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Fast measurement of total atomic attenuation, total atomic photoelectric and total atomic scattering cross sections in the range 58⩽Z⩽68 using radioisotope X-ray fluorescence
Nuclear Instruments and Methods in Physics Research B 152 (1999) 202±206
Fast measurement of total atomic attenuation, total atomic photoelectric and total atomic scattering cross sections in the range 58 6 Z 6 68 using radioisotope X-ray ¯uorescence A. Karabulut b
a,*
, G. Budak a, M. Ertu grul
b
a Department of Physics, Faculty of Arts and Sciences, Atat urk University, 25240 Erzurum, Turkey Department of Physics, Faculty of Kazim Karabekir Education, Atat urk University, 25240 Erzurum, Turkey
Received 24 November 1998; received in revised form 5 January 1999
Abstract Cross sections for total atomic attenuation, total atomic photoelectric and total atomic scattering in nine elements (58 6 Z 6 68) at 59.537 keV are reported. The experimental values of the cross sections were determined by measuring the transmission factor. Measurements have been performed using an Am-241 point source and an Si(Li) solid state detector. Experimental results have been compared with theoretically calculated values and other available experimental results. Good agreement was observed among the experimental, theoretical and other experimental values. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction XRF is important in both basic and applied research. The comparison of cross section, relative line intensities and other characteristic features of X-rays induced by dierent excitation modes oers an experimental basis for understanding the radiation-atom interaction mechanism and photo cross section processes. A precise value of photoelectric cross section in dierent materials is required for the accurate estimation of total photon absorption and photon transport phenomena, for
* Corresponding author. Fax:+00-90-442-2331062; e-mail: [email protected]
the design of shielding, and in a variety of radiation detection devices. K X-ray ¯uorescence cross sections for all elements at various excitation energies are important because of their use in applied ®elds such as radiation transport in matter, dosimetry and trace elemental analysis using either traditional photon sources or synchrotron radiation. The use of X-ray ¯uorescence scattering cross sections in quantitative analysis using the X-rays plays an important role, but requires their accurate determination. Attenuation measurements in good geometrical set-up have proved useful in nuclear spectroscopy but such measurements in this context have limited practical applicability. A systematic study of K XRF cross sections for Er, Gd, Dy and Tb has been undertaken
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 0 7 0 - 1
A. Karabulut et al. / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 202±206
previously [1]. In the our previous work, we have reported K XRF cross sections for dierent elements in the atomic range 40 6 Z 6 52 [2]. In a continuation of this work, a simple, fast and direct method which is explained by earlier investigators [3] was used to obtained fairly accurate total atomic attenuation, total atomic photoelectric and total atomic scattering cross sections in the range 58 6 Z 6 68 at 59.537 keV. The measured cross sections were compared with the corresponding theoretical values and other experimental values. 2. Experimental details The XRF experimental set-up consists of a point Am-241 radioisotope 100 mCi activity, an Si(Li) solid state detector of 12.5 mm2 active area and a resolution of 160 eV at 5.9 keV. The detector coupled to a 1024 multichannel analyzer. Net counts under the photopeak were determined by a method proposed by our previous work [4]. The experimental set-up employed in the present work has been described in previous work [2]. The present work is carried out such that the ¯uorescence X-rays reach the detector at an angle 0 with respect to the incident gamma photon beam. Thin elemental samples of Ce, Pr, Nd, Eu, Gd, Tb, Dy, Ho and Er were photoionized using a radioactive point source of 241 Am of strength 100 mCi and gamma photon energy 59.537 keV. High purity (99.95%) light-tight, thin uniform foils of Gd and Er (each thickness 25 lm) were used for the measurements. Spectroscopically pure powder of Ce, Pr, Nd, Eu, Tb, Dy and Ho of thickness ranging from 0.0145 to 0.02252 g/cm2 , of concentration ranging from 99.9% to 99.99% was used for measurement. The whole samples are circularly done with 8 mm diameter. The run has been carried out for each target at dierent times to check the stability of the target used, with time intervals ranging from 10 000 to 40 000 s. The spectrometer was calibrated and tested for its linearity and stability using several c-ray sources covering the energy range 13±59.537 keV (Am-241 and Ba-133 with 10 lCi) and also using a precision pulse generator. Eciency calibration of Si(Li) detector
203
was determined to the two sources in the energy range 13±59.537 keV. The total atomic attenuation cross section rt i of an element i at an excitation energy of 59.537 keV is given by LambertÕs law rt i ÿ
ln I=I0 M ; T N
1
where I and I0 are the c-rays intensity after and before absorption by target, respectively; T is the target thickness in mass per unit area; M is the atomic weight and N is AvagadroÕs number. The Ka X-ray photoionization cross section rKa i of an element i at an excitation energy Ei is given by the relation rKa i
IKa i M ; I0 GebT N
2
where IKa i is the measured net intensity of the Ka peaks of the elements; I0 G is the intensity of the exciting radiation at the experimental geometry measured directly; e is the eciency of the detector at the Ka X-ray energy; b is the self-absorption correction factor. The b was calculated from the following equation: b
1 ÿ exp ÿ li le T ; li le T
3
where li and le are the total mass attenuation absorption coecient of the target at primer and emitter radiation energy [5], respectively. In this work, the angles of primer and emitted photons with the sample surface normal are equal to zero. The total atomic photoelectric cross sections were evaluated by the following equation rtp i
rKa i ; JK wK fK
4
where JK , wK and fKa are absorption jump factors, ¯uorescence yield and the fraction of Ka X-ray emission rate, respectively. Using this relation, the total atomic photoelectric cross section of an element at Ei can be determined using the measured value of rKa i from Eq. (2) and the tabulated quantities of JK ; wK and fKa . The parameters were taken from the table of Broll [6].
b
a
58 59 60 61 62 63 64
65
66
67 68
Ce Pr Nd Pm Sm Eu Gd
Tb
Dy
Ho Er
Fitted experimental values; Ref. [1].
Z
Elements
2135 145 2397 165 2548 153 2590a 2735a 2872 181 3050 195 3071 220b 3178 207 3224 260b 3396 224 3399 235b 3528 236 3749 255 3774 255b 3590 3790
3410
3240
2190 2330 2460 2610 2760 2910 3060
2046 139 2305 159 2241 157 2462a 2603a 2759 174 2940 188 2950 197b 3047 198 3085 193b 3260 215 3284 173b 3387 227 3621 246 3613 224b
Exp.
Exp.
Theo.
rtp i
rt i
Table 1 rt i, rtp i, rKa i and rts i values (barns/atom) in the range 58 6 Z 6 68
3460 3660
3290
3120
2100 2230 2360 2510 2650 2800 2950
Theo. 1258 85 1418 98 1393 84 1524a 1613a 1709 108 1829 117 1829 123b 1883 122 1907 119b 2014 133 2029 107b 2083 140 2245 153 2240 139b
Exp.
rKa i
2128 2269
2033
1928
1292 1373 1467 1560 1644 1735 1835
Theo.
89 6 91 6 106 7 128a 132a 112 7 110 7 131 9b 131 9 138 9b 135 9 115 8b 141 10 128 9 161 9b
Exp.
rts i
130 130
120
120
90 100 100 100 110 110 110
Theo.
204 A. Karabulut et al. / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 202±206
A. Karabulut et al. / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 202±206
205
The total atomic scattering cross sections of elements were evaluated by the following equation: rts i rt i ÿ rtp i:
5
3. Results and discussion Experimental cross sections measured in the present investigations are summarised in Table 1. These results constitute the important experimental report of total atomic attenuation, total atomic photoelectric and total atomic scattering cross sections for 59.537 keV gamma rays for the 11 elements as there are limited experimental reports [1±3,7,8] in the literature. In order to do the comparison, theoretical Storm and Israel cross sections are given in Table 1. It can be seen from Table 1 that there is qualitative agreement between the present experimental results and theoretical values. Experimental cross sections are plotted as a function of the atomic number, and the experimental values that were ®tted to a second-order polynomial is listed in Table 1. In order to facilitate a better and closer comparison between theory and experiment, the results are presented in graphical form in Fig. 1. It is seen clearly from the ®gures that the experimental results are in good agreement with the theoretical values within error ¯uctuation. In order to reduce the absorption, very thin foils of uniform thickness were used as target. Furthermore, an absorption correction was also done to each sample. In order to reduce the statistical error, the spectra were recorded for a long time and about 104 (and more) counts were collected under incoherent peaks and characteristic peaks. The error associated in evaluating the photopeak area is less than 1%. The errors of the geometry changes [9,10], target thickness and absorption factor are less than 2, 1, 1, respectively. The uncertainties in the transmission factor are known better than 1%. The overall error comes to less than 3%. In conclusion, the present agreement between the theoretical and the experimental values leads
Fig. 1. (a) rt , (b) rtp , (c) rKa as functions of atomic number.
to the conclusion that the data presented here will bene®t those using radioisotope XRF technique because of their use in applied ®elds such as radiation transport in matter, absorbed-dose and radiation-eect determinations, trace elemental analysis using either traditional photon sources or synchrotron radiation.
206
A. Karabulut et al. / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 202±206
References S [1] M. Ertugrul, O. gan, U. Turgut, J. ß imsßek, O. Do Radioanal. Nucl. Chem. Lett. 213 (1) (1996) 37. S [2] G. Budak, A. Karabulut, O. ß imsßek, M. Ertugrul, Nucl. Instr. and Meth. B, in press. [3] H.A. Jahagirdar, B. Hanumaiah, S.R. Thontadarya, Appl. Radiat. Isot. 43 (1992) 399. [4] Y. S ß ahin, A. Karabulut, G. Budak, Appl. Spectrosc. Rev. 31 (3) (1996) 333.
[5] E. Storm, H.I. Israel, Nucl. Data A 7 (1970) 565. [6] N. Broll, X-ray Spectrosc. 15 (1986) 271. [7] C. Ranganathaiah, R. Gowda, R. Sanjeevaiah, J. Phys. B: At. Mol. Opt. Phys. 12 (1979) 1915. [8] V. Viswesvara Rao, V. Shahanawas, D.V. Rao, Physica 11c (1981) 107. [9] Y. S ß ahin, G. Budak, A. Karabulut, Il Nuovo Cimento 17D (1995) 221. [10] G. Budak, A. Karabulut, Y. S ß ahin, Appl. Spectrosc. Rev. 13 (3) (1996) 321.
Fast measurement of total atomic attenuation, total atomic photoelectric and total atomic scattering cross sections in the range 58 6 Z 6 68 using radioisotope X-ray ¯uorescence A. Karabulut b
a,*
, G. Budak a, M. Ertu grul
b
a Department of Physics, Faculty of Arts and Sciences, Atat urk University, 25240 Erzurum, Turkey Department of Physics, Faculty of Kazim Karabekir Education, Atat urk University, 25240 Erzurum, Turkey
Received 24 November 1998; received in revised form 5 January 1999
Abstract Cross sections for total atomic attenuation, total atomic photoelectric and total atomic scattering in nine elements (58 6 Z 6 68) at 59.537 keV are reported. The experimental values of the cross sections were determined by measuring the transmission factor. Measurements have been performed using an Am-241 point source and an Si(Li) solid state detector. Experimental results have been compared with theoretically calculated values and other available experimental results. Good agreement was observed among the experimental, theoretical and other experimental values. Ó 1999 Elsevier Science B.V. All rights reserved.
1. Introduction XRF is important in both basic and applied research. The comparison of cross section, relative line intensities and other characteristic features of X-rays induced by dierent excitation modes oers an experimental basis for understanding the radiation-atom interaction mechanism and photo cross section processes. A precise value of photoelectric cross section in dierent materials is required for the accurate estimation of total photon absorption and photon transport phenomena, for
* Corresponding author. Fax:+00-90-442-2331062; e-mail: [email protected]
the design of shielding, and in a variety of radiation detection devices. K X-ray ¯uorescence cross sections for all elements at various excitation energies are important because of their use in applied ®elds such as radiation transport in matter, dosimetry and trace elemental analysis using either traditional photon sources or synchrotron radiation. The use of X-ray ¯uorescence scattering cross sections in quantitative analysis using the X-rays plays an important role, but requires their accurate determination. Attenuation measurements in good geometrical set-up have proved useful in nuclear spectroscopy but such measurements in this context have limited practical applicability. A systematic study of K XRF cross sections for Er, Gd, Dy and Tb has been undertaken
0168-583X/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 0 7 0 - 1
A. Karabulut et al. / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 202±206
previously [1]. In the our previous work, we have reported K XRF cross sections for dierent elements in the atomic range 40 6 Z 6 52 [2]. In a continuation of this work, a simple, fast and direct method which is explained by earlier investigators [3] was used to obtained fairly accurate total atomic attenuation, total atomic photoelectric and total atomic scattering cross sections in the range 58 6 Z 6 68 at 59.537 keV. The measured cross sections were compared with the corresponding theoretical values and other experimental values. 2. Experimental details The XRF experimental set-up consists of a point Am-241 radioisotope 100 mCi activity, an Si(Li) solid state detector of 12.5 mm2 active area and a resolution of 160 eV at 5.9 keV. The detector coupled to a 1024 multichannel analyzer. Net counts under the photopeak were determined by a method proposed by our previous work [4]. The experimental set-up employed in the present work has been described in previous work [2]. The present work is carried out such that the ¯uorescence X-rays reach the detector at an angle 0 with respect to the incident gamma photon beam. Thin elemental samples of Ce, Pr, Nd, Eu, Gd, Tb, Dy, Ho and Er were photoionized using a radioactive point source of 241 Am of strength 100 mCi and gamma photon energy 59.537 keV. High purity (99.95%) light-tight, thin uniform foils of Gd and Er (each thickness 25 lm) were used for the measurements. Spectroscopically pure powder of Ce, Pr, Nd, Eu, Tb, Dy and Ho of thickness ranging from 0.0145 to 0.02252 g/cm2 , of concentration ranging from 99.9% to 99.99% was used for measurement. The whole samples are circularly done with 8 mm diameter. The run has been carried out for each target at dierent times to check the stability of the target used, with time intervals ranging from 10 000 to 40 000 s. The spectrometer was calibrated and tested for its linearity and stability using several c-ray sources covering the energy range 13±59.537 keV (Am-241 and Ba-133 with 10 lCi) and also using a precision pulse generator. Eciency calibration of Si(Li) detector
203
was determined to the two sources in the energy range 13±59.537 keV. The total atomic attenuation cross section rt i of an element i at an excitation energy of 59.537 keV is given by LambertÕs law rt i ÿ
ln I=I0 M ; T N
1
where I and I0 are the c-rays intensity after and before absorption by target, respectively; T is the target thickness in mass per unit area; M is the atomic weight and N is AvagadroÕs number. The Ka X-ray photoionization cross section rKa i of an element i at an excitation energy Ei is given by the relation rKa i
IKa i M ; I0 GebT N
2
where IKa i is the measured net intensity of the Ka peaks of the elements; I0 G is the intensity of the exciting radiation at the experimental geometry measured directly; e is the eciency of the detector at the Ka X-ray energy; b is the self-absorption correction factor. The b was calculated from the following equation: b
1 ÿ exp ÿ li le T ; li le T
3
where li and le are the total mass attenuation absorption coecient of the target at primer and emitter radiation energy [5], respectively. In this work, the angles of primer and emitted photons with the sample surface normal are equal to zero. The total atomic photoelectric cross sections were evaluated by the following equation rtp i
rKa i ; JK wK fK
4
where JK , wK and fKa are absorption jump factors, ¯uorescence yield and the fraction of Ka X-ray emission rate, respectively. Using this relation, the total atomic photoelectric cross section of an element at Ei can be determined using the measured value of rKa i from Eq. (2) and the tabulated quantities of JK ; wK and fKa . The parameters were taken from the table of Broll [6].
b
a
58 59 60 61 62 63 64
65
66
67 68
Ce Pr Nd Pm Sm Eu Gd
Tb
Dy
Ho Er
Fitted experimental values; Ref. [1].
Z
Elements
2135 145 2397 165 2548 153 2590a 2735a 2872 181 3050 195 3071 220b 3178 207 3224 260b 3396 224 3399 235b 3528 236 3749 255 3774 255b 3590 3790
3410
3240
2190 2330 2460 2610 2760 2910 3060
2046 139 2305 159 2241 157 2462a 2603a 2759 174 2940 188 2950 197b 3047 198 3085 193b 3260 215 3284 173b 3387 227 3621 246 3613 224b
Exp.
Exp.
Theo.
rtp i
rt i
Table 1 rt i, rtp i, rKa i and rts i values (barns/atom) in the range 58 6 Z 6 68
3460 3660
3290
3120
2100 2230 2360 2510 2650 2800 2950
Theo. 1258 85 1418 98 1393 84 1524a 1613a 1709 108 1829 117 1829 123b 1883 122 1907 119b 2014 133 2029 107b 2083 140 2245 153 2240 139b
Exp.
rKa i
2128 2269
2033
1928
1292 1373 1467 1560 1644 1735 1835
Theo.
89 6 91 6 106 7 128a 132a 112 7 110 7 131 9b 131 9 138 9b 135 9 115 8b 141 10 128 9 161 9b
Exp.
rts i
130 130
120
120
90 100 100 100 110 110 110
Theo.
204 A. Karabulut et al. / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 202±206
A. Karabulut et al. / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 202±206
205
The total atomic scattering cross sections of elements were evaluated by the following equation: rts i rt i ÿ rtp i:
5
3. Results and discussion Experimental cross sections measured in the present investigations are summarised in Table 1. These results constitute the important experimental report of total atomic attenuation, total atomic photoelectric and total atomic scattering cross sections for 59.537 keV gamma rays for the 11 elements as there are limited experimental reports [1±3,7,8] in the literature. In order to do the comparison, theoretical Storm and Israel cross sections are given in Table 1. It can be seen from Table 1 that there is qualitative agreement between the present experimental results and theoretical values. Experimental cross sections are plotted as a function of the atomic number, and the experimental values that were ®tted to a second-order polynomial is listed in Table 1. In order to facilitate a better and closer comparison between theory and experiment, the results are presented in graphical form in Fig. 1. It is seen clearly from the ®gures that the experimental results are in good agreement with the theoretical values within error ¯uctuation. In order to reduce the absorption, very thin foils of uniform thickness were used as target. Furthermore, an absorption correction was also done to each sample. In order to reduce the statistical error, the spectra were recorded for a long time and about 104 (and more) counts were collected under incoherent peaks and characteristic peaks. The error associated in evaluating the photopeak area is less than 1%. The errors of the geometry changes [9,10], target thickness and absorption factor are less than 2, 1, 1, respectively. The uncertainties in the transmission factor are known better than 1%. The overall error comes to less than 3%. In conclusion, the present agreement between the theoretical and the experimental values leads
Fig. 1. (a) rt , (b) rtp , (c) rKa as functions of atomic number.
to the conclusion that the data presented here will bene®t those using radioisotope XRF technique because of their use in applied ®elds such as radiation transport in matter, absorbed-dose and radiation-eect determinations, trace elemental analysis using either traditional photon sources or synchrotron radiation.
206
A. Karabulut et al. / Nucl. Instr. and Meth. in Phys. Res. B 152 (1999) 202±206
References S [1] M. Ertugrul, O. gan, U. Turgut, J. ß imsßek, O. Do Radioanal. Nucl. Chem. Lett. 213 (1) (1996) 37. S [2] G. Budak, A. Karabulut, O. ß imsßek, M. Ertugrul, Nucl. Instr. and Meth. B, in press. [3] H.A. Jahagirdar, B. Hanumaiah, S.R. Thontadarya, Appl. Radiat. Isot. 43 (1992) 399. [4] Y. S ß ahin, A. Karabulut, G. Budak, Appl. Spectrosc. Rev. 31 (3) (1996) 333.
[5] E. Storm, H.I. Israel, Nucl. Data A 7 (1970) 565. [6] N. Broll, X-ray Spectrosc. 15 (1986) 271. [7] C. Ranganathaiah, R. Gowda, R. Sanjeevaiah, J. Phys. B: At. Mol. Opt. Phys. 12 (1979) 1915. [8] V. Viswesvara Rao, V. Shahanawas, D.V. Rao, Physica 11c (1981) 107. [9] Y. S ß ahin, G. Budak, A. Karabulut, Il Nuovo Cimento 17D (1995) 221. [10] G. Budak, A. Karabulut, Y. S ß ahin, Appl. Spectrosc. Rev. 13 (3) (1996) 321.