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Measurement of K to L shell vacancy transfer probabilities for the elements 52⩽Z⩽68
Journal of Quantitative Spectroscopy & Radiative Transfer 78 (2003) 163 – 169
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Measurement of K to L shell vacancy transfer probabilities for the elements 52 6 Z 6 68 B. Ertugrala, U. Cevika , E. Tirasoglua , A.I. Kopyaa , M. Ertugrulb;∗ , O. Doganb a
Department of Physics, Science Faculty, Karadeniz Technical University, 61080 Trabzon, Turkey b Department of Physics, K. K. Education Faculty, Atat%urk University, 25240 Ezurum, Turkey Received 9 May 2002; accepted 13 August 2002
Abstract The probabilities for transfer of vacancies from K to L shell were measured using intensity ratio of K and total Lx X-rays. The K and total Lx X-rays yields from the targets excited by 59:5 keV incident photon were obtained using a Si(Li) detector. These experimental results were compared with the theoretically calculated values using radiative and radiationless transitions. The radiative transitions of these elements were observed from the relativistic Hartree–Slater model, which was proposed by Sco?eld (Atom. Data Nucl. Data Tables 14 (1974) 121). The radiationless transitions were observed from the Dirac–Hartree–Slater model, which was proposed by Chen et al. (Atom. Data Nucl. Data Tables 24 (1979) 13). A fairly good agreement is found between the experimental and calculated values. ? 2003 Elsevier Science Ltd. All rights reserved. Keywords: Vacancy transfer; Intensity ratio; Photoionisation; EDXRF
1. Introduction When the atom’s K or L shell/subshell has been ionized, it is excited through radiative [1] or radiationless (Auger) [2] transitions. A knowledge of average vacancy distributions is also important for the study of such processes as nuclear electron capture, internal conversion of -rays, photoelectric eIect and generally, whenever primary vacancies produced in the shell must be distinguished from multiple ionization due to the decay of inner vacancy [3]. The L and M X-rays production cross-sections and average L and M shell Juorescence yield were measured experimentally in recent years [4–6]. Ertugrul et al. [7] measured K to L shell ∗
Corresponding author. Fax: +90-4422-1841-72. E-mail addresses: [email protected] (B. Ertugral), [email protected] (M. Ertugrul).
0022-4073/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 2 ) 0 0 1 8 9 - 9
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radiative vacancy transfer probabilities for elements in the atomic range 69 6 Z 6 92 using a Co-57 radioisotope source. The enhancement eIect of K to L shell vacancy transfer on K to L intensity ratio was measured for lanthanides [8]. K to L shell and L to M shell vacancy transfer probabilities were measured experimentally using two radioisotope sources [9–11]. In addition, Puri et al. [12] have calculated values and ?tted them versus atomic number Z values and ?tted coeOcients for vacancy transfer probabilities of K to L1 , K to L2 , K to L (average), L1 to M, L2 to M, L3 to M shells. The values of the KLi (i = 1; 2; 3) for elements in the atomic range 20 6 Z 6 94 have been calculated [3]. In these calculations, the contributions due to Auger and radiative transitions were derived using the best ?tted experimental data on the Juorescence yields and intensity ratios of diIerent components of KLX (X = L; M; N, etc.) Auger electrons and K X-rays currently available. In the earlier measurements [9–11], the authors used two radioisotope sources for excitation of targets. The method is 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. Ertugrul [13,14] has measured total, radiative and radiationless vacancy transfer probabilities from K to Li subshell for some elements in the mean atomic number region. In this study, we measured K to L shell vacancy transfer probabilities for the atomic range 52 6 Z 6 68. Targets were irradiated by an 241 Am radioisotope source. The energy of primary photon that is 59:5 keV yields from 241 Am can excite K, L and other shells. The measured values have been compared with the calculated values deduced using Auger transition rates [2] and radiative X-ray emissions [1].
2. Experimental procedure The experimental set-up for the annular source in the direct excitation mode used in this study is shown in Fig. 1. The experiment was carried out using an annular source 241 Am (50 mCi), which emits monoenergetic (59:5 keV) -rays. The -rays of 26:4 keV and N p L X-rays coming from 241 Am are completely (∼ 99:99%) ?ltered out with their help of graded ?lter of Pb, Cu and Al of thickness 0.1, 0.1 and 1 mm, respectively, because even a small fraction of these radiations would produce sizable interference due to their large interaction cross-sections with K-shell electrons. Spectroscopically, pure targets of Te, Ba(CO3 ), La2 O3 , CeO2 , Pr 3 O4 , Nd 2 O3 , Sm2 O3 , Eu3 O3 , Gd 2 O3 , Tb4 O7 , Dy2 O3 , Ho2 O3 and Er 2 O3 of thickness ranging from 15 to 22 g=cm2 have been used for measurements. The Juorescent K and L X-rays from the sample were detected by collimated an Si(Li) detector having a thickness of 3 mm and energy resolution of 147 eV at 5:96 keV. The output from the preampli?er with a pulse pile-up rejection capability, and fed to a multi-channel analyzer interface with a personal computer provided with suitable software for data acquisition and peak analysis. The live time was taken as 1000 s for all elements. The samples were placed at 45◦ angle with respect to the direct beam and Juorescent X-rays emitted 90◦ to the detector. The K X-ray production cross-sections at excitation energy are given by K = K !K fK ;
(1)
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165
Fig. 1. Geometry of the experimental setup.
where K is the total K shell ionization cross-section, !K is the K shell Juorescence yield and fK is given by IK −1 fK = 1 + ; (2) IK IK =IK values are taken from [1]. The total L X-ray production cross-section at excitation energy above the K edge of the elements are given by Lx = ( L + KL K )$L ;
(3)
where L is the total L shell photoionization cross-section, KL is the K to L shell vacancy transfer probabilities and $L is the average L shell Juorescence yields. The term of KL K $L is the enhanced part from K to L shell vacancy transfer for the L shell X-ray production cross-sections. The intensity ratio of Lx and K X-rays are resolved from Eqs. (1) and (3): I Lx ( L + KL K )$L = : IK K ! K f K
(4)
The ILx =IK was obtained experimentally as follows: IL x N L K jK = x ; IK N K L x jL x
(5)
where NLx and NK are the net counts under the Lx and K peaks, Lx and K are the self-absorption correction factor for energies of Lx and K peaks and jLx and jK are the detector eOciency at
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the energies of the Lx and K X-ray energies, respectively. The detector eOciency was evaluated using the 133 Ba, 137 Cs and 241 Am radioisotope. The method for measuring the detector eOciency is explained earlier [15]. The absorption correction factor at the excitation energy has been calculated using the following equation: =
1 − exp[ − (inc =sin + emt =sin )t] ; (inc =sin + emt =sin )t
(6)
where inc and emt are the total mass absorption coeOcients of target material at the incident photon energy and at the emitted K and average L X-ray energy [16] and t is the thickness of the target. and are the angles of incident photon and emitted X-rays with respect to the normal at the surface of the sample. It can be written from Eqs. (4) and (5) as KL =
N L x K jK ! K L fK − ; N K L x jL x $ L K
(7)
where !K and $L values are taken from the table of Hubbell et al. [17], fK is calculated from Eq. (2) and K and L are interpolated from the table of Sco?eld [18]. 3. Theoretical calculations The probabilities for vacancy transfer from K to L shell is de?ned as the number of Li subshell vacancies produced in the decay of one K shell vacancy through radiate K–Li transitions or through Auger K–Li Lj and K–Li X (X = M; N; O, etc.) transitions. The average number KLi = KLi (R) + KLi (A);
(8)
where KLi (R) and KLi (A) are the radiative and Auger transition probabilities of the K to Li subshell, respectively. The number of KLi (R) is proportional to the probability that a K–Li radiative transitions takes place KLi (R) = !K [I (KLi )=IK (R)];
(9)
where I (KLi ) is the K–Li X-ray intensity and IK (R) is the total intensity of the K X-rays. The KLi have been calculated using the following equations [3]: KL1 =
1 [R (KL1 ) + 2A (KL1 L1 ) + A (KL1 L2 ) + A (KL1 L3 ) + A (KL1 X)]; (K)
KL2 =
1 [R (KL2 ) + 2A (KL2 L2 ) + A (KL1 L2 ) + A (KL2 L3 ) + A (KL2 X)]; (K)
KL3 =
1 [R (KL3 ) + 2A (KL3 L3 ) + A (KL2 L3 ) + A (KL1 L3 ) + A (KL3 X)]; (K)
(X = M; N; O; etc:):
(10)
In these equations, R and A are the radiative and the Auger partial widths corresponding to the transitions between the shells written the brackets, and is the total level width. The radiative
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167
transition rates and Auger transition rates were tabulated by Sco?eld [1] and Chen et al. [2], respectively.
4. Results and discussion The measured values of the K to L shell vacancy transfer probability, KL , for 13 elements, namely, Te, Ba, La, Ce, Pr, Nd, Sm, Eu, Cd, Tb, Dy, Ho, and Er are listed in Table 1. The overall error in the present measurements is estimated to be 3– 6%. This error is attributed to the uncertainties in diIerent parameters used to deduce KL values; namely, the error in the area evaluation under the K and L shell X-ray peak (6 3%), in the absorption correction factor ratio (6 2%) and the other systematic errors (2–3%). The experimental results alongside with the theoretically calculated values are represented graphically as vacancy transfer probabilities versus atomic numbers in Fig. 2. As shown in Fig. 2, values of the KL decrease with the rising atomic numbers. The experimental values KL are compared with the calculated values. These values are found to be in good agreement with calculated values for the elements 52 6 Z 6 68. In the calculated values, the radiative transition rates were taken from [1] and the radiationless (Auger) transition rates were taken from [2]. The basic idea of Puri et al. [9] and Ertugrul et al. [11] to determine experimentally the K to L shell vacancy transfer was the use of two kinds of vacancy-generating photons: one of them below, and other one above the K edge of the corresponding target element. Firstly, the all L shell was excited with the radioisotope which emits photons energy below K edge and L X-ray production cross-sections were determined. Secondly, the all L and K shells were excited with the other radioisotope, which emits photon energy above the K edge. Since the L X-ray intensity is enhanced with the K to L shell vacancy transfer, the L X-ray production cross-sections increased. The vacancy transfer probabilities for K to L shell were determined using this increasing. The experimental K to L shell vacancy transfer probabilities in the earlier method [9,11] strongly depends on the primary photon intensity (I0 ) and geometrical factor (G) for both set-ups. For this reason the experimental errors increase in the earlier method. In the present experiment, only 241 Am source has been used. It is shown in Eq. (7) that the present equation for determining K to L shell vacancy transfer probabilities is wholly independent of the primary photon intensity at the
Table 1 Comparison of experimental and theoretical results for K to L shell vacancy transfer probability Elements
KL (exper.)
KL (theor.)
Elements
KL (exper.)
KL (theor.)
52
0:908 ± 0:03 0:905 ± 0:04 0:892 ± 0:04 0:869 ± 0:03 0:866 ± 0:04 0:861 ± 0:05 0:864 ± 0:04
0.917 0.888 0.881 0.877 0.871 0.866 0.858
63
0:861 ± 0:03 0:844 ± 0:04 0:847 ± 0:05 0:832 ± 0:03 0:834 ± 0:04 0:839 ± 0:03
0.855 0.850 0.848 0.843 0.843 0.836
Te Ba 57 La 58 Ce 59 Pr 60 Nd 62 Sm 56
Eu Gd 65 Tb 66 Dy 67 Ho 68 Er 64
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Present Experimental Theoretical 0.95
ηKL
0.90
0.85
0.80
0.75 50
55
60
65
70
Atomic number Fig. 2. KL versus atomic number (Z).
present geometry (I0 G). Since the intensity ratio for K and Lx X-rays is independent of geometrical factor, sample composition and K and Lx X-rays peaks were synchronously determined, the present experimental results for K to L shell vacancy transfer using K to Lx intensity ratio gives more realistic results than the earlier experiments [9,11]. The accuracy of the numbers given is of the same size as in the earlier paper. However, while the atomic number region is 52 6 Z 6 68 in the present work, the atomic number region is the 73 6 Z 6 92 in the earlier paper [11]. As known, the statistical accuracy of peak areas is better for the high Z elements than the low Z elements. In our other experiment [8], the I K =I L intensity ratio of lanthanides was measured and the enhancement factor of L X-rays was calculated for the K to L shell vacancy transfer. The enhancement factor for L X-rays was found to be in the interval 7.75 –9.90. These enhancement factors involve L1 to L3 , L2 to L3 and together L1 to L2 and L2 to L3 Coster–Kronig transitions. For the lanthanides, while the I K =I L intensity ratio is in the interval 7–13 in earlier experiment [8], the I K =I Lx intensity ratio is in the interval 4 – 6.25 in the present experiment. Since the L X-ray intensity (I Lx ) is the sum of the Ll , L , L and L X-rays intensities, the present values for I K =I Lx intensity ratio are lower than the earlier I K =I L intensity ratio values [8]. Since the K and L X-rays were simultaneously counted, the present method is reliable according to earlier method [9,11]. Earlier method [9,11] becomes independent of both the target thickness and the eOciency of the detector. Present method becomes independent of the I0 G product and target thickness. Generally, in the literature, the errors in these measurements are approximately 2–3% and 3– 6% for the detector eOciency and the I0 G product, respectively. In conclusion, the present agreement between the theoretical and experimental values leads to the conclusion that the present method will be bene?cial for determining of vacancy transfer probability.
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169
References [1] Sco?eld JH. Relativistic Hartree–Slater values for K and L X-ray emission rates. Atom Data Nucl Data Tables 1974;14:121–37. [2] Chen MH, Crasemann B, Mark H. Relativistic radiationless transition probabilities for atomic K- and L-shells. Atom Data Nucl Data Tables 1979;24:13. [3] Rao VP, Chen MH, Crasemann B. Atomic vacancy distributions produced by inner-shell ionization. Phys Rev A 1972;5:997. [4] Ertugrul M, TiraSsoTglu E, Kurucu Y, ErzeneoTglu S, Durak R, SSahin Y. Measurement of M shell X-ray production cross section and Juorescence yields for the elements in the atomic range 70 6 Z 6 92 at 5:96 keV. Nucl Instrum Methods B 1996;108:18. [5] Garg RR, Puri S, Singh S, Mehta D, Shahi JS, Garg ML, Singh N, Mangal PC, Trehan PN. Measurement of L X-ray Juorescence cross sections and yields for the elements in the atomic range 41 6 Z 6 52 at 5:96 keV. Nucl Instrum Methods B 1992;72:147. [6] Puri S, Mehta D, Singh N, Mangal PC, Trehan PN. M-shell X-ray production cross-sections and Juorescence yields for the elements with 71 6 Z 6 92 at 5:96 keV. Nucl Instrum Methods B 1993;73:319. V Measurement of radiative vacancy distributions for the L2 , L3 subshell and M [7] ErtuTgrul M, DoTgan O, SSimSsek O. shell of some elements with atomic range 69 6 Z 6 92. Radiat Phys Chem 1997;49:221. [8] Ertugrul M. Measurement of K to L intensity ratios of lanthanides following photoionization at 59:5 keV. J Phys B 1995;28:4037. [9] Puri S, Mehta D, Chand B, Singh N, Trehan PN. Measurements of K-shell to L-shell vacancy transfer probabilities for the elements 37 6 Z 6 42. Nucl Instrum Methods B 1993;73:443. [10] Puri S, Mehta D, Chand B, Singh N, Trehan PN. Measurements of L to M shell vacancy transfer probabilities for the elements in the atomic region 70 6 Z 6 92. Nucl Instrum Methods B 1993;74:347. V Turgut U. V Measurement of probabilities for vacancy transfer from K to L shell [11] ErtuTgrul M, DoTgan O, SSimSsek O, of the elements 73 6 Z 6 92. Phys Rev A 1997;55:303. [12] Puri S, Mehta D, Chand B, Singh N, Hubbell JH, Trehan PN. Production of Li subshell and M shell vacancies following inner-shell vacancy production. Nucl Instrum Methods B 1993;83:21. [13] Ertugrul M. Measurement of total, radiative and radiationless (Auger) vacancy transfer probabilities from K to Li sub-shells of Cs, Ba and La. J Anal Atom Spectrum 2002;17:64. [14] Ertugrul M. Measurement of total, radiative and radiationless (Auger) vacancy transfer probabilities from K to Li (i = 1; 2; 3) subshell of Ho and Er. Spectrochim Acta B 2002;57:63. V Ertugrul M. Measurement of the eOciency of a Si(Li) detector in the 5.5 –60 keV [15] Budak G, Karabulut A, SSimSsek O, energy region. Instrum Sci Technol 1999;27:357. [16] Storm E, Israel IH. Photon cross sections from 1 keV to 100 MeV for elements Z = 1 to Z = 100. Nucl Data Tables 1970;A7:565. [17] Hubbell JH, Trehan PN, Singh N, Chand B, Mehta D, Garg ML, Garg RR, Singh S, Puri S. A review, bibliography, and tabulation of K, L, and higher atomic shell X-ray Juorescence yields. J Phys Chem Ref Data 1994;23:339. [18] Sco?eld JH. Theoretical photoionization cross sections from 1 to 1500 keV. Lawrence Livermore Laboratory (UCRL) No: 513626, 1973.
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Measurement of K to L shell vacancy transfer probabilities for the elements 52 6 Z 6 68 B. Ertugrala, U. Cevika , E. Tirasoglua , A.I. Kopyaa , M. Ertugrulb;∗ , O. Doganb a
Department of Physics, Science Faculty, Karadeniz Technical University, 61080 Trabzon, Turkey b Department of Physics, K. K. Education Faculty, Atat%urk University, 25240 Ezurum, Turkey Received 9 May 2002; accepted 13 August 2002
Abstract The probabilities for transfer of vacancies from K to L shell were measured using intensity ratio of K and total Lx X-rays. The K and total Lx X-rays yields from the targets excited by 59:5 keV incident photon were obtained using a Si(Li) detector. These experimental results were compared with the theoretically calculated values using radiative and radiationless transitions. The radiative transitions of these elements were observed from the relativistic Hartree–Slater model, which was proposed by Sco?eld (Atom. Data Nucl. Data Tables 14 (1974) 121). The radiationless transitions were observed from the Dirac–Hartree–Slater model, which was proposed by Chen et al. (Atom. Data Nucl. Data Tables 24 (1979) 13). A fairly good agreement is found between the experimental and calculated values. ? 2003 Elsevier Science Ltd. All rights reserved. Keywords: Vacancy transfer; Intensity ratio; Photoionisation; EDXRF
1. Introduction When the atom’s K or L shell/subshell has been ionized, it is excited through radiative [1] or radiationless (Auger) [2] transitions. A knowledge of average vacancy distributions is also important for the study of such processes as nuclear electron capture, internal conversion of -rays, photoelectric eIect and generally, whenever primary vacancies produced in the shell must be distinguished from multiple ionization due to the decay of inner vacancy [3]. The L and M X-rays production cross-sections and average L and M shell Juorescence yield were measured experimentally in recent years [4–6]. Ertugrul et al. [7] measured K to L shell ∗
Corresponding author. Fax: +90-4422-1841-72. E-mail addresses: [email protected] (B. Ertugral), [email protected] (M. Ertugrul).
0022-4073/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 2 ) 0 0 1 8 9 - 9
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radiative vacancy transfer probabilities for elements in the atomic range 69 6 Z 6 92 using a Co-57 radioisotope source. The enhancement eIect of K to L shell vacancy transfer on K to L intensity ratio was measured for lanthanides [8]. K to L shell and L to M shell vacancy transfer probabilities were measured experimentally using two radioisotope sources [9–11]. In addition, Puri et al. [12] have calculated values and ?tted them versus atomic number Z values and ?tted coeOcients for vacancy transfer probabilities of K to L1 , K to L2 , K to L (average), L1 to M, L2 to M, L3 to M shells. The values of the KLi (i = 1; 2; 3) for elements in the atomic range 20 6 Z 6 94 have been calculated [3]. In these calculations, the contributions due to Auger and radiative transitions were derived using the best ?tted experimental data on the Juorescence yields and intensity ratios of diIerent components of KLX (X = L; M; N, etc.) Auger electrons and K X-rays currently available. In the earlier measurements [9–11], the authors used two radioisotope sources for excitation of targets. The method is 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. Ertugrul [13,14] has measured total, radiative and radiationless vacancy transfer probabilities from K to Li subshell for some elements in the mean atomic number region. In this study, we measured K to L shell vacancy transfer probabilities for the atomic range 52 6 Z 6 68. Targets were irradiated by an 241 Am radioisotope source. The energy of primary photon that is 59:5 keV yields from 241 Am can excite K, L and other shells. The measured values have been compared with the calculated values deduced using Auger transition rates [2] and radiative X-ray emissions [1].
2. Experimental procedure The experimental set-up for the annular source in the direct excitation mode used in this study is shown in Fig. 1. The experiment was carried out using an annular source 241 Am (50 mCi), which emits monoenergetic (59:5 keV) -rays. The -rays of 26:4 keV and N p L X-rays coming from 241 Am are completely (∼ 99:99%) ?ltered out with their help of graded ?lter of Pb, Cu and Al of thickness 0.1, 0.1 and 1 mm, respectively, because even a small fraction of these radiations would produce sizable interference due to their large interaction cross-sections with K-shell electrons. Spectroscopically, pure targets of Te, Ba(CO3 ), La2 O3 , CeO2 , Pr 3 O4 , Nd 2 O3 , Sm2 O3 , Eu3 O3 , Gd 2 O3 , Tb4 O7 , Dy2 O3 , Ho2 O3 and Er 2 O3 of thickness ranging from 15 to 22 g=cm2 have been used for measurements. The Juorescent K and L X-rays from the sample were detected by collimated an Si(Li) detector having a thickness of 3 mm and energy resolution of 147 eV at 5:96 keV. The output from the preampli?er with a pulse pile-up rejection capability, and fed to a multi-channel analyzer interface with a personal computer provided with suitable software for data acquisition and peak analysis. The live time was taken as 1000 s for all elements. The samples were placed at 45◦ angle with respect to the direct beam and Juorescent X-rays emitted 90◦ to the detector. The K X-ray production cross-sections at excitation energy are given by K = K !K fK ;
(1)
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165
Fig. 1. Geometry of the experimental setup.
where K is the total K shell ionization cross-section, !K is the K shell Juorescence yield and fK is given by IK −1 fK = 1 + ; (2) IK IK =IK values are taken from [1]. The total L X-ray production cross-section at excitation energy above the K edge of the elements are given by Lx = ( L + KL K )$L ;
(3)
where L is the total L shell photoionization cross-section, KL is the K to L shell vacancy transfer probabilities and $L is the average L shell Juorescence yields. The term of KL K $L is the enhanced part from K to L shell vacancy transfer for the L shell X-ray production cross-sections. The intensity ratio of Lx and K X-rays are resolved from Eqs. (1) and (3): I Lx ( L + KL K )$L = : IK K ! K f K
(4)
The ILx =IK was obtained experimentally as follows: IL x N L K jK = x ; IK N K L x jL x
(5)
where NLx and NK are the net counts under the Lx and K peaks, Lx and K are the self-absorption correction factor for energies of Lx and K peaks and jLx and jK are the detector eOciency at
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the energies of the Lx and K X-ray energies, respectively. The detector eOciency was evaluated using the 133 Ba, 137 Cs and 241 Am radioisotope. The method for measuring the detector eOciency is explained earlier [15]. The absorption correction factor at the excitation energy has been calculated using the following equation: =
1 − exp[ − (inc =sin + emt =sin )t] ; (inc =sin + emt =sin )t
(6)
where inc and emt are the total mass absorption coeOcients of target material at the incident photon energy and at the emitted K and average L X-ray energy [16] and t is the thickness of the target. and are the angles of incident photon and emitted X-rays with respect to the normal at the surface of the sample. It can be written from Eqs. (4) and (5) as KL =
N L x K jK ! K L fK − ; N K L x jL x $ L K
(7)
where !K and $L values are taken from the table of Hubbell et al. [17], fK is calculated from Eq. (2) and K and L are interpolated from the table of Sco?eld [18]. 3. Theoretical calculations The probabilities for vacancy transfer from K to L shell is de?ned as the number of Li subshell vacancies produced in the decay of one K shell vacancy through radiate K–Li transitions or through Auger K–Li Lj and K–Li X (X = M; N; O, etc.) transitions. The average number KLi = KLi (R) + KLi (A);
(8)
where KLi (R) and KLi (A) are the radiative and Auger transition probabilities of the K to Li subshell, respectively. The number of KLi (R) is proportional to the probability that a K–Li radiative transitions takes place KLi (R) = !K [I (KLi )=IK (R)];
(9)
where I (KLi ) is the K–Li X-ray intensity and IK (R) is the total intensity of the K X-rays. The KLi have been calculated using the following equations [3]: KL1 =
1 [R (KL1 ) + 2A (KL1 L1 ) + A (KL1 L2 ) + A (KL1 L3 ) + A (KL1 X)]; (K)
KL2 =
1 [R (KL2 ) + 2A (KL2 L2 ) + A (KL1 L2 ) + A (KL2 L3 ) + A (KL2 X)]; (K)
KL3 =
1 [R (KL3 ) + 2A (KL3 L3 ) + A (KL2 L3 ) + A (KL1 L3 ) + A (KL3 X)]; (K)
(X = M; N; O; etc:):
(10)
In these equations, R and A are the radiative and the Auger partial widths corresponding to the transitions between the shells written the brackets, and is the total level width. The radiative
B. Ertugral et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 78 (2003) 163 – 169
167
transition rates and Auger transition rates were tabulated by Sco?eld [1] and Chen et al. [2], respectively.
4. Results and discussion The measured values of the K to L shell vacancy transfer probability, KL , for 13 elements, namely, Te, Ba, La, Ce, Pr, Nd, Sm, Eu, Cd, Tb, Dy, Ho, and Er are listed in Table 1. The overall error in the present measurements is estimated to be 3– 6%. This error is attributed to the uncertainties in diIerent parameters used to deduce KL values; namely, the error in the area evaluation under the K and L shell X-ray peak (6 3%), in the absorption correction factor ratio (6 2%) and the other systematic errors (2–3%). The experimental results alongside with the theoretically calculated values are represented graphically as vacancy transfer probabilities versus atomic numbers in Fig. 2. As shown in Fig. 2, values of the KL decrease with the rising atomic numbers. The experimental values KL are compared with the calculated values. These values are found to be in good agreement with calculated values for the elements 52 6 Z 6 68. In the calculated values, the radiative transition rates were taken from [1] and the radiationless (Auger) transition rates were taken from [2]. The basic idea of Puri et al. [9] and Ertugrul et al. [11] to determine experimentally the K to L shell vacancy transfer was the use of two kinds of vacancy-generating photons: one of them below, and other one above the K edge of the corresponding target element. Firstly, the all L shell was excited with the radioisotope which emits photons energy below K edge and L X-ray production cross-sections were determined. Secondly, the all L and K shells were excited with the other radioisotope, which emits photon energy above the K edge. Since the L X-ray intensity is enhanced with the K to L shell vacancy transfer, the L X-ray production cross-sections increased. The vacancy transfer probabilities for K to L shell were determined using this increasing. The experimental K to L shell vacancy transfer probabilities in the earlier method [9,11] strongly depends on the primary photon intensity (I0 ) and geometrical factor (G) for both set-ups. For this reason the experimental errors increase in the earlier method. In the present experiment, only 241 Am source has been used. It is shown in Eq. (7) that the present equation for determining K to L shell vacancy transfer probabilities is wholly independent of the primary photon intensity at the
Table 1 Comparison of experimental and theoretical results for K to L shell vacancy transfer probability Elements
KL (exper.)
KL (theor.)
Elements
KL (exper.)
KL (theor.)
52
0:908 ± 0:03 0:905 ± 0:04 0:892 ± 0:04 0:869 ± 0:03 0:866 ± 0:04 0:861 ± 0:05 0:864 ± 0:04
0.917 0.888 0.881 0.877 0.871 0.866 0.858
63
0:861 ± 0:03 0:844 ± 0:04 0:847 ± 0:05 0:832 ± 0:03 0:834 ± 0:04 0:839 ± 0:03
0.855 0.850 0.848 0.843 0.843 0.836
Te Ba 57 La 58 Ce 59 Pr 60 Nd 62 Sm 56
Eu Gd 65 Tb 66 Dy 67 Ho 68 Er 64
168
B. Ertugral et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 78 (2003) 163 – 169 1.00
Present Experimental Theoretical 0.95
ηKL
0.90
0.85
0.80
0.75 50
55
60
65
70
Atomic number Fig. 2. KL versus atomic number (Z).
present geometry (I0 G). Since the intensity ratio for K and Lx X-rays is independent of geometrical factor, sample composition and K and Lx X-rays peaks were synchronously determined, the present experimental results for K to L shell vacancy transfer using K to Lx intensity ratio gives more realistic results than the earlier experiments [9,11]. The accuracy of the numbers given is of the same size as in the earlier paper. However, while the atomic number region is 52 6 Z 6 68 in the present work, the atomic number region is the 73 6 Z 6 92 in the earlier paper [11]. As known, the statistical accuracy of peak areas is better for the high Z elements than the low Z elements. In our other experiment [8], the I K =I L intensity ratio of lanthanides was measured and the enhancement factor of L X-rays was calculated for the K to L shell vacancy transfer. The enhancement factor for L X-rays was found to be in the interval 7.75 –9.90. These enhancement factors involve L1 to L3 , L2 to L3 and together L1 to L2 and L2 to L3 Coster–Kronig transitions. For the lanthanides, while the I K =I L intensity ratio is in the interval 7–13 in earlier experiment [8], the I K =I Lx intensity ratio is in the interval 4 – 6.25 in the present experiment. Since the L X-ray intensity (I Lx ) is the sum of the Ll , L , L and L X-rays intensities, the present values for I K =I Lx intensity ratio are lower than the earlier I K =I L intensity ratio values [8]. Since the K and L X-rays were simultaneously counted, the present method is reliable according to earlier method [9,11]. Earlier method [9,11] becomes independent of both the target thickness and the eOciency of the detector. Present method becomes independent of the I0 G product and target thickness. Generally, in the literature, the errors in these measurements are approximately 2–3% and 3– 6% for the detector eOciency and the I0 G product, respectively. In conclusion, the present agreement between the theoretical and experimental values leads to the conclusion that the present method will be bene?cial for determining of vacancy transfer probability.
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