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Experimental determination of effective resonance energies for the (n,γ) reactions of 71Ga, 75As, 164Dy, 170Er by the cadmium ratio method
Available online at www.sciencedirect.com annals of
NUCLEAR ENERGY Annals of Nuclear Energy 35 (2008) 1433–1439 www.elsevier.com/locate/anucene
Experimental determination of effective resonance energies for the (n,c) reactions of 71Ga, 75As, 164Dy, 170Er by the cadmium ratio method M.G. Budak a, H. Yu¨cel b,*, M. Karadag a, M. Tan a a
Gazi University, Gazi Education Faculty, 06500 Teknikokullar, Ankara, Turkey b Turkish Atomic Energy Authority, Besevler Campus, 06100 Ankara, Turkey
Received 31 August 2007; received in revised form 18 January 2008; accepted 19 January 2008 Available online 4 March 2008
Abstract The effective resonance energy Er -values for the (n, c) reactions of 71Ga, 75As, 164Dy, 170Er were determined by the cadmium ratio method using dual monitor (55Mn–98Mo) having favorable resonance properties. The powder samples with and without a 1 mm thick Cd cylindrical box were irradiated in an isotropic neutron field obtained from three 241Am–Be neutron sources. The induced activities were measured with a 120.8% relative efficient p-type Ge detector. The necessary correction factors for thermal neutron self-shielding (Gth) and resonance neutron self-shielding (Gepi) effects were taken into account. Thus, the experimentally determined Er -values were 174 ± 36 eV for 71Ga, 112 ± 23 eV for 75As, 225 ± 47 eV for 164Dy and 129 ± 27 eV for 170Er, respectively. The present experimental results for the Er -values were also theoretically calculated from the newest resonance data. Since the experimentally determined Er -values for the 71Ga, 75As, 164Dy and 170Er isotopes are not available in literature, the present experimental results are compared only with the present and earlier calculated ones. It is found that there are still large discrepancies (within range of 3–15%) between the experimentally determined Er -values and the calculated ones obtained by recent resonance data for the above isotopes. A wide variation of the available Er -values implies the need for the new experimental determinations of Er -values for other isotopes, especially used in k0 standardization studies. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Over the past 30 years, great efforts have been made to perform neutron activation analysis (NAA) technique in absolute or single comparator standardization mode for the neutron capture (n, c) activation analysis of any analyte (Simonits et al., 1975). However, single comparator and absolute standardizations suffer from two important drawbacks (De Corte and Simonits, 2003). The first one is that the inflexibility of single comparator method is strictly bound to a given set of local irradiation and counting conditions. The second one is that the inaccuracy of the abso*
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07. E-mail address: [email protected] (H. Yu¨cel). 0306-4549/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2008.01.010
lute method is caused by the introduction of occasionally unreliable absolute nuclear data for activation and decay. In the neutron capture (n, c) activation analysis, for instance, the absolute standardization (e.g., the k0-method) uses the concept of effective resonance energy Er to correct for the effect of non-ideal nature of the epithermal neutron flux distribution, which is often represented by a non-ideal 1/E1+a with a spectrum shape factor, a. It is well known that in case non-ideal epithermal spectrum shape (deviation from ideal 1/E behavior) in an irradiation position has been neglected, this may lead to significant errors on the analytical result due to the inaccuracy of the essential nuclear parameter I0(a), which is resonance integral cross section (Simonits et al., 1984). As well as the epithermal spectrum shape factor (a), the effective resonance energy (Er ) parameter of the nuclide to be activated is also an
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essential parameter for the correction of resonance integral to thermal neutron cross section ratio, Q0(a) (=I0(a)/r0) in a real 1/E1+a epithermal flux distribution (Moens et al., 1979; De Corte et al., 1986). Therefore, the inaccurate of effective resonance energy (Er ) value can also give rise to more serious error on the analytical result because it is directly related to the ð1=Er Þa in the I0(a) definition (Simonits et al., 1984; Jovanovic et al., 1987). On the other hand, it is reported that some Er -values had to be corrected by about a factor of 2; for instance, 45 Sc: from Er ¼ 2120 eV to 4110 eV (Op De Beeck, 1985). In view of the use of Er -values for accurate NAA purposes, the question arises as to whether they are not as vulnerable to updates of experimental resonance data, as the individual resonance energies. The extent of the experimental instability of Er -values, as well as the degree of inaccuracy of the resonance integral values need to look into carefully the experimental determination of Er -values. The present study for the Er -value determination is based on cadmium (Cd) ratio measurements of the isotope being investigated because the Cd-ratio method allows one to obtain the reproducible results and eliminate the possible differences in the neutron spectrum between the thermal and epithermal activation, providing that the same irradiation and counting conditions apply to each measurement. By definition, since the Er term represents ‘‘the energy of
a single virtual resonance which gives the same resonance activation rate as all actual resonances for the isotope”, the Er -value for the isotope is taken as an effective or average value estimated from all the resonances in the epithermal spectrum region. That is, a single virtual energy Er , is important because it replaces all the resonance energies lying in epithermal region, which is described by a modified 1/E1+a behaviour in H/gdahl formalism (De Corte et al., 1986). In addition, in some cases when the theoretical resonance data for Er -values are incomplete, obsolete, inaccurate or even not known at all, the experimental determination of the Er -value for an isotope should be carried out (Simonits et al., 1984). When applying the single comparator method in the thermal activation analysis and when in addition the H/ gdahl formalism serves as a base for this method (Verheijke, 2000), the Er -value is sensitive to the accuracy of the Q0(a) value for the monitor used. Because the neutron spectrum is divided into two parts, namely: the thermal and the epithermal region in which the (n, c) activation due to fast neutrons can generally be neglected. Moreover, by definition, the separation between the thermal and epithermal part of the spectrum is arbitrary and the so-called Cd cutoff energy is used, which is internationally accepted as 0.55 eV in H/gdahl convention. Hence, it is not possible to avoid the error in the Er -value to be measured for the
Table 1 Nuclear and decay data for the isotopes used in the analyses Cadmium transmission factor, FCda
Effective resonance energy, Er (eV)b
Q0 (=I0/r0)b S (%)
Half-lifec
1.00 1.00
468 ± 51 241 ± 48
1.053(2.6%) 53.1(6.3%)
0.991 1.00
5.65 ± 0.40 –
1.00
164
170
Nuclear reaction
55
Mn(n, c)56Mn Mo(n, c)99Mo(b-)99mTc
98
197
Au(n, c)198Au Ga(n, c)72Ga
71
75
As(n, c)76As
Dy(n, c)165Dy
Er(n, c)171Er
a b c d
The measured gammarayc
Notes
Energy (keV)
Emission probability, c (%)
2.5789(1) h 65.94(1) h
846.754(20) 140.511(1)
98.9(3) 4.52(24)
Monitor Monitor
15.7(1.8%) 6.69(1.2%)
2.695(21) d 14.10(1) h
13.6
26.24(9) h
1.00
–
0.19
2.334(1) h
1.00
–
4.42(3.3%)
7.516(2) h
95.58 25.9(5) 100 10.33(17) 7.23(12) 45.0 1.20(8) 6.2(4) 1.44(11) 3.42(24) 3.80(5) 0.534(8) 0.904(13) 0.613(9) 0.578(9) 28.9(12) 64(3)
Monitor Investigated isotope
–
411.802(17) 629.96(4) 834.03(3) 894.25(10) 1050.69(5) 559.10(5) 563.23(5) 657.05(5) 1212.92(5) 1216.08(5) 94.700(3) 279.763(12) 361.68(2) 633.415(20) 715.328(20) 295.901(14) 308.291(18)
El Nimr et al. (1981). Kolotov and De Corte (2003). NUDAT (Sonzogni et al., 2005). Simonits et al. (1981).
Asp(Mo)/Asp(Mo+Tc), =0.05992d, where Asp is specific activities of isotope investigated.
Investigated isotope
Investigated isotope
Investigated isotope
The suitable waiting period was used for decay of isomeric transition (97.6%) of 165mDy with a half-life of 1.257b min
M.G. Budak et al. / Annals of Nuclear Energy 35 (2008) 1433–1439
isotope due to an uncertainty in the Q0(a) value of the monitor. However, this can be adjusted in the determination of Er -values by choosing the appropriate Er monitor isotopes whose Q0(a) values and other parameters are more accurate. Accordingly, 55Mn and 98Mo isotopes having favourable nuclear properties were used as the Er monitor in the present work. They have good 1/v-behaviors with Westcott-factors, g(20 °C) 1 and moderate values for 2200 m s1 thermal neutron cross section and resonance integral values to minimize burn-up of atoms. In addition, most of the resonance captures of 55Mn and 98Mo occurs at a relatively higher energy region (for instance, the first principal resonance of 55Mn is at 337 eV and that of 98Mo is at 468 eV) (JENDL-3.3 et al., 2002), which are quite far from the 1/v region, thus making their well established effective resonance energies, as given in Table 1. In this study, it is aimed to measure effective resonance energy values for the (n, c) reactions of 71Ga, 75As, 164Dy and 170Er by the activation method using cadmium ratios of the isotopes being investigated relative to those of Cd-ratios of dual monitors (55Mn and 98Mo). Further, the Er -values for the above isotopes also theoretically calculated using the recent resonance parameter data since the quantity and quality of the available resonance parameter data appeared in the literature continuously improve. 2. Experimental The sample irradiations were performed in an isotropic neutron field obtained from the three 241Am–Be neutron sources each having 592 GBq activity, immersed in a paraffin moderator and shielded with 1 mm thick Cd sheet and 10 cm thick lead bricks. The geometrical configuration of this neutron irradiator installed at ex-Ankara Nuclear Research and Training Center (ANRTC) has been previously described in detail elsewhere (Karadag et al., 2003; Yu¨cel and Karadag, 2004). The analytical grade oxide powder samples obtained from Aldrich Inc. and Merck were diluted by mixing Al2O3 powder as a matrix so as to minimize errors due to neutron self-shielding effect. Because 27Al (100% abundance) isotope has sufficiently low neutron absorption cross section, ra = 0.231 b. The percentages of dilution for the samples were experimentally determined in order to obtain optimum counting statistics in the measurements. Ten samples for each element were individually prepared. A set of 5 samples prepared for each element were used for obtaining Cd covered-irradiation data. The remaining 5 samples for each element were used for obtaining bare irradiation data. In addition, the thin Au and Mo foils were used as monitors. The powder samples were filled in the polystyrene tubes (6.5 mm diameter and 15 mm height). They were exposed to the neutrons in a fixed position of the irradiation hole. The samples were irradiated with 1 mm thick cylindrical Cd filter (10 mm diameter and 20 mm height) to obtain Cd-ratio values.
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The irradiated samples were measured by a high resolution c-ray spectrometer equipped with a coaxial p-type HP Ge detector (Canberra GC 11021) with a measured relative efficiency of 120.8%, an energy resolution of 1.95 keV, and a peak-to-Compton ratio of 85.7:1 at 1332.5 keV of 60Co. For c-ray shielding, a 10 cm thick Pb shield lined with a 1 mm thick Sn and 1.5 mm Cu thick (Canberra Model 767) was used. The shield is also jacketed by a 9.5 mm steel outer housing. To minimize scattered radiation from the shield, the detector was centred in it. The detector was interfaced to a Digital Spectrum Analyzer (DSA-1000) with a full featured 16 K channels ADC conversion/ MCA memory analyzer based on digital signal processing. DSA-1000 gamma spectrum analyzer operates through a commercial Genie-2000 software. The net peak areas under the full energy peaks were evaluated both manually and the interactive peak fitting module of the Genie-2000 software. Each spectrum was collected in 4096 channels memory with a gain of 0.52 keV/channel, and in the live-time mode. The samples were counted at a distance of 10 cm from the detector to keep possible true coincidence effects at a reasonably low level (Yu¨cel et al., 2007), although the Cdratios can cancel out the true coincidence effects. The counting periods were high enough to ensure good statistical quality of data. Background measurements were subtracted from the sample spectra. The suitable waiting times were employed to minimize dead time losses and eliminate the possible contributions of 843.8 keV gamma ray from 27Mg (9.45 min) activity to the 846.7 keV peak of 56Mn and ensure the isomer (m) level, 165mDy (1.257 min) with a 97.6% IT (isomeric transition) decaying to the ground (g) level, 165gDy (2.334 h). For the efficiency calibration of the used Ge detector as a function of energy, the powder radioactive standard containing a mixture of 241Am, 109Cd, 57Co, 123mTe, 51Cr, 113 Sn, 85Sr, 137Cs, 60Co and 88Y radionuclides (purchased from the NIST traceable Isotope Products Laboratories Inc.) was used. 3. Determination of effective resonance energy 3.1. Experimental determination of Er value The effective resonance energy, Er valid in a non-ideal epithermal neutron spectrum was firstly defined in the past by Ryves (1969) as follows: a Eref I 0 ðaÞ ¼ 00 ð1Þ I0 Er where I 00 and I 00 ðaÞ are the reduced resonance integral cross sections (i.e., 1/v-tail subtracted) for ideal 1/E and nonideal 1/E1+a epithermal neutron flux distribution. Eref is a suitably chosen reference energy, which general1y is taken as 1 eV. In theoretical basis, Er is assumed to vary slightly with the a parameter. However, it is reported that it can to a good approximation be calculated as an independent
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value of a shape parameter according to the term a ð1 eVÞ ffi 1 (De Wispelaere and De Corte, 2003). Accordingly, the Q0(a) = (I0(a)/r0) in a real epithermal 1/ E1+a flux distribution at a given irradiation position, can also be related to Q0(=I0/r0) in an ideal 1/E epithermal flux distribution (De Corte et al., 1979; Simonits et al., 1984). Q0 0:429 0:429 þ ð2Þ Q0 ðaÞ ¼ ð1 eVÞa ð2a þ 1Þ EaCd Ear 1=2
With 0:429 ¼ 2 ðE0 =ECd Þ . In Eq. (2) above, thermal energy is E0 = 0.0253 eV, cadmium cut-off energy, ECd = 0.55 eV and effective resonance energy, Er (in eV). Since the cadmium cut-off energy, ECd is set at 0.55 eV for a small sample in a 1 mm thick Cd box (height/diameter ffi 2), Eq. (2) is only valid for the case of ECd = 0.55 eV in a non-ideal 1/E1+a epithermal distribution. On the other hand, since the Cd-ratio, RCd to be measured for an isotope is also related to the thermal to epithermal flux ratio, f by the following formula: f ¼ Q0 ðaÞ ½F Cd RCd 1
ð3Þ
For the effective resonance energy, Er the above Eqs. (1) and (2) can be rewritten as follows: 1=a f 0:429 Er;i ¼ ðQ0 0:429Þ F Cd RCd 1 ð2a þ 1Þ EaCd ð4Þ Taking into account neutron self-shielding factors, Gth and Gepi for a comparator (c) and an investigated isotope (x), the logarithmic form of Eq. (4) can be used as follows (Jovanovic et al., 1984, 1985): 0 1 f Gth;c Q0;x 0:429 ðF Cd;c RCd;c 1ÞGepi;c C a Er;x 1 A ln ¼ ln @ f Gth;x a Q0;c 0:429 Er;c Ca
et al., 1981). Nuclear and decay data used in the analyses for effective resonance energy determinations are given in Table 1. The equivalent 2200 m s1 thermal and epithermal neutron fluxes at the sample irradiation position of the 241 Am–Be neutron irradiator were measured to be /th = (1.5 ± 0.2) 104 and /epi = (1.4 ± 0.1) 103 n cm2 s1, respectively. The thermal to epithermal neutron flux ratio at the same position was determined to be f = 10.42 ± 0.31 using 197Au monitor (Yu¨cel and Karadag, 2004). In addition, the deviation of the epithermal neutron flux distribution (characterized by the parameter a) in the particular irradiation should be known in advance (De Corte et al., 1979,1981). Hence, the extent of non-ideality of epithermal flux shape, a-shape factor at the sample irradiation position for the irradiation hole used of the present neutron irradiator was taken to be 0.083 ± 0.016, which was experimentally determined by dual monitor method using 98Mo and 197Au isotopes (Yu¨cel and Karadag, 2004). The thermal and epithermal self-shielding factors (Gth and Gepi) used in Eq. (5) for the powder mixtures filled in the polystyrene tubes were calculated using the procedures for the case of the irradiations in an isotopic neutron field (Karadag et al., 2003; Karadag and Yu¨cel, 2004,2005; Yu¨cel and Karadag 2005). But those factors for the case of Au and Mo-foils exposed to the same neutron field were calculated by the Nisle’s approximation (Gilat and Gurfinkel, 1963). The required nuclear data (e.g., resonance parameters, absorption, scattering, total microscopic cross-sections, etc.) were taken from JENDL-3.3 and NUDAT online data libraries. The calculated neutron self-shielding factors are given in Table 2. 3.2. Theoretical calculation of Er value
ðF Cd;x RCd;x 1ÞGepi;x
ð5Þ Ca ¼
0:429 ð2a þ 1Þ EaCd
þ In Eq. (5) the cadmium ratio, RCd ¼ A sp =Asp can easily be calculated from the measured specific activities of the isotope, by the following: N p =tc N p =tc þ Asp ¼ and Asp ¼ ð6Þ w S D C bare w S D C Cd þ where A sp and Asp are specific activities obtained after a bare and Cd-covered isotope irradiation; Np is net number of counts under the full-energy peak collected during measuring (live) time, tc; w is mass of irradiated element; S=1 ektirr is saturation factor with k = decay constant, tirr = irradiation time; D ¼ ektd is decay factor with td = decay time; C ¼ ½1 expðktr Þ=ktr is measurement factor correcting for decay during the true time, tr for a measurement. Cadmium transmission factors for epithermal neutrons, FCd for the isotopes of interest, according to the definition of ECd = 0.55 eV are taken as unity but may be different from unity fore some isotopes (El Nimr
In neutron activation analysis of elemental composition of materials, the occurrence of ‘‘resonances” in total and capture cross sections is a function of neutron energy. Therefore, for the aspect of the effective resonance energy
Table 2 The calculated neutron self-shielding factors for the diluted powder samples and foils The samples
Isotope
Thermal self-shielding factor including scattering, Gth
Epithermal self-shielding factor, Gepi
Al2O3–3.4% MnO2 Mo 0.025 mm-foil Au 0.0005 mm-foil Al2O3–4.1% Ga2O3 Al2O3–2.4% As2O3 Al2O3–3.8% Dy2O3 Al2O3–5.0% Er2O3
55
0.997 0.999a 1.000a 0.998 0.998 0.947 0.983
0.903 0.992b 0.925c 0.907 0.900 0.830 0.822
Mn Mo 197 Au 71 Ga 75 As 164 Dy 170 Er 98
a Calculated by Nisle’s approximation, including scattering effect, given in Gilat and Gurfinkel (1963). b Calculated by approximation given in Beckurts and Wirtz (1964). c IAEA and Technical Reports (1970).
M.G. Budak et al. / Annals of Nuclear Energy 35 (2008) 1433–1439
of an isotope, it can usually be utilized by the following approximate expressions. One obtains: P ri Cc;i ln Er;i ln Er ¼
i
Er;i
P
ð7Þ
ri Cc ;i Er;i
i
where ri is partial capture cross-section at the maximum of the ith resonance energy, Er,i and Cc,i is the radiative width of the ith resonance energy. It is assumed in Eq. (7) that resonance self-shielding is negligible, which is certainly the case when using sufficiently diluted samples. The latest resonance data taken from JENDL 3.3 (Shibata et al., 2002) and JEFF-3.1 (2005), General Purpose Neutron File OECD-NEA evaluated data library are used in this study. The Er -values resulted from Eq. (7) are also given in Table 4. This approximation was first used by Moens et al. (1979), in which neutron widths, Cn are neglected. The latter is that Er -value can also to a good approximation be calculated by assuming its a independence according to the term (1 eV)a 1 that are omitted. P wi ln Er;i ln Er ¼ i P ð8Þ wi i
where the weighting factor wi is given by gCc Cn 1 wi ¼ 2 C i E r;i
ð9Þ
Table 3 The measured effective resonance energy values obtained by dual monitors Reaction
71
Ga(n, c)72Ga As(n, c)76As 164 Dy(n, c)165Dy 170 Er(n, c)171Er 75
Experimental effective resonance energy value, Er (eV) Using 55Mn monitor
Using 98Mo monitor
Weighted average
173.3 ± 47.1 111.7 ± 30.3 223.8 ± 60.7 128.5 ± 35.1
175.8 ± 57.0 113.3 ± 36.7 227.0 ± 73.5 130.4 ± 42.4
174 ± 36 112 ± 23 225 ± 47 129 ± 27
where g = (2J + 1)/2(2I + 1) is the statistical weight factor being I and J the spin of the target nucleus and the resonance state of the neutron captured compound nucleus, Cc is the radiative width, Cn is the neutron width, and C = Cc + Cn is the total width of resonance. The resonance data taken from the recent literature (Mughabghab, 1984; JENDL-3.3 et al., 2002; JEFF-3.1, 2005) are used to calculate the Er -values by Eq. (8). 4. Results and discussion The Er -values for the isotopes being investigated were obtained by Eq. (5) using the experimentally determined Cd-ratios and the adopted nuclear data given in Table 1, respectively. The obtained results for Er -values relative to the Er -value of 55Mn and 98Mo monitors are given in Table 3. The Er -values of 55Mn and 98Mo monitors used in the present experiment are remarkably different each other but they are intermediate Er -values and cover the range of Er -values for the isotopes of interest, thus allowing to be appropriate range for the resonance energy regions ( 50–10,000 eV) of some isotopes. As can be seen in Table 3, a consistency between the results obtained by 55Mn and those obtained by 98Mo for each isotope being measured is found. This leads to more accurate results since, in general, the main feature of the comparator methods compensate for some systematic errors, which may contribute to the measured results. Two different monitors with the sufficiently known cross sections also allowed to check for the possible differences in the measured results. The main sources of uncertainty in the experimentally determined Er -values given Table 3 are mainly due to the a-shape factor(19.3%), the monitor effective resonance energy values (10.9% for 55Mn and 19.9% for 98Mo), and the resonance integral to thermal neutron cross section ratio, Q0 (within range of 0.2–13.6%). On the other hand, the measurement uncertainties on the Cd-ratios determined from the specific activities are generally found to be less than 2.5%, and thus they are not an important component
Table 4 Experimentally an theoretically determined effective resonance energy, Er -values for Reaction
Ga(n, c)72Ga As(n, c)76As 164 Dy(n, c)165Dy 170 Er(n, c)171Er 71
75
a b c d e f
1437
71
Ga,
75
As,
164
Dy and
Experimental effective resonance energy value
Theoretically calculated effective resonance energy values
This work
This workc
170
Er
Literature
Er (eV)
Er (eV) [from Eq. (7)]a
[C/E]
174 ± 36 112 ± 23 225 ± 47 129 ± 27
180 117 146 114
1.034 1.045 0.649 0.884
b
Er (eV) [from Eq. (8)]d
[C/E]
153 115 221 123
1.027 1.027 0.982 0.953
b
Er (eV) [from Eq. (7)]e
[C/E]b
Er (eV) [from Eq. (8)]f
[C/E]b
152 102 145 –
0.874 0.911 0.644 –
154 ± 18 106 ± 36 224 ± 11 129 ± 3
0.885 0.946 0.996 1.000
Calculated by Eq. (7) based on Moens et al. (1979)’s approximation using recent resonance data taken from JENDL 3.3 and JEFF 3.1 data libraries. C/E means that the ratio of the theoretically calculated value/the experimentally determined value. Uncertainties are not given due to no uncertainty quoted in the used data. Calculated by Eq. (8), using recent resonance data taken from JENDL 3.3 and JEFF 3.1 data libraries. Referenced by Moens et al. (1979). Referenced by Jovanovic et al. (1987).
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M.G. Budak et al. / Annals of Nuclear Energy 35 (2008) 1433–1439
in the overall uncertainty estimation. However, in the overall uncertainty budget, it is not possible to reduce the overall uncertainty of about 20% on the final results for Er -values of the isotopes being investigated since the magnitudes of uncertainties on the nuclear data propagated in Eq. (5). In addition, it was noted by Simonits et al. (1984) that 20% uncertainty on any Er -value obtained by Cd-ratio method could be acceptable, thanks to the large uncertainty reduction in the conversion of Q0 into Q0(a), as shown in Eq. (4). The present experimental results for the Er -values were compared with the present theoretically calculated values and the older ones, as given in Table 4. In general, the present experimental values agree with the calculated ones when using the newest resonance data within limits of the estimated uncertainty, except for the Er -value of 225 ± 47 eV for 164Dy. However, it implies that when Moens’ approximation based on Eq. (7) is used to calculate the Er -values, the results are not satisfactorily accurate even if currently available most accurate neutron resonance data are used. Because this Moens’s approximation was used in past, neglecting neutron widths, Cn. Whereas the Cn widths of the resonances vary in the range of 103–10 eV, and should not overlook although the Cn widths are considerably even for resonances of the same isotope. On contrary, the radiative widths, Cc taken into account in Eq. (7) vary within the range of 0.1–1 eV, and they are fairly constant, within one isotope, because of many c-ray exit channels (Postma et al., 2001). On the other hand, since there is no evidence that the Er value is dependent on the a-shape factor over the resonances (De Wispelaere and De Corte, 2003), the expanding of ðEr Þa factors in series should not be ignored for higher order terms for Er and a-values in the integrated Breit–Wigner expressions for all resonances as given by Moens et al. (1979). Consequently it seems that it may be regarded to the experimentally determined Er -values rather than the theoretical ones. The experimental results in Table 4 agree with the commonly used calculated values of Jovanovic et al. (1987) by 0.4–11.5%. For the above isotopes being investigated, it is found that there are still discrepancies within range of 3–15%, excepting the Er result for 164Dy isotope between the experimentally determined Er -values and the theoretical values when the recent resonance data used. It may suggest that the new experimental determinations of Er -values for other isotopes should have to be done, especially those used in k0 NAA standardization studies. Since the quantity and quality of the available resonance parameter data for the theoretical calculations of Er -values continuously improve, it is expected that discrepancies between the old calculated Er values and the recent ones have been observed in some degree. Acknowledgments The experiments in this work were performed in ex-Ankara Nuclear Research and Training Center (ANRTC) in
2004. Authors are grateful to the directorate of ex-ANRTC of Turkish Atomic Energy Authority for the permission to use the experimental facilities. References Beckurts, K.H., Wirtz, K., 1964. Neutron Physics. Springer-Verlag OGH, Berlin. De Corte, F., Simonits, A., 2003. Recommended nuclear data for use in the k0 standardization of neutron activation analysis. Atom. Data Nucl. Data 85, 47–67. De Corte, F., Moens, L., Sordo-El Hammami, K., Simonits, A., Hoste, J., 1979. Modification and generalization of some methods to improve the accuracy of a-determination in the 1/E1+a epithermal neutron spectrum. J. Radioanal. Chem. 52 (2), 305–317. De Corte, F., Sordo-El Hammami, K., Moens, L., Simonits, A., De Wispelaere, A., Hoste, J., 1981. The accuracy and precision of the experimental a-determination in the 1/E1+a epithermal reactor neutron spectrum. J. Radioanal. Chem. 62 (1–2), 209–255. De Corte, F., Moens, L., Jovanovic, S., Simonits, A., De Wispelaere, A., 1986. J. Radioanal. Nucl. Chem. 102, 37. De Wispelaere, A., De Corte, F., 2003. Recalibration of the irradiation facilities in the Thetis reactor, with an examination of the a versus E behavior in the keV neutron energy range. J. Radioanal. Nucl. Chem. 257 (3), 519–523. El Nimr, T., De Corte, F., Moens, L., Simonits, A., Hoste, J., 1981. Epicadmium neutron activation analysis (ENAA) based on the k0comparator method. J. Radioanal. Chem. 67 (2), 421–435. Gilat, J., Gurfinkel, Y., 1963. Self-shielding in activation analysis. Nucleonics 21 (8), 143–144. IAEA, Technical Reports, 1970. Series No: 107. Neutron Fluence Measurements. IAEA, Vienna. JEFF-3.1, 2005. Evaluated Data Library (updated on May, 2005). OECD Nuclear Energy Agency. http://www.nea.fr/html/dbdata/JEFF/ JEFF31/JEFF31N6649_0.ASC. JENDL-3.3, K. Shibata, et al., 2002. Japanese Evaluated Nuclear Data Library Version 3 Revision-3: Program for Nuclear Data on the Web (). Nuclear Data Center, Japan Atomic Energy Agency (JAEA). Jovanovic, S., De Corte, F., Moens, L., Simonits, A., Hoste, J., 1984. Some elucidations to the concept of the effective resonance energy Er. J. Radioanal. Nucl. Chem., Art. 82, 379–383. Jovanovic, S., De Corte, F., Simonits, A., Hoste, J., 1985. The ‘‘Ercomparator” technique for the experimental determination of effective resonance energies. J. Radioanal. Nucl. Chem., Art. 92, 399–406. Jovanovic, S., De Corte, F., Simonits, A., Moens, L., Vukotic, P., Hoste, J., 1987. The effective resonance energy as a parameter in (n, c) activation analysis with reactor neutrons. J. Radioanal. Nucl. Chem., Art. 113, 177–185. Karadag, M., Yu¨cel, H., 2004. Measurement of thermal neutron crosssection and resonance integral for186W(n, c)187W reaction by the activation method using a single monitor. Ann. Nucl. Energy 31, 1285– 1297. Karadag, M., Yu¨cel, H., 2005. Thermal neutron cross-section and resonance integral for164Dy(n,c165Dy reaction. Nucl. Instr. and Meth. A 550, 626–636. ¨ zmen, A., 2003. Measurement of Karadag, M., Yu¨cel, H., Tan, M., O thermal neutron cross-section and resonance integrals for 71 Ga(n, c)72Ga and 75As(n, c)76As by using241Am–Be isotopic neutron source. Nucl. Instr. and Meth. A 501, 524–535. Kolotov, V.P., De Corte, F., 2003. An electronic database with a compilation of k0 and related data for NAA. J. Radioanal. Nucl. Chem. 257 (3), 501–508. Moens, L., De Corte, F., Simonits, A., De Wispelaere, A., Hoste, J., 1979. The effective resonance energy Er as a parameter for the correction of resonance integrals in 1/E1+a epithermal neutron spectra; tabulation of Er values for 96 isotopes. J. Radioanal. Chem. 52, 379–387.
M.G. Budak et al. / Annals of Nuclear Energy 35 (2008) 1433–1439 Mughabghab, S.F., 1984. In: Neutron Cross Sections, Part B, Z = 61–100, NNDC, BNL, Uptown, vol. 1. Academic Press, Inc., New York. NuDat, Nuclear Data Retrieval Program (
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Simonits, A., Moens, L., De Corte, F., De Wispelaere, A., Hoste, J., 1981. Absolute intensity of the 1405 keV gamma-ray of 99Mo. J. Radioanal. Nucl. Chem. 67 (1), 61–74. Simonits, A., Jovanovic, S., De Corte, F., Moens, L., Hoste, J., 1984. A method for experimental determination of effective resonance energies related to (n, c) reactions. J. Radioanal. Nucl. Chem. Articles 82, 169– 179. Verheijke, M.L., 2000. On the relation between the effective resonance energy and infinite dilution resonance integral for (n, c) reactions. J. Radioanal. Nucl. Chem. 246 (1), 161–163. Yu¨cel, H., Karadag, M., 2004. Experimental determination of the a-shape factor in the 1/E1+a epithermal-isotopic neutron source-spectrum by dual monitor method. Ann. Nucl. Energy 31, 681–695. Yu¨cel, H., Karadag, M., 2005. Measurement of thermal neutron cross section and resonance integral for 165Ho(n, c)166gHo reaction by the activation method. Ann. Nucl. Energy 32, 1–11. Yu¨cel, H., Budak, M.G., Karadag, M., 2007. Measurement of thermal neutron cross section and resonance integral for the 170Er(n, c)171Er reaction by using a 55Mn monitor. Phys. Rev. C 76, 034610.
NUCLEAR ENERGY Annals of Nuclear Energy 35 (2008) 1433–1439 www.elsevier.com/locate/anucene
Experimental determination of effective resonance energies for the (n,c) reactions of 71Ga, 75As, 164Dy, 170Er by the cadmium ratio method M.G. Budak a, H. Yu¨cel b,*, M. Karadag a, M. Tan a a
Gazi University, Gazi Education Faculty, 06500 Teknikokullar, Ankara, Turkey b Turkish Atomic Energy Authority, Besevler Campus, 06100 Ankara, Turkey
Received 31 August 2007; received in revised form 18 January 2008; accepted 19 January 2008 Available online 4 March 2008
Abstract The effective resonance energy Er -values for the (n, c) reactions of 71Ga, 75As, 164Dy, 170Er were determined by the cadmium ratio method using dual monitor (55Mn–98Mo) having favorable resonance properties. The powder samples with and without a 1 mm thick Cd cylindrical box were irradiated in an isotropic neutron field obtained from three 241Am–Be neutron sources. The induced activities were measured with a 120.8% relative efficient p-type Ge detector. The necessary correction factors for thermal neutron self-shielding (Gth) and resonance neutron self-shielding (Gepi) effects were taken into account. Thus, the experimentally determined Er -values were 174 ± 36 eV for 71Ga, 112 ± 23 eV for 75As, 225 ± 47 eV for 164Dy and 129 ± 27 eV for 170Er, respectively. The present experimental results for the Er -values were also theoretically calculated from the newest resonance data. Since the experimentally determined Er -values for the 71Ga, 75As, 164Dy and 170Er isotopes are not available in literature, the present experimental results are compared only with the present and earlier calculated ones. It is found that there are still large discrepancies (within range of 3–15%) between the experimentally determined Er -values and the calculated ones obtained by recent resonance data for the above isotopes. A wide variation of the available Er -values implies the need for the new experimental determinations of Er -values for other isotopes, especially used in k0 standardization studies. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction Over the past 30 years, great efforts have been made to perform neutron activation analysis (NAA) technique in absolute or single comparator standardization mode for the neutron capture (n, c) activation analysis of any analyte (Simonits et al., 1975). However, single comparator and absolute standardizations suffer from two important drawbacks (De Corte and Simonits, 2003). The first one is that the inflexibility of single comparator method is strictly bound to a given set of local irradiation and counting conditions. The second one is that the inaccuracy of the abso*
Corresponding author. Tel.: +90 312 212 03 84; fax: +90 312 215 33
07. E-mail address: [email protected] (H. Yu¨cel). 0306-4549/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.anucene.2008.01.010
lute method is caused by the introduction of occasionally unreliable absolute nuclear data for activation and decay. In the neutron capture (n, c) activation analysis, for instance, the absolute standardization (e.g., the k0-method) uses the concept of effective resonance energy Er to correct for the effect of non-ideal nature of the epithermal neutron flux distribution, which is often represented by a non-ideal 1/E1+a with a spectrum shape factor, a. It is well known that in case non-ideal epithermal spectrum shape (deviation from ideal 1/E behavior) in an irradiation position has been neglected, this may lead to significant errors on the analytical result due to the inaccuracy of the essential nuclear parameter I0(a), which is resonance integral cross section (Simonits et al., 1984). As well as the epithermal spectrum shape factor (a), the effective resonance energy (Er ) parameter of the nuclide to be activated is also an
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essential parameter for the correction of resonance integral to thermal neutron cross section ratio, Q0(a) (=I0(a)/r0) in a real 1/E1+a epithermal flux distribution (Moens et al., 1979; De Corte et al., 1986). Therefore, the inaccurate of effective resonance energy (Er ) value can also give rise to more serious error on the analytical result because it is directly related to the ð1=Er Þa in the I0(a) definition (Simonits et al., 1984; Jovanovic et al., 1987). On the other hand, it is reported that some Er -values had to be corrected by about a factor of 2; for instance, 45 Sc: from Er ¼ 2120 eV to 4110 eV (Op De Beeck, 1985). In view of the use of Er -values for accurate NAA purposes, the question arises as to whether they are not as vulnerable to updates of experimental resonance data, as the individual resonance energies. The extent of the experimental instability of Er -values, as well as the degree of inaccuracy of the resonance integral values need to look into carefully the experimental determination of Er -values. The present study for the Er -value determination is based on cadmium (Cd) ratio measurements of the isotope being investigated because the Cd-ratio method allows one to obtain the reproducible results and eliminate the possible differences in the neutron spectrum between the thermal and epithermal activation, providing that the same irradiation and counting conditions apply to each measurement. By definition, since the Er term represents ‘‘the energy of
a single virtual resonance which gives the same resonance activation rate as all actual resonances for the isotope”, the Er -value for the isotope is taken as an effective or average value estimated from all the resonances in the epithermal spectrum region. That is, a single virtual energy Er , is important because it replaces all the resonance energies lying in epithermal region, which is described by a modified 1/E1+a behaviour in H/gdahl formalism (De Corte et al., 1986). In addition, in some cases when the theoretical resonance data for Er -values are incomplete, obsolete, inaccurate or even not known at all, the experimental determination of the Er -value for an isotope should be carried out (Simonits et al., 1984). When applying the single comparator method in the thermal activation analysis and when in addition the H/ gdahl formalism serves as a base for this method (Verheijke, 2000), the Er -value is sensitive to the accuracy of the Q0(a) value for the monitor used. Because the neutron spectrum is divided into two parts, namely: the thermal and the epithermal region in which the (n, c) activation due to fast neutrons can generally be neglected. Moreover, by definition, the separation between the thermal and epithermal part of the spectrum is arbitrary and the so-called Cd cutoff energy is used, which is internationally accepted as 0.55 eV in H/gdahl convention. Hence, it is not possible to avoid the error in the Er -value to be measured for the
Table 1 Nuclear and decay data for the isotopes used in the analyses Cadmium transmission factor, FCda
Effective resonance energy, Er (eV)b
Q0 (=I0/r0)b S (%)
Half-lifec
1.00 1.00
468 ± 51 241 ± 48
1.053(2.6%) 53.1(6.3%)
0.991 1.00
5.65 ± 0.40 –
1.00
164
170
Nuclear reaction
55
Mn(n, c)56Mn Mo(n, c)99Mo(b-)99mTc
98
197
Au(n, c)198Au Ga(n, c)72Ga
71
75
As(n, c)76As
Dy(n, c)165Dy
Er(n, c)171Er
a b c d
The measured gammarayc
Notes
Energy (keV)
Emission probability, c (%)
2.5789(1) h 65.94(1) h
846.754(20) 140.511(1)
98.9(3) 4.52(24)
Monitor Monitor
15.7(1.8%) 6.69(1.2%)
2.695(21) d 14.10(1) h
13.6
26.24(9) h
1.00
–
0.19
2.334(1) h
1.00
–
4.42(3.3%)
7.516(2) h
95.58 25.9(5) 100 10.33(17) 7.23(12) 45.0 1.20(8) 6.2(4) 1.44(11) 3.42(24) 3.80(5) 0.534(8) 0.904(13) 0.613(9) 0.578(9) 28.9(12) 64(3)
Monitor Investigated isotope
–
411.802(17) 629.96(4) 834.03(3) 894.25(10) 1050.69(5) 559.10(5) 563.23(5) 657.05(5) 1212.92(5) 1216.08(5) 94.700(3) 279.763(12) 361.68(2) 633.415(20) 715.328(20) 295.901(14) 308.291(18)
El Nimr et al. (1981). Kolotov and De Corte (2003). NUDAT (Sonzogni et al., 2005). Simonits et al. (1981).
Asp(Mo)/Asp(Mo+Tc), =0.05992d, where Asp is specific activities of isotope investigated.
Investigated isotope
Investigated isotope
Investigated isotope
The suitable waiting period was used for decay of isomeric transition (97.6%) of 165mDy with a half-life of 1.257b min
M.G. Budak et al. / Annals of Nuclear Energy 35 (2008) 1433–1439
isotope due to an uncertainty in the Q0(a) value of the monitor. However, this can be adjusted in the determination of Er -values by choosing the appropriate Er monitor isotopes whose Q0(a) values and other parameters are more accurate. Accordingly, 55Mn and 98Mo isotopes having favourable nuclear properties were used as the Er monitor in the present work. They have good 1/v-behaviors with Westcott-factors, g(20 °C) 1 and moderate values for 2200 m s1 thermal neutron cross section and resonance integral values to minimize burn-up of atoms. In addition, most of the resonance captures of 55Mn and 98Mo occurs at a relatively higher energy region (for instance, the first principal resonance of 55Mn is at 337 eV and that of 98Mo is at 468 eV) (JENDL-3.3 et al., 2002), which are quite far from the 1/v region, thus making their well established effective resonance energies, as given in Table 1. In this study, it is aimed to measure effective resonance energy values for the (n, c) reactions of 71Ga, 75As, 164Dy and 170Er by the activation method using cadmium ratios of the isotopes being investigated relative to those of Cd-ratios of dual monitors (55Mn and 98Mo). Further, the Er -values for the above isotopes also theoretically calculated using the recent resonance parameter data since the quantity and quality of the available resonance parameter data appeared in the literature continuously improve. 2. Experimental The sample irradiations were performed in an isotropic neutron field obtained from the three 241Am–Be neutron sources each having 592 GBq activity, immersed in a paraffin moderator and shielded with 1 mm thick Cd sheet and 10 cm thick lead bricks. The geometrical configuration of this neutron irradiator installed at ex-Ankara Nuclear Research and Training Center (ANRTC) has been previously described in detail elsewhere (Karadag et al., 2003; Yu¨cel and Karadag, 2004). The analytical grade oxide powder samples obtained from Aldrich Inc. and Merck were diluted by mixing Al2O3 powder as a matrix so as to minimize errors due to neutron self-shielding effect. Because 27Al (100% abundance) isotope has sufficiently low neutron absorption cross section, ra = 0.231 b. The percentages of dilution for the samples were experimentally determined in order to obtain optimum counting statistics in the measurements. Ten samples for each element were individually prepared. A set of 5 samples prepared for each element were used for obtaining Cd covered-irradiation data. The remaining 5 samples for each element were used for obtaining bare irradiation data. In addition, the thin Au and Mo foils were used as monitors. The powder samples were filled in the polystyrene tubes (6.5 mm diameter and 15 mm height). They were exposed to the neutrons in a fixed position of the irradiation hole. The samples were irradiated with 1 mm thick cylindrical Cd filter (10 mm diameter and 20 mm height) to obtain Cd-ratio values.
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The irradiated samples were measured by a high resolution c-ray spectrometer equipped with a coaxial p-type HP Ge detector (Canberra GC 11021) with a measured relative efficiency of 120.8%, an energy resolution of 1.95 keV, and a peak-to-Compton ratio of 85.7:1 at 1332.5 keV of 60Co. For c-ray shielding, a 10 cm thick Pb shield lined with a 1 mm thick Sn and 1.5 mm Cu thick (Canberra Model 767) was used. The shield is also jacketed by a 9.5 mm steel outer housing. To minimize scattered radiation from the shield, the detector was centred in it. The detector was interfaced to a Digital Spectrum Analyzer (DSA-1000) with a full featured 16 K channels ADC conversion/ MCA memory analyzer based on digital signal processing. DSA-1000 gamma spectrum analyzer operates through a commercial Genie-2000 software. The net peak areas under the full energy peaks were evaluated both manually and the interactive peak fitting module of the Genie-2000 software. Each spectrum was collected in 4096 channels memory with a gain of 0.52 keV/channel, and in the live-time mode. The samples were counted at a distance of 10 cm from the detector to keep possible true coincidence effects at a reasonably low level (Yu¨cel et al., 2007), although the Cdratios can cancel out the true coincidence effects. The counting periods were high enough to ensure good statistical quality of data. Background measurements were subtracted from the sample spectra. The suitable waiting times were employed to minimize dead time losses and eliminate the possible contributions of 843.8 keV gamma ray from 27Mg (9.45 min) activity to the 846.7 keV peak of 56Mn and ensure the isomer (m) level, 165mDy (1.257 min) with a 97.6% IT (isomeric transition) decaying to the ground (g) level, 165gDy (2.334 h). For the efficiency calibration of the used Ge detector as a function of energy, the powder radioactive standard containing a mixture of 241Am, 109Cd, 57Co, 123mTe, 51Cr, 113 Sn, 85Sr, 137Cs, 60Co and 88Y radionuclides (purchased from the NIST traceable Isotope Products Laboratories Inc.) was used. 3. Determination of effective resonance energy 3.1. Experimental determination of Er value The effective resonance energy, Er valid in a non-ideal epithermal neutron spectrum was firstly defined in the past by Ryves (1969) as follows: a Eref I 0 ðaÞ ¼ 00 ð1Þ I0 Er where I 00 and I 00 ðaÞ are the reduced resonance integral cross sections (i.e., 1/v-tail subtracted) for ideal 1/E and nonideal 1/E1+a epithermal neutron flux distribution. Eref is a suitably chosen reference energy, which general1y is taken as 1 eV. In theoretical basis, Er is assumed to vary slightly with the a parameter. However, it is reported that it can to a good approximation be calculated as an independent
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M.G. Budak et al. / Annals of Nuclear Energy 35 (2008) 1433–1439
value of a shape parameter according to the term a ð1 eVÞ ffi 1 (De Wispelaere and De Corte, 2003). Accordingly, the Q0(a) = (I0(a)/r0) in a real epithermal 1/ E1+a flux distribution at a given irradiation position, can also be related to Q0(=I0/r0) in an ideal 1/E epithermal flux distribution (De Corte et al., 1979; Simonits et al., 1984). Q0 0:429 0:429 þ ð2Þ Q0 ðaÞ ¼ ð1 eVÞa ð2a þ 1Þ EaCd Ear 1=2
With 0:429 ¼ 2 ðE0 =ECd Þ . In Eq. (2) above, thermal energy is E0 = 0.0253 eV, cadmium cut-off energy, ECd = 0.55 eV and effective resonance energy, Er (in eV). Since the cadmium cut-off energy, ECd is set at 0.55 eV for a small sample in a 1 mm thick Cd box (height/diameter ffi 2), Eq. (2) is only valid for the case of ECd = 0.55 eV in a non-ideal 1/E1+a epithermal distribution. On the other hand, since the Cd-ratio, RCd to be measured for an isotope is also related to the thermal to epithermal flux ratio, f by the following formula: f ¼ Q0 ðaÞ ½F Cd RCd 1
ð3Þ
For the effective resonance energy, Er the above Eqs. (1) and (2) can be rewritten as follows: 1=a f 0:429 Er;i ¼ ðQ0 0:429Þ F Cd RCd 1 ð2a þ 1Þ EaCd ð4Þ Taking into account neutron self-shielding factors, Gth and Gepi for a comparator (c) and an investigated isotope (x), the logarithmic form of Eq. (4) can be used as follows (Jovanovic et al., 1984, 1985): 0 1 f Gth;c Q0;x 0:429 ðF Cd;c RCd;c 1ÞGepi;c C a Er;x 1 A ln ¼ ln @ f Gth;x a Q0;c 0:429 Er;c Ca
et al., 1981). Nuclear and decay data used in the analyses for effective resonance energy determinations are given in Table 1. The equivalent 2200 m s1 thermal and epithermal neutron fluxes at the sample irradiation position of the 241 Am–Be neutron irradiator were measured to be /th = (1.5 ± 0.2) 104 and /epi = (1.4 ± 0.1) 103 n cm2 s1, respectively. The thermal to epithermal neutron flux ratio at the same position was determined to be f = 10.42 ± 0.31 using 197Au monitor (Yu¨cel and Karadag, 2004). In addition, the deviation of the epithermal neutron flux distribution (characterized by the parameter a) in the particular irradiation should be known in advance (De Corte et al., 1979,1981). Hence, the extent of non-ideality of epithermal flux shape, a-shape factor at the sample irradiation position for the irradiation hole used of the present neutron irradiator was taken to be 0.083 ± 0.016, which was experimentally determined by dual monitor method using 98Mo and 197Au isotopes (Yu¨cel and Karadag, 2004). The thermal and epithermal self-shielding factors (Gth and Gepi) used in Eq. (5) for the powder mixtures filled in the polystyrene tubes were calculated using the procedures for the case of the irradiations in an isotopic neutron field (Karadag et al., 2003; Karadag and Yu¨cel, 2004,2005; Yu¨cel and Karadag 2005). But those factors for the case of Au and Mo-foils exposed to the same neutron field were calculated by the Nisle’s approximation (Gilat and Gurfinkel, 1963). The required nuclear data (e.g., resonance parameters, absorption, scattering, total microscopic cross-sections, etc.) were taken from JENDL-3.3 and NUDAT online data libraries. The calculated neutron self-shielding factors are given in Table 2. 3.2. Theoretical calculation of Er value
ðF Cd;x RCd;x 1ÞGepi;x
ð5Þ Ca ¼
0:429 ð2a þ 1Þ EaCd
þ In Eq. (5) the cadmium ratio, RCd ¼ A sp =Asp can easily be calculated from the measured specific activities of the isotope, by the following: N p =tc N p =tc þ Asp ¼ and Asp ¼ ð6Þ w S D C bare w S D C Cd þ where A sp and Asp are specific activities obtained after a bare and Cd-covered isotope irradiation; Np is net number of counts under the full-energy peak collected during measuring (live) time, tc; w is mass of irradiated element; S=1 ektirr is saturation factor with k = decay constant, tirr = irradiation time; D ¼ ektd is decay factor with td = decay time; C ¼ ½1 expðktr Þ=ktr is measurement factor correcting for decay during the true time, tr for a measurement. Cadmium transmission factors for epithermal neutrons, FCd for the isotopes of interest, according to the definition of ECd = 0.55 eV are taken as unity but may be different from unity fore some isotopes (El Nimr
In neutron activation analysis of elemental composition of materials, the occurrence of ‘‘resonances” in total and capture cross sections is a function of neutron energy. Therefore, for the aspect of the effective resonance energy
Table 2 The calculated neutron self-shielding factors for the diluted powder samples and foils The samples
Isotope
Thermal self-shielding factor including scattering, Gth
Epithermal self-shielding factor, Gepi
Al2O3–3.4% MnO2 Mo 0.025 mm-foil Au 0.0005 mm-foil Al2O3–4.1% Ga2O3 Al2O3–2.4% As2O3 Al2O3–3.8% Dy2O3 Al2O3–5.0% Er2O3
55
0.997 0.999a 1.000a 0.998 0.998 0.947 0.983
0.903 0.992b 0.925c 0.907 0.900 0.830 0.822
Mn Mo 197 Au 71 Ga 75 As 164 Dy 170 Er 98
a Calculated by Nisle’s approximation, including scattering effect, given in Gilat and Gurfinkel (1963). b Calculated by approximation given in Beckurts and Wirtz (1964). c IAEA and Technical Reports (1970).
M.G. Budak et al. / Annals of Nuclear Energy 35 (2008) 1433–1439
of an isotope, it can usually be utilized by the following approximate expressions. One obtains: P ri Cc;i ln Er;i ln Er ¼
i
Er;i
P
ð7Þ
ri Cc ;i Er;i
i
where ri is partial capture cross-section at the maximum of the ith resonance energy, Er,i and Cc,i is the radiative width of the ith resonance energy. It is assumed in Eq. (7) that resonance self-shielding is negligible, which is certainly the case when using sufficiently diluted samples. The latest resonance data taken from JENDL 3.3 (Shibata et al., 2002) and JEFF-3.1 (2005), General Purpose Neutron File OECD-NEA evaluated data library are used in this study. The Er -values resulted from Eq. (7) are also given in Table 4. This approximation was first used by Moens et al. (1979), in which neutron widths, Cn are neglected. The latter is that Er -value can also to a good approximation be calculated by assuming its a independence according to the term (1 eV)a 1 that are omitted. P wi ln Er;i ln Er ¼ i P ð8Þ wi i
where the weighting factor wi is given by gCc Cn 1 wi ¼ 2 C i E r;i
ð9Þ
Table 3 The measured effective resonance energy values obtained by dual monitors Reaction
71
Ga(n, c)72Ga As(n, c)76As 164 Dy(n, c)165Dy 170 Er(n, c)171Er 75
Experimental effective resonance energy value, Er (eV) Using 55Mn monitor
Using 98Mo monitor
Weighted average
173.3 ± 47.1 111.7 ± 30.3 223.8 ± 60.7 128.5 ± 35.1
175.8 ± 57.0 113.3 ± 36.7 227.0 ± 73.5 130.4 ± 42.4
174 ± 36 112 ± 23 225 ± 47 129 ± 27
where g = (2J + 1)/2(2I + 1) is the statistical weight factor being I and J the spin of the target nucleus and the resonance state of the neutron captured compound nucleus, Cc is the radiative width, Cn is the neutron width, and C = Cc + Cn is the total width of resonance. The resonance data taken from the recent literature (Mughabghab, 1984; JENDL-3.3 et al., 2002; JEFF-3.1, 2005) are used to calculate the Er -values by Eq. (8). 4. Results and discussion The Er -values for the isotopes being investigated were obtained by Eq. (5) using the experimentally determined Cd-ratios and the adopted nuclear data given in Table 1, respectively. The obtained results for Er -values relative to the Er -value of 55Mn and 98Mo monitors are given in Table 3. The Er -values of 55Mn and 98Mo monitors used in the present experiment are remarkably different each other but they are intermediate Er -values and cover the range of Er -values for the isotopes of interest, thus allowing to be appropriate range for the resonance energy regions ( 50–10,000 eV) of some isotopes. As can be seen in Table 3, a consistency between the results obtained by 55Mn and those obtained by 98Mo for each isotope being measured is found. This leads to more accurate results since, in general, the main feature of the comparator methods compensate for some systematic errors, which may contribute to the measured results. Two different monitors with the sufficiently known cross sections also allowed to check for the possible differences in the measured results. The main sources of uncertainty in the experimentally determined Er -values given Table 3 are mainly due to the a-shape factor(19.3%), the monitor effective resonance energy values (10.9% for 55Mn and 19.9% for 98Mo), and the resonance integral to thermal neutron cross section ratio, Q0 (within range of 0.2–13.6%). On the other hand, the measurement uncertainties on the Cd-ratios determined from the specific activities are generally found to be less than 2.5%, and thus they are not an important component
Table 4 Experimentally an theoretically determined effective resonance energy, Er -values for Reaction
Ga(n, c)72Ga As(n, c)76As 164 Dy(n, c)165Dy 170 Er(n, c)171Er 71
75
a b c d e f
1437
71
Ga,
75
As,
164
Dy and
Experimental effective resonance energy value
Theoretically calculated effective resonance energy values
This work
This workc
170
Er
Literature
Er (eV)
Er (eV) [from Eq. (7)]a
[C/E]
174 ± 36 112 ± 23 225 ± 47 129 ± 27
180 117 146 114
1.034 1.045 0.649 0.884
b
Er (eV) [from Eq. (8)]d
[C/E]
153 115 221 123
1.027 1.027 0.982 0.953
b
Er (eV) [from Eq. (7)]e
[C/E]b
Er (eV) [from Eq. (8)]f
[C/E]b
152 102 145 –
0.874 0.911 0.644 –
154 ± 18 106 ± 36 224 ± 11 129 ± 3
0.885 0.946 0.996 1.000
Calculated by Eq. (7) based on Moens et al. (1979)’s approximation using recent resonance data taken from JENDL 3.3 and JEFF 3.1 data libraries. C/E means that the ratio of the theoretically calculated value/the experimentally determined value. Uncertainties are not given due to no uncertainty quoted in the used data. Calculated by Eq. (8), using recent resonance data taken from JENDL 3.3 and JEFF 3.1 data libraries. Referenced by Moens et al. (1979). Referenced by Jovanovic et al. (1987).
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in the overall uncertainty estimation. However, in the overall uncertainty budget, it is not possible to reduce the overall uncertainty of about 20% on the final results for Er -values of the isotopes being investigated since the magnitudes of uncertainties on the nuclear data propagated in Eq. (5). In addition, it was noted by Simonits et al. (1984) that 20% uncertainty on any Er -value obtained by Cd-ratio method could be acceptable, thanks to the large uncertainty reduction in the conversion of Q0 into Q0(a), as shown in Eq. (4). The present experimental results for the Er -values were compared with the present theoretically calculated values and the older ones, as given in Table 4. In general, the present experimental values agree with the calculated ones when using the newest resonance data within limits of the estimated uncertainty, except for the Er -value of 225 ± 47 eV for 164Dy. However, it implies that when Moens’ approximation based on Eq. (7) is used to calculate the Er -values, the results are not satisfactorily accurate even if currently available most accurate neutron resonance data are used. Because this Moens’s approximation was used in past, neglecting neutron widths, Cn. Whereas the Cn widths of the resonances vary in the range of 103–10 eV, and should not overlook although the Cn widths are considerably even for resonances of the same isotope. On contrary, the radiative widths, Cc taken into account in Eq. (7) vary within the range of 0.1–1 eV, and they are fairly constant, within one isotope, because of many c-ray exit channels (Postma et al., 2001). On the other hand, since there is no evidence that the Er value is dependent on the a-shape factor over the resonances (De Wispelaere and De Corte, 2003), the expanding of ðEr Þa factors in series should not be ignored for higher order terms for Er and a-values in the integrated Breit–Wigner expressions for all resonances as given by Moens et al. (1979). Consequently it seems that it may be regarded to the experimentally determined Er -values rather than the theoretical ones. The experimental results in Table 4 agree with the commonly used calculated values of Jovanovic et al. (1987) by 0.4–11.5%. For the above isotopes being investigated, it is found that there are still discrepancies within range of 3–15%, excepting the Er result for 164Dy isotope between the experimentally determined Er -values and the theoretical values when the recent resonance data used. It may suggest that the new experimental determinations of Er -values for other isotopes should have to be done, especially those used in k0 NAA standardization studies. Since the quantity and quality of the available resonance parameter data for the theoretical calculations of Er -values continuously improve, it is expected that discrepancies between the old calculated Er values and the recent ones have been observed in some degree. Acknowledgments The experiments in this work were performed in ex-Ankara Nuclear Research and Training Center (ANRTC) in
2004. Authors are grateful to the directorate of ex-ANRTC of Turkish Atomic Energy Authority for the permission to use the experimental facilities. References Beckurts, K.H., Wirtz, K., 1964. Neutron Physics. Springer-Verlag OGH, Berlin. De Corte, F., Simonits, A., 2003. Recommended nuclear data for use in the k0 standardization of neutron activation analysis. Atom. Data Nucl. Data 85, 47–67. De Corte, F., Moens, L., Sordo-El Hammami, K., Simonits, A., Hoste, J., 1979. Modification and generalization of some methods to improve the accuracy of a-determination in the 1/E1+a epithermal neutron spectrum. J. Radioanal. Chem. 52 (2), 305–317. De Corte, F., Sordo-El Hammami, K., Moens, L., Simonits, A., De Wispelaere, A., Hoste, J., 1981. The accuracy and precision of the experimental a-determination in the 1/E1+a epithermal reactor neutron spectrum. J. Radioanal. Chem. 62 (1–2), 209–255. De Corte, F., Moens, L., Jovanovic, S., Simonits, A., De Wispelaere, A., 1986. J. Radioanal. Nucl. Chem. 102, 37. De Wispelaere, A., De Corte, F., 2003. Recalibration of the irradiation facilities in the Thetis reactor, with an examination of the a versus E behavior in the keV neutron energy range. J. Radioanal. Nucl. Chem. 257 (3), 519–523. El Nimr, T., De Corte, F., Moens, L., Simonits, A., Hoste, J., 1981. Epicadmium neutron activation analysis (ENAA) based on the k0comparator method. J. Radioanal. Chem. 67 (2), 421–435. Gilat, J., Gurfinkel, Y., 1963. Self-shielding in activation analysis. Nucleonics 21 (8), 143–144. IAEA, Technical Reports, 1970. Series No: 107. Neutron Fluence Measurements. IAEA, Vienna. JEFF-3.1, 2005. Evaluated Data Library (updated on May, 2005). OECD Nuclear Energy Agency. http://www.nea.fr/html/dbdata/JEFF/ JEFF31/JEFF31N6649_0.ASC. JENDL-3.3, K. Shibata, et al., 2002. Japanese Evaluated Nuclear Data Library Version 3 Revision-3: Program for Nuclear Data on the Web (
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