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Measurement of vacancy transfer probabilities from K to L shell for high atomic number elements
Spectrochimica Acta Part B 60 (2005) 519 – 524 www.elsevier.com/locate/sab
Measurement of vacancy transfer probabilities from K to L shell for high atomic number elements B. Ertugrala,*, G. Apaydina, H. Baltasa, U. C ¸ evika, A.I˙. Kobyaa, M. Ertugrulb a b
Department of Physics, Faculty of Art and Sciences, Karadeniz Technical University, 61080 Trabzon, Turkey Department of Electrical and Electronic, Faculty of Engineering, Ataturk University, 25240 Erzurum, Turkey Received 19 November 2004; accepted 22 March 2005 Available online 27 April 2005
Abstract The probabilities for vacancy transfer from K to L shell, g KL, were obtained by measuring the Kh/Ka intensity ratios in 25 elements over the range 57 Z 92 using a 25 mCi 57Co filtered source for excitation. The K X-rays were measured by using a Si(Li) detector. The theoretical values were calculated via the radiative and radiationless transition rates of these elements. The comparison between present experimental results and theoretical predictions showed that both results agreed well. The experimental and theoretical values were fitted against atomic number (Z). The measured values of g KL for Tm, Yb, Lu, Hf and Ir are being reported here for the first time. D 2005 Elsevier B.V. All rights reserved. Keywords: Intensity ratios; Vacancy transfer; X-ray fluorescence (XRF); Radiative and radiationless transition rates
1. Introduction Atomic shell data are relevant in nuclear physics. Vacancies in the atomic shell give rise to rearrangements in the shells which are accompanied by the emission of Xray quanta and the ejection of Auger electrons [1]. The vacancy transfer coefficient g KL describes the mean number of vacancies produced in the L shell by one vacancy in the K shell. Accurate experimental data regarding the vacancy transfer probability are important in many practical applications, such as nuclear electron capture, internal conversion of g-rays, photoelectric effect, atomic processes leading to the emission of X-rays, Auger electrons and computations for medical physics and irradiational processes. In recent times, some works were done on the K and L X-ray fluorescence cross-sections [2 –7], L X-ray intensity ratio [8,9], K, L and M X-ray production cross-sections [10 –13], chemical effect [14], for many elements by using energy-dispersive X-ray fluorescence (EDXRF).
* Corresponding author. Tel.: +90 462 3772539; fax: +90 462 3253195. E-mail address: [email protected] (B. Ertugral). 0584-8547/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2005.03.009
A review of the literature shows that a number of experimental studies on the vacancy transfer probabilities in the atomic shell (K to L and M) or subshell (K to Li i = 1, 2, 3) were reported. As a result of this, Ertugrul et al. [15] measured K to L shell radiative vacancy transfer probabilities for some elements. The Ka to La intensity ratios of 11 lanthanide elements were measured and the effect of vacancy transfer of K to L shell on these ratios was also investigated at 59.5 keV by using a Si(Li) detector by Ertugrul [16]. Total, radiative and radionless vacancy transfer probabilities from K to Li subshell of Cs, Ba and La were measured with a new approach by Ertugrul [17]. In adition, Ertugrul et al. [18] measured K to L shell vacancy transfer probabilities using L X-rays yields in the atomic region 73 Z 92 at 59.5 and 122 keV energies. Ertugral et al. [19] measured K to L shell vacancy transfer probabilities using intensity ratio of Ka and Lx total X-rays for some elements in the atomic region 52 Z 68 at 59.5 keV. Simsek et al. [20] determined K to L shell vacancy transfer probabilities for nine elements in the atomic region 46 Z 55 measuring the L X-ray yields from targets excited by 5.96 and 59.5 keV photons. K to L shell vacancy transfer probabilities were measured in the
520
B. Ertugral et al. / Spectrochimica Acta Part B 60 (2005) 519 – 524
Mylar Sample
Annular source (57Co) Pb annular colimator
Berillium window
X-ray fluorescence radiation Si(Li) Detector
Holder
Fig. 1. Experimental setup.
atomic region 37 Z 42 at 5.96 and 22.6 keV energies by Puri et al. [21]. In addition, Puri et al. [22] have calculated and fitted them against atomic number Z and also fitted coefficients for vacancy transfer probabilities from K to L1, K to L2, K to L3, K to L (average), L1 to M, L2 to M and L3 to M shells. The values of the vacancy transfer probabilities from the K to the L1, L2 and L3 shells (g KL) for elements in the atomic range 20 Z 94 have been calculated by Rao et al. [23]. In these calculations, the contribution due to Auger and radiative transitions was made using the best fitted experimental data on the fluorescence yields and intensity ratios of different components of KLX (X = L, M, N, etc.) Auger electrons and K X-rays currently available. From the literature review, there is no work done on the measurements of vacancy transfer probabilities of K to L shell for Tm, Yb, Lu, Hf, and Ir elements. In this study, we determined K to L shell vacancy transfer probabilities for 25 elements in the atomic range 58 Z 92 by measuring the K X-ray yields from targets excited by 123.6 keV photons and using I Kh/I Ka intensity ratios. Finally the measured
values of g KL were compared with all available data and the theoretical values deduced using the calculated radiative Xray emission rates [24] and Auger transition rates [25] based on the relativistic Dirac –Hartree – Slater (RDHS) model.
2. Method of measurement The geometry and the shielding arrangements of the experimental set-up employed in the present work are as shown schematically in Fig. 1. The samples were irradiated with a 57Co radioisotope source at 123.6 keV photons with strength of approximately 25 mCi. Spectroscopically, high purity (99.90%) targets of Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Re, Ir, Au, Hg, Tl, Pb, Bi, Th and U of thickness ranging from 20 to 40 mg/cm2 have been used for the measurement. The samples were then placed at 45- angle with respect to the direct beam and fluorescent X-rays emitted 90- to the detector. The incident beam and fluorescence X-rays emitted from the target were
TaKα 1 40000 TaKα 2
Counts
30000
20000 TaKβ 1
10000
TaKβ 2 0 700
7 50
800
850
Channel Fig. 2. Typical K X-ray spectrum for Ta.
900
950
B. Ertugral et al. / Spectrochimica Acta Part B 60 (2005) 519 – 524
detected with a Si(Li) detector manufactured by Canberra (FWHM = 160 eV at 5.9 keV, active area 13 mm2, thickness 3 mm and Be window thickness = 30 Am). The output from the preamplifier, with pulse pile-up rejection capability, was fed to a multi-channel analyzer interfaced with a personal computer provided with suitable software (Tennelec PCA II) for data acquisition and peak analysis. The live time was selected to be 5000 s for all elements. Fig. 2 shows a typical K X-ray spectrum for Ta.
3. Experimental K to L shell vacancy transfer probabilities The experimental K to L shell total vacancy transfer probabilities, g KL, were evaluated by using following equation [1] gKL ¼
2 xK 1 þ ðIKh =IKa Þ
ð1Þ
where x K is the fluorescence yield of the K shell [26] and I Kh/I Ka is the intensity ratio of the K X-rays. The I Kh/I Ka intensity ratio is obtained from the following equation [19] IKh NKh bKa eKa ¼ IKa NKa bKh eKh
ð2Þ
where N Kh and N Ka are the net counts under the Kh and Ka peaks, b Kh and b Ka are the self-absorption correction factor for energies of Kh and Ka peaks. The self absorption correction factor b Kx (x = a, h) at the excitation energy has been calculated by using the following 1,20E+008
521
expression, assuming that the fluorescence X-rays are incident normally at the detector. bKx ¼
1 exp½ ðl1 =sinh þ l2 =sin/Þt ðl1 =sinh þ l2 =sin/Þt
where l 1 and l 2 are the total mass absorption coefficients (from XCOM [27]) of target material at the incident photon energy and at the emitted average Ka and Kh X-ray energy [28] and t is the thickness of the target in g/cm2, h and / are the angles of incident photon and emitted X-rays with respect to the normal at the surface of the sample. e Kh and e Ka are the detector efficiencies at the Kx X-ray energies and were evaluated using the equation eKi ¼
NKi I0 GbKi mi rKi
ð4Þ
where N K and b K have the same meaning as in Eq. (2). The term I 0 is the intensity of exciting radiation, G is the geometry factor, m i is the mass of the element in the sample (g cm2). The absolute efficiency e of the X-ray detector was determined by collecting the K X-ray spectra of samples of Ce, Nd, Gd, Dy, Er, Yb, Ta, Ir, Hg, Bi, Th, and U in the same experimental set-up. The term r Ki represents the K X-ray fluorescence crosssections and is given as rKi ¼ rPK xK fKi
ð5Þ
where r KP is the K shell photoionization cross-section [29] and f Ki is fractional X-ray emission rate [30]. The measured variation of I 0Ge was fitted to a third-order polynomial as a function of the mean K X-ray energy and fitted coefficients are as shown in Fig. 3.
I0Gε =418558110-13885694 EKx+157914 EKx2-597 EKx3
1,00E+008
I0Gε
8,00E+007
6,00E+007
4,00E+007
2,00E+007
0,00E+000 30
40
50
ð3Þ
60
70
Energy (keV) Fig. 3. The variation of I 0Ge versus energy.
80
90
100
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4. Theoretical calculation of K to L shell vacancy transfer probabilities
The g KLi was calculated using the following equations [23]:
The vacancy transfer probabilities from K to L shell are defined as the number of Li subshell vacancies produced in the decay of one K shell vacancy through radiative K – Li transitions or through Auger K – Li Lj and K –Li X (X = M, N, O, etc.) transitions. The average number of g KL is
gKL1 ¼
gKLi ¼ gKLi ðRÞ þ gKLi ðAÞ;
1 ½CR ðKL1 Þ þ 2CA ðKL1 L1 Þ þ CA ðKL1 L2 Þ C ðK Þ þ CA ðKL1 L3 Þ þ CA ðKL1 XÞ
gKL2 ¼
ð6Þ
1 ½CR ðKL2 Þ þ 2CA ðKL2 L2 Þ þ CA ðKL1 L2 Þ C ðK Þ þ CA ðKL2 L3 Þ þ CA ðKL2 XÞ
where g KLi (R) and g KLi (A) are the radiative and Auger transition probabilities of the K to Li subshell, respectively. The number of g KLi (R) is proportional to the probability of radiative transition which takes place at K –Li transition and is given by
gKL3 ¼
gKLi ðRÞ ¼ xK ½ I ðKLi Þ=IK ðRÞ
ðX ¼ M; N; O; etc:Þ:
ð7Þ
where I(KLi ) is the K – Li X-ray intensity and I K(R) is the total intensity of the K X-rays.
1 ½CR ðKL3 Þ þ 2CA ðKL3 L3 Þ þ CA ðKL2 L3 Þ C ðK Þ þ CA ðKL1 L3 Þ þ CA ðKL3 XÞ ð8Þ
In these equations, C R and C A are the radiative and the Auger partial widths corresponding to the transitions
Table 1 Comparison of experimental and theoretical results for K to L shell vacancy transfer probabilities Elements
g KL Present experimental values
58
Ce Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 87 Fr 88 Ra 89 Ac 90 Th 91 Pa 92 U 59
0.874 T 0.053 0.877 T 0.026 0.872 T 0.035 – 0.862 T 0.026 0.853 T 0.034 0.846 T 0.042 0.851 T 0.025 0.852 T 0.025 0.841 T 0.034 0.843 T 0.051 0.836 T 0.033 0.831 T 0.025 0.836 T 0.042 0.827 T 0.050 0.822 T 0.049 0.823 T 0.041 0.824 T 0.058 – 0.819 T 0.025 – 0.820 T 0.024 0.811 T 0.032 0.816 T 0.024 0.809 T 0.040 0.803 T 0.032 – – – – – – 0.774 T 0.056 – 0.770 T 0.055
Fitted experimental values
0.879 0.874 0.868 0.863 0.859 0.854 0.850 0.847 0.843 0.840 0.838 0.835 0.833 0.830 0.828 0.826 0.824 0.823 0.821 0.819 0.817 0.816 0.814 0.812 0.810 0.808 0.806 0.803 0.800 0.798 0.795 0.791 0.787 0.783 0.779
Theoretical values
0.876 0.871 0.867 0.863 0.859 0.855 0.852 0.849 0.846 0.843 0.841 0.839 0.836 0.834 0.832 0.830 0.828 0.826 0.823 0.821 0.819 0.817 0.815 0.812 0.810 0.808 0.806 0.803 0.801 0.799 0.797 0.796 0.794 0.793 0.792
Other experimental values Ref. [18]
Ref. [19]
– – – – – – – –
0.869 0.866 0.861 – 0.864 0.861 0.844 0.847 0.832 0.834 0.839 – – – – – – – – – – – –
– – – – – – 0.829 0.855 0.904 – – – 0.815 0.815 0.795 0.805 0.637 – – – – – – 0.636 – 0.682
– – – – – – – – – – –
B. Ertugral et al. / Spectrochimica Acta Part B 60 (2005) 519 – 524
between the shells written in the parenthesis, and C is the total level width. The radiative and Auger transition rates were tabulated by Scofield [24] and Chen et al. [25], respectively.
5. Result and discussion The measured values of the K to L shell vacancy transfer probability, g KL, for 25 elements namely, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Re, Ir, Au, Hg, Tl, Pb, Bi, Th and U listed in Table 1 with the theoretical and other experimental values. The uncertainties in the values of the K to L shell vacancy transfer are estimated to be ranged from 3% to 8%. This uncertainties are sum of the several errors caused by the area evaluation under the Ka and Kh X-ray peak (3%), in the absorption correction factor ratio (2%), the product I oGe (5– 7%) and the other systematic errors (2– 3%). In earlier measurements [18,20,21], the authors used two radioisotope sources for excitation of targets to determine the K to L shell vacancy transfer experimentally. The method was based on the number of L X-rays produced at the photon excitation energy below the K edge and at the excitation energy above the K edge, where the major contribution to L shell vacancies comes from the decay K shell vacancies. As a result, their methods strongly depend on the L X-ray cross-sections. The method of other investigators [19] was based on the Ka and total Lx Xrays yields from the targets used a radioisotope source for excitation targets. In present work, K X-ray line intensities and K shell fluorescence yields were used to measure the same
523
quantity at 123.6 keV. K shell fluorescence yields values are the well known values for high atomic number elements. In addition, the statistical accuracy of peak areas is better for the Kx X-rays peaks than the Lx Xray peaks. The experimental results alongside with the theoretically calculated values of Scofield [24] and Chen et al. [25] are represented graphically as vacancy transfer probabilities versus atomic numbers in Fig. 4. As seen from this figure the values of the g KL decrease with the rising atomic number. It can be seen from Table 1 and Fig. 4 that there is a good agreement between the present experimental results and the theoretical values. Experimental data of the K to L shell vacancy transfer probabilities are plotted as a function of the atomic number. The unknown experimental values were approximated in the atomic range 58 Z 92 by fitting the third-order polynomial by using known experimental values and these fitted values are listed in Table 1. The fitted polynomial is shown in Fig. 4. In order to facilitate a better and closer comparison between theory and experiment the results are presented in the graphical form as shown in Fig. 4. It is clearly seen from this figure then experimental results are in good agreement with the theoretical values within the range 0.23– 1.26% for the K to L shell vacancy transfer probabilities in the atomic range 58 Z 92. Finally, the comparison between the experimental results and the theoretical values leads to the conclusion that the present method will be beneficial for determining vacancy transfer probabilities in high atomic number elements and satisfactory for many other applications employing the fundamental parameter approach.
K to L Shell Vacancy Transfer Probability (ηKL)
0,900
Experimental Theoretical Fitted
0,875
0,850
0,825
0,800
0,775
ηKL=2.7919-0.07349.Z+9.332.10-4.Z2-4,0456.10-6.Z3 55
60
65
70
75
80
85
Atomic Number (Z) Fig. 4. The variation of g KL versus atomic number (Z).
90
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Acknowledgements This work was done with the support of the Karadeniz Technical University Research Fund under Project No(s). 2002.111.1.4.
[14]
[15]
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[29]
[30]
and average fluorescence yields in eleven elements from Tm to U at photon energy of 5.96 keV, Radiat. Phys. Chem. 72 (5) (2005) 549 – 554. E. TNrasoglu, U. C ¸ evik, B. Ertugral, G. ApaydNn, M. Ertugrul, A.I. Kobya, Chemical effects on La, Lh, Lg, Ll and LD X-ray fluorescence cross-section and Li/La X-ray Intensity Ratios of Hg, Pb and Bi compounds at 59.54 keV, Eur. Phys. J. D 26 (2003) 231 – 236. M. Ertugrul, O. Dogan, O. Simsek, Measurement of radiative vacancy distributions for the L2, L3 subshell and M shell of some elements with atomic range 69 Z 92, Radiat. Phys. Chem. 49 (1997) 221 – 224. M. Ertugrul, Measurement of Ka to La intensity ratio of lanthanides following photoionization at 59.5 keV, J. Phys., At. Mol. Opt. Phys. 28 (1995) 4037. M. Ertugrul, Measurement of total, radiative and radiationless (Auger) vacancy transfer probabilities from K to Li (i = 1,2,3) subshell of Cs, Ba, and La, J. Anal. At. Spectrom. 17 (2002) 64 – 68. M. Ertugrul, O. Dogan, O. Simsek, U. Turgut, Measurement of Probabilities for vacancy transfer from K to L Shell of the elements 73 Z 92, Phys. Rev., A 55 (1997) 303 – 306. B. Ertugral, U. C ¸ evik, E. TNrasoglu, A.I. Kobya, M. Ertugrul, O. Dogan, Measurement of K to L shell vacancy transfer probabilities for the elements 52 Z 68, J. Quant. Spect. R.A. 78 (2003) 163 – 169. O. Simsek, D. KaragOz, M. Ertugrul, Measurement of K to L shell vacancy transfer probabilities for the elements 46 Z 55, Spectrochim. Acta, Part B 58 (2003) 1859 – 1865. S. Puri, D. Mehta, B. Chand, S. Nirmal, P.N. Trehan, Measurements of K to L shell vacancy transfer probabilities for the elements 37 Z 42, Nucl. Instrum. Methods B 73 (1993) 443 – 446. S. Puri, D. Metha, B. Chand, N. Singh, J.H. Hubbell, P.N. Trehan, Production of L subshell and M shell i vacancies following inner shell vacancy production, Nucl. Instrum. Methods B 83 (1993) 21 – 30. V.P. Rao, M.H. Chen, B. Crasemann, Atomic vacancy distributions produced by inner-shell ionization, Phys. Rev., A 5 (1972) 997 – 1012. J.H. Scofield, Relativistic Hartree – Slater values for K and L X-ray emission rates, Atom Data Tables 14 (1974) 121 – 137. M.H. Chen, B. Crasemann, H. Mark, Relativistic radiationless transition probabilities for atomic K and L shell, At. Data Nucl. Data Tables 24 (1979) 13. W. Bambynek, X-ray and inner shell processes in atoms, Molecules and Solids A Meisel, Leipzig DDR (1984) Paper P I. M.J. Berger, J.H. Hubbell, S.M. Seltzer, J.S. Coursey, D.S. Zucker, ´ ST Standard Reference XCOM: Photon Cross Sections Database, NY Database 8 (XGAM) (1998). E. Storm, I.H. Israel, Photon cross sections from 1 keV to 100 MeV for elements Z = 1 to Z = 100, Nucl. Data Tables A 7 (1970) 565 – 681. J.H. Scofield, Theoretical photoionization cross sections from 1 to 1500 keV, Lawrence Livermore Laboratory (UCRL), vol. 51326, 1973. N. Broll, Qantitative X-ray fluorescence analysis, X-ray Spectrom. 15 (1986) 271 – 285.
Measurement of vacancy transfer probabilities from K to L shell for high atomic number elements B. Ertugrala,*, G. Apaydina, H. Baltasa, U. C ¸ evika, A.I˙. Kobyaa, M. Ertugrulb a b
Department of Physics, Faculty of Art and Sciences, Karadeniz Technical University, 61080 Trabzon, Turkey Department of Electrical and Electronic, Faculty of Engineering, Ataturk University, 25240 Erzurum, Turkey Received 19 November 2004; accepted 22 March 2005 Available online 27 April 2005
Abstract The probabilities for vacancy transfer from K to L shell, g KL, were obtained by measuring the Kh/Ka intensity ratios in 25 elements over the range 57 Z 92 using a 25 mCi 57Co filtered source for excitation. The K X-rays were measured by using a Si(Li) detector. The theoretical values were calculated via the radiative and radiationless transition rates of these elements. The comparison between present experimental results and theoretical predictions showed that both results agreed well. The experimental and theoretical values were fitted against atomic number (Z). The measured values of g KL for Tm, Yb, Lu, Hf and Ir are being reported here for the first time. D 2005 Elsevier B.V. All rights reserved. Keywords: Intensity ratios; Vacancy transfer; X-ray fluorescence (XRF); Radiative and radiationless transition rates
1. Introduction Atomic shell data are relevant in nuclear physics. Vacancies in the atomic shell give rise to rearrangements in the shells which are accompanied by the emission of Xray quanta and the ejection of Auger electrons [1]. The vacancy transfer coefficient g KL describes the mean number of vacancies produced in the L shell by one vacancy in the K shell. Accurate experimental data regarding the vacancy transfer probability are important in many practical applications, such as nuclear electron capture, internal conversion of g-rays, photoelectric effect, atomic processes leading to the emission of X-rays, Auger electrons and computations for medical physics and irradiational processes. In recent times, some works were done on the K and L X-ray fluorescence cross-sections [2 –7], L X-ray intensity ratio [8,9], K, L and M X-ray production cross-sections [10 –13], chemical effect [14], for many elements by using energy-dispersive X-ray fluorescence (EDXRF).
* Corresponding author. Tel.: +90 462 3772539; fax: +90 462 3253195. E-mail address: [email protected] (B. Ertugral). 0584-8547/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.sab.2005.03.009
A review of the literature shows that a number of experimental studies on the vacancy transfer probabilities in the atomic shell (K to L and M) or subshell (K to Li i = 1, 2, 3) were reported. As a result of this, Ertugrul et al. [15] measured K to L shell radiative vacancy transfer probabilities for some elements. The Ka to La intensity ratios of 11 lanthanide elements were measured and the effect of vacancy transfer of K to L shell on these ratios was also investigated at 59.5 keV by using a Si(Li) detector by Ertugrul [16]. Total, radiative and radionless vacancy transfer probabilities from K to Li subshell of Cs, Ba and La were measured with a new approach by Ertugrul [17]. In adition, Ertugrul et al. [18] measured K to L shell vacancy transfer probabilities using L X-rays yields in the atomic region 73 Z 92 at 59.5 and 122 keV energies. Ertugral et al. [19] measured K to L shell vacancy transfer probabilities using intensity ratio of Ka and Lx total X-rays for some elements in the atomic region 52 Z 68 at 59.5 keV. Simsek et al. [20] determined K to L shell vacancy transfer probabilities for nine elements in the atomic region 46 Z 55 measuring the L X-ray yields from targets excited by 5.96 and 59.5 keV photons. K to L shell vacancy transfer probabilities were measured in the
520
B. Ertugral et al. / Spectrochimica Acta Part B 60 (2005) 519 – 524
Mylar Sample
Annular source (57Co) Pb annular colimator
Berillium window
X-ray fluorescence radiation Si(Li) Detector
Holder
Fig. 1. Experimental setup.
atomic region 37 Z 42 at 5.96 and 22.6 keV energies by Puri et al. [21]. In addition, Puri et al. [22] have calculated and fitted them against atomic number Z and also fitted coefficients for vacancy transfer probabilities from K to L1, K to L2, K to L3, K to L (average), L1 to M, L2 to M and L3 to M shells. The values of the vacancy transfer probabilities from the K to the L1, L2 and L3 shells (g KL) for elements in the atomic range 20 Z 94 have been calculated by Rao et al. [23]. In these calculations, the contribution due to Auger and radiative transitions was made using the best fitted experimental data on the fluorescence yields and intensity ratios of different components of KLX (X = L, M, N, etc.) Auger electrons and K X-rays currently available. From the literature review, there is no work done on the measurements of vacancy transfer probabilities of K to L shell for Tm, Yb, Lu, Hf, and Ir elements. In this study, we determined K to L shell vacancy transfer probabilities for 25 elements in the atomic range 58 Z 92 by measuring the K X-ray yields from targets excited by 123.6 keV photons and using I Kh/I Ka intensity ratios. Finally the measured
values of g KL were compared with all available data and the theoretical values deduced using the calculated radiative Xray emission rates [24] and Auger transition rates [25] based on the relativistic Dirac –Hartree – Slater (RDHS) model.
2. Method of measurement The geometry and the shielding arrangements of the experimental set-up employed in the present work are as shown schematically in Fig. 1. The samples were irradiated with a 57Co radioisotope source at 123.6 keV photons with strength of approximately 25 mCi. Spectroscopically, high purity (99.90%) targets of Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Re, Ir, Au, Hg, Tl, Pb, Bi, Th and U of thickness ranging from 20 to 40 mg/cm2 have been used for the measurement. The samples were then placed at 45- angle with respect to the direct beam and fluorescent X-rays emitted 90- to the detector. The incident beam and fluorescence X-rays emitted from the target were
TaKα 1 40000 TaKα 2
Counts
30000
20000 TaKβ 1
10000
TaKβ 2 0 700
7 50
800
850
Channel Fig. 2. Typical K X-ray spectrum for Ta.
900
950
B. Ertugral et al. / Spectrochimica Acta Part B 60 (2005) 519 – 524
detected with a Si(Li) detector manufactured by Canberra (FWHM = 160 eV at 5.9 keV, active area 13 mm2, thickness 3 mm and Be window thickness = 30 Am). The output from the preamplifier, with pulse pile-up rejection capability, was fed to a multi-channel analyzer interfaced with a personal computer provided with suitable software (Tennelec PCA II) for data acquisition and peak analysis. The live time was selected to be 5000 s for all elements. Fig. 2 shows a typical K X-ray spectrum for Ta.
3. Experimental K to L shell vacancy transfer probabilities The experimental K to L shell total vacancy transfer probabilities, g KL, were evaluated by using following equation [1] gKL ¼
2 xK 1 þ ðIKh =IKa Þ
ð1Þ
where x K is the fluorescence yield of the K shell [26] and I Kh/I Ka is the intensity ratio of the K X-rays. The I Kh/I Ka intensity ratio is obtained from the following equation [19] IKh NKh bKa eKa ¼ IKa NKa bKh eKh
ð2Þ
where N Kh and N Ka are the net counts under the Kh and Ka peaks, b Kh and b Ka are the self-absorption correction factor for energies of Kh and Ka peaks. The self absorption correction factor b Kx (x = a, h) at the excitation energy has been calculated by using the following 1,20E+008
521
expression, assuming that the fluorescence X-rays are incident normally at the detector. bKx ¼
1 exp½ ðl1 =sinh þ l2 =sin/Þt ðl1 =sinh þ l2 =sin/Þt
where l 1 and l 2 are the total mass absorption coefficients (from XCOM [27]) of target material at the incident photon energy and at the emitted average Ka and Kh X-ray energy [28] and t is the thickness of the target in g/cm2, h and / are the angles of incident photon and emitted X-rays with respect to the normal at the surface of the sample. e Kh and e Ka are the detector efficiencies at the Kx X-ray energies and were evaluated using the equation eKi ¼
NKi I0 GbKi mi rKi
ð4Þ
where N K and b K have the same meaning as in Eq. (2). The term I 0 is the intensity of exciting radiation, G is the geometry factor, m i is the mass of the element in the sample (g cm2). The absolute efficiency e of the X-ray detector was determined by collecting the K X-ray spectra of samples of Ce, Nd, Gd, Dy, Er, Yb, Ta, Ir, Hg, Bi, Th, and U in the same experimental set-up. The term r Ki represents the K X-ray fluorescence crosssections and is given as rKi ¼ rPK xK fKi
ð5Þ
where r KP is the K shell photoionization cross-section [29] and f Ki is fractional X-ray emission rate [30]. The measured variation of I 0Ge was fitted to a third-order polynomial as a function of the mean K X-ray energy and fitted coefficients are as shown in Fig. 3.
I0Gε =418558110-13885694 EKx+157914 EKx2-597 EKx3
1,00E+008
I0Gε
8,00E+007
6,00E+007
4,00E+007
2,00E+007
0,00E+000 30
40
50
ð3Þ
60
70
Energy (keV) Fig. 3. The variation of I 0Ge versus energy.
80
90
100
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4. Theoretical calculation of K to L shell vacancy transfer probabilities
The g KLi was calculated using the following equations [23]:
The vacancy transfer probabilities from K to L shell are defined as the number of Li subshell vacancies produced in the decay of one K shell vacancy through radiative K – Li transitions or through Auger K – Li Lj and K –Li X (X = M, N, O, etc.) transitions. The average number of g KL is
gKL1 ¼
gKLi ¼ gKLi ðRÞ þ gKLi ðAÞ;
1 ½CR ðKL1 Þ þ 2CA ðKL1 L1 Þ þ CA ðKL1 L2 Þ C ðK Þ þ CA ðKL1 L3 Þ þ CA ðKL1 XÞ
gKL2 ¼
ð6Þ
1 ½CR ðKL2 Þ þ 2CA ðKL2 L2 Þ þ CA ðKL1 L2 Þ C ðK Þ þ CA ðKL2 L3 Þ þ CA ðKL2 XÞ
where g KLi (R) and g KLi (A) are the radiative and Auger transition probabilities of the K to Li subshell, respectively. The number of g KLi (R) is proportional to the probability of radiative transition which takes place at K –Li transition and is given by
gKL3 ¼
gKLi ðRÞ ¼ xK ½ I ðKLi Þ=IK ðRÞ
ðX ¼ M; N; O; etc:Þ:
ð7Þ
where I(KLi ) is the K – Li X-ray intensity and I K(R) is the total intensity of the K X-rays.
1 ½CR ðKL3 Þ þ 2CA ðKL3 L3 Þ þ CA ðKL2 L3 Þ C ðK Þ þ CA ðKL1 L3 Þ þ CA ðKL3 XÞ ð8Þ
In these equations, C R and C A are the radiative and the Auger partial widths corresponding to the transitions
Table 1 Comparison of experimental and theoretical results for K to L shell vacancy transfer probabilities Elements
g KL Present experimental values
58
Ce Pr 60 Nd 61 Pm 62 Sm 63 Eu 64 Gd 65 Tb 66 Dy 67 Ho 68 Er 69 Tm 70 Yb 71 Lu 72 Hf 73 Ta 74 W 75 Re 76 Os 77 Ir 78 Pt 79 Au 80 Hg 81 Tl 82 Pb 83 Bi 84 Po 85 At 86 Rn 87 Fr 88 Ra 89 Ac 90 Th 91 Pa 92 U 59
0.874 T 0.053 0.877 T 0.026 0.872 T 0.035 – 0.862 T 0.026 0.853 T 0.034 0.846 T 0.042 0.851 T 0.025 0.852 T 0.025 0.841 T 0.034 0.843 T 0.051 0.836 T 0.033 0.831 T 0.025 0.836 T 0.042 0.827 T 0.050 0.822 T 0.049 0.823 T 0.041 0.824 T 0.058 – 0.819 T 0.025 – 0.820 T 0.024 0.811 T 0.032 0.816 T 0.024 0.809 T 0.040 0.803 T 0.032 – – – – – – 0.774 T 0.056 – 0.770 T 0.055
Fitted experimental values
0.879 0.874 0.868 0.863 0.859 0.854 0.850 0.847 0.843 0.840 0.838 0.835 0.833 0.830 0.828 0.826 0.824 0.823 0.821 0.819 0.817 0.816 0.814 0.812 0.810 0.808 0.806 0.803 0.800 0.798 0.795 0.791 0.787 0.783 0.779
Theoretical values
0.876 0.871 0.867 0.863 0.859 0.855 0.852 0.849 0.846 0.843 0.841 0.839 0.836 0.834 0.832 0.830 0.828 0.826 0.823 0.821 0.819 0.817 0.815 0.812 0.810 0.808 0.806 0.803 0.801 0.799 0.797 0.796 0.794 0.793 0.792
Other experimental values Ref. [18]
Ref. [19]
– – – – – – – –
0.869 0.866 0.861 – 0.864 0.861 0.844 0.847 0.832 0.834 0.839 – – – – – – – – – – – –
– – – – – – 0.829 0.855 0.904 – – – 0.815 0.815 0.795 0.805 0.637 – – – – – – 0.636 – 0.682
– – – – – – – – – – –
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between the shells written in the parenthesis, and C is the total level width. The radiative and Auger transition rates were tabulated by Scofield [24] and Chen et al. [25], respectively.
5. Result and discussion The measured values of the K to L shell vacancy transfer probability, g KL, for 25 elements namely, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta, W, Re, Ir, Au, Hg, Tl, Pb, Bi, Th and U listed in Table 1 with the theoretical and other experimental values. The uncertainties in the values of the K to L shell vacancy transfer are estimated to be ranged from 3% to 8%. This uncertainties are sum of the several errors caused by the area evaluation under the Ka and Kh X-ray peak (3%), in the absorption correction factor ratio (2%), the product I oGe (5– 7%) and the other systematic errors (2– 3%). In earlier measurements [18,20,21], the authors used two radioisotope sources for excitation of targets to determine the K to L shell vacancy transfer experimentally. The method was based on the number of L X-rays produced at the photon excitation energy below the K edge and at the excitation energy above the K edge, where the major contribution to L shell vacancies comes from the decay K shell vacancies. As a result, their methods strongly depend on the L X-ray cross-sections. The method of other investigators [19] was based on the Ka and total Lx Xrays yields from the targets used a radioisotope source for excitation targets. In present work, K X-ray line intensities and K shell fluorescence yields were used to measure the same
523
quantity at 123.6 keV. K shell fluorescence yields values are the well known values for high atomic number elements. In addition, the statistical accuracy of peak areas is better for the Kx X-rays peaks than the Lx Xray peaks. The experimental results alongside with the theoretically calculated values of Scofield [24] and Chen et al. [25] are represented graphically as vacancy transfer probabilities versus atomic numbers in Fig. 4. As seen from this figure the values of the g KL decrease with the rising atomic number. It can be seen from Table 1 and Fig. 4 that there is a good agreement between the present experimental results and the theoretical values. Experimental data of the K to L shell vacancy transfer probabilities are plotted as a function of the atomic number. The unknown experimental values were approximated in the atomic range 58 Z 92 by fitting the third-order polynomial by using known experimental values and these fitted values are listed in Table 1. The fitted polynomial is shown in Fig. 4. In order to facilitate a better and closer comparison between theory and experiment the results are presented in the graphical form as shown in Fig. 4. It is clearly seen from this figure then experimental results are in good agreement with the theoretical values within the range 0.23– 1.26% for the K to L shell vacancy transfer probabilities in the atomic range 58 Z 92. Finally, the comparison between the experimental results and the theoretical values leads to the conclusion that the present method will be beneficial for determining vacancy transfer probabilities in high atomic number elements and satisfactory for many other applications employing the fundamental parameter approach.
K to L Shell Vacancy Transfer Probability (ηKL)
0,900
Experimental Theoretical Fitted
0,875
0,850
0,825
0,800
0,775
ηKL=2.7919-0.07349.Z+9.332.10-4.Z2-4,0456.10-6.Z3 55
60
65
70
75
80
85
Atomic Number (Z) Fig. 4. The variation of g KL versus atomic number (Z).
90
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Acknowledgements This work was done with the support of the Karadeniz Technical University Research Fund under Project No(s). 2002.111.1.4.
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