimental and theoretical results in literature. References [1] C.V. Barros Leite, A.G. De Pinho, N.V. De C. Faria, Rev. Bras. Fis. 7 (1977) 311. [2] S. Kumar, R. Mittal, K.L. Allawadhi, B.S. Sood, J. Phys. B: At. Mol. Opt. Phys. 15 (1982) 3377. [3] K. Shatendra, K.L. Allawadhi, B.S. Sood, J. Phys. B: At. Mol. Opt. Phys. 16 (1983) 4313. [4] M.L. Garg, J. Singh, H.R. Verma, N. Singh, P.C. Mangal, P.N. Trehan, J. Phys. B: At. Mol. Opt. Phys. 17 (1984) 577. [5] H.R. Verma, P. Dharminder, M.L. Garg, P.N. Trehan, J. Phys. B: At. Mol. Opt. Phys. 18 (1985) 1133. [6] M.L. Garg, D. Mehta, H.R. Verma, N. Singh, P.C. Mangal, P.N. Trehan, J. Phys. B: At. Mol. Opt. Phys. 19 (1986) 1615.
[7] C.V. Raghavaiah, N. Venkateswara Rao, S. Bhuloka Reddy, G. Satyanarayana, D.L. Sastry, J. Phys. B: At. Mol. Opt. Phys. 20 (1987) 5647. [8] S. Singh, D. Mehta, M.L. Garg, S. Kumar, N. Singh, P.C. Mangal, P.N. Trehan, J. Phys. B: At. Mol. Opt. Phys. 20 (1987) 5345. [9] S. Singh, D. Mehta, M.L. Garg, P.N. Trehan, N. Singh, S. Kumar, P.C. Mangal, J. Phys. B: At. Mol. Opt. Phys. 20 (1987) 3325. [10] G. Sree Krishna Murty, M.V.S. Chandrasekhar Rao, C.V. Raghavaiah, S. Bhuloka Reddy, G. Satyanarayana, D.L. Sastry, Phys. Rev. A 39 (1989) 1541. [11] J.B. Darko, G.K. Tetteh, X-Ray Spectr. 21 (1992) 111. [12] D.V. Rao, R. Cesareo, G.E. Gigante, Phys. Rev. A 47 (1993) 1087. [13] D.V. Rao, G.E. Gigante, R. Cesareo, Phys. Scr. 47 (1993) 765. [14] M. Ertu˘grul, J. Phys. B: At. Mol. Opt. Phys. 28 (1995) 4037. [15] M. Ertu˘grul, Nucl. Instrum. Methods B 111 (1996) 229. [16] M. Ertugrul, Spectrochim. Acta, Part B 52 (1997) 201. [17] O. Dogan, Ö. Simsek, U. Turgut, M. Ertugrul, J. Radioanal. Nucl. Chem. 232 (1998) 143. [18] M. Ismaill, N.B. Malhi, X-Ray Spectr. 29 (2000) 317. [19] R. Durak, Y. Özdemir, Phys. Lett. A 284 (2001) 43. [20] E. Tırasoglu, ¸ U. Çevik, B. Ertu˘gral, G. Apaydın, M. Ertu˘grul, A.I˙ . Kobya, Eur. Phys. J. D 26 (2003) 231. [21] U. Turgut, M. Ertugrul, Nucl. Instrum. Methods B 222 (2004) 432. [22] A.B. Hallak, X-Ray Spectr. 29 (2004) 30. [23] A. Carreras, J. Trincavelli, R. Bonetto, G. Castellano, X-Ray Spectr. 34 (2005) 124. [24] S.J. Cipolla, Nucl. Instrum. Methods B 261 (2007) 153. [25] P.V. Rao, R.E. Wood, J.M. Palms, Phys. Rev. 178 (1969) 2005. [26] E. Büyükkasap, A. Küçükönder, Y. Sahin, ¸ H. Erdo˘gan, J. Radioanal. Nucl. Chem. Lett. 186 (1994) 471. [27] P. Yalçın, Nucl. Instrum. Methods B 254 (2007) 182. [28] Y. Sahin, ¸ R. Durak, Y. Kurucu, S. Erzeneo˘glu, J. Radioanal. Nucl. Chem. 177 (1994) 403. [29] P. Yalçın, A. Sülün, A. Bastu˘ ¸ g, Y. Kurucu, Y. Sahin, ¸ Can. J. Anal. Sci. Spectrosc. 50 (2005) 103. [30] E. Storm, I.H. Israel, Nucl. Data Tables A 7 (1970) 565. [31] J.H. Scofield, Theoretical photoionization cross sections from 1 to 1500 keV. UCRL report 51326, Lawrence Livermore Laboratory, Livermore, CA, 1973. [32] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [33] J.H. Scofield, At. Data Nucl. Data Tables 14 (1974) 121. [34] V.P. Rao, M.H. Chen, B. Crasemann, Phys. Rev. A 5 (1972) 997. [35] M.A. Chesta, T.S. Plivelic, R.T. Mainardi, Nucl. Instrum. Methods B 187 (2002) 259. [36] X. Long, M. Liu, F. Ho, X. Peng, At. Data Nucl. Data Tables 45 (1990) 353.
Contents lists available at ScienceDirect
Physics Letters B www.elsevier.com/locate/physletb
Measurement of relative L X-ray intensity ratio following radioactive decay and photoionization b P. Yalçın a,∗ , S. Porikli b , Y. Kurucu b , Y. Sahin ¸ a b
Department of Science Education, Faculty of Education, Erzincan University, 24030 Erzincan, Turkey Department of Physics, Faculty of Sciences, Atatürk University, 25240 Erzurum, Turkey
a r t i c l e
i n f o
Article history: Received 26 November 2007 Received in revised form 28 February 2008 Accepted 11 April 2008 Available online 16 April 2008 Editor: V. Metag Keywords: Intensity ratio following radioactive decay Intensity ratio by photoionization L X-ray intensity ratio Radioisotopes L X-rays
a b s t r a c t The measurements of the L X-ray intensity ratio I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) for elements Dy, Ho, Yb, W, Hg, Tl and Pb were experimentally determined both by photon excitation, in which 59.5 keV γ -rays from a filtered radioisotope 241 Am was used, and by the radioactive decay of 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi. L X-rays emitted by samples were counted by a Si(Li) detector with resolution 160 eV at 5.9 keV. Obtained values were compared with the calculated theoretical values. Theoretical values of the I ( L α / L β), I ( L α / L γ ), I ( L α / L ι), I ( L β/ L γ ) and I ( L ι/ L γ ) intensity ratios were calculated using theoretically tabulated values of subshell photoionization cross-section, fluorescence yield, fractional X-ray emission rates, Coster–Kronig transition probabilities. It was observed that present values agree with previous theoretical and other available experimental results. © 2008 Elsevier B.V. All rights reserved.
1. Introduction
2. Experimental detail
The accurate determination of L-shell X-ray line intensities for elements is important because of their wide use in non-destructive trace fluorescence techniques, in geological and medical research, in basic studies of nuclear and atomic physics. It is also important for developing more reliable theoretical models describing fundamental inner-shell ionization processes. Several experiments regarding the X-ray intensity ratios for heavy elements were carried out [1–24]. Rao et al. studied L-subshell fluorescence yields and Coster–Kronig transition probabilities of Pb following electroncapture decay 207 Bi [25]. However, with this study the ratio of L X-ray intensity ratios obtained following the radioactive decay to those from photoionization was computed for the first time. Merely, K X-ray intensity ratios I ( K β)/ I ( K α ), I ( K α2 )/ I ( K α1 ) and I ( K β1 )/ I ( K α1 ) for some elements have been in comparison with measured following radioactive decay and photon excitation by Büyükkasap et al. [26] and Yalçın [27]. The purpose of this study is to compare the L X-ray intensity ratio I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) obtained both for elements Dy, Ho, Yb, W, Hg, Tl and Pb by radioactive decay of radioisotopes 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi, and photon excitation of 59.5 keV γ -rays with energy-dispersive X-ray deduction system.
As shown in Fig. 1, the lead shield prevented the detector from the direct exposure of radiation from the source and the environment. An iron lining on its inner side was used to reduce the Pb L X-rays. The aluminum lining was used to reduce the K X-rays from the iron. Photons by 59.5 keV γ -rays from a filtered radioisotope 241 Am (100 mCi) annular source was used for excitation of the samples. The purity of commercially obtained in powder form materials was higher than 99.5%. All of the samples were sieved using −325 + 400 mesh. The powder materials were pelletized into the size of 10 mm diameter and 2 mm thick for final use in the experiments. The geometry used for the results obtained by photon excitation is shown in Fig. 1(a) and the geometry used for the results obtained by the decay of radioactive isotope is shown in Fig. 1(b). The present X-ray intensity measurements were performed using a Si(Li) detector (Manufacturer: Canberra, Model: SL12160, Series No. 1290538) with an active area of 12 mm2 , a sensitive crystal depth of 3 mm and Be window of 0.025 mm thickness. Si(Li) detector was adopted using electronic system and was kept at the temperature of liquid nitrogen. The measured energy resolution of the detector system was 160 eV FWHM for the Mn K α line at 5.96 keV. The electronic set up was a standard one consisting of a stabilized detector voltage supply unit, FET preamplifier, a main amplifier, an analogue to digital converter and 1024-channel pulse height analyzer. To keep the counting error in minimum, X-ray spectra were accumulated in time intervals ranging from 6 to 12 h.
*
Corresponding author. Tel.: +90 446 2240089; fax: +90 446 2231901. E-mail address: [email protected] (P. Yalçın).
0370-2693/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.physletb.2008.04.021
P. Yalçın et al. / Physics Letters B 663 (2008) 186–190
187
Fig. 1. The experimental set-up.
given by I (L i ) I (L j )
=
N ( L i ) ε ( L j ) β( L j ) N ( L i ) ε ( L i ) β( L i )
(1)
,
where N ( L i )/ N ( L j ) represents the ratio of the counting rates under the L i (i = α , β and ι) and L j ( j = β, ι and γ ) peaks. ε ( L j )/ε ( L i ) is the ratio of the detector efficiency values for L j and L i Xrays, respectively. In this work, the photopeak efficiency of the Si(Li) semiconductor detector was determined by Yalçın et al. [29]. β( L j )/β( L i ) is the target self-absorption correction factors for both the incident and the emitted radiations. The self-absorption correction factor βi is calculated for both L j and L i separately by using the following expression,
βi =
Fig. 2. Typical L X-ray spectrum both for element Tl by radioactive decay of radioisotope 203 Pb, and photon excitation of 59.5 keV γ -rays.
Fig. 2 shows a typical L shell X-ray spectrum both for element Tl by radioactive decay of radioisotope 203 Pb, and photon excitation of 59.5 keV γ -rays with energy-dispersive X-ray deduction system. The present work was performed by positioning fluorescence X-rays reach in front of the detector (Fig. 1(b)). The radioisotope sources were housed at the center of a cylindrical shield of 1 cm diameter and 3.4 cm length. The cylindrical shield consists of a concentrically placed glass tube covered by Mylar film, located inside of a cylindrical aluminum and lead cap as is shown Fig. 1(b). The experiment was carried out using polyester coated radioisotopes of 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi provided by Amersham International Limited. The source activities were separately measured in equipment experimental in our laboratory and theoretical was calculated. The uncertainties in the activities of the sources used were 0.7% for 160 Tb; 1.5% for 160 Er; less than 0.1% for 173 Lu; 1.8% for 182 Re; 1.4% for 201 Tl; 2.4% for 203 Pb and less than 0.05% 207 Bi. The polyester coating sources, purity better then 99.8% and thickness ∼ 15 μg/cm2 absorb less than 1% for X-rays of energy above 2 keV. The net peak areas of the L X-rays of each target were determined after background subtraction, tailing and escape-peak corrections [28]. The experimental values of I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) X-ray intensity ratios are
1 − exp[−(μinc sec θ1 + μemt sec θ2 )t ]
(μinc sec θ1 + μemt sec θ2 )t
,
(2)
where μinc (cm2 g−1 ) and μemt (cm2 g−1 ) are the mass absorption coefficients for incident and emitted radiation [30], t is the mass thickness of the 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 sample. Relative intensities are associated with the radiative transition rates from different occupied atomic states, and accurate values for them may be used in testing theoretical models for atomic structure descriptions. L X-ray intensity ratios in the literature are given in Table 1. Theoretical values of I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) were calculated by using the relation
σL α = (σ1 + σ K n K L1 )( f 13 + f 12 f 23 ) + (σ2 + σ K n K L2 ) f 23 + (σ3 + σ K n K L3 ) w 3 f 3α , σLl = (σ1 + σ K n K L1 )( f 13 + f 12 f 23 )
σLβ
+ (σ2 + σ K n K L2 ) f 23 + (σ3 + σ K n K L3 ) w 3 f 3l , = (σ1 + σ K n K L1 ) w 1 F 1β + (σ2 + σ K n K L2 ) + (σ1 + σ K n K L1 ) f 12 w 2 F 2β + (σ1 + σ K n K L1 )( f 13 + f 12 f 23 ) + (σ2 + σ K n K L2 ) f 23 + (σ3 + σ K n K L3 ) w 3 f 3β ,
(3)
(4)
σL γ = (σ1 + σ K n K L1 ) w 1 F 1γ
+ (σ2 + σ K n K L2 ) + (σ1 + σ K n K L1 ) f 12 w 2 F 2γ ,
(5)
188
P. Yalçın et al. / Physics Letters B 663 (2008) 186–190
Table 1 Comparison of present and literature and theoretical values of I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) intensity ratios Radioactive isotope (decay mode) → daughter nucleus
L X-rays intensity ratios
Excitation modes Decay
Decay Photoionization
Litera.
Theo.
Photoionization
160
Tb (β − ) → Dy = 66
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
1.189 ± 0.087 8.217 ± 0.098 23.13 ± 0.130 6.591 ± 0.033 0.313 ± 0.019
1.272 ± 0.005 8.427 ± 0.012 23.32 ± 0.035 6.663 ± 0.031 0.348 ± 0.014
0.856 0.978 0.992 0.988 0.899
1.267a 8.452a 23.38b 6.672a 0.357a
1.263 8.412 23.39 6.656 0.351
160
Er (EC) → Ho = 67
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
1.105 ± 0.069 8.122 ± 0.026 23.16 ± 0.175 6.458 ± 0.098 0.293 ± 0.029
1.230 ± 0.016 8.259 ± 0.008 23.62 ± 0.055 6.645 ± 0.004 0.362 ± 0.006
0.898 0.986 0.989 0.972 0.805
1.205a 8.333a 23.39b 6.986a 0.366a
1.243 8.274 23.51 6.653 0.350
173
Lu (EC) → Yb = 70
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.686 ± 0.017 2.811 ± 0.021 22.10 ± 0.230 4.012 ± 0.044 0.119 ± 0.006
0.704 ± 0.008 2.971 ± 0.019 22.34 ± 0.110 4.128 ± 0.014 0.132 ± 0.011
0.974 0.980 0.989 0.982 0.902
0.690a 2.950a 22.28b 4.272a 0.132a
0.720 2.952 22.56 4.100 0.131
182
Re (EC + β + ) → W = 74
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.625 ± 0.014 3.082 ± 0.053 21.14 ± 0.005 4.677 ± 0.108 0.127 ± 0.011
0.653 ± 0.071 3.213 ± 0.070 21.27 ± 0.018 4.856 ± 0.013 0.156 ± 0.004
0.957 0.963 0.994 0.963 0.814
0.628a 2.781a 21.44b 4.030a 0.131a
0.653 3.198 21.13 4.892 0.150
201
Tl (EC) → Hg = 80
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.838 ± 0.106 4.624 ± 0.301 18.83 ± 0.120 4.930 ± 0.244 0.218 ± 0.015
0.924 ± 0.013 4.836 ± 0.015 19.11 ± 0.020 5.249 ± 0.066 0.261 ± 0.006
0.797 0.882 0.895 0.882 0.896
1.011a 5.597a 19.28b 5.500a 0.280a
0.950 4.866 19.07 5.117 0.248
203
Pb (EC) → Tl = 81
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.938 ± 0.019 4.303 ± 0.287 17.69 ± 0.350 5.004 ± 0.039 0.230 ± 0.011
0.973 ± 0.007 4.785 ± 0.046 18.43 ± 0.020 5.432 ± 0.175 0.266 ± 0.007
0.947 0.895 0.954 0.921 0.865
0.967a 5.514a 18.05b 5.702a 0.284a
0.959 4.876 18.39 5.082 0.252
207
Bi (EC + β + ) → Pb = 82
I ( L α )/ I ( L β) I ( L α )/ I ( L γ ) I ( L α )/ I ( L ι) I ( L β)/ I ( L γ ) I ( L ι)/ I ( L γ )
0.915 ± 0.023 4.164 ± 0.319 18.65 ± 0.140 4.480 ± 0.261 0.218 ± 0.017
0.941 ± 0.015 4.558 ± 0.122 18.74 ± 0.095 4.646 ± 0.178 0.243 ± 0.018
0.972 0.914 0.995 0.964 0.987
0.939a 5.063a 18.75b 5.387a 0.278a
0.960 4.802 18.93 5.001 0.253
a
Ref. [15].
b
Ref. [19].
where σ K and σ1 , σ2 and σ3 are the K shell and L subshell photoionization cross-section [31], w i (i = 1, 2 and 3) are L subshell fluorescence yields [32], f i j are Coster–Kronig transitions probabilities from the i to j subshell fluorescence yields [32]. F ny (F 3l , F 3α , F 3β , . . .) are the fractional X-ray emission rates [33], n K Li are the number of additional vacancies transferred to the L i subshell from the K shell through radiative n K Li ( R ) and nonradiative n K Li ( A ) transitions [34]. n K Li is given by n K Li = n K Li ( R ) + n K Li ( A ).
(6)
3. Results and discussion The measured relative intensities I ( L α )/ I ( L β), I ( L α )/ I ( L γ ), I ( L α )/ I ( L ι), I ( L β)/ I ( L γ ) and I ( L ι)/ I ( L γ ) both for elements daughter/product-nucleus Dy, Ho, Yb, W, Hg, Tl and Pb by radioactive decay of radioisotopes 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi, and those elements photon excitation of 59.5 keV γ -rays have been compared with theoretical L-shell intensity ratios in Table 1. The values of the intensity ratio for seven elements, determined experimentally using Eq. (1), are listed both for product elements by radioactive decay of radioisotopes and photon excitation of 59.5 keV γ -rays in Table 1. The theoretical values were calculated by using Eqs. (3)–(6).
In this Letter, the errors in the intensity ratios have been calculated using Eqs. (1) and (2). As a result, the overall error in the measured relative intensities are estimated to be about 7%; this error arises as a result of uncertainties in different parameters; namely, the statistical and other possible errors in the area of evaluation of the L X-ray peaks N ( L i , j ) (< 0.5–5%), errors in the self-absorption correction factor at incident and emitted photon energies β( Li , j ) (0.2–3%), errors in the parameters used to photopeak efficiency ε ( L i , j ) (< 0.3–5%), errors activities of the radioisotope sources used (about 0.05–3%). The present results support the theoretical and other experimental results that are presented in Table 1 and Fig. 3. However, the L X-ray intensity ratios for the elements by radioactive decay of radioisotopes are found to deviate from both experimental and theoretical values in literature. One of the reasons of the deviation may be recoiling of the decayed nucleus, consequently relevant decay parameters. That is, the shape of every shell electron cloud is changed by recoiling of the nucleus during the decay process [26,27]. Actually, the reason for the decrease in intensity ratio of radioactive decay is that every beta decay lead to a sudden change of the proton number of the nucleus, and therefore necessarily triggers a re-arrangement of the electron cloud, accompanied mostly also by the emission of electrons (“shake-off”). Additionally, when beta particles with energies ranging between hundreds of keV and a few MeV penetrate mat-
P. Yalçın et al. / Physics Letters B 663 (2008) 186–190
189
(a)
(b)
(c)
(d)
(e) Fig. 3. Comparison of decay of radioisotope, photon excitation and theoretical predictions of L X-ray intensity ratios ((a) I ( L α )/ I ( L β), (b) I ( L α )/ I ( L γ ), (c) I ( L α )/ I ( L ι), (d) I ( L β)/ I ( L γ ) and (e) I ( L ι)/ I ( L γ )).
ter, they strongly interact with the atomic electron cloud and with the atomic nucleus [35]. As a consequence the incident electrons lose energy by radiation and by collision with a relative probabil-
ity that depends on its kinetic energy and on the atomic number of the target atoms. Vacancies in the K , L, M, N, etc., shells are thus produced, which in turn yield the characteristic lines [36].
190
P. Yalçın et al. / Physics Letters B 663 (2008) 186–190
Consequently, the transmission probabilities change from transition between energy levels. To compare theoretical values and measured intensity ratios by radioactive decay of radioisotopes together with photon excitation, L X-ray intensity ratios were plotted as a function of atomic number in Figs. 3(a), (b), (c), (d) and (e). As shown in Table 1 and Figs. 3, L X-ray intensity ratios generally decrease together with increasing atomic number. 4. Conclusion The measurements of the L X-ray intensity ratio for elements Dy, Ho, Yb, W, Hg, Tl and Pb were experimentally determined both by photon excitation and by the radioactive decay of 160 Tb, 160 Er, 173 Lu, 182 Re, 201 Tl, 203 Pb and 207 Bi. The values of the intensity ratio determined experimentally using Eq. (1), were listed both for product elements by radioactive decay of radioisotopes and photon excitation of 59.5 keV γ -rays in Table 1. The theoretical values were calculated by using Eqs. (3)–(6). L X-rays emitted by samples were counted by a Si(Li) detector. Although the present results of this study support the theoretical and other experimental results, the L X-ray intensity ratios for elements by radioactive decay of radioisotopes deviated significantly from both experimental and theoretical results in literature. References [1] C.V. Barros Leite, A.G. De Pinho, N.V. De C. Faria, Rev. Bras. Fis. 7 (1977) 311. [2] S. Kumar, R. Mittal, K.L. Allawadhi, B.S. Sood, J. Phys. B: At. Mol. Opt. Phys. 15 (1982) 3377. [3] K. Shatendra, K.L. Allawadhi, B.S. Sood, J. Phys. B: At. Mol. Opt. Phys. 16 (1983) 4313. [4] M.L. Garg, J. Singh, H.R. Verma, N. Singh, P.C. Mangal, P.N. Trehan, J. Phys. B: At. Mol. Opt. Phys. 17 (1984) 577. [5] H.R. Verma, P. Dharminder, M.L. Garg, P.N. Trehan, J. Phys. B: At. Mol. Opt. Phys. 18 (1985) 1133. [6] M.L. Garg, D. Mehta, H.R. Verma, N. Singh, P.C. Mangal, P.N. Trehan, J. Phys. B: At. Mol. Opt. Phys. 19 (1986) 1615.
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