- Email: [email protected]
Measurement of L3 subshell fluorescence yields of some elements in the atomic range 57⩽Z⩽68 using photoionisation
Applied Radiation and Isotopes 57 (2002) 57–61
Measurement of L3 subshell fluorescence yields of some elements in the atomic range 57pZp68 using photoionisation Mehmet Ertugrul* Kazim Karabekir Faculty of Education, Department of Physics, Ataturk University, 25240 Erzurum, Turkey Received 6 March 2001; received in revised form 5 November 2001; accepted 19 November 2001
Abstract L3 X-ray production cross sections have been measured for the elements in the atomic range 57pZp68 at 59.5 keV. The values of L3 subshell fluorescence yields (o3 ) have been measured for the same elements using the presently measured cross section values and the theoretical Li subshell photoionisation cross sections, Coster–Kronig transition probabilities, emission rates and vacancy transfer probabilities. The measured X-ray production cross section values are in general agreement with the theoretical values evaluated using L3 subshell fluorescence yields, Coster–Kronig transition probabilities, emission rates, vacancy transfer probabilities and subshell photoionisation cross sections. Furthermore, the values of L3 subshell fluorescence yields are in good agreement with the theoretical values. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Production cross sections; Fluorescence yields; Photoionisation; EDXRF; L3 subshell; Lanthanides
1. Introduction Accurate experimental data regarding the X-ray production cross sections and the Li subshell fluorescence yields (o1 ; o2 and o3 ) are important in many practical applications like elemental analysis by X-ray emission technique, basic studies of nuclear and atomic processes leading to the emission of X-rays and Auger electrons and domestic computations for medical physics and irradiational processes. The primary vacancies in the Li subshells can arise from either direct ionisation by photons, electrons, heavy charged or from a shift of a K shell vacancy to the L shell. These vacancies decay through radiative, Auger and Coster– Kronig transitions. The number of Li subshell X-rays produced per Li subshell vacancy decay defines the subshell fluorescence yield oi : Recently, Ll ; La ; Lb and Lg X-ray production cross sections for elements with the atomic range 57pZp69 were measured at the 60 keV photon energy (Ertugrul, 1996a). Three sets of values of Li subshell fluorescence yields oi and Coster–Kronig *Fax: +90-4422-1841-72. E-mail address: [email protected] (M. Ertugrul).
transition probabilities fij are available in the literature. The first set, complied by Krause (1979), consist of the semi-empirically fitted values of o3 and fij for all elements in the atomic range 12pZp110: The second set of these parameters, based on the relativistic DirecHartree-Slater model was tabulated by Chen et al. (1981) for 25 elements in the atomic range 18pZp96: The third set of these values, using radiative and nonradiative transition rates based on the relativistic Dirac-Hartree-Slater model for all elements in the atomic range 25pZp96 has been evaluated by Puri et al. (1993). Sarkar et al. (1997) have obtained an analytical expression for L3 subshell fluorescence yield using 155 experimental data of 52 elements in the atomic number range 23pZp96: A systematic study of L X-ray production cross sections and L shell fluorescence yields for different elements, in the atomic range 40pZp92 as a function of incident photon energy has previously been undertaken (Ertugrul, 1996a; Sahota et al., 1988; Garg et al., 1992; Ertu$grul, 1997, 1998). In this study, the accuracy in the data of fluorescence yields and Coster–Kronig transition probabilities had an important bearing on the accuracy of final calculations of cross sections. The
0969-8043/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 0 1 ) 0 0 2 7 8 - 0
M. Ertugrul / Applied Radiation and Isotopes 57 (2002) 57–61
58
Fig. 1. Experimental set-up.
Coster–Kronig transition effect on X-ray production cross sections have been investigated for heavy elements in the atomic range 79pZp92 (Ertugrul, 1996b). In the present investigation, the L3 subshell X-ray fluorescence cross sections and o3 fluorescence yields for the elements in the region 57pZp68 have been measured using thin targets. The measured values were compared with the theoretical results.
2. Experimental procedure The experimental arrangement used in this study is shown in Fig. 1. The targets are irradiated, in turn,
with 59.5 keV g-rays from a filtered annular radioactive source of 241Am of intensity 100 mCi which essentially emits monoenergetic (59.5 keV) g-rays and the radiation emitted from the 241Am is collimated to fall on the targets. 26 keV g-rays and Np L X-rays are also emitted in addition to 59.5 keV g-rays. It can be seen that the 26 keV g-rays and Np L X-rays can excite the L1, L2 and L3 subshells of the present elements. There is a graded filter on the 241Am annular source that almost completely absorbs all the Np L X-rays and 26 keV g-rays. The L shell fluorescent X-rays emitted from targets are recorded with Si(Li) X-ray detector, with resolution of B160 eV at 5.9 keV, coupled to an Nd 66B multichannel analyser. The shielding in the arrangement is so arranged that the source can only see the primary target. Spectroscopically pure targets of La2O3, CeO2, Pr6O11, Nd2O3, Sm2O3, Eu2O3, Gd2O3, Tb4O7, Dy2O3, Ho2O3 and Er2O3 of thickness ranging from 20 to 30 mg/cm2 have been used. These targets were irradiated by photons at 59.5 keV. For each element two or more targets of different thickness have been used. In order to reduce the statistical error in the measurements, three spectra were recorded for the time intervals ranging from 3600, 7200 and 10,800 s. To minimise the errors, the data for each target has been taken on different occasions. A typical L X-ray spectra of Pr is shown in Fig. 2. The experimental L3 subshell X-ray production cross section ðsxL3 Þ and fluorescence yield (o3 ) were evaluated
Fig. 2. L X-ray spectrum of Pr with recorded Si(Li) detector.
M. Ertugrul / Applied Radiation and Isotopes 57 (2002) 57–61
from the tables of Hubbell and Seltzer (1995). yð¼ 451Þ and fð¼ 01Þ are the angles of the incident and emitted X-rays on target surface normal. si (i ¼ 1; 2, 3 and K) is the photoionisation cross section of Li subshell and K shell (Scofield, 1973), oi (i ¼ 1; 2, 3) is the Li subshell
using the following relations, NLa I0 GeLa bLa mF3a
sxL3 ¼
ð1Þ
and o3 ¼
59
NLa ; I0 GeLa bLa m½ðs3 þ ZKL3 sK Þ þ ðs2 þ ZKL2 sK Þf23 þ ðs1 þ ZKL1 sK Þðf13 þ f12 f23 ÞF3a
fluorescence yield (Krause, 1979) and fij (i ¼ 1; 2 and j ¼ 2; 3) is the Coster–Kronig transition probability (Krause, 1979). The ZKLi (i ¼ 1; 2 and 3) values are the vacancy transfer probability of the same elements (Scofield, 1974). F3a is the fraction of L X-rays originating from the L3 transition that contribute to the La peak.
where NLa is the number of counts per unit time under the photopeak corresponding to La X-rays of elements, the product I0 G is the intensity of exciting radiation falling on the area of the target, eLa is the detector efficiency at the La X-ray energy, m is the mass per area of the element in g/cm2. The bLa is the self-absorption correction factor for the incident and emitted photon energies. The values of I0 G are evaluated by collecting the K X-ray spectra of thin targets of Zr in the same geometry in which the L X-ray production cross sections were measured and using the similar relation Eq. (1) but for K instead of L X-rays. In these calculations, the theoretical values of Ka X-ray production cross sections, sKa ¼ sPK oK fKa calculated using photoionisation cross sections (sPK ) based on the Hartree-Fock-Slater model (Scofield, 1973), fKa is the fraction rate of Ka X-ray in K X-rays (Scofield, 1974) and fluorescence yields (oK ) from tables of Krause (1979) have been used. The detector efficiency (eLa ) in the La X-ray energy regions of present elements was determined using 54Mn, 241Am and 133 Ba radioisotope sources according to our earlier method (Budak et al., 1999). The values of bLa have been calculated by using the following expression, bLa ¼
1 exp½ðminc sec y þ mLa sec fÞm ; ðminc sec y þ mLa sec fÞm
ð2Þ
F3a ¼
G3a ; G3
ð4Þ
where G3 is the theoretical total radiation rate of the L3 subshell and G3a is the sum of the radiative transition rates, which contribute to the La line associated with the hole filling in the shell. That is G3a ¼ G3 ðM4 L3 Þ þ GðM5 L3 Þ;
ð5Þ
where G3 ðM5 L3 Þ is the radiative transition rate from M4 to L3 subshell (Scofield, 1974).
3. Results and discussion The present values of L3 subshell X-ray production cross sections, F3a and ðs3 þ ZKL3 sK Þ þ ðs2 þ ZKL2 sK Þf23 þ ðs1 þ ZKL1 sK Þðf13 þ f12 f23 Þ values for La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho and Er at 60 keV incident photon energy are listed in Table 1. The comparison of experimental and theoretical results for
ð3Þ
where minc and mLa are the attenuation coefficients at the incident and La X-ray energy. Their values are taken
Table 1 The experimental and theoretical values of L3 subshell X-ray production cross sections of the elements with the atomic region 57pZp68 Element
sxL3 (E) (barns/atom)
sxL3 (T) (barns/atom)
F3a
K
57La 58Ce 59Pr 60Nd 62Sm 63Eu 64Gd 65Tb 66Dy 67Ho 68Er
11977 138710 146710 170711 214714 230718 257722 286723 299723 338724 388727
118 133 151 168 207 230 255 282 314 345 382
0.822 0.824 0.822 0.822 0.820 0.820 0.817 0.817 0.816 0.815 0.815
1135 1202 1278 1324 1491 1567 1642 1706 1802 1894 1987
E-means experimentally; T-means theoretically; K ¼ ðs3 þ ZKL3 sK Þ þ ðs2 þ ZKL2 sK Þf23 þ ðs1 þ ZKL1 sK Þðf13 þ f12 f23 Þ:
M. Ertugrul / Applied Radiation and Isotopes 57 (2002) 57–61
60
Table 2 The comparison of present o3 values with the Krause (1979), Chen et al. (1981), Sarkar et al. (1997) and Puri et al. (1993) values for the elements in the atomic region 57pZp68 Element
57La 58Ce 59Pr 60Nd 62Sm 63Eu 64Gd 65Tb 66Dy 67Ho 68Er
o3 Experimental
Sarkar et al. (1997)
Krause (1979)
Chen et al. (1981)
Puri et al. (1993)
0.10470.006 0.11570.008 0.11470.007 0.12870.008 0.14370.009 0.14670.011 0.15670.013 0.16770.013 0.16570.012 0.17870.012 0.19570.013
0.09770.008 F F 0.12270.010 F 0.14870.040 0.15770.019 0.16670.016 0.17570.055 0.18470.015 0.19470.022
0.104 0.111 0.118 0.125 0.139 0.147 0.155 0.164 0.174 0.182 0.192
F F F 0.136 F 0.166 F F F 0.196 F
0.112 0.119 0.126 0.134 0.150 0.158 0.167 0.175 0.184 0.193 0.203
o3 is given in Table 1. The overall error in the present measurements is estimated to be 3–7%. This error is the sum of the uncertainties in different parameters used to calculate the La X-ray production cross sections, namely, the evaluation of peak areas (p3%), I0Ge product (5–7%), target thickness measurements (p5%) and in the absorption correction factor (p2%). It is clear from Table 1 that the present experimental results for all elements are in general agreement with the theoretical values. The values of L3 subshell fluorescence yields (o3 ) decided using Eq. (2), for same elements are presented in Table 2. Present results are different than 1–5%, 5–12% and 3–8% for values of Krause (1979), Chen et al. (1981) and Puri et al. (1993), respectively. The values of o3 based on RDHS (Chen et al., 1981) are available for the limited number of elements only in the range 18pZp94: The semi-empirical values of Krause (1979), fitted values of Sarkar et al. (1997) and the calculated values by Puri et al. (1993) are also given in Table 2. In the calculation of Puri et al. (1993), the oi and fij values for all the elements with 25pZp96 were calculated from the RDHS model based radiative emission rates of Scofield (1974) and nonradiative emission rates of Chen et al. (1979). Fitted values of (Sarkar et al., 1997) were obtained using to all available data on L3 subshell fluorescence yields. It is clear from Table 2 that the present experimental values are in general agreement with the other results for all elements.
References . Ertugrul, M., 1999. Budak, G., Karabulut, A., S, im,sek, O., Measurement of the efficiency of a Si(Li) detector in the 5.5– 60 keV energy region. Instrum. Sci. Technol. 27, 357.
Chen, M.H., Crasemann, B., Mark, H., 1979. Relativistic radionless transition probabilities for atomic K- and Lshells. At. Data Nucl. Data Tables 24, 13. Chen, M.H., Crasemann, B., Mark, H., 1981. Widths and fluorescence yields of atomic L-shell vacancy states. Phys. Rev. A 2, 177. Ertugrul, M., 1996a. Measurement of L X-ray production cross-sections by 60 keV photons and average L shell fluorescence yields of lanthanides. Z. Phys. D 38, 91. Ertugrul, M., 1996b. Measurement of cross-sections and Coster–Kronig transition effect on L subshell X-rays of some heavy elements in the atomic range 79pZp92 at 59.5 keV. Nucl. Instrum. Meth. B 119, 345. Ertugrul, M., 1997. Determination of L3 subshell fluorescence yield of Nd with a Si(Li) detector. Nucl. Instrum. Meth. B 124, 475. Ertu&grul, M., 1998. Measurement of L subshell X-ray fluorescence cross-sections and L subshell fluorescence yields for elements in the atomic range 73pZp92 at 60 keV. J. Radioanal. Nucl. Chem. 237, 139. Garg, R.R., Puri, S., Singh, S., Mehta, D., Shahi, J.S., Garg, M.L., Singh, N., Mangal, P.C., Trehan, P.N., 1992. Measurement of L X-ray production cross sections and yields for elements in the atomic range 41pZp52. Nucl. Instrum. Meth. B 72, 147. Hubbell, J.H., Seltzer, S.M., 1995. Tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients 1 keV to 20 MeV for elements Z=1 to 92 and 48 additional substances of dosimetric interest. National Institute of Standards and Technology, NISTIR 5632. Krause, M.O., 1979. Atomic radiative and radionless yields for K and L shells. J. Phys. Chem. Ref. Data 8, 3307. Puri, S., Mehta, D., Chand, B., Trehan, P.N., 1993. L shell fluorescence yields and Coster–Kronig transition probabilities for the elements with 25pZp96. X-ray Spectrom. 22, 358.
M. Ertugrul / Applied Radiation and Isotopes 57 (2002) 57–61 Sahota, H.S., Singh, R., Sidhu, N.P.S., 1988. Average L shell fluorescence fluorescence yields from L shell vacancies in radionuclides. X-ray Spectrometry 17, 99. Sarkar, M., Mitra, D., Bhattacharya, Sen, P., 1997. Analytical expression for the L3 subshell fluorescence yield in the range Z=23–96. Radiat. Phys. Chem. 50, 125.
61
Scofield, J.H., 1973. Theoretical photoionization cross sections from 1 to 1500 keV. Lawrence Livermore National Laboratory Report No: UCRL No: 51326. Scofield, J.H., 1974. Relativistic Hartree-Slater values for K and L shell X-ray emission rates. At. Nucl. Data Tables 14, 121.
Measurement of L3 subshell fluorescence yields of some elements in the atomic range 57pZp68 using photoionisation Mehmet Ertugrul* Kazim Karabekir Faculty of Education, Department of Physics, Ataturk University, 25240 Erzurum, Turkey Received 6 March 2001; received in revised form 5 November 2001; accepted 19 November 2001
Abstract L3 X-ray production cross sections have been measured for the elements in the atomic range 57pZp68 at 59.5 keV. The values of L3 subshell fluorescence yields (o3 ) have been measured for the same elements using the presently measured cross section values and the theoretical Li subshell photoionisation cross sections, Coster–Kronig transition probabilities, emission rates and vacancy transfer probabilities. The measured X-ray production cross section values are in general agreement with the theoretical values evaluated using L3 subshell fluorescence yields, Coster–Kronig transition probabilities, emission rates, vacancy transfer probabilities and subshell photoionisation cross sections. Furthermore, the values of L3 subshell fluorescence yields are in good agreement with the theoretical values. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Production cross sections; Fluorescence yields; Photoionisation; EDXRF; L3 subshell; Lanthanides
1. Introduction Accurate experimental data regarding the X-ray production cross sections and the Li subshell fluorescence yields (o1 ; o2 and o3 ) are important in many practical applications like elemental analysis by X-ray emission technique, basic studies of nuclear and atomic processes leading to the emission of X-rays and Auger electrons and domestic computations for medical physics and irradiational processes. The primary vacancies in the Li subshells can arise from either direct ionisation by photons, electrons, heavy charged or from a shift of a K shell vacancy to the L shell. These vacancies decay through radiative, Auger and Coster– Kronig transitions. The number of Li subshell X-rays produced per Li subshell vacancy decay defines the subshell fluorescence yield oi : Recently, Ll ; La ; Lb and Lg X-ray production cross sections for elements with the atomic range 57pZp69 were measured at the 60 keV photon energy (Ertugrul, 1996a). Three sets of values of Li subshell fluorescence yields oi and Coster–Kronig *Fax: +90-4422-1841-72. E-mail address: [email protected] (M. Ertugrul).
transition probabilities fij are available in the literature. The first set, complied by Krause (1979), consist of the semi-empirically fitted values of o3 and fij for all elements in the atomic range 12pZp110: The second set of these parameters, based on the relativistic DirecHartree-Slater model was tabulated by Chen et al. (1981) for 25 elements in the atomic range 18pZp96: The third set of these values, using radiative and nonradiative transition rates based on the relativistic Dirac-Hartree-Slater model for all elements in the atomic range 25pZp96 has been evaluated by Puri et al. (1993). Sarkar et al. (1997) have obtained an analytical expression for L3 subshell fluorescence yield using 155 experimental data of 52 elements in the atomic number range 23pZp96: A systematic study of L X-ray production cross sections and L shell fluorescence yields for different elements, in the atomic range 40pZp92 as a function of incident photon energy has previously been undertaken (Ertugrul, 1996a; Sahota et al., 1988; Garg et al., 1992; Ertu$grul, 1997, 1998). In this study, the accuracy in the data of fluorescence yields and Coster–Kronig transition probabilities had an important bearing on the accuracy of final calculations of cross sections. The
0969-8043/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 8 0 4 3 ( 0 1 ) 0 0 2 7 8 - 0
M. Ertugrul / Applied Radiation and Isotopes 57 (2002) 57–61
58
Fig. 1. Experimental set-up.
Coster–Kronig transition effect on X-ray production cross sections have been investigated for heavy elements in the atomic range 79pZp92 (Ertugrul, 1996b). In the present investigation, the L3 subshell X-ray fluorescence cross sections and o3 fluorescence yields for the elements in the region 57pZp68 have been measured using thin targets. The measured values were compared with the theoretical results.
2. Experimental procedure The experimental arrangement used in this study is shown in Fig. 1. The targets are irradiated, in turn,
with 59.5 keV g-rays from a filtered annular radioactive source of 241Am of intensity 100 mCi which essentially emits monoenergetic (59.5 keV) g-rays and the radiation emitted from the 241Am is collimated to fall on the targets. 26 keV g-rays and Np L X-rays are also emitted in addition to 59.5 keV g-rays. It can be seen that the 26 keV g-rays and Np L X-rays can excite the L1, L2 and L3 subshells of the present elements. There is a graded filter on the 241Am annular source that almost completely absorbs all the Np L X-rays and 26 keV g-rays. The L shell fluorescent X-rays emitted from targets are recorded with Si(Li) X-ray detector, with resolution of B160 eV at 5.9 keV, coupled to an Nd 66B multichannel analyser. The shielding in the arrangement is so arranged that the source can only see the primary target. Spectroscopically pure targets of La2O3, CeO2, Pr6O11, Nd2O3, Sm2O3, Eu2O3, Gd2O3, Tb4O7, Dy2O3, Ho2O3 and Er2O3 of thickness ranging from 20 to 30 mg/cm2 have been used. These targets were irradiated by photons at 59.5 keV. For each element two or more targets of different thickness have been used. In order to reduce the statistical error in the measurements, three spectra were recorded for the time intervals ranging from 3600, 7200 and 10,800 s. To minimise the errors, the data for each target has been taken on different occasions. A typical L X-ray spectra of Pr is shown in Fig. 2. The experimental L3 subshell X-ray production cross section ðsxL3 Þ and fluorescence yield (o3 ) were evaluated
Fig. 2. L X-ray spectrum of Pr with recorded Si(Li) detector.
M. Ertugrul / Applied Radiation and Isotopes 57 (2002) 57–61
from the tables of Hubbell and Seltzer (1995). yð¼ 451Þ and fð¼ 01Þ are the angles of the incident and emitted X-rays on target surface normal. si (i ¼ 1; 2, 3 and K) is the photoionisation cross section of Li subshell and K shell (Scofield, 1973), oi (i ¼ 1; 2, 3) is the Li subshell
using the following relations, NLa I0 GeLa bLa mF3a
sxL3 ¼
ð1Þ
and o3 ¼
59
NLa ; I0 GeLa bLa m½ðs3 þ ZKL3 sK Þ þ ðs2 þ ZKL2 sK Þf23 þ ðs1 þ ZKL1 sK Þðf13 þ f12 f23 ÞF3a
fluorescence yield (Krause, 1979) and fij (i ¼ 1; 2 and j ¼ 2; 3) is the Coster–Kronig transition probability (Krause, 1979). The ZKLi (i ¼ 1; 2 and 3) values are the vacancy transfer probability of the same elements (Scofield, 1974). F3a is the fraction of L X-rays originating from the L3 transition that contribute to the La peak.
where NLa is the number of counts per unit time under the photopeak corresponding to La X-rays of elements, the product I0 G is the intensity of exciting radiation falling on the area of the target, eLa is the detector efficiency at the La X-ray energy, m is the mass per area of the element in g/cm2. The bLa is the self-absorption correction factor for the incident and emitted photon energies. The values of I0 G are evaluated by collecting the K X-ray spectra of thin targets of Zr in the same geometry in which the L X-ray production cross sections were measured and using the similar relation Eq. (1) but for K instead of L X-rays. In these calculations, the theoretical values of Ka X-ray production cross sections, sKa ¼ sPK oK fKa calculated using photoionisation cross sections (sPK ) based on the Hartree-Fock-Slater model (Scofield, 1973), fKa is the fraction rate of Ka X-ray in K X-rays (Scofield, 1974) and fluorescence yields (oK ) from tables of Krause (1979) have been used. The detector efficiency (eLa ) in the La X-ray energy regions of present elements was determined using 54Mn, 241Am and 133 Ba radioisotope sources according to our earlier method (Budak et al., 1999). The values of bLa have been calculated by using the following expression, bLa ¼
1 exp½ðminc sec y þ mLa sec fÞm ; ðminc sec y þ mLa sec fÞm
ð2Þ
F3a ¼
G3a ; G3
ð4Þ
where G3 is the theoretical total radiation rate of the L3 subshell and G3a is the sum of the radiative transition rates, which contribute to the La line associated with the hole filling in the shell. That is G3a ¼ G3 ðM4 L3 Þ þ GðM5 L3 Þ;
ð5Þ
where G3 ðM5 L3 Þ is the radiative transition rate from M4 to L3 subshell (Scofield, 1974).
3. Results and discussion The present values of L3 subshell X-ray production cross sections, F3a and ðs3 þ ZKL3 sK Þ þ ðs2 þ ZKL2 sK Þf23 þ ðs1 þ ZKL1 sK Þðf13 þ f12 f23 Þ values for La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho and Er at 60 keV incident photon energy are listed in Table 1. The comparison of experimental and theoretical results for
ð3Þ
where minc and mLa are the attenuation coefficients at the incident and La X-ray energy. Their values are taken
Table 1 The experimental and theoretical values of L3 subshell X-ray production cross sections of the elements with the atomic region 57pZp68 Element
sxL3 (E) (barns/atom)
sxL3 (T) (barns/atom)
F3a
K
57La 58Ce 59Pr 60Nd 62Sm 63Eu 64Gd 65Tb 66Dy 67Ho 68Er
11977 138710 146710 170711 214714 230718 257722 286723 299723 338724 388727
118 133 151 168 207 230 255 282 314 345 382
0.822 0.824 0.822 0.822 0.820 0.820 0.817 0.817 0.816 0.815 0.815
1135 1202 1278 1324 1491 1567 1642 1706 1802 1894 1987
E-means experimentally; T-means theoretically; K ¼ ðs3 þ ZKL3 sK Þ þ ðs2 þ ZKL2 sK Þf23 þ ðs1 þ ZKL1 sK Þðf13 þ f12 f23 Þ:
M. Ertugrul / Applied Radiation and Isotopes 57 (2002) 57–61
60
Table 2 The comparison of present o3 values with the Krause (1979), Chen et al. (1981), Sarkar et al. (1997) and Puri et al. (1993) values for the elements in the atomic region 57pZp68 Element
57La 58Ce 59Pr 60Nd 62Sm 63Eu 64Gd 65Tb 66Dy 67Ho 68Er
o3 Experimental
Sarkar et al. (1997)
Krause (1979)
Chen et al. (1981)
Puri et al. (1993)
0.10470.006 0.11570.008 0.11470.007 0.12870.008 0.14370.009 0.14670.011 0.15670.013 0.16770.013 0.16570.012 0.17870.012 0.19570.013
0.09770.008 F F 0.12270.010 F 0.14870.040 0.15770.019 0.16670.016 0.17570.055 0.18470.015 0.19470.022
0.104 0.111 0.118 0.125 0.139 0.147 0.155 0.164 0.174 0.182 0.192
F F F 0.136 F 0.166 F F F 0.196 F
0.112 0.119 0.126 0.134 0.150 0.158 0.167 0.175 0.184 0.193 0.203
o3 is given in Table 1. The overall error in the present measurements is estimated to be 3–7%. This error is the sum of the uncertainties in different parameters used to calculate the La X-ray production cross sections, namely, the evaluation of peak areas (p3%), I0Ge product (5–7%), target thickness measurements (p5%) and in the absorption correction factor (p2%). It is clear from Table 1 that the present experimental results for all elements are in general agreement with the theoretical values. The values of L3 subshell fluorescence yields (o3 ) decided using Eq. (2), for same elements are presented in Table 2. Present results are different than 1–5%, 5–12% and 3–8% for values of Krause (1979), Chen et al. (1981) and Puri et al. (1993), respectively. The values of o3 based on RDHS (Chen et al., 1981) are available for the limited number of elements only in the range 18pZp94: The semi-empirical values of Krause (1979), fitted values of Sarkar et al. (1997) and the calculated values by Puri et al. (1993) are also given in Table 2. In the calculation of Puri et al. (1993), the oi and fij values for all the elements with 25pZp96 were calculated from the RDHS model based radiative emission rates of Scofield (1974) and nonradiative emission rates of Chen et al. (1979). Fitted values of (Sarkar et al., 1997) were obtained using to all available data on L3 subshell fluorescence yields. It is clear from Table 2 that the present experimental values are in general agreement with the other results for all elements.
References . Ertugrul, M., 1999. Budak, G., Karabulut, A., S, im,sek, O., Measurement of the efficiency of a Si(Li) detector in the 5.5– 60 keV energy region. Instrum. Sci. Technol. 27, 357.
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