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Measurement of Kα to Lα and Kβ to Lβ intensity ratios of seven elements in the atomic number range 56≤Z≤66 using photoionization at 59.54 keV
Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
Measurement of K to ¸ and K to ¸ intensity ratios of seven elements in the atomic number range 564Z466 using photoionization at 59.54 keV Rmdvan Durak*, YuK ksel OG zdemir, Yusuf S7 ahin Atatu( rk U$ niversitesi, Fen & Edebiyat Faku( ltesi, Fizik Bo( lu( mu( , 25240, Erzurum, Turkey Received 31 July 2000; accepted 8 November 2000
Abstract K to ¸ and K to ¸ intensity ratios for elements Ba, La, Ce, Nd, Sm, Tb, and Dy have been measured at the excitation energy of 59.54 keV -rays from Am radioactive source of strength 100 mCi. Intensity ratios were determined by measuring K and ¸ X-rays emitted from standard target of a given element. Theoretical values of the K to ¸ and K to ¸ intensity ratios were calculated using theoretically tabulated values of shell/subshell photoionization cross-sections, #uorescence yields, Coster}Kronig transition probabilities and radiative decay rates for O0 and "0. Experimental results were compared with the theoretical )*G )*G values. 2001 Elsevier Science Ltd. All rights reserved. Keywords: X-ray intensity ratios; Cross sections; Fluorescense yields
1. Introduction K- and ¸-shell X-ray intensity ratios for di!erent elements at various photoionization energies are important because of the wide use of this technique in atomic, molecular, and radiation physics and in the nondestructive elemental analysis of materials using energy-dispersive X-ray #uorescence. Several attempts have been made to measure X-ray intensity ratios. K and ¸ X-ray intensity ratios were measured experimentally [1}5]. Rebohle et al. [6] have measured K/K intensity ratio for pure 3d elements and some of their chemical compounds. Garg et al. [7] have reported ¸ X-ray #uorescence cross sections and relative intensities for Ho, Er and Yb in the energy range
* Corresponding author. Fax: #90-442-2331062. E-mail address: [email protected] (R. Durak). 0022-4073/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 0 ) 0 0 1 4 6 - 1
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11}41 keV. Shatendra et al. [8] have measured energy dependence of photon-induced ¸-shell X-ray intensity ratios in some high-Z elements. Rao et al. [9] have measured ¸ X-ray #uorescence cross sections and intensity ratios in some high-Z elements excited by 23.62- and 24.68-keV photons. Accurate measurement of K X-ray intensities of elements with Z"79.82 [10] and K to K X-ray intensity ratios after ionization by -rays [11] have been reported. In this study, K to ¸ and K to ¸ intensity ratios for elements Ba, La, Ce, Nd, Sm, Tb, and Dy have been measured. We have measured Ba and some lanthanide elements 554Z466 with K-edge energies lower than 59.54 keV. The K edge energies of the elements under investigation are below incident photon energy 59.54 keV when, in addition to K shell, ¸, M and higher shells are also ionized. In this case, the initial inner-shell vacancy is transferred to a higher shell/subshell and additional vacancies may be created. The enhancement of ¸-shell X-rays depends on the transfer of vacancies from the K-shell to various ¸-subshells and the corresponding Coster}Kronig transition probabilities. The transfer of vacancies from the K-shell to various ¸-subshells was investigated by experimental and semiempirical methods in this study.
2. Experimental The experimental arrangement and geometry used in the present study are shown in Fig. 1. The target K and ¸ X-rays spectra were recorded with a Si(Li) detector with an active area of 12.5 mm and a sensitive crystal depth of 3 mm and Be window of 0.025 mm thickness coupled to 1024 multichannel analyzer. The ampli"er shaping time constant that resulted in the best resolution was 6 s and this value was used in the present measurements. The measured energy resolution of the detector system was 188 eV FWHM for the Mn K line at 5.9 keV. Spectroscopically pure
Fig. 1. Experimental setup used for measurements of K- and ¸-shell X-ray intensity ratios.
R. Durak et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
335
Fig. 2. (a) Typical K X-ray spectrum for Tb irradiated with 59.54 keV gamma rays from Am. (b) Typical ¸ X-ray spectrum for Tb irradiated with 59.54 keV gamma rays from Am.
rectangular samples of 1.72 cm area and thickness ranging from 3 to 35 m g/cm\ have been used. Photons of 59.54 keV energy from a 100 mCi Am point source were used for excitation of the samples. To keep the counting error to a minimum, X-ray spectra were accumulated in time intervals ranging from 1800 to 64,800 s. Figs. 2a, b show a typical K and ¸ shell X-ray spectrum of dysprosium, respectively. AXIL (V3.0) X-ray analysis computer program was used for peak resolving background subtraction and determination of the net peak areas of K and ¸ X-rays of the targets.
3. Theoretical method The theoretical values of K and K line intensity of elements were calculated using the equations "N (E) f , )? ) ) )? "N (E) f , )@ ) ) )@
(1) (2)
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where N (E) is the K-shell photoionization cross-section for the given element at the excitation ) energy E, is the K-shell #uorescence yield and f and f are fractional X-ray emission rates ) )? )@ for K and K X-rays and are de"ned as f "(1#I /I )\, (3) )? )@ )? f "(1#I /I )\, (4) )@ )? )@ where I /I is the K to K X-ray intensity ratio. In the present calculations, the values of N (E) )@ )? ) were taken from Sco"eld [12] based on the Hartree}Slater potential theory, and the values of were taken from the tables of Hubbell et al. [13]. I /I values based on relativistic ) )@ )? Hartree}Slater theory were used for the evaluation of theoretical K X-ray #uorescence cross sections [14]. The theoretical values of ¸ and ¸ line intensity of elements were calculated using the equations "[(N #N )( f #f f )#(N #N ) f #(N #N )] F , (5) *? * ) )* * ) )* * ) )* ? "(N #N ) F #[(N #N ) f #(N #N )] F *@ * ) )* @ * ) )* * ) )* @ #[(N #N );( f #f f )#(N #N ) f #(N #N )] F , (6) ) )* * ) )* * ) )* @ * where N and N G (i"1,2,3) are K and ¸ subshell photoionization cross sections at the excitation ) * energy [15], are the ¸ subshell #uorescence yields [16], f are Coster}Kronig transition G GH probabilities from the i to j subshell #uorescence yields [16], F are the fractional X-ray emission GH rates [17], G are the number of additional vacancies transferred to the ¸ subshell from the G )* K shell through radiative G (R) and nonradiative G (A) transitions [18]. G is given by )* )* )* (7) G " G (R)# G (A). )* )* )* 4. Experimental method The experimental values of K to ¸ and K to ¸ line intensity of elements were given by I G N ¹ ) " )G *G *G (i", ), (8) I G N G ¹ G G * * ) ) where N(K )/N(¸ ) represents the ratio of the counting rates under the K and ¸ peaks. G G G G ¹(¸ )/¹(K ) is the ratio of the self-absorption correction factor of the target. (¸ )/(K ) is the ratio G G G G of the detector e$ciency values for ¸ and K X-rays, respectively. The e$ciency values at various G G energies were taken from the variation of the factor I G with energy, where I is the intensity of the incident radiation, G is a geometrical factor and is the detector e$ciency for characteristic X-rays. In the present study, the values of the factor I G were determined by collecting the K ) X-ray yields from thin standard samples of Zn, Se, Sn, Cs, Pr, Gd, and Ho in the same geometry, and using the equation I )? , I G " )? ¹ m )? )?
(9)
R. Durak et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
337
where I is the net number of counts under the corresponding photopeak, theoretical values )? )? were calculated using Eq. (1) and ¹ is the self-absorption correction factor for the incident )? photons and emitted K X-ray photons and is given by 1!exp[!( sec # sec )m] ¹" , (10) ( sec # sec )m where and are the total mass absorption of the target material for the incident photon and the emitted characteristic X-rays, respectively [19]. m is the mass of the sample in g/cm. The angles of incident photons and emitted X-rays with respect to the normal at the surface of the sample and were equal to 453 in the present setup. The measured I G values for the present setup are plotted as a function of the energy in Fig. 3.
Fig. 3. Plot of the factor I G vs. K X-rays energy.
Table 1 Comparison of the present work and theoretical predictions of K to ¸ intensity ratios Z
Element
Present work
Theoretical values
Theoretical values
56 57 58 60 62 65 66
Ba La Ce Nd Sm Tb Dy
12.81$0.55 12.51$0.45 11.83$0.37 11.50$0.37 9.25$0.35 7.70$0.30 7.71$0.32
13.74 12.66 12.23 10.98 9.99 8.16 8.17
144.42 125.35 121.19 102.80 89.44 72.04 66.76
Values calculated using relations (1) and (5). Values calculated using relations (1) and (5), when G "0. )*
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Table 2 Comparison of the present work and theoretical predictions of K to ¸ intensity ratios Z
Element
Present work
Theoretical values
Theoretical values
56 57 58 60 62 65 66
Ba La Ce Nd Sm Tb Dy
3.79$0.21 3.90$0.20 3.58$0.20 3.45$0.19 3.37$0.19 2.74$0.18 2.84$0.19
3.91 3.71 3.89 3.22 2.93 2.58 2.39
21.22 19.97 18.70 16.69 14.80 12.48 11.38
Values calculated using relations (2) and (6). Values calculated using relations (2) and (6), when G "0. )*
Fig. 4. (a) Comparison of the present work and theoretical predictions of K to ¸ intensity ratios. (b) Comparison of the present work and theoretical predictions of K to ¸ intensity ratios.
R. Durak et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
339
Table 3 Uncertainties in the quantities used to determine K to ¸ and K to ¸ intensity ratios in Eq. (8) Quantity
Nature of uncertainty
Uncertainty (%)
N G (i",) ) N G * I G G )
Counting statistic Counting statistic Errors in di!erent parameters used to evaluate this factor Errors in di!erent parameters used to evaluate this factor Error in the absorption coe$cients at incident and emitted photon energies Nonuniform thickness
(3 2 5
I G G * ¹ m
5 (1 1
5. Results and discussion The measured relative intensities K to ¸ for the elements in the atomic number range 564Z466 at 59.54 keV excitation energy are presented in Table 1 together with values calculated using relations (1) and (5) and values calculated using relations (1) and (5), when G "0. Measured relative intensities K to ¸ for the same elements 59.54 keV excitation energy )* are also presented in Table 2 together with calculated values using relations (2), (6) and calculated values using relations (2), (6), when G "0. For comparison, theoretical and measured intensity )* ratios are plotted as a function of atomic number in Figs. 4a, b. The overall errors in the measured K to ¸ and K to ¸ intensity ratios are estimated to be less than 5 and 7% respectively, which arise due to the uncertainties in the various physical parameters required to evaluate the experimental results using Eq (8). The uncertainties in the parameters are listed in Table 3. The experimental values are in good agreement with theoretical values, when G O0. )* Consequently, to determine K to ¸ and K to ¸ relative intensities for a given element, vacancy transfer probabilities G O0 must be taken. )* Acknowledgements We are very grateful to Mr. J.H. Hubbell for providing us with the necessary documents for this study. This work was supported by the AtatuK rk University Research Fund, project No(s). 1997-69, 1998-65.
References [1] Garg ML, Sing J, Sharma AK, Verma HR, Singh N, Mangal PC, Trehan PN. Ind J Phys A 1984;58:242. [2] Md Khan R, Karimi M. X-Ray Spectrom 1980;9:32.
340
R. Durak et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
[3] Kumar S, Mittal R, Allawadhi KL, Sood BS. J Phys B 1982;15:3377. [4] Rao DV, Gigante GE, Cesareo R. Phys Scripta 1993;47:765. [5] Darko JB, Tetteh GK. X-Ray Spectrom 1992;21:111. [6] Rebohle L, Lehnert U, Zschornack G. X-Ray Spectrom 1996;25:295. [7] Garg ML, Mehta D, Verma HR, Singh N, Mangal PC, Trehan PN. J Phys B 1986;19:1615. [8] Shatendra K, Allawadhi KL, Sood BS. J Phys B 1983;16:4313. [9] Rao DV, Cesareo R, Gigante GE. Phys Rev A 1993;47:1087. [10] Dasmahapatra B, Mukherjee A. Phys Rev A 1995;51:3546. [11] Coelho LFS, Gaspar MB, Eichler J. Phys Rev A 1989;40:4093. [12] Sco"eld JH. Report UCRL 51326, Lawrence Livermore Lab, Livermore, CA, 1973. [13] Hubbell JH et al. J Phys Chem Ref Data 1994;23:339. [14] Sco"eld JH. At Data Nucl Data Tables 1974;14:121. [15] Sco"eld JH. Lawrence Livermore National report no. UCRL 51326, 1973, unpublished. [16] Krause MO. J Phys Chem Ref Data 1979;8:307. [17] Sco"eld JH. At Data Nucl Data Tables 1974;14:121. [18] Rao PV, Chen MH, Crasemann B. Phys Rev A 1972;5:997. [19] Hubbell JH, Seltzer SM. National Institute of Standards and Technology report no. 5632 NISTIR, 1995, unpublished.
Measurement of K to ¸ and K to ¸ intensity ratios of seven elements in the atomic number range 564Z466 using photoionization at 59.54 keV Rmdvan Durak*, YuK ksel OG zdemir, Yusuf S7 ahin Atatu( rk U$ niversitesi, Fen & Edebiyat Faku( ltesi, Fizik Bo( lu( mu( , 25240, Erzurum, Turkey Received 31 July 2000; accepted 8 November 2000
Abstract K to ¸ and K to ¸ intensity ratios for elements Ba, La, Ce, Nd, Sm, Tb, and Dy have been measured at the excitation energy of 59.54 keV -rays from Am radioactive source of strength 100 mCi. Intensity ratios were determined by measuring K and ¸ X-rays emitted from standard target of a given element. Theoretical values of the K to ¸ and K to ¸ intensity ratios were calculated using theoretically tabulated values of shell/subshell photoionization cross-sections, #uorescence yields, Coster}Kronig transition probabilities and radiative decay rates for O0 and "0. Experimental results were compared with the theoretical )*G )*G values. 2001 Elsevier Science Ltd. All rights reserved. Keywords: X-ray intensity ratios; Cross sections; Fluorescense yields
1. Introduction K- and ¸-shell X-ray intensity ratios for di!erent elements at various photoionization energies are important because of the wide use of this technique in atomic, molecular, and radiation physics and in the nondestructive elemental analysis of materials using energy-dispersive X-ray #uorescence. Several attempts have been made to measure X-ray intensity ratios. K and ¸ X-ray intensity ratios were measured experimentally [1}5]. Rebohle et al. [6] have measured K/K intensity ratio for pure 3d elements and some of their chemical compounds. Garg et al. [7] have reported ¸ X-ray #uorescence cross sections and relative intensities for Ho, Er and Yb in the energy range
* Corresponding author. Fax: #90-442-2331062. E-mail address: [email protected] (R. Durak). 0022-4073/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 0 ) 0 0 1 4 6 - 1
334
R. Durak et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
11}41 keV. Shatendra et al. [8] have measured energy dependence of photon-induced ¸-shell X-ray intensity ratios in some high-Z elements. Rao et al. [9] have measured ¸ X-ray #uorescence cross sections and intensity ratios in some high-Z elements excited by 23.62- and 24.68-keV photons. Accurate measurement of K X-ray intensities of elements with Z"79.82 [10] and K to K X-ray intensity ratios after ionization by -rays [11] have been reported. In this study, K to ¸ and K to ¸ intensity ratios for elements Ba, La, Ce, Nd, Sm, Tb, and Dy have been measured. We have measured Ba and some lanthanide elements 554Z466 with K-edge energies lower than 59.54 keV. The K edge energies of the elements under investigation are below incident photon energy 59.54 keV when, in addition to K shell, ¸, M and higher shells are also ionized. In this case, the initial inner-shell vacancy is transferred to a higher shell/subshell and additional vacancies may be created. The enhancement of ¸-shell X-rays depends on the transfer of vacancies from the K-shell to various ¸-subshells and the corresponding Coster}Kronig transition probabilities. The transfer of vacancies from the K-shell to various ¸-subshells was investigated by experimental and semiempirical methods in this study.
2. Experimental The experimental arrangement and geometry used in the present study are shown in Fig. 1. The target K and ¸ X-rays spectra were recorded with a Si(Li) detector with an active area of 12.5 mm and a sensitive crystal depth of 3 mm and Be window of 0.025 mm thickness coupled to 1024 multichannel analyzer. The ampli"er shaping time constant that resulted in the best resolution was 6 s and this value was used in the present measurements. The measured energy resolution of the detector system was 188 eV FWHM for the Mn K line at 5.9 keV. Spectroscopically pure
Fig. 1. Experimental setup used for measurements of K- and ¸-shell X-ray intensity ratios.
R. Durak et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
335
Fig. 2. (a) Typical K X-ray spectrum for Tb irradiated with 59.54 keV gamma rays from Am. (b) Typical ¸ X-ray spectrum for Tb irradiated with 59.54 keV gamma rays from Am.
rectangular samples of 1.72 cm area and thickness ranging from 3 to 35 m g/cm\ have been used. Photons of 59.54 keV energy from a 100 mCi Am point source were used for excitation of the samples. To keep the counting error to a minimum, X-ray spectra were accumulated in time intervals ranging from 1800 to 64,800 s. Figs. 2a, b show a typical K and ¸ shell X-ray spectrum of dysprosium, respectively. AXIL (V3.0) X-ray analysis computer program was used for peak resolving background subtraction and determination of the net peak areas of K and ¸ X-rays of the targets.
3. Theoretical method The theoretical values of K and K line intensity of elements were calculated using the equations "N (E) f , )? ) ) )? "N (E) f , )@ ) ) )@
(1) (2)
336
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where N (E) is the K-shell photoionization cross-section for the given element at the excitation ) energy E, is the K-shell #uorescence yield and f and f are fractional X-ray emission rates ) )? )@ for K and K X-rays and are de"ned as f "(1#I /I )\, (3) )? )@ )? f "(1#I /I )\, (4) )@ )? )@ where I /I is the K to K X-ray intensity ratio. In the present calculations, the values of N (E) )@ )? ) were taken from Sco"eld [12] based on the Hartree}Slater potential theory, and the values of were taken from the tables of Hubbell et al. [13]. I /I values based on relativistic ) )@ )? Hartree}Slater theory were used for the evaluation of theoretical K X-ray #uorescence cross sections [14]. The theoretical values of ¸ and ¸ line intensity of elements were calculated using the equations "[(N #N )( f #f f )#(N #N ) f #(N #N )] F , (5) *? * ) )* * ) )* * ) )* ? "(N #N ) F #[(N #N ) f #(N #N )] F *@ * ) )* @ * ) )* * ) )* @ #[(N #N );( f #f f )#(N #N ) f #(N #N )] F , (6) ) )* * ) )* * ) )* @ * where N and N G (i"1,2,3) are K and ¸ subshell photoionization cross sections at the excitation ) * energy [15], are the ¸ subshell #uorescence yields [16], f are Coster}Kronig transition G GH probabilities from the i to j subshell #uorescence yields [16], F are the fractional X-ray emission GH rates [17], G are the number of additional vacancies transferred to the ¸ subshell from the G )* K shell through radiative G (R) and nonradiative G (A) transitions [18]. G is given by )* )* )* (7) G " G (R)# G (A). )* )* )* 4. Experimental method The experimental values of K to ¸ and K to ¸ line intensity of elements were given by I G N ¹ ) " )G *G *G (i", ), (8) I G N G ¹ G G * * ) ) where N(K )/N(¸ ) represents the ratio of the counting rates under the K and ¸ peaks. G G G G ¹(¸ )/¹(K ) is the ratio of the self-absorption correction factor of the target. (¸ )/(K ) is the ratio G G G G of the detector e$ciency values for ¸ and K X-rays, respectively. The e$ciency values at various G G energies were taken from the variation of the factor I G with energy, where I is the intensity of the incident radiation, G is a geometrical factor and is the detector e$ciency for characteristic X-rays. In the present study, the values of the factor I G were determined by collecting the K ) X-ray yields from thin standard samples of Zn, Se, Sn, Cs, Pr, Gd, and Ho in the same geometry, and using the equation I )? , I G " )? ¹ m )? )?
(9)
R. Durak et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
337
where I is the net number of counts under the corresponding photopeak, theoretical values )? )? were calculated using Eq. (1) and ¹ is the self-absorption correction factor for the incident )? photons and emitted K X-ray photons and is given by 1!exp[!( sec # sec )m] ¹" , (10) ( sec # sec )m where and are the total mass absorption of the target material for the incident photon and the emitted characteristic X-rays, respectively [19]. m is the mass of the sample in g/cm. The angles of incident photons and emitted X-rays with respect to the normal at the surface of the sample and were equal to 453 in the present setup. The measured I G values for the present setup are plotted as a function of the energy in Fig. 3.
Fig. 3. Plot of the factor I G vs. K X-rays energy.
Table 1 Comparison of the present work and theoretical predictions of K to ¸ intensity ratios Z
Element
Present work
Theoretical values
Theoretical values
56 57 58 60 62 65 66
Ba La Ce Nd Sm Tb Dy
12.81$0.55 12.51$0.45 11.83$0.37 11.50$0.37 9.25$0.35 7.70$0.30 7.71$0.32
13.74 12.66 12.23 10.98 9.99 8.16 8.17
144.42 125.35 121.19 102.80 89.44 72.04 66.76
Values calculated using relations (1) and (5). Values calculated using relations (1) and (5), when G "0. )*
338
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Table 2 Comparison of the present work and theoretical predictions of K to ¸ intensity ratios Z
Element
Present work
Theoretical values
Theoretical values
56 57 58 60 62 65 66
Ba La Ce Nd Sm Tb Dy
3.79$0.21 3.90$0.20 3.58$0.20 3.45$0.19 3.37$0.19 2.74$0.18 2.84$0.19
3.91 3.71 3.89 3.22 2.93 2.58 2.39
21.22 19.97 18.70 16.69 14.80 12.48 11.38
Values calculated using relations (2) and (6). Values calculated using relations (2) and (6), when G "0. )*
Fig. 4. (a) Comparison of the present work and theoretical predictions of K to ¸ intensity ratios. (b) Comparison of the present work and theoretical predictions of K to ¸ intensity ratios.
R. Durak et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
339
Table 3 Uncertainties in the quantities used to determine K to ¸ and K to ¸ intensity ratios in Eq. (8) Quantity
Nature of uncertainty
Uncertainty (%)
N G (i",) ) N G * I G G )
Counting statistic Counting statistic Errors in di!erent parameters used to evaluate this factor Errors in di!erent parameters used to evaluate this factor Error in the absorption coe$cients at incident and emitted photon energies Nonuniform thickness
(3 2 5
I G G * ¹ m
5 (1 1
5. Results and discussion The measured relative intensities K to ¸ for the elements in the atomic number range 564Z466 at 59.54 keV excitation energy are presented in Table 1 together with values calculated using relations (1) and (5) and values calculated using relations (1) and (5), when G "0. Measured relative intensities K to ¸ for the same elements 59.54 keV excitation energy )* are also presented in Table 2 together with calculated values using relations (2), (6) and calculated values using relations (2), (6), when G "0. For comparison, theoretical and measured intensity )* ratios are plotted as a function of atomic number in Figs. 4a, b. The overall errors in the measured K to ¸ and K to ¸ intensity ratios are estimated to be less than 5 and 7% respectively, which arise due to the uncertainties in the various physical parameters required to evaluate the experimental results using Eq (8). The uncertainties in the parameters are listed in Table 3. The experimental values are in good agreement with theoretical values, when G O0. )* Consequently, to determine K to ¸ and K to ¸ relative intensities for a given element, vacancy transfer probabilities G O0 must be taken. )* Acknowledgements We are very grateful to Mr. J.H. Hubbell for providing us with the necessary documents for this study. This work was supported by the AtatuK rk University Research Fund, project No(s). 1997-69, 1998-65.
References [1] Garg ML, Sing J, Sharma AK, Verma HR, Singh N, Mangal PC, Trehan PN. Ind J Phys A 1984;58:242. [2] Md Khan R, Karimi M. X-Ray Spectrom 1980;9:32.
340
R. Durak et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 70 (2001) 333}340
[3] Kumar S, Mittal R, Allawadhi KL, Sood BS. J Phys B 1982;15:3377. [4] Rao DV, Gigante GE, Cesareo R. Phys Scripta 1993;47:765. [5] Darko JB, Tetteh GK. X-Ray Spectrom 1992;21:111. [6] Rebohle L, Lehnert U, Zschornack G. X-Ray Spectrom 1996;25:295. [7] Garg ML, Mehta D, Verma HR, Singh N, Mangal PC, Trehan PN. J Phys B 1986;19:1615. [8] Shatendra K, Allawadhi KL, Sood BS. J Phys B 1983;16:4313. [9] Rao DV, Cesareo R, Gigante GE. Phys Rev A 1993;47:1087. [10] Dasmahapatra B, Mukherjee A. Phys Rev A 1995;51:3546. [11] Coelho LFS, Gaspar MB, Eichler J. Phys Rev A 1989;40:4093. [12] Sco"eld JH. Report UCRL 51326, Lawrence Livermore Lab, Livermore, CA, 1973. [13] Hubbell JH et al. J Phys Chem Ref Data 1994;23:339. [14] Sco"eld JH. At Data Nucl Data Tables 1974;14:121. [15] Sco"eld JH. Lawrence Livermore National report no. UCRL 51326, 1973, unpublished. [16] Krause MO. J Phys Chem Ref Data 1979;8:307. [17] Sco"eld JH. At Data Nucl Data Tables 1974;14:121. [18] Rao PV, Chen MH, Crasemann B. Phys Rev A 1972;5:997. [19] Hubbell JH, Seltzer SM. National Institute of Standards and Technology report no. 5632 NISTIR, 1995, unpublished.