- Email: [email protected]
Lγ X-ray intensity ratios for elements in the atomic range 57⩽Z⩽92 using radioisotope X-ray fluorescence
28 May 2001
Physics Letters A 284 (2001) 43–48 www.elsevier.nl/locate/pla
Measurement of Lα/L, Lα/Lβ and Lα/Lγ X-ray intensity ratios for elements in the atomic range 57 Z 92 using radioisotope X-ray fluorescence Rıdvan Durak ∗ , Yüksel Özdemir Atatürk Üniversitesi, Fen-Edebiyat Fakültesi, Fizik Bölümü, 25240 Erzurum, Turkey Received 17 January 2001; received in revised form 26 March 2001; accepted 29 March 2001 Communicated by B. Fricke
Abstract Lα/L, Lα/Lβ and Lα/Lγ intensity ratios have been measured for some elements with atomic range 57 Z 92 by using characteristic L X-rays from targets excited by 59.54 keV photons from a filtered radioisotope 241 Am point source. Theoretical values of the Lα/L, Lα/Lβ and Lα/Lγ intensity ratios were calculated using theoretically tabulated values of subshell photoionization cross-sections, fluorescence yields, fractional X-ray emission rates, Coster–Kronig transition probabilities. Experimental results have been compared with the theoretical values and other available experimental results. Good agreement was observed between experimental results, other available experimental results and theoretically calculated values. 2001 Elsevier Science B.V. All rights reserved. PACS: 32.30.Rj; 32.80.Cy; 32.80.Hd
1. Introduction Accurate experimental result regarding the X-ray intensity ratios are important because of their extensive use in basic studies of nuclear and atomic physics and developing more reliable theoretical models describing fundamental inner-shell ionization processes. Several attempts have been made for measuring K and L X-ray intensity ratios for heavy elements [1–12]. Among others, Kα to Lα intensity ratio of lanthanides following photoionization at 59.5 keV [1], measurement of L X-ray fluorescence cross-sections and relative intensity for Ho, Er and Yb in the energy range
* Corresponding author.
E-mail address: [email protected] (R. Durak).
11–41 keV [2], energy dependence of photon-induced L shell X-ray intensity ratios in some high-Z elements [3], L X-ray fluorescence cross-sections and intensity ratios in some high-Z elements excited by 23.62 and 24.68 keV photons [4], Lα/L X-ray intensity ratios for elements in the region 55 Z 80 [5], Lα/Lβ and Lα/Lγ X-ray intensity ratios for elements in the range Z = 55–80 [6] and L X-ray fluorescence cross-sections and relative intensities for elements 56 Z 66 in the energy range 11–41 keV [7] have been reported. Extensive literature search reveals that the individual Lα/L, Lα/Lβ and Lα/Lγ intensity ratios for the elements La, Ce, Pr, Nd, Sm, Tb, Dy, Ho, Er, Yb, Hf, W, Os, Hg, Tl, Pb, Th and U are scarce, to the best of our knowledge, Lα/Lβ and Lα/Lγ intensity ratios for Hf and Os are reported for the first time. This investigations Lα/L, Lα/Lβ and Lα/Lγ
0375-9601/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 ( 0 1 ) 0 0 2 2 3 - 7
44
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
Fig. 1. Experimental setup used for measurements of Lα/L, Lα/Lβ and Lα/Lγ X-ray intensity ratios.
intensity ratios have been measured for these elements. The results of our work have been compared with the literature experimental results and theoretical predictions.
2. Experimental The experimental arrangement and geometry used in the present study are shown in Fig. 1. The target L X-rays spectra were recorded with a Si (Li) detector with an active area of 12.5 mm2 and a sensitive crystal depth of 3 mm and Be window of 0.025 mm thickness coupled to 1024 multichannel analyzer. The amplifier shaping time constant that resulted in the best resolution was 6 µs and this value was used in the present measurements. The measured energy resolution of the detector system was 188 eV FWHM for the Mn Kα line at 5.9 keV. Spectroscopically pure rectangular samples of 1.72 cm2 area and thickness ranging from 3 to 35 mg cm−2 have been used. Photons of 59.54 keV energy from a 100 mCi 241 Am point source were used for excitation of the samples. To keep the counting error to minimum, X-ray spec-
Fig. 2. Typical L X-ray spectrum for Tb irradiated with 59.54 keV gamma rays from 241 Am.
tra were accumulated in time intervals ranging from 1800 to 64800 s. Fig. 2 shows a typical L shell X-ray spectrum of Tb. AXIL (V3.0) X-ray analysis computer program was used for peak resolving background subtraction and determination of the net peak areas of L X-rays of the targets.
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
45
3. Experimental method The experimental values of Lα/L, Lα/Lβ and Lα/Lγ intensity ratios of elements were given by ILi NLi TLj εLj = ILj NLj TLi εLi
(i = α, j = , β, γ ),
(1)
where NLi /NLj represents the ratio of the counting rates under the Li and Lj peaks. εLj /εLi is the ratio of the detector efficiency values for Lj and Li Xrays, respectively, and TLj /TLi is the ratio of the self absorption correction factor of the target. In the present study, the values of the factors I0 GεKα , which contain terms related to the incident photon flux, geometrical factor and the efficiency of the X-ray detector, were determined by collecting the K X-ray spectra of thin samples of Cl, Ca, Fe, Zn, Se, Sr, Nb and Ag in the same geometry in which the K X-ray fluorescence cross-sections were measured and using the equation IKα , I0 GεKα = σKα TKα m
(2)
where IKα is the net number of counts under the corresponding photopeak , εKα is the detector efficiency for Kα X-rays and TKα is the self-absorption correction factor for the incident photons and emitted Kα X-ray photons and is given by T=
1 − exp[−(µi sec θ1 + µe sec θ2 )m] , (µi sec θ1 + µe sec θ2 )m
(3)
where µi and µe are the total mass absorption of the target material for the incident photon and the emitted characteristic X-rays, respectively [13]. m is the mass of the sample in g/cm2. The angles incident photons and emitted X-rays with respect to the normal at the surface of the sample θ1 and θ2 were equal to 45◦ in the present setup. The measured I0 Gεα values for the present setup are plotted as a function of the energy in Fig. 3.
Fig. 3. Plot of the factor I0 Gε vs. K X-rays energy.
equations p p X σL = σL1 + σK ηKL1 (f13 + f12 f23 ) p p + σL2 + σK ηKL2 f23 p p + σL3 + σK ηKL3 ω3 F3 , p p X = σL1 + σK ηKL1 (f13 + f12 f23 ) σLα p p + σL2 + σK ηKL2 f23 p p + σL3 + σK ηKL3 ω3 F3α , p p X σLβ = σL1 + σK ηKL1 ω1 F1β p p + σL1 + σK ηKL1 f12 p p + σL2 + σK ηKL2 ω2 F2β p p + σL1 + σK ηKL1 (f13 + f12 f23 ) p p + σL2 + σK ηKL2 f23 p p + σL3 + σK ηKL3 ω3 F3β , p p X = σL1 + σK ηKL1 ω1 F1γ σLγ p p + σL1 + σK ηKL1 f12 p p + σL2 + σK ηKL2 ω2 F2γ , p
4. Theoretical method The theoretical values of L, Lα, Lβ and Lγ line intensity of elements were calculated using the
p
(4)
(5)
(6)
(7)
where σK and σLi (i = 1, 2, 3) are K and L subshell photoionization cross-sections [14], ωi are the L subshell fluorescence yields [15], fij are Coster–Kronig transitions probabilities from the i to j subshell fluorescence yields [15], Fij are the fractional X-ray emis-
46
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
Table 1 Comparison of present and literature experimental values and theoretical predictions of Lα/L intensity ratios
Table 2 Comparison of present and literature experimental values and theoretical predictions of Lα/Lβ intensity ratios
Lα/L
Lα/Lβ
Z
Target
Present
Exp.b
57
La
–a
27.86
25.77
57
La
1.29 ± 0.10
1.250
1.32
Ce
–a
26.46
25.73
58
Ce
1.28 ± 0.10
1.325
1.31
Pr
–a
25.51
25.32
59
Pr
1.26 ± 0.11
1.247
1.25
60
Nd
–a
24.94
24.96
60
Nd
1.28 ± 0.10
1.254
1.24
62
Sm
–a
25.77
24.85
62
Sm
1.28 ± 0.11
1.268
1.22
65
Tb
24.43 ± 1.61
23.81
24.09
65
Tb
1.21 ± 0.09
1.264
1.20
66
Dy
23.38 ± 1.51
23.70
23.29
66
Dy
1.21 ± 0.10
1.267
1.23
58 59
Theo.
Z
Target
Present
Exp.a
Theo.
67
Ho
23.39 ± 1.52
22.78
23.51
67
Ho
1.16 ± 0.09
1.205
1.17
68
Er
22.38 ± 1.51
22.73
23.41
68
Er
1.19 ± 0.08
1.227
1.22
70
Yb
22.28 ± 1.53
–
22.56
70
Yb
0.66 ± 0.08
0.690
0.69
72
Hf
22.11 ± 1.50
–
21.79
72
Hf
0.70 ± 0.08
–
0.71
74
W
21.44 ± 1.45
–
21.13
74
W
0.80 ± 0.07
0.628
0.70
76
Os
20.57 ± 1.36
–
19.98
76
Os
0.94 ± 0.10
–
0.87
80
Hg
19.28 ± 1.34
–
19.07
80
Hg
0.91 ± 0.09
1.011
0.95
81
Tl
18.05 ± 1.35
–
18.39
81
Tl
0.96 ± 0.11
0.967
0.95
82
Pb
18.75 ± 1.22
–
18.93
82
Pb
0.97 ± 0.09
0.939
0.96
90
Th
16.83 ± 1.28
–
16.66
290
Th
0.90 ± 0.09
0.896
0.89
92
U
16.66 ± 1.11
–
16.08
92
U
0.96 ± 0.09
0.845
0.93
a The L peaks of the elements could not be measured due to poor
a Ref. [19].
statistics in the regions. b Ref. [18].
sion rates [16], ηKLi are the number of additional vacancies transferred to the Li subshell from the K shell through radiative ηKLi (R) and nonradiative ηKLi (A) transitions [17]. ηKLi is given by ηKLi = ηKLi (R) + ηKLi (A).
(8)
5. Results and discussion Lα/L, Lα/Lβ and Lα/Lγ intensity ratios for thin targets of La, Ce, Pr, Nd, Sm, Tb Dy, Ho, Er, Yb, Hf, W, Os, Hg, Tl, Pb, Th and U at 59.5 keV excitation energy are measured and the results are compared
with other experimental results and theoretical predictions. These results are given in Tables 1–3 and, for comparison, theoretical predictions, literature experimental results and measured intensity ratios are plotted as a function of atomic number in Figs. 4(a)–(c). The overall error in the measured Lα/L, Lα/Lβ and Lα/Lγ intensity ratios is estimated to be less than 6.5–11.5%, which arises due to the uncertainties in the various physical parameters required to evaluate the experimental results using Eq. (1). The uncertainties in the parameters are listed in Table 4. It can be seen from Tables 1–3 and Figs. 4(a)–(c) that our measurements values are in good agreement, within the experimental uncertainties, with literature experimental values [18,19] and the calculated theoretical values. The agreements between the present Lα/L, Lα/Lβ and Lα/Lγ results and the theoretical predictions
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
47
Table 3 Comparison of present and literature experimental values and theoretical predictions of Lα/Lγ intensity ratios Lα/Lγ Z
Target
Present
Exp.a
Theo.
57
La
8.84 ± 0.90
9.692
8.35
58
Ce
8.77 ± 0.71
9.363
8.47
59
Pr
8.21 ± 0.69
9.205
8.42
60
Nd
8.50 ± 0.70
9.326
8.40
62
Sm
7.64 ± 0.45
8.766
8.15
65
Tb
7.92 ± 0.49
8.616
7.90
66
Dy
7.87 ± 0.42
8.452
7.86
67
Ho
7.38 ± 0.45
8.333
7.59
68
Er
7.62 ± 0.44
7.840
7.64
70
Yb
3.33 ± 0.26
2.950
3.47
72
Hf
3.65 ± 0.23
–
3.73
74
W
3.02 ± 0.25
2.781
3.47
76
Os
3.85 ± 0.21
–
4.14
80
Hg
4.93 ± 0.32
5.597
4.83
81
Tl
4.67 ± 0.32
5.514
4.77
82
Pb
4.23 ± 0.31
5.063
4.75
90
Th
4.06 ± 0.30
4.044
3.98
92
U
4.30 ± 0.30
3.651
4.23
a Ref. [19].
(a)
(b)
are within the range 0.38–4.30%, 0.80–12.5% and 0.20–14.9%, respectively. The present results agree better with the experimental values reported by Ertu˘grul [18,19] the values being within 1.36–2.60%, 0.44–21.5% and 0.40–19.69% for Lα/L, Lα/Lβ and Lα/Lγ , respectively. To obtain a more definite conclusions on L X-ray intensity ratios, more experimental and theoretical data are clearly needed, particularly in the heavy elements region.
Acknowledgement This work was supported by the Atatürk University Research Fund, project no. 1998-65.
(c) Fig. 4. Comparison of present L shell X-ray intensity ratios, literature experimental results and theoretical predictions. (a) Lα/L, (b) Lα/Lβ and (c) Lα/Lγ .
48
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
Table 4 Uncertainties in the quantities used to determine Lα/L, Lα/Lβ and Lα/Lγ intensity ratios in Eq. (1) Quantity
Nature of uncertainty
NLi (i = , α, β and γ )
Counting statistic
2
I0 GεKα
Errors in different parameters used to evaluate this factor
5
T
Error in the absorption coefficients at incident and emitted photon energies
m
Nonuniform thickness
References [1] M. Ertu˘grul, J. Phys. B 28 (1995) 4037. [2] M.L. Garg, D. Mehta, H.R. Verma, N. Singh, P.C. Mangal, P.N. Trehan, J. Phys. B 19 (1986) 1615. [3] K. Shatendra, K.L. Allawadhi, B.S. Sood, J. Phys. B 16 (1983) 4313. [4] D.V. Rao, R. Cesareo, G.E. Gigante, Phys. Rev. A 47 (1993) 1087. [5] C.V. Raghavaiah, N. Venkateswara Rao, S. Bhuloka Reddy, G. Satyanarayana, D.L. Sastry, J. Phys. B 20 (1987) 5647. [6] C.V. Raghavaiah, N. Venkateswara Rao, S. Bhuloka Reddy, G. Satyanarayana, G. Sree Krishna Murty, M.V.S. Chandrasekhar Rao, D.L. Sastry, X-Ray Spectrom. 19 (1990) 23. [7] S. Singh, D. Mehta, M.L. Garg, S. Kumar, N. Singh, P.C. Mangal, P.N. Trehan, J. Phys. B 20 (1987) 5345. [8] M.L. Garg, J. Sing, A.K. Sharma, H.R. Verma, N. Singh, P.C. Mangal, P.N. Trehan, Ind. J. Phys. A 58 (1984) 242.
Uncertainty (%)
<1 1
[9] R. Md Khan, M. Karimi, X-Ray Spectrom. 9 (1980) 32. [10] S. Kumar, R. Mittal, K.L. Allawadhi, B.S. Sood, J. Phys. B 15 (1982) 3377. [11] D.V. Rao, G.E. Gigante, R. Cesareo, Phys. Scr. 47 (1993) 765. [12] J.B. Darko, G.K. Tetteh, X-Ray Spectrom. 21 (1992) 111. [13] J.H. Hubbell, S.M. Seltzer, National Institute of Standards and Technology Report No. 5632 NISTIR (1995), unpublished. [14] J.H. Scofield, Lawrence Livermore National Report No. UCRL 51326 (1973), unpublished. [15] M.O. Krause, J. Phys. Chem. Ref. Data 8 (1979) 307. [16] J.H. Scofield, At. Data Nucl. Data Tables 14 (1974) 121. [17] P.V. Rao, M.H. Chen, B. Crasemann, Phys. Rev. A 5 (1972) 997. [18] M. Ertu˘grul, Spectrochim. Acta B 52 (1997) 201. [19] M. Ertu˘grul, Nucl. Instrum. Meth. B 111 (1996) 229.
Physics Letters A 284 (2001) 43–48 www.elsevier.nl/locate/pla
Measurement of Lα/L, Lα/Lβ and Lα/Lγ X-ray intensity ratios for elements in the atomic range 57 Z 92 using radioisotope X-ray fluorescence Rıdvan Durak ∗ , Yüksel Özdemir Atatürk Üniversitesi, Fen-Edebiyat Fakültesi, Fizik Bölümü, 25240 Erzurum, Turkey Received 17 January 2001; received in revised form 26 March 2001; accepted 29 March 2001 Communicated by B. Fricke
Abstract Lα/L, Lα/Lβ and Lα/Lγ intensity ratios have been measured for some elements with atomic range 57 Z 92 by using characteristic L X-rays from targets excited by 59.54 keV photons from a filtered radioisotope 241 Am point source. Theoretical values of the Lα/L, Lα/Lβ and Lα/Lγ intensity ratios were calculated using theoretically tabulated values of subshell photoionization cross-sections, fluorescence yields, fractional X-ray emission rates, Coster–Kronig transition probabilities. Experimental results have been compared with the theoretical values and other available experimental results. Good agreement was observed between experimental results, other available experimental results and theoretically calculated values. 2001 Elsevier Science B.V. All rights reserved. PACS: 32.30.Rj; 32.80.Cy; 32.80.Hd
1. Introduction Accurate experimental result regarding the X-ray intensity ratios are important because of their extensive use in basic studies of nuclear and atomic physics and developing more reliable theoretical models describing fundamental inner-shell ionization processes. Several attempts have been made for measuring K and L X-ray intensity ratios for heavy elements [1–12]. Among others, Kα to Lα intensity ratio of lanthanides following photoionization at 59.5 keV [1], measurement of L X-ray fluorescence cross-sections and relative intensity for Ho, Er and Yb in the energy range
* Corresponding author.
E-mail address: [email protected] (R. Durak).
11–41 keV [2], energy dependence of photon-induced L shell X-ray intensity ratios in some high-Z elements [3], L X-ray fluorescence cross-sections and intensity ratios in some high-Z elements excited by 23.62 and 24.68 keV photons [4], Lα/L X-ray intensity ratios for elements in the region 55 Z 80 [5], Lα/Lβ and Lα/Lγ X-ray intensity ratios for elements in the range Z = 55–80 [6] and L X-ray fluorescence cross-sections and relative intensities for elements 56 Z 66 in the energy range 11–41 keV [7] have been reported. Extensive literature search reveals that the individual Lα/L, Lα/Lβ and Lα/Lγ intensity ratios for the elements La, Ce, Pr, Nd, Sm, Tb, Dy, Ho, Er, Yb, Hf, W, Os, Hg, Tl, Pb, Th and U are scarce, to the best of our knowledge, Lα/Lβ and Lα/Lγ intensity ratios for Hf and Os are reported for the first time. This investigations Lα/L, Lα/Lβ and Lα/Lγ
0375-9601/01/$ – see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 ( 0 1 ) 0 0 2 2 3 - 7
44
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
Fig. 1. Experimental setup used for measurements of Lα/L, Lα/Lβ and Lα/Lγ X-ray intensity ratios.
intensity ratios have been measured for these elements. The results of our work have been compared with the literature experimental results and theoretical predictions.
2. Experimental The experimental arrangement and geometry used in the present study are shown in Fig. 1. The target L X-rays spectra were recorded with a Si (Li) detector with an active area of 12.5 mm2 and a sensitive crystal depth of 3 mm and Be window of 0.025 mm thickness coupled to 1024 multichannel analyzer. The amplifier shaping time constant that resulted in the best resolution was 6 µs and this value was used in the present measurements. The measured energy resolution of the detector system was 188 eV FWHM for the Mn Kα line at 5.9 keV. Spectroscopically pure rectangular samples of 1.72 cm2 area and thickness ranging from 3 to 35 mg cm−2 have been used. Photons of 59.54 keV energy from a 100 mCi 241 Am point source were used for excitation of the samples. To keep the counting error to minimum, X-ray spec-
Fig. 2. Typical L X-ray spectrum for Tb irradiated with 59.54 keV gamma rays from 241 Am.
tra were accumulated in time intervals ranging from 1800 to 64800 s. Fig. 2 shows a typical L shell X-ray spectrum of Tb. AXIL (V3.0) X-ray analysis computer program was used for peak resolving background subtraction and determination of the net peak areas of L X-rays of the targets.
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
45
3. Experimental method The experimental values of Lα/L, Lα/Lβ and Lα/Lγ intensity ratios of elements were given by ILi NLi TLj εLj = ILj NLj TLi εLi
(i = α, j = , β, γ ),
(1)
where NLi /NLj represents the ratio of the counting rates under the Li and Lj peaks. εLj /εLi is the ratio of the detector efficiency values for Lj and Li Xrays, respectively, and TLj /TLi is the ratio of the self absorption correction factor of the target. In the present study, the values of the factors I0 GεKα , which contain terms related to the incident photon flux, geometrical factor and the efficiency of the X-ray detector, were determined by collecting the K X-ray spectra of thin samples of Cl, Ca, Fe, Zn, Se, Sr, Nb and Ag in the same geometry in which the K X-ray fluorescence cross-sections were measured and using the equation IKα , I0 GεKα = σKα TKα m
(2)
where IKα is the net number of counts under the corresponding photopeak , εKα is the detector efficiency for Kα X-rays and TKα is the self-absorption correction factor for the incident photons and emitted Kα X-ray photons and is given by T=
1 − exp[−(µi sec θ1 + µe sec θ2 )m] , (µi sec θ1 + µe sec θ2 )m
(3)
where µi and µe are the total mass absorption of the target material for the incident photon and the emitted characteristic X-rays, respectively [13]. m is the mass of the sample in g/cm2. The angles incident photons and emitted X-rays with respect to the normal at the surface of the sample θ1 and θ2 were equal to 45◦ in the present setup. The measured I0 Gεα values for the present setup are plotted as a function of the energy in Fig. 3.
Fig. 3. Plot of the factor I0 Gε vs. K X-rays energy.
equations p p X σL = σL1 + σK ηKL1 (f13 + f12 f23 ) p p + σL2 + σK ηKL2 f23 p p + σL3 + σK ηKL3 ω3 F3 , p p X = σL1 + σK ηKL1 (f13 + f12 f23 ) σLα p p + σL2 + σK ηKL2 f23 p p + σL3 + σK ηKL3 ω3 F3α , p p X σLβ = σL1 + σK ηKL1 ω1 F1β p p + σL1 + σK ηKL1 f12 p p + σL2 + σK ηKL2 ω2 F2β p p + σL1 + σK ηKL1 (f13 + f12 f23 ) p p + σL2 + σK ηKL2 f23 p p + σL3 + σK ηKL3 ω3 F3β , p p X = σL1 + σK ηKL1 ω1 F1γ σLγ p p + σL1 + σK ηKL1 f12 p p + σL2 + σK ηKL2 ω2 F2γ , p
4. Theoretical method The theoretical values of L, Lα, Lβ and Lγ line intensity of elements were calculated using the
p
(4)
(5)
(6)
(7)
where σK and σLi (i = 1, 2, 3) are K and L subshell photoionization cross-sections [14], ωi are the L subshell fluorescence yields [15], fij are Coster–Kronig transitions probabilities from the i to j subshell fluorescence yields [15], Fij are the fractional X-ray emis-
46
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
Table 1 Comparison of present and literature experimental values and theoretical predictions of Lα/L intensity ratios
Table 2 Comparison of present and literature experimental values and theoretical predictions of Lα/Lβ intensity ratios
Lα/L
Lα/Lβ
Z
Target
Present
Exp.b
57
La
–a
27.86
25.77
57
La
1.29 ± 0.10
1.250
1.32
Ce
–a
26.46
25.73
58
Ce
1.28 ± 0.10
1.325
1.31
Pr
–a
25.51
25.32
59
Pr
1.26 ± 0.11
1.247
1.25
60
Nd
–a
24.94
24.96
60
Nd
1.28 ± 0.10
1.254
1.24
62
Sm
–a
25.77
24.85
62
Sm
1.28 ± 0.11
1.268
1.22
65
Tb
24.43 ± 1.61
23.81
24.09
65
Tb
1.21 ± 0.09
1.264
1.20
66
Dy
23.38 ± 1.51
23.70
23.29
66
Dy
1.21 ± 0.10
1.267
1.23
58 59
Theo.
Z
Target
Present
Exp.a
Theo.
67
Ho
23.39 ± 1.52
22.78
23.51
67
Ho
1.16 ± 0.09
1.205
1.17
68
Er
22.38 ± 1.51
22.73
23.41
68
Er
1.19 ± 0.08
1.227
1.22
70
Yb
22.28 ± 1.53
–
22.56
70
Yb
0.66 ± 0.08
0.690
0.69
72
Hf
22.11 ± 1.50
–
21.79
72
Hf
0.70 ± 0.08
–
0.71
74
W
21.44 ± 1.45
–
21.13
74
W
0.80 ± 0.07
0.628
0.70
76
Os
20.57 ± 1.36
–
19.98
76
Os
0.94 ± 0.10
–
0.87
80
Hg
19.28 ± 1.34
–
19.07
80
Hg
0.91 ± 0.09
1.011
0.95
81
Tl
18.05 ± 1.35
–
18.39
81
Tl
0.96 ± 0.11
0.967
0.95
82
Pb
18.75 ± 1.22
–
18.93
82
Pb
0.97 ± 0.09
0.939
0.96
90
Th
16.83 ± 1.28
–
16.66
290
Th
0.90 ± 0.09
0.896
0.89
92
U
16.66 ± 1.11
–
16.08
92
U
0.96 ± 0.09
0.845
0.93
a The L peaks of the elements could not be measured due to poor
a Ref. [19].
statistics in the regions. b Ref. [18].
sion rates [16], ηKLi are the number of additional vacancies transferred to the Li subshell from the K shell through radiative ηKLi (R) and nonradiative ηKLi (A) transitions [17]. ηKLi is given by ηKLi = ηKLi (R) + ηKLi (A).
(8)
5. Results and discussion Lα/L, Lα/Lβ and Lα/Lγ intensity ratios for thin targets of La, Ce, Pr, Nd, Sm, Tb Dy, Ho, Er, Yb, Hf, W, Os, Hg, Tl, Pb, Th and U at 59.5 keV excitation energy are measured and the results are compared
with other experimental results and theoretical predictions. These results are given in Tables 1–3 and, for comparison, theoretical predictions, literature experimental results and measured intensity ratios are plotted as a function of atomic number in Figs. 4(a)–(c). The overall error in the measured Lα/L, Lα/Lβ and Lα/Lγ intensity ratios is estimated to be less than 6.5–11.5%, which arises due to the uncertainties in the various physical parameters required to evaluate the experimental results using Eq. (1). The uncertainties in the parameters are listed in Table 4. It can be seen from Tables 1–3 and Figs. 4(a)–(c) that our measurements values are in good agreement, within the experimental uncertainties, with literature experimental values [18,19] and the calculated theoretical values. The agreements between the present Lα/L, Lα/Lβ and Lα/Lγ results and the theoretical predictions
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
47
Table 3 Comparison of present and literature experimental values and theoretical predictions of Lα/Lγ intensity ratios Lα/Lγ Z
Target
Present
Exp.a
Theo.
57
La
8.84 ± 0.90
9.692
8.35
58
Ce
8.77 ± 0.71
9.363
8.47
59
Pr
8.21 ± 0.69
9.205
8.42
60
Nd
8.50 ± 0.70
9.326
8.40
62
Sm
7.64 ± 0.45
8.766
8.15
65
Tb
7.92 ± 0.49
8.616
7.90
66
Dy
7.87 ± 0.42
8.452
7.86
67
Ho
7.38 ± 0.45
8.333
7.59
68
Er
7.62 ± 0.44
7.840
7.64
70
Yb
3.33 ± 0.26
2.950
3.47
72
Hf
3.65 ± 0.23
–
3.73
74
W
3.02 ± 0.25
2.781
3.47
76
Os
3.85 ± 0.21
–
4.14
80
Hg
4.93 ± 0.32
5.597
4.83
81
Tl
4.67 ± 0.32
5.514
4.77
82
Pb
4.23 ± 0.31
5.063
4.75
90
Th
4.06 ± 0.30
4.044
3.98
92
U
4.30 ± 0.30
3.651
4.23
a Ref. [19].
(a)
(b)
are within the range 0.38–4.30%, 0.80–12.5% and 0.20–14.9%, respectively. The present results agree better with the experimental values reported by Ertu˘grul [18,19] the values being within 1.36–2.60%, 0.44–21.5% and 0.40–19.69% for Lα/L, Lα/Lβ and Lα/Lγ , respectively. To obtain a more definite conclusions on L X-ray intensity ratios, more experimental and theoretical data are clearly needed, particularly in the heavy elements region.
Acknowledgement This work was supported by the Atatürk University Research Fund, project no. 1998-65.
(c) Fig. 4. Comparison of present L shell X-ray intensity ratios, literature experimental results and theoretical predictions. (a) Lα/L, (b) Lα/Lβ and (c) Lα/Lγ .
48
R. Durak, Y. Özdemir / Physics Letters A 284 (2001) 43–48
Table 4 Uncertainties in the quantities used to determine Lα/L, Lα/Lβ and Lα/Lγ intensity ratios in Eq. (1) Quantity
Nature of uncertainty
NLi (i = , α, β and γ )
Counting statistic
2
I0 GεKα
Errors in different parameters used to evaluate this factor
5
T
Error in the absorption coefficients at incident and emitted photon energies
m
Nonuniform thickness
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Uncertainty (%)
<1 1
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