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The effect of an external magnetic field on the L subshell X-ray fluorescence cross sections and L subshell fluorescence yields in elements 73 ≤ Z ≤ 92 by 59.54 keV photons
Available online at www.sciencedirect.com
Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
The effect of an external magnetic field on the L subshell X-ray fluorescence cross sections and L subshell fluorescence yields in elements 73 ≤ Z ≤ 92 by 59.54 keV photons D. Demir ∗ , Y. S¸ahin Atat¨urk University, Faculty of Arts and Sciences, Department of Physics, 25240 Erzurum, Turkey Received 15 November 2006; received in revised form 5 July 2007; accepted 12 July 2007 Available online 24 July 2007
Abstract Li (i = 1, 2 and 3) X-ray fluorescence cross sections for Ta, W, Au, Hg, Tl, Pb, Bi, Th and U have been measured using the 59.54 keV incident photons energy in the external magnetic field of intensity +0.60 T. The values of Li subshell fluorescence yields (w1 , w2 and w3 ) have been measured for the same elements using the previously measured cross section values and the theoretical Li subshell photoionisation cross sections, Coster–Kronig transition probabilities and emission rates. It is observed that the measured Li subshell X-ray fluorescence cross section and Li subshell fluorescence yield values for B = 0 are in good agreement with the theoretical ones evaluated using Li subshell fluorescence yield and Li subshell photoionization cross section. Furthermore, the results show that the atomic parameters such as spectral linewidth, radiation rates, photoionization cross section and fluorescence yield can change when the irradiation is conducted in a magnetic field. © 2007 Elsevier B.V. All rights reserved. Keywords: Photoionization; Fluorescence yields; Level widths; External magnetic field
1. Introduction X-ray fluorescence parameters such as fluorescence yields and cross sections, are very important in understanding the ionization of atoms as well as for non-destructive elemental analysis in several fields such as material science, medical physics, industry and environmental science. Besides, these parameters are needed to develop more reliable theoretical models for describing the fundamental inner shell ionization processes. Therefore, studies of the L XRF cross sections and yields were focused on this subject [1–5]. The primary vacancies in the Li subshells can arise from either direct ionization by photons, electrons, heavy charged particles or from a shift of a K shell vacancy to the L shell. These vacancies decay through radiative, Auger and Coster–Kronig transitions. The number of Li subshell X-rays produced per Li subshell vacancy decay defines the subshell fluorescence yield wi . L XRF cross sections can be calculated theoretically by
∗
Corresponding author. Tel.: +90 442 231 4078; fax: +90 442 236 0948. E-mail address: [email protected] (D. Demir).
0368-2048/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2007.07.001
using photoelectric (or photoionization) cross sections, fluorescence yields, and fractional emission rates. Uncertainties in these tabulated quantities largely reflect the error in the L XRF cross sections. For this reason, most users prefer the experimental values of the cross sections whenever large discrepancies are observed between theoretical and experimental results. For quantitative analytical applications, it is necessary to know the different relative intensities of the photons which contribute to the fluorescence. Since fluorescence cross sections increase as the energy decrease, the contributions to the X-ray fluorescence of low-energy, low intensity transitions can be very important. Experimental L X-ray fluorescence cross sections of many elements have been measured by different groups [6–10]. Limited work [11–14] has been conducted for L subshell fluorescence yield. An atom in a field of electromagnetic radiation experiences interactions between its magnetic moments and the magnetic field and also between its electric charges and the electric field. The elementary electromagnetic theory explains the behavior of a magnetic dipole of moment μl when it is replaced in an applied magnetic field B. The dipole will experience a torque tending to align the dipole with the field, and (τ = μ l × B)
D. Demir, Y. S¸ahin / Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
that, associated with this torque, there is a potential energy of orientation. E = −μ l · B
9
literature experimental results and theoretical predictions. It is found that they are in good agreement.
(1) 2. Experimental set-up and method of measurement
The slight difference in energy is associated with these different orientations in the magnetic field. Thus, the atomic parameters as the shapes and the circulation properties of the electronic charge clouds, spectral linewidth, radiation rates, atomic lifetimes, photoionization cross sections and fluorescence yields can change when the irradiated atom is placed in an external magnetic field. In this work, the effect of the external magnetic field on the L1 , L2 and L3 subshell X-ray fluorescence cross sections and w1 , w2 and w3 fluorescence yields for various elements, namely Ta, W, Au, Hg, Tl, Pb, Bi, Th and U in the region 73 ≤ Z ≤ 92, have been measured using an energy-dispersive X-ray fluorescence set-up involving a 241 Am radioisotope source as an exciter. To our knowledge, Li subshell X-ray fluorescence cross sections and Li subshell fluorescence yields in the external magnetic field have not been reported in the literature and appear to have been measured here for the first time. In the absence of external magnetic field, the results of our work have been compared with the
The geometry and shielding of the experimental set-up are shown in Fig. 1. Gamma photons of 59.54 keV from a filtered radioisotope 241 Am point source was used for direct excitation of spectroscopically pure (purity better than 99.6%) foil of Ta, Au, Pb and powders of W, Hg2 (NO3 )2 ·2H2 O, Tl2 O3 , Bi, Th(NO3 )4 ·5H2 O and UO2 (CH3 COO)·2H2 O. The 241 Am gamma source was housed at the center of a cylindrical lead shield of 10 mm diameter and 36 mm depth. The L X-ray spectra from different samples were detected by a Si(Li) detector (FWHM = 180 eV at 5.9 keV, an active diameter = 6.2 mm, sensitive crystal depth = 5 mm, Be window thickness = 0.008 mm). The detector was shielded by a graded filter of Pb, Fe and Al, to obtain a thin beam of photons scattered from the target and to prevent undesirable radiation (Np L X-rays from 241 Am source, L X-rays from the Pb mask, environmental background and background arising from the scattering from the sample holder and
Fig. 1. Experimental set-up.
10
D. Demir, Y. S¸ahin / Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
electromagnet). The data were collected into 16384 channels of a digital spectrum analyzer DSA-1000. The samples were mounted in a sample holder placed between the pole pieces of an electromagnet capable of producing the magnetic field of approximately 3 T at 1 mm pole range. During the study, the magnetic field intensities of +0.60 T were applied to the samples. The continuity and stability of the current feeding the electromagnet were monitored by an ammeter. In order to check the systematic and the statistical counting errors arising from radiation emanating from the exciting source, a thin indium wire reference sample positioned at the collimator of the Si(Li) detector. The pulse height spectrum of L X-rays emitted from each sample was acquired for a period of 10 h to obtain good statistics in the evaluation of each L X-ray peaks and the measurements were repeated 5 times. A typical L X-ray spectrum of Au at the B = +0.60 T is shown in Fig. 2. The peaks due to the Ll, Lα, Lβ and Lγ group of lines are well resolved. The spectra were analyzed by using Microcal Origin 7.5 Demo Version. The counting electronics included a pile-up rejection circuit and live time clock which was used for the dead time correction. Since there is no escape peak and any other undesired effects contributing to the spectrum, the mean count of twenty channels at each side of the peaks used to calculate the background and to define the net peak area. Since the background is constant in this region a linear background function was selected to all L X-ray peaks. The background count rate was subtracted from the measurements. The experimental L subshell X-ray fluorescence cross sections have been obtained using the equation: σLi
ILi = I0 GεLi βLi t
(2)
where ILi is the observed intensity (area under the photopeak) corresponding to the Li group of X-rays, I0 the intensity of the exciting radiation, G is a geometrical factor dependent on the source-sample geometry, εLi the detector efficiency for the Li group of X-rays, βLi the target self-absorption correction factor
Fig. 3. A typical K X-ray spectrum of the Mo target.
for the target material, which accounts for absorption in the target of incident photons and the emitted characteristic X-rays and t is the mass per area of the element in g/cm2 . The I0 Gε values corresponding to the 59.54 keV incident photons energy were determined by measuring the K X-ray yields from spectroscopically pure targets in the atomic range 23 ≤ Z ≤ 47. For these measurements the targets under investigation were replaced, in turn, with targets V, Fe, Co, Ni, Cu, As, Mo and Ag with the mass thickness 0.060–0.38 g/cm2 . A typical K X-ray spectrum of Mo is shown in Fig. 3. The I0 Gε values for the present set-up were determined by the following relationship: I0 Gε =
IKα σKα tβKα
(3)
where IKα is the number of counts per second under the K␣ Xray peak. σKα is the fluorescence cross sections. The theoretical values of σKα fluorescence cross sections are calculated using the equation: σKα = σK (E)wK FKα
(4)
where σ K (E) is the K shell photoionization cross section of the given element for the excitation energy E. The values of σ K (E) were taken from Scofield [15] based on Hartree–Slater calculations. wK is the K shell fluorescence yield and was taken from the tables of Krause [16]. FKα is the fractional X-ray emission rate for Kα X-rays and is defined as FKα =
IKα IKα + IKβ
(5)
where IKα and IKβ are the K␣ and Kβ X-ray intensities, respectively. The values of IKα and IKβ were taken from Scofield [17]. The self-absorption correction factor has been calculated using the following relation: 1 − exp −(μinc /cos θ1 + μemt /cos θ2 )t β= (6) (μinc /cos θ1 + μemt /cos θ2 )t
Fig. 2. A typical L X-ray spectrum of the Au target in B = +0.60 T.
where μinc and μemt are the attenuation coefficients (cm2 g−1 ) of the incident photons and emitted characteristic X-rays, respectively, θ 1 and θ 2 are the angles of incident photon and emitted
F2β F1γ − F1β F2γ σLα F3α
(16) (17)
The experimental L subshell fluorescence yields were calculated using the following expressions: w1 = w2 = w3 =
σLx 1
(18)
σ1 σLx 2
(19)
σ2 + σ1 f12 σLx 3 [σ3 + σ2 f23 + σ1 (f13 + f12 f23 )]
(20)
σLx 1 , σLx 2 and σLx 3 values were evaluated from Eqs. (14)–(16). σ 1 , σ 2 and σ 3 were interpolated from Scofield’s table [15] and f12 , f13 and f23 were taken from table of Krause [16]. 3. Results and discussion The effect of the external magnetic field on Li (σLx 1 , σLx 2 and x σL3 ) X-ray fluorescence cross sections for thin targets of Ta, W,
3.4 4.7 9.2 14.2 11.4 14.1 18.9 19.2 30.7 ± ± ± ± ± ± ± ± ±
σLx 3 (E) B = +0.60 T
74.43 85.053 257.04 251.00 193.75 284.84 308.69 411.95 454.09 3.4 4.5 10.2 15.4 10.4 14.7 19.7 20.4 31.4 ± ± ± ± ± ± ± ± ± 81.89 94.46 190.42 205.92 222.44 249.78 268.47 436.77 519.65 61.12 67.49 109.82 122.34 118.07 132.10 161.13 298.60 323.70 4.2 14.1 5.4 10.1 20.8 13.8 13.2 19.4 21.2 ± ± ± ± ± ± ± ± ± 79.25 112.22 146.52 183.87 87.01 189.77 188.01 181.80 173.98 E = experimental. T = theoretical.
(σLβ F1γ − σLγ F1β − σLx 3 F3β F1γ )
(15)
a
σLx 3 =
F1β
b
σLx 2 =
(σLβ − σLx 2 F2β − σLx 3 F3β )
4.4 14.2 5.4 10.2 20.2 13.2 14.4 20.4 24.5
σLx 1 =
± ± ± ± ± ± ± ± ±
where Γ (L3 – M1 ) is the partial emission rate and Γ 3 is the total emission rate of L3 subshell [17]. Using Eqs. (8)–(10), we can resolve the values of σLx 1 , σLx 2 and σLx 3 as follows:
68.60 76.55 110.07 103.61 123.02 128.20 148.72 237.60 246.11
(14)
47.96 53.68 47.50 49.29 51.09 50.54 59.85 103.39 118.06
Γ (L3 − M1 ) Γ3
1.8 3.7 4.1 3.2 3.4 4.2 4.5 3.2 7.2
F3l =
± ± ± ± ± ± ± ± ±
where σ i (i = 1, 2 and 3) is the photoionization cross section of the Li subshell [15] wi (i = 1, 2 and 3) is the Li subshell fluorescence yield [16] and fij (i = 1, 2 and j = 2, 3) is the Coster Kronig transition probability [16]. The Li emission rate per total L3 emission rate (F3l ) is written as
42.55 36.84 74.16 64.19 53.25 83.31 90.25 129.56 108.23
(13)
= [σ3 + σ2 f23 + σ1 (f13 + f12 f23 )]w3
1.9 3.7 4.1 3.1 3.4 4.1 4.7 3.1 7.4
(12)
σLx 3
± ± ± ± ± ± ± ± ±
σLx 2 = (σ2 + σ1 f12 )w2
40.25 44.89 53.65 59.90 66.34 68.95 70.55 125.89 133.98
(11)
73 Ta 74 W 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 90 Th 92 U
σLx 1 = σ1 w1
σLx 3 (E) B = 0
and L subshell X-ray production cross sections are given by the following expression:
σLx 2 (T ) B = 0
(10)
σLx 2 (E) B = +0.60 T
σLγ = σLx 1 F1γ + σLx 2 F2γ
σLx 2 (E) B = 0
(9)
σLx 1 (T)b B = 0
σLβ = σLx 1 F1β + σLx 2 F2β + σLx 3 F3β
σLx 1 (E) B = +0.60 T
(8)
σLx 1 (E)a B = 0
σLα = σLx 3 F3α
Z
(7)
Table 1 The experimental and theoretical values of Li subshell X-ray fluorescence cross sections of the elements within the atomic region 73 ≤ Z ≤ 92 in the external magnetic field
σLl = σLx 3 F3l
σLx 3 (T ) B = 0
X-ray with the target. μinc and μemt were obtained from WinXcom. This is a Windows version of XCOM [18] the well-known program for calculating X- and ␥-rays attenuation coefficients. Ll , Lα , L and Lγ X-ray production cross sections are given by the following expressions:
11
80.62 89.70 194.76 206.12 225.40 211.18 270.49 460.49 547.83
D. Demir, Y. S¸ahin / Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
12
D. Demir, Y. S¸ahin / Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
Table 2 Comparison of present wi values with the values of Krause [16] Z
w1
w2
B=0 73 Ta 74 W 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 90 Th 92 U
0.115 0.123 0.121 0.130 0.139 0.153 0.138 0.196 0.200
B = +0.60 T ± ± ± ± ± ± ± ± ±
0.005 0.010 0.010 0.006 0.012 0.014 0.015 0.005 0.016
0.122 0.101 0.167 0.139 0.112 0.185 0.176 0.202 0.161
± ± ± ± ± ± ± ± ±
0.005 0.010 0.010 0.006 0.011 0.014 0.016 0.005 0.016
w3
Ref. [16]
B=0
B = +0.60 T
Ref. [16]
B=0
B = +0.60 T
Ref. [16]
0.137 0.147 0.107 0.107 0.107 0.112 0.117 0.161 0.176
0.290 ± 0.020 0.296 ± 0.018 0.282 ± 0.024 0.314 ± 0.024 0.335 ± 0.027 0.382 ± 0.020 0.397 ± 0.025 0.481 ± 0.034 0.455 ± 0.034
0.335 ± 0.020 0.439 ± 0.018 0.362 ± 0.026 0.422 ± 0.027 0.245 ± 0.026 0.436 ± 0.021 0.452 ± 0.024 0.392 ± 0.035 0.351 ± 0.034
0.258 0.271 0.334 0.347 0.361 0.373 0.387 0.479 0.467
0.247 ± 0.016 0.269 ± 0.017 0.313 ± 0.019 0.333 ± 0.022 0.342 ± 0.020 0.356 ± 0.023 0.370 ± 0.027 0.439 ± 0.020 0.464 ± 0.029
0.224 ± 0.015 0.242 ± 0.017 0.422 ± 0.018 0.405 ± 0.022 0.298 ± 0.019 0.412 ± 0.025 0.426 ± 0.026 0.414 ± 0.020 0.405 ± 0.031
0.243 0.255 0.321 0.333 0.347 0.361 0.373 0.463 0.489
Au, Hg, Tl, Pb, Bi, Th and U at 59.54 keV excitation energy is measured and the results are compared with theoretical predictions and experimental values at 59.54 keV taken from the literature [8]. These results are given in Table 1. It is clear from Table 1 that the present experimental results agree with the theoretical results and with the results in Ref. [8] for B = 0. To the best our knowledge, no other experimental data available for comparison with the results obtained by us for B = 0. The total error in the measured Li subshell X-ray fluorescence cross sections arises due to peak area evaluation, I0 Gε factor, the target thickness measurement and self-absorption correction. The errors given in Table 1 are estimated using the propagation of errors based on classical rules. The standard deviation of five repeated measurements obtained for Th sample is 1.04% of the arithmetic mean of these measurements. For Bi sample, this ratio is 0.92%. This means that the fluctuation of each measured value about the mean of each series or the statistical counting errors is small. It can be seen from Table 1 that σLx 1 , σLx 2 and σLx 3 change with the external magnetic field. The magnetic field dependency of Li subshell X-ray fluorescence cross sections can be explained with the interaction of magnetic dipole moment with the external magnetic field. To show the accuracy of the present results in the external magnetic field, we applied the t-test to Li X-ray fluorescence cross sections of Th in B = 0 and B = +0.60 T. The t-test compares the actual difference between two means in relation to the variation in the data (expressed as the standard deviation of the difference between the means). It was found that texpt is 7.48, 30.5 and 19.9 for σLx 1 , σLx 2 and σLx 3 , respectively. The critical t value is 1.613 at the 5% level of significance and 8 degrees of freedom. According to the t-test result, the difference of the means of σLx 1 , σLx 2 and σLx 3 obtained for B = 0 and B = +0.60 T is significantly different than the t-test difference. We can say that the data collected in Table 1 shows sensitivity with respect to the external magnetic field. The values for Li subshell X-ray fluorescence yields (w1 , w2 and w3 ) deduced using Eqs. (8)–(20) for the same elements are presented in Table 2. In Table 2, the values of the determined w1 , w2 and w3 X-ray fluorescence yield are also compared with the theoretical [16] and experimental values taken from the literature [8]. It is concluded that the experimental Li subshell X-ray fluorescence yields for B = 0 are in good agreement with the theoretical and experimental results for all elements. The dis-
crepancies, experimentally, probably arise from the inaccuracy in the net Li peak area measurement. Furthermore, two effects; non-electric-dipole effect and the relativistic effects may change the theoretical values of Li subshell fluorescence yield. It can be seen from Table 2 that Li subshell X-ray fluorescence yields change with the external magnetic field as expected. In conclusion, the magnetic field dependency of Li subshell fluorescence cross sections and Li subshell fluorescence yields clearly establish that the atomic parameters such as the shapes and the circulation properties of the electronic charge clouds, spectral linewidth, radiation rates, photoionization cross sections and fluorescence yields can change due to irradiated atom is placed in an external magnetic field. The best of our knowledge there are no reports regarding effect of an external magnetic field to the σLx i and ωi (i = 1, 2 and 3). To obtain more definite conclusions on the magnetic field dependency of the atomic parameters, more experimental data are clearly needed, particularly in the heavy elements region. References [1] J.H. Hubbell, National Institute of Standards and Technology NISTIR 894144, 1989. [2] 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. [3] D.V. Rao, R. Cesareo, G.E. Gigante, Radiat. Phys. Chem. 46 (1995) 17. ¨ S¸ims¸ek, U. ¨ Turgut, M. Ertu˘grul, Phys. Scr. 56 (1997) 580. [4] O. Do˘gan, O. [5] A. G¨urol, R. Polat, A. Karabulut, G. Budak, X-ray Spectrom. 32 (2003) 161. ¨ S¨og˘ u¨ t, M. Ertu˘grul, O. ˙Ic¸elli, J. Phys. B: At. Mol. [6] M. S¸ahin, L. Demir, O. Opt. Phys. 33 (2000) 93. [7] R.R. Garg, S. Puri, S. Singh, D. Mehta, J.S. Shahi, M.L. Garg, N. Singh, P.C. Mangal, P.N. Trehan, Nucl. Instrum. Methods B 72 (1992) 147. [8] M. Ertu˘grul, J. Radioanal. Nucl. Chem. 237 (1998) 139. [9] A.C. Mandal, S. Santra, D. Mitra, M. Sarkar, D. Bhattacharya, Nucl. Instrum. Methods B 234 (2005) 176. [10] K.A. Al-Saleh, N.S. Saleh, Radiat. Phys. Chem. 54 (1999) 117. [11] A. Rani, N. Nath, S.N. Chaturvedi, X-ray Spectrom. 18 (1989) 7780. [12] E.V. Bonzi, N.M. Badiger, Nucl. Instrum. Methods B 248 (2006) 242. ¨ [13] R. Durak, Y. Ozdemir, J. Anal. At. Spectrom. 16 (2001) 1167. [14] W. Jitschin, R. Stotzel, T. Papp, M. Sarkar, Phys. Rev. A 59 (1999) 3408. [15] J.H. Scofield, Lawrence Livermore Laboratory Report UCRL 51326, 1973. [16] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [17] J.H. Scofıeld, At. Data Nucl. Data Tables 14 (1974) 121. [18] L. Gerward, N. Guilbert, K. Bjorn, H. Levring, Radiat. Phys. Chem. 60 (2001) 23.
Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
The effect of an external magnetic field on the L subshell X-ray fluorescence cross sections and L subshell fluorescence yields in elements 73 ≤ Z ≤ 92 by 59.54 keV photons D. Demir ∗ , Y. S¸ahin Atat¨urk University, Faculty of Arts and Sciences, Department of Physics, 25240 Erzurum, Turkey Received 15 November 2006; received in revised form 5 July 2007; accepted 12 July 2007 Available online 24 July 2007
Abstract Li (i = 1, 2 and 3) X-ray fluorescence cross sections for Ta, W, Au, Hg, Tl, Pb, Bi, Th and U have been measured using the 59.54 keV incident photons energy in the external magnetic field of intensity +0.60 T. The values of Li subshell fluorescence yields (w1 , w2 and w3 ) have been measured for the same elements using the previously measured cross section values and the theoretical Li subshell photoionisation cross sections, Coster–Kronig transition probabilities and emission rates. It is observed that the measured Li subshell X-ray fluorescence cross section and Li subshell fluorescence yield values for B = 0 are in good agreement with the theoretical ones evaluated using Li subshell fluorescence yield and Li subshell photoionization cross section. Furthermore, the results show that the atomic parameters such as spectral linewidth, radiation rates, photoionization cross section and fluorescence yield can change when the irradiation is conducted in a magnetic field. © 2007 Elsevier B.V. All rights reserved. Keywords: Photoionization; Fluorescence yields; Level widths; External magnetic field
1. Introduction X-ray fluorescence parameters such as fluorescence yields and cross sections, are very important in understanding the ionization of atoms as well as for non-destructive elemental analysis in several fields such as material science, medical physics, industry and environmental science. Besides, these parameters are needed to develop more reliable theoretical models for describing the fundamental inner shell ionization processes. Therefore, studies of the L XRF cross sections and yields were focused on this subject [1–5]. The primary vacancies in the Li subshells can arise from either direct ionization by photons, electrons, heavy charged particles or from a shift of a K shell vacancy to the L shell. These vacancies decay through radiative, Auger and Coster–Kronig transitions. The number of Li subshell X-rays produced per Li subshell vacancy decay defines the subshell fluorescence yield wi . L XRF cross sections can be calculated theoretically by
∗
Corresponding author. Tel.: +90 442 231 4078; fax: +90 442 236 0948. E-mail address: [email protected] (D. Demir).
0368-2048/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.elspec.2007.07.001
using photoelectric (or photoionization) cross sections, fluorescence yields, and fractional emission rates. Uncertainties in these tabulated quantities largely reflect the error in the L XRF cross sections. For this reason, most users prefer the experimental values of the cross sections whenever large discrepancies are observed between theoretical and experimental results. For quantitative analytical applications, it is necessary to know the different relative intensities of the photons which contribute to the fluorescence. Since fluorescence cross sections increase as the energy decrease, the contributions to the X-ray fluorescence of low-energy, low intensity transitions can be very important. Experimental L X-ray fluorescence cross sections of many elements have been measured by different groups [6–10]. Limited work [11–14] has been conducted for L subshell fluorescence yield. An atom in a field of electromagnetic radiation experiences interactions between its magnetic moments and the magnetic field and also between its electric charges and the electric field. The elementary electromagnetic theory explains the behavior of a magnetic dipole of moment μl when it is replaced in an applied magnetic field B. The dipole will experience a torque tending to align the dipole with the field, and (τ = μ l × B)
D. Demir, Y. S¸ahin / Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
that, associated with this torque, there is a potential energy of orientation. E = −μ l · B
9
literature experimental results and theoretical predictions. It is found that they are in good agreement.
(1) 2. Experimental set-up and method of measurement
The slight difference in energy is associated with these different orientations in the magnetic field. Thus, the atomic parameters as the shapes and the circulation properties of the electronic charge clouds, spectral linewidth, radiation rates, atomic lifetimes, photoionization cross sections and fluorescence yields can change when the irradiated atom is placed in an external magnetic field. In this work, the effect of the external magnetic field on the L1 , L2 and L3 subshell X-ray fluorescence cross sections and w1 , w2 and w3 fluorescence yields for various elements, namely Ta, W, Au, Hg, Tl, Pb, Bi, Th and U in the region 73 ≤ Z ≤ 92, have been measured using an energy-dispersive X-ray fluorescence set-up involving a 241 Am radioisotope source as an exciter. To our knowledge, Li subshell X-ray fluorescence cross sections and Li subshell fluorescence yields in the external magnetic field have not been reported in the literature and appear to have been measured here for the first time. In the absence of external magnetic field, the results of our work have been compared with the
The geometry and shielding of the experimental set-up are shown in Fig. 1. Gamma photons of 59.54 keV from a filtered radioisotope 241 Am point source was used for direct excitation of spectroscopically pure (purity better than 99.6%) foil of Ta, Au, Pb and powders of W, Hg2 (NO3 )2 ·2H2 O, Tl2 O3 , Bi, Th(NO3 )4 ·5H2 O and UO2 (CH3 COO)·2H2 O. The 241 Am gamma source was housed at the center of a cylindrical lead shield of 10 mm diameter and 36 mm depth. The L X-ray spectra from different samples were detected by a Si(Li) detector (FWHM = 180 eV at 5.9 keV, an active diameter = 6.2 mm, sensitive crystal depth = 5 mm, Be window thickness = 0.008 mm). The detector was shielded by a graded filter of Pb, Fe and Al, to obtain a thin beam of photons scattered from the target and to prevent undesirable radiation (Np L X-rays from 241 Am source, L X-rays from the Pb mask, environmental background and background arising from the scattering from the sample holder and
Fig. 1. Experimental set-up.
10
D. Demir, Y. S¸ahin / Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
electromagnet). The data were collected into 16384 channels of a digital spectrum analyzer DSA-1000. The samples were mounted in a sample holder placed between the pole pieces of an electromagnet capable of producing the magnetic field of approximately 3 T at 1 mm pole range. During the study, the magnetic field intensities of +0.60 T were applied to the samples. The continuity and stability of the current feeding the electromagnet were monitored by an ammeter. In order to check the systematic and the statistical counting errors arising from radiation emanating from the exciting source, a thin indium wire reference sample positioned at the collimator of the Si(Li) detector. The pulse height spectrum of L X-rays emitted from each sample was acquired for a period of 10 h to obtain good statistics in the evaluation of each L X-ray peaks and the measurements were repeated 5 times. A typical L X-ray spectrum of Au at the B = +0.60 T is shown in Fig. 2. The peaks due to the Ll, Lα, Lβ and Lγ group of lines are well resolved. The spectra were analyzed by using Microcal Origin 7.5 Demo Version. The counting electronics included a pile-up rejection circuit and live time clock which was used for the dead time correction. Since there is no escape peak and any other undesired effects contributing to the spectrum, the mean count of twenty channels at each side of the peaks used to calculate the background and to define the net peak area. Since the background is constant in this region a linear background function was selected to all L X-ray peaks. The background count rate was subtracted from the measurements. The experimental L subshell X-ray fluorescence cross sections have been obtained using the equation: σLi
ILi = I0 GεLi βLi t
(2)
where ILi is the observed intensity (area under the photopeak) corresponding to the Li group of X-rays, I0 the intensity of the exciting radiation, G is a geometrical factor dependent on the source-sample geometry, εLi the detector efficiency for the Li group of X-rays, βLi the target self-absorption correction factor
Fig. 3. A typical K X-ray spectrum of the Mo target.
for the target material, which accounts for absorption in the target of incident photons and the emitted characteristic X-rays and t is the mass per area of the element in g/cm2 . The I0 Gε values corresponding to the 59.54 keV incident photons energy were determined by measuring the K X-ray yields from spectroscopically pure targets in the atomic range 23 ≤ Z ≤ 47. For these measurements the targets under investigation were replaced, in turn, with targets V, Fe, Co, Ni, Cu, As, Mo and Ag with the mass thickness 0.060–0.38 g/cm2 . A typical K X-ray spectrum of Mo is shown in Fig. 3. The I0 Gε values for the present set-up were determined by the following relationship: I0 Gε =
IKα σKα tβKα
(3)
where IKα is the number of counts per second under the K␣ Xray peak. σKα is the fluorescence cross sections. The theoretical values of σKα fluorescence cross sections are calculated using the equation: σKα = σK (E)wK FKα
(4)
where σ K (E) is the K shell photoionization cross section of the given element for the excitation energy E. The values of σ K (E) were taken from Scofield [15] based on Hartree–Slater calculations. wK is the K shell fluorescence yield and was taken from the tables of Krause [16]. FKα is the fractional X-ray emission rate for Kα X-rays and is defined as FKα =
IKα IKα + IKβ
(5)
where IKα and IKβ are the K␣ and Kβ X-ray intensities, respectively. The values of IKα and IKβ were taken from Scofield [17]. The self-absorption correction factor has been calculated using the following relation: 1 − exp −(μinc /cos θ1 + μemt /cos θ2 )t β= (6) (μinc /cos θ1 + μemt /cos θ2 )t
Fig. 2. A typical L X-ray spectrum of the Au target in B = +0.60 T.
where μinc and μemt are the attenuation coefficients (cm2 g−1 ) of the incident photons and emitted characteristic X-rays, respectively, θ 1 and θ 2 are the angles of incident photon and emitted
F2β F1γ − F1β F2γ σLα F3α
(16) (17)
The experimental L subshell fluorescence yields were calculated using the following expressions: w1 = w2 = w3 =
σLx 1
(18)
σ1 σLx 2
(19)
σ2 + σ1 f12 σLx 3 [σ3 + σ2 f23 + σ1 (f13 + f12 f23 )]
(20)
σLx 1 , σLx 2 and σLx 3 values were evaluated from Eqs. (14)–(16). σ 1 , σ 2 and σ 3 were interpolated from Scofield’s table [15] and f12 , f13 and f23 were taken from table of Krause [16]. 3. Results and discussion The effect of the external magnetic field on Li (σLx 1 , σLx 2 and x σL3 ) X-ray fluorescence cross sections for thin targets of Ta, W,
3.4 4.7 9.2 14.2 11.4 14.1 18.9 19.2 30.7 ± ± ± ± ± ± ± ± ±
σLx 3 (E) B = +0.60 T
74.43 85.053 257.04 251.00 193.75 284.84 308.69 411.95 454.09 3.4 4.5 10.2 15.4 10.4 14.7 19.7 20.4 31.4 ± ± ± ± ± ± ± ± ± 81.89 94.46 190.42 205.92 222.44 249.78 268.47 436.77 519.65 61.12 67.49 109.82 122.34 118.07 132.10 161.13 298.60 323.70 4.2 14.1 5.4 10.1 20.8 13.8 13.2 19.4 21.2 ± ± ± ± ± ± ± ± ± 79.25 112.22 146.52 183.87 87.01 189.77 188.01 181.80 173.98 E = experimental. T = theoretical.
(σLβ F1γ − σLγ F1β − σLx 3 F3β F1γ )
(15)
a
σLx 3 =
F1β
b
σLx 2 =
(σLβ − σLx 2 F2β − σLx 3 F3β )
4.4 14.2 5.4 10.2 20.2 13.2 14.4 20.4 24.5
σLx 1 =
± ± ± ± ± ± ± ± ±
where Γ (L3 – M1 ) is the partial emission rate and Γ 3 is the total emission rate of L3 subshell [17]. Using Eqs. (8)–(10), we can resolve the values of σLx 1 , σLx 2 and σLx 3 as follows:
68.60 76.55 110.07 103.61 123.02 128.20 148.72 237.60 246.11
(14)
47.96 53.68 47.50 49.29 51.09 50.54 59.85 103.39 118.06
Γ (L3 − M1 ) Γ3
1.8 3.7 4.1 3.2 3.4 4.2 4.5 3.2 7.2
F3l =
± ± ± ± ± ± ± ± ±
where σ i (i = 1, 2 and 3) is the photoionization cross section of the Li subshell [15] wi (i = 1, 2 and 3) is the Li subshell fluorescence yield [16] and fij (i = 1, 2 and j = 2, 3) is the Coster Kronig transition probability [16]. The Li emission rate per total L3 emission rate (F3l ) is written as
42.55 36.84 74.16 64.19 53.25 83.31 90.25 129.56 108.23
(13)
= [σ3 + σ2 f23 + σ1 (f13 + f12 f23 )]w3
1.9 3.7 4.1 3.1 3.4 4.1 4.7 3.1 7.4
(12)
σLx 3
± ± ± ± ± ± ± ± ±
σLx 2 = (σ2 + σ1 f12 )w2
40.25 44.89 53.65 59.90 66.34 68.95 70.55 125.89 133.98
(11)
73 Ta 74 W 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 90 Th 92 U
σLx 1 = σ1 w1
σLx 3 (E) B = 0
and L subshell X-ray production cross sections are given by the following expression:
σLx 2 (T ) B = 0
(10)
σLx 2 (E) B = +0.60 T
σLγ = σLx 1 F1γ + σLx 2 F2γ
σLx 2 (E) B = 0
(9)
σLx 1 (T)b B = 0
σLβ = σLx 1 F1β + σLx 2 F2β + σLx 3 F3β
σLx 1 (E) B = +0.60 T
(8)
σLx 1 (E)a B = 0
σLα = σLx 3 F3α
Z
(7)
Table 1 The experimental and theoretical values of Li subshell X-ray fluorescence cross sections of the elements within the atomic region 73 ≤ Z ≤ 92 in the external magnetic field
σLl = σLx 3 F3l
σLx 3 (T ) B = 0
X-ray with the target. μinc and μemt were obtained from WinXcom. This is a Windows version of XCOM [18] the well-known program for calculating X- and ␥-rays attenuation coefficients. Ll , Lα , L and Lγ X-ray production cross sections are given by the following expressions:
11
80.62 89.70 194.76 206.12 225.40 211.18 270.49 460.49 547.83
D. Demir, Y. S¸ahin / Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
12
D. Demir, Y. S¸ahin / Journal of Electron Spectroscopy and Related Phenomena 162 (2008) 8–12
Table 2 Comparison of present wi values with the values of Krause [16] Z
w1
w2
B=0 73 Ta 74 W 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 90 Th 92 U
0.115 0.123 0.121 0.130 0.139 0.153 0.138 0.196 0.200
B = +0.60 T ± ± ± ± ± ± ± ± ±
0.005 0.010 0.010 0.006 0.012 0.014 0.015 0.005 0.016
0.122 0.101 0.167 0.139 0.112 0.185 0.176 0.202 0.161
± ± ± ± ± ± ± ± ±
0.005 0.010 0.010 0.006 0.011 0.014 0.016 0.005 0.016
w3
Ref. [16]
B=0
B = +0.60 T
Ref. [16]
B=0
B = +0.60 T
Ref. [16]
0.137 0.147 0.107 0.107 0.107 0.112 0.117 0.161 0.176
0.290 ± 0.020 0.296 ± 0.018 0.282 ± 0.024 0.314 ± 0.024 0.335 ± 0.027 0.382 ± 0.020 0.397 ± 0.025 0.481 ± 0.034 0.455 ± 0.034
0.335 ± 0.020 0.439 ± 0.018 0.362 ± 0.026 0.422 ± 0.027 0.245 ± 0.026 0.436 ± 0.021 0.452 ± 0.024 0.392 ± 0.035 0.351 ± 0.034
0.258 0.271 0.334 0.347 0.361 0.373 0.387 0.479 0.467
0.247 ± 0.016 0.269 ± 0.017 0.313 ± 0.019 0.333 ± 0.022 0.342 ± 0.020 0.356 ± 0.023 0.370 ± 0.027 0.439 ± 0.020 0.464 ± 0.029
0.224 ± 0.015 0.242 ± 0.017 0.422 ± 0.018 0.405 ± 0.022 0.298 ± 0.019 0.412 ± 0.025 0.426 ± 0.026 0.414 ± 0.020 0.405 ± 0.031
0.243 0.255 0.321 0.333 0.347 0.361 0.373 0.463 0.489
Au, Hg, Tl, Pb, Bi, Th and U at 59.54 keV excitation energy is measured and the results are compared with theoretical predictions and experimental values at 59.54 keV taken from the literature [8]. These results are given in Table 1. It is clear from Table 1 that the present experimental results agree with the theoretical results and with the results in Ref. [8] for B = 0. To the best our knowledge, no other experimental data available for comparison with the results obtained by us for B = 0. The total error in the measured Li subshell X-ray fluorescence cross sections arises due to peak area evaluation, I0 Gε factor, the target thickness measurement and self-absorption correction. The errors given in Table 1 are estimated using the propagation of errors based on classical rules. The standard deviation of five repeated measurements obtained for Th sample is 1.04% of the arithmetic mean of these measurements. For Bi sample, this ratio is 0.92%. This means that the fluctuation of each measured value about the mean of each series or the statistical counting errors is small. It can be seen from Table 1 that σLx 1 , σLx 2 and σLx 3 change with the external magnetic field. The magnetic field dependency of Li subshell X-ray fluorescence cross sections can be explained with the interaction of magnetic dipole moment with the external magnetic field. To show the accuracy of the present results in the external magnetic field, we applied the t-test to Li X-ray fluorescence cross sections of Th in B = 0 and B = +0.60 T. The t-test compares the actual difference between two means in relation to the variation in the data (expressed as the standard deviation of the difference between the means). It was found that texpt is 7.48, 30.5 and 19.9 for σLx 1 , σLx 2 and σLx 3 , respectively. The critical t value is 1.613 at the 5% level of significance and 8 degrees of freedom. According to the t-test result, the difference of the means of σLx 1 , σLx 2 and σLx 3 obtained for B = 0 and B = +0.60 T is significantly different than the t-test difference. We can say that the data collected in Table 1 shows sensitivity with respect to the external magnetic field. The values for Li subshell X-ray fluorescence yields (w1 , w2 and w3 ) deduced using Eqs. (8)–(20) for the same elements are presented in Table 2. In Table 2, the values of the determined w1 , w2 and w3 X-ray fluorescence yield are also compared with the theoretical [16] and experimental values taken from the literature [8]. It is concluded that the experimental Li subshell X-ray fluorescence yields for B = 0 are in good agreement with the theoretical and experimental results for all elements. The dis-
crepancies, experimentally, probably arise from the inaccuracy in the net Li peak area measurement. Furthermore, two effects; non-electric-dipole effect and the relativistic effects may change the theoretical values of Li subshell fluorescence yield. It can be seen from Table 2 that Li subshell X-ray fluorescence yields change with the external magnetic field as expected. In conclusion, the magnetic field dependency of Li subshell fluorescence cross sections and Li subshell fluorescence yields clearly establish that the atomic parameters such as the shapes and the circulation properties of the electronic charge clouds, spectral linewidth, radiation rates, photoionization cross sections and fluorescence yields can change due to irradiated atom is placed in an external magnetic field. The best of our knowledge there are no reports regarding effect of an external magnetic field to the σLx i and ωi (i = 1, 2 and 3). To obtain more definite conclusions on the magnetic field dependency of the atomic parameters, more experimental data are clearly needed, particularly in the heavy elements region. References [1] J.H. Hubbell, National Institute of Standards and Technology NISTIR 894144, 1989. [2] 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. [3] D.V. Rao, R. Cesareo, G.E. Gigante, Radiat. Phys. Chem. 46 (1995) 17. ¨ S¸ims¸ek, U. ¨ Turgut, M. Ertu˘grul, Phys. Scr. 56 (1997) 580. [4] O. Do˘gan, O. [5] A. G¨urol, R. Polat, A. Karabulut, G. Budak, X-ray Spectrom. 32 (2003) 161. ¨ S¨og˘ u¨ t, M. Ertu˘grul, O. ˙Ic¸elli, J. Phys. B: At. Mol. [6] M. S¸ahin, L. Demir, O. Opt. Phys. 33 (2000) 93. [7] R.R. Garg, S. Puri, S. Singh, D. Mehta, J.S. Shahi, M.L. Garg, N. Singh, P.C. Mangal, P.N. Trehan, Nucl. Instrum. Methods B 72 (1992) 147. [8] M. Ertu˘grul, J. Radioanal. Nucl. Chem. 237 (1998) 139. [9] A.C. Mandal, S. Santra, D. Mitra, M. Sarkar, D. Bhattacharya, Nucl. Instrum. Methods B 234 (2005) 176. [10] K.A. Al-Saleh, N.S. Saleh, Radiat. Phys. Chem. 54 (1999) 117. [11] A. Rani, N. Nath, S.N. Chaturvedi, X-ray Spectrom. 18 (1989) 7780. [12] E.V. Bonzi, N.M. Badiger, Nucl. Instrum. Methods B 248 (2006) 242. ¨ [13] R. Durak, Y. Ozdemir, J. Anal. At. Spectrom. 16 (2001) 1167. [14] W. Jitschin, R. Stotzel, T. Papp, M. Sarkar, Phys. Rev. A 59 (1999) 3408. [15] J.H. Scofield, Lawrence Livermore Laboratory Report UCRL 51326, 1973. [16] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [17] J.H. Scofıeld, At. Data Nucl. Data Tables 14 (1974) 121. [18] L. Gerward, N. Guilbert, K. Bjorn, H. Levring, Radiat. Phys. Chem. 60 (2001) 23.