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Determination of effective resonance energies for the (n,γ) reactions of 152Sm and 165Ho by using dual monitors
Nuclear Instruments and Methods in Physics Research B 268 (2010) 2578–2584
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Determination of effective resonance energies for the (n,c) reactions of 152Sm and 165Ho by using dual monitors M.G. Budak a,1, M. Karadag a, H. Yücel b,* a b
Gazi University, Gazi Education Faculty, 06500 Teknikokullar-Ankara, Turkey Ankara University, Institute of Nuclear Sciences, 06100 Tandogan-Ankara, Turkey
a r t i c l e
i n f o
Article history: Received 26 May 2010 Received in revised form 29 June 2010 Available online 7 July 2010 Keywords: Effective resonance energy Thermal neutron Cross section 152 Sm 165 Ho Monitor Activation
a b s t r a c t The effective resonance energies Er for the (n,c) reactions of 152Sm and 165Ho isotopes were determined by using dual monitors (55Mn–98Mo) due to their favourable resonance properties. The samples were irradiated in an isotropic neutron field obtained from 241Am–Be neutron sources. The induced activities were measured with a high efficient, p-type Ge detector. The necessary correction factors for thermal neutron self-shielding (Gth), resonance neutron self-shielding (Gepi), self absorption (Fs) and true coincidence summing (Fcoi) effects for the measured c-rays were taken into account. Thus, the experimental Er values for above (n,c) reactions are found to be 8.65 ± 1.80 eV for 152Sm and 12.90 ± 2.69 eV for 165Ho isotopes, respectively. The Er -values for both 152Sm and 165Ho isotopes were also theoretically calculated from the newest resonance data in the literature. Theoretically calculated Er -values are estimated to be 8.34 eV and 8.53 eV for 152Sm by two different approaches, which are generally, much smaller than that the present experimental value by 1.4–3.6% for 152Sm. In case of 165Ho isotope, the theoretically calculated Er -value of 8.63 eV from the first approach deviates substantially from the measured value by about 33%, whereas the theoretical Er -value of 12.95 eV from the second approach agrees very well with our experimentally determined Er -value. The results show that the present experimental Er -values for 152 Sm and 165Ho isotopes agree with the calculated ones from the second approach within limits of the estimated uncertainty if the recently evaluated resonance data are used. However, it is worth noting that the results for Er -value calculated from the first approach are not satisfactorily accurate because of neglecting the neutron widths in that approach. Therefore, this study implies that it be regarded to the experimentally determined Er -value introduced in k0–NAA method for the determination of any analytical result rather than its theoretical value. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction In recent years, Holmium (Ho) and Samarium (Sm) are commonly used rare-earth elements that are attractive for therapeutic radionuclide production. For instance, 166mHo (1.21 103 years) and 166gHo (26.83 h) could be produced from the neutron capture reaction of 165Ho (100%) stable isotope. The first one is the longlived isotope which is generally used in laboratory calibration source. But the latter one is mostly used in radiotherapy due to its good decay properties such as high beta energies 1.773 MeV (48.7%) and 1.854 MeV (50.0%) and its prominent c-ray energy 80.574 keV (6.71%) [1,2]. It is reported that 166gHo due to favourable decay characteristics could be used in endovascular
* Corresponding author. Tel.: +90 3122128577; fax: +90 3122153307. E-mail addresses: [email protected] (M.G. Budak), [email protected], [email protected] (H. Yücel). 1 Tel.:+903122028275. 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.06.037
radionuclide therapy technique in liquid filled low pressure balloon angioplasty, which is a well known standard treatment for atherosclerotic coronary artery disease [3]. On the other hand, Sm is also mostly used in nuclear reactors as an absorber material because of high thermal and epithermal neutron cross sections. Apart from this, some Samarium isotopes have also a great importance in nuclear medicine for therapeutic purposes. For example, the radioactive isotope 153Sm, which is produced from 152Sm(n,c) reaction, is used as one of the b emitting therapeutic radioisotope in nuclear medicine for tumour therapy and bone pain palliation due to its high local beta dose per disintegration and suitable half-life (46.284 h) with beta energies 0.635 MeV (32.2%) and 0.705 MeV (49.6%), Because 153Sm disintegrates beta transitions to excited levels and to the ground state of 153Eu by emission of the prominent c-rays with 69.67 keV (4.85%) and 103.18 keV (30%) energy, while other c-ray emissions with energy up to 763.8 keV are relatively weak [4]. Additionally, it is reported that 153Sm has been tested and used in insect ecology (insects
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behaviors, such as dispersal) as ingested marker of some insects and detected to using neutron activation analysis (NAA) because the sensitivity of its detection by NAA is high [5]. The motivation for the present measurements for the reactions 165 Ho(n,c)166gHo and 152Sm(n,c)153gSm was the discrepancies among effective resonance energies. Because the effective resonance energies as well as thermal neutron and resonance integral cross sections are important in NAA analysis, e.g. in k0–NAA method. Additionally neutron activation cross section data are also commonly used in other studies related to the interaction of neutrons with matter [6–8]. On the other hand, since the launching of the NAA k0-standardization concept [9], great efforts have been made to perform NAA technique in absolute or single-comparator standardization mode for the neutron capture (n,c) activation analysis of any analyte. However, single comparator and absolute standardizations suffer from two important drawbacks [10]. 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 latter one, i.e., absolute standardization 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–NAA method) uses the concept of effective energy Er to correct for the effect of non-ideality 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-ideality of epithermal spectrum shape (deviation from ideal 1/E behaviour) 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 [11]. As well as the epithermal spectrum shape factor (a), the effective resonance energy (Er ) parameter of the nuclide to be activated is also another 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 [12,13]. Therefore, the inaccurate of effective resonance energy ðEr Þvalue can also give rise to more serious error on the analytical result because it is directly related to the 1/(Ear ) in the I0(a) definition [11,14]. From point of view of accurate NAA analysis, the question arises whether the used Er -values used are susceptible to updates of experimental resonance data due to their dependencies on individual resonance energies and resonance widths. 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 [15]. In addition, it is reported that, in some cases when the theoretical resonance data for Er -values are still incomplete, obsolete, inaccurate or even not known at all. Hence, the experimental determination of the Er -value for an isotope should be carried out [11]. It is therefore that in the present study it is aimed to determine the new experimental Er -values for the particular (n,c) reactions of 165 Ho and 152Sm target isotopes by using two different monitors 55 ( Mn–98Mo). The determination ofEr -values is based on the well-reliable cadmium ratio (Cd-ratio) measurements of the isotope being investigated since the Cd-ratio method greatly allows to obtain the reproducible results and thus eliminate the possible differences in the neutron spectrum between the thermal and epithermal activation on the condition that same irradiation and counting conditions is applied to each measurement. On the other hand, since the experimentally determined Er values for 165Ho and 152Sm isotopes do not appear at all in surveying literature, those Er -values theoretically calculated for the above isotopes using the recent resonance parameter data could also be compared with each other. It is thought that this would be helpful in determination of Er -values since the quantity
and quality of the available resonance parameters’ data in the present literature improve continuously. 2. Experimental Each of the samples was separately mixed with a sufficient amount of Al2O3 powder to reduce to some degree the neutron self shielding effects. Then, the samples (Al2O3 + Ho2O3 and Al2O3 + Sm2O3) were filled in the 1 mm thick polystyrene tubes (6.5 mm radius and 6.25 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 to obtain Cd-ratio values. 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 as given in Table 1, together with the percentage dilution, and their neutron self-shielding factors. The thermal and epithermal self-shielding factors (Gth and Gepi) for the powder mixtures filled in the polystyrene sample tubes were calculated using the procedures for the case of the irradiations in an isotopic neutron field [6,16–18]. But those factors for the case of Au and Mo-foils exposed to the same neutron field were calculated by the Nisle’ approximation [19]. The required nuclear data (e.g. resonance parameters, absorption, scattering, total microscopic cross-sections, etc.) were taken from JENDL-3.3 [20] and NUDAT [21] online data libraries. A set of five samples was prepared for each element for obtaining Cd covered-irradiation data. The remaining a set of five samples for each element was then used for obtaining bare irradiation data. In addition, the thin foils of Au and Mo were also irradiated as monitor isotopes. The irradiations were performed in an isotropic neutron field obtained from 241Am–Be neutron sources with total activity 3 592 GBq. The sources were immersed in a paraffin moderator and shielded with 1 mm thick Cd sheet and lead bricks, which was installed at ex-Ankara Nuclear Research and Training Center (ANRTC). The detailed geometrical configuration of this neutron irradiator has been previously described, elsewhere [7,16,22]. The irradiated samples were measured by using a c-ray spectrometer with a p-type, coaxial high pure Ge detector (Canberra Model 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. The Ge crystal has 82 mm diameter and 85.5 mm length mounted in a 101.6 mm diameter Al-end cap. The detector was installed in a 10 cm thick Pb shield lined with a 1 mm thick Sn and 1.5 mm Cu thick (Canberra Model 767) for reducing Pb X-rays in the 72–88 keV. The lead shield was also jacketed by a 9.5 mm steel outer housing. The detector was interfaced to a digital spectrum analyzer (Canberra DSA-1000) with a full featured 16 K ADC/MCA analyzer, based on digital signal pro-
Table 1 The calculated neutron self-shielding factors for the used samples. Irradiated samples
Target isotope
Thermal neutron self shielding factor including scattering, Gth
Epithermal neutron self shielding factor, Gepi
Al2O3-3.4% MnO2 Al2O3-1.05% Sm2O3 Al2O3-1.2% Ho2O3 Mo 0.025 mm-foil Au 0.0005 mm-foil
55
0.997 0.913 0.997 0.999a 1.000a
0.903 0.812 0.890 0.992b 0.925c
Mn Sm 165 Ho 98 Mo 197 Au 152
a Calculated by Nisle approximation, including scattering effect, given in Gilat and Gurfinkel (1963) [19]. b Calculated by approximation given in Beckurtz and Wirtz (1964) [23]. c IAEA (1970) [24].
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Table 2 Measured and calculated efficiencies for a small cylinder tube placed at a 10 cm distance far from a 120.8% relative efficient Ge detector. Nuclide
241
Am Cd Co 123m Te 113 Sn 137 Cs 88 Y 60 Co 60 Co 88 Y 109 57
Gamma ray energy (keV)
59.54120 88.03360 122.0606 159.000 391.698 661.657 898.0420 1173.228 1332.492 1836.063
Full-energy peak efficiency, ep Experimental*
Fitted**
MCNP calculated***
0.0110 ± 0.0005 0.0193 ± 0.0007 0.0207 ± 0.0007 0.0187 ± 0.0006 0.0119 ± 0.0004 0.0087 ± 0.0003 0.0072 ± 0.0002 0.0059 ± 0.0002 0.0056 ± 0.0002 0.0046 ± 0.0001
0.0122 0.0214 0.0206 0.0187 0.0119 0.0087 0.0071 0.0060 0.0056 0.0046
0.0110 0.0184 0.0200 0.0191 0.0118 0.0085 0.0072 0.0062 0.0057 0.0046
True coincidence summing Factor**** Fcoi
Self attenuation factor***** Fs
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9811 0.9808 0.9799 0.9801
1.123 1.090 1.078 1.071 1.050 1.041 1.035 1.031 1.029 1.025
*
The main uncertainty sources are 1.5–2% due to source activities, 0.1–1.2% due to counting statistics, and <1% due to systematic ones. 2 Efficiency data were fitted to a logarithmic polynomial function in the form: ep ¼ expða þ b:ln E þ c:ln E þ d:ln 3 EÞ, where a = 1.918828, b = 5.037222, c = 3.444946, d = 0.698902 in the low energy region of 59–159 keV, and a = 5.010486, b = 0.636695, c = 0.000219, d = 0.022974 in the high energy region of 159–1836 keV. *** The MCNP calculated efficiency data were obtained from GESPECOR Ver. 4.2 program in which both Fcoi and Fs factors were taken into account. **** Fcoi factors calculated for a 1 mm-thick polystyrene cylinder tube of 13 mm diameter and 6.25 mm height, placed at a 10 cm distance far from the 120.8% relative efficient Ge detector. ***** Fs factors were estimated for the same tube geometry but containing SiO2 matrix spiked with nuclides. **
cessing operating through a Genie-2000 gamma spectroscopy software. Each spectrum was collected in 4096 channels memory with an amplifier gain of 0.52 keV/channel, thus covering up to about 2.2 MeV c-ray energy. The net peak areas under the full-energy peaks were evaluated both manually and the interactive peak fitting module of the Genie-2000 software in which the observed counts can be fitted to a normal Gaussian peak without tail, and subtracted either a linear or a stepwise background continuum. The samples were counted at a distance of 10 cm from the detector in order to keep possible true coincidence (TCS) effects at a reasonably low level although the Cd-ratios cancel out the true coincidence effects on the peak areas resulting in specific activities [25]. The chosen 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 not also the dead time and pile-up losses and but for eliminating the possible contributions from the interfering 843.74 keV (71.8%) c-ray emitted from 27Mg (9.458 min) to the 846.77 keV (98.9%) analytical peak of 56Mn (2.5785 h). For the characterization of thermal flux, thermal to epithermal ratio factor (f) of the neutron irradiator unit, it was required to obtain a full-energy efficiency calibration of the Ge detector as a function of energy. To do this, the multi-nuclide standard containing 241 Am, 109Cd, 57Co, 123mTe, 51Cr, 113Sn, 85Sr, 137Cs, 60Co and 88Y radio nuclides spiked in sand matrix (SiO2, density:1.7 ± 0.1 g cm3) purchased from Isotope Products Laboratories Inc traceable to NIST was used. Full-energy peak efficiencies, TCS correction factors (Fcoi) are given in Table 2 together with self absorption (Fs) coefficients for the c-rays of interest. 3. Effective resonance energy determination By a definition, 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 has an importance because it replaces all the resonance energies lying in epithermal region, which is described by a modified 1/E1+a behaviour in Høgdahl formalism [13]. It should be noted that the-value is very sensitive to the accuracy of the Q0(a) value for the monitor used, while applying the single comparator method in the thermal activation analysis [26]. In Høgdahl formal-
ism, the neutron spectrum is divided into two parts, i.e., the thermal and the epithermal region in which the (n,c) activation due to fast neutrons could generally be neglected. Moreover, the division between the thermal and epithermal part of the spectrum is definitely arbitrary and the so-called Cd cut-off energy for a 1 mm thick Cd cover, which is internationally accepted as ECd = 0.55 eV in Høgdahl convention in which for a small sample in a 1 mm thick Cd box. ECd = 0.55 eV value is the lower limit of the resonance integral cross section valid in a non-ideal 1/E1+a epithermal distribution. Although it is not possible to avoid the error in the Er -value to be measured for the isotope due to an uncertainty in the Q0(a) value of the monitor. This can be adjusted in the determination of Er -values by choosing the appropriate Er;c monitor isotopes whose Q0(a) values and other parameters are more accurate and close to those of the isotopes being measured. Accordingly, 55Mn and 98Mo target isotopes having favourable nuclear properties were chosen as the Er;c monitor in the present work. As previously described in detail [15,25], these monitor isotopes 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, especially in high flux irradiations. In addition, most of the resonance captures of 55 Mn and 98Mo occurs at a relatively higher neutron energy region, for example, the first principal resonance of 55Mn is seen at 337 eV and that of 98Mo is at 468 eV [20], which are quite far from 1/v region, thus making their well-established effective resonance energies, as given in Table 3. In following sections of the paper, experimental and theoretical bases of the Er -value determination is briefly given, for the description of data analysis is required to determine effective resonance energy concept for the (n,c) reactions of the target isotopes by the activation method when using Cd-ratios of the isotopes being investigated relative to those of Cd-ratios of monitors such as 55Mn and 98Mo. 3.1. Data analysis for experimentally determined Er -value As is known, the ideal 1/E epithermal neutron spectrum, the resonance integral cross section, I0, including 1/v tail of thermal neutron spectrum defined in the literature [27] is not valid in a non-ideal, real epithermal neutron spectrum and that such a deviating epithermal neutron fluence distribution can be approximated by U(E) = 1/E1+a. Accordingly, a resonance integral I0(a) for a real epithermal neutron spectrum characterized by a-shape factor
Ho (t1/2 = 1200 y, ra = 3.4 b) gives no IT to 166Hof
ln
a
b
El Nimr et al. (1981) [35]. Kolotov and De Corte (2003) [36]. c NUDAT (Sonzogni et al., 2005)[21]. d Simonits et al. (1981)[37]. e El Nimr, T. and Ela-Assaly, F.M. (1987) [38]. f De Corte et al. (1989; 2003) [10,39]. * Self attenuation calculated using mass attenuation coefficients taken from NIST [40] and KORDATEN databases, respectively. ** True coincidence summing correction factors calculated by using GESPECOR Ver 4.2 software with a MCNP modelling for the present detector-source geometry.
165m
26.824(12) h 10.9(2.4%) – 0.99 Ho(n,c)166gHo 165165
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[28]. The effective resonance energy, Er -value as the basis firstly defined by Ryves [29] can be estimated by the following equation [11,28,30].
Monitor Investigated isotope Investigated isotope 0.9998 0.9878 0.9973 0.9996 0.9951 0.9950 1.0041 1.0019 1.0973 1.0666 1.0602 1.0133 1.0124 1.0121 95.58 4.73(5) 29.25 6.71(8) 0.92 0.182(3) 0119(20) 411.802(17) 69.67300(13) 103.1801(17) 80.574(8) 1379.437(6) 1581.834(7) 1662.439(6) 2.695(21) days 46.50(21) h 15.7(1.8%) 14.4(2.1%) 0.991 0.982 152
197
Au(n,c)198Au Sm(n,c)153Sm
5.65 ± 0.40 –
1.053(2.6%) 53.1(6.3%) 468 ± 51 241 ± 48 1.00 1.00 Mn(n,c)56Mn Mo(n,c)99Mo(b)99mTc 98
55
energy, Er (eV)b
1.0001 1.0531 1.0358 1.0042 1.0052 1.0053 1.0053
0.9921 0.9988 1.0140 98.9(3) 4.52(24) 2.5789(1) h 65.94(1) h
846.754(20) 140.511(1)
1.0104 1.0062
Fcoi Fs (from GESPECOR) Fs (from NIST) Emission probability,c (%) Energy (keV)
The measured gamma-rayc Half-lifec Q0 (=I0/r0)b s(%) Effective resonance
Cadmium transmission factor, FCda,e Nuclear reaction
Table 3 Nuclear data for the isotopes, self attenuation and true coincidence summing correction factors for the measured gamma-rays.
Self attenuation factor*
True coincidence summing**
Notes
Asp(Mo)/Asp(Mo + Tc),=0.05992d, where Asp is specific activities of isotope investigated.
Monitor Monitor
M.G. Budak et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2578–2584
Q 0 0:429 f Gth ð2a0:429 Gepi ðF cd Rcd 1Þ þ1ÞEaCd
¼ a ln Er
ð1Þ
In Eq. (1), the a parameter exists in both sides of the equation. It can therefore be initially set to zero, followed by an iterative procedure until it converges to a constant value [31,32]. In this work, the a parameter determined by using the measured Cd-ratios of monitor isotopes 55Mn and 98Mo, because their Q0(a), Er -values and other essential parameters are known more accurately. The presently used iterative procedure is required to fit the experimental data, when plotting left hand term of the Eq. (1) versus ‘‘ln Er ” for each monitor. Thus from the expected straight line, a-shape factor is derived from the slope of the obtained straight line as shown in Fig. 1. Thus, in this work, the extent of non-ideality of epithermal flux shape, i.e., the a-shape factor at the sample irradiation position was determined to be 0.0828 ± 0.0097 for all irradiations. For the effective resonance energy, Eq. (1) can also be re-written for the investigated (Er ) and the monitor isotopes (Er;c ) as follows [33,34]:
1=a Er ¼ ðQ o 0:429Þ= ð½f Gth =½ðF Cd RCd 1ÞGepi Þ C a
ð2Þ
where pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C a ¼ 0:429=½ð2a þ 1ÞEaCd and 0:429 ¼ 2 E0 =ECd ¼ 2 0:0253=0:55. Thus, the effective resonance energy of the investigated isotope from the ratio of (Er =Er;c ) can easily be determined by taking into account the necessary factors such as neutron self-shielding factors, Gth and Gepi for both monitor (c) and investigated isotope [15,34]. þ The Cd-ratio RCd ¼ A sp =Asp can easily be calculated from the measured specific activities of the isotope, as follows:
Asp ¼ fNp =ðwSDCtm Þgbare and Aþsp ¼ fNp =ðwSDCtm ÞgCd
ð3Þ
þ where A sp and Asp are specific activities obtained after a bare and Cdcovered isotope irradiation; Np is net number of counts under the full-energy peak collected during measuring (live) time, tm; w is mass of irradiated element; S ¼ 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=kt r 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 [35]. Nuclear data used for the investigated isotopes, self attenuation and true coincidence summing correction factors for the measured gamma-rays are given in Table 3. The equivalent 2200 m s1 thermal and epithermal neutron fluxes at the sample irradiation position of the 241Am–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 [22].
3.2. Theoretically calculation of Er -value 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 of an isotope, it can usually be
M.G. Budak et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2578–2584
-
-
-
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ln Fig. 1. Experimental determination of a-shape factor in the irradiation position in the used Am–Be source geometry.
utilized by the following approximate expressions. As the first approach, one can use:
ln Er ¼
X
X
ri Cc;i ln Er;i =Er;i =
i
ri Cc;i =Er;i
ð4Þ
i
where ri is partial capture cross-section, Eri is the i-th resonance energy and Cc,i is the radiative width at the maximum of the i-th resonance energy. It is assumed in Eq. (4) that resonance self-shielding is negligible, which is the case when using sufficiently diluted samples. The newest resonance data is taken from JENDL 3.3. [20] and JEFF 3.1. [41], General Purpose Neutron File OECD-NEA Evaluated Data Library is used in this study. The Er -values resulted from Eq. (4) are also given in Table 5. This approximation was first used by Moens et al. [12], in which neutron widths, Cn are neglected. The second approach suggested by Jovanovic et al. [14] 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.
ln Er ¼
X
wi ln Er;i =
i
X
wi
ð5Þ
i
where the weighting factor wi is given by
wi ¼ ðg Cc Cn =CÞi ð1=E2r;i Þ
ð6Þ
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. For the evaluation of Eq. (5) for the Er -values, the newest resonance data are taken from the available recent literature [20,41–46]. 4. Results and Discussion The Er -values for the isotopes of interest were obtained by Eq. (2) using experimentally determined Cd-ratios and the relevant nuclear data given in Table 3, respectively. The results for Er -values Table 4 The measured effective resonance energy values obtained by dual monitors. Reaction
152 165
Sm(n,c)153gSm Ho(n,c)166gHo
Experimental effective resonance energy value, Er (eV) Using 55Mn monitor
Using 98Mo monitor
Weighted average
8.59 ± 2.34 12.82 ± 3.49
8.72 ± 2.83 13.01 ± 4.22
8.65 ± 1.80 12.90 ± 2.69
obtained by using dual monitor are given in Table 4. The 55Mn and Mo monitors used in the present experiment have intermediate Er -values that cover the range of Er -values for the isotopes of interest, thus allowing being appropriate range for the resonance energy regions (approximately 50–10,000 eV) of some isotopes. As can be seen in Table 4, a consistency between the results obtained by 55Mn and those obtained by 98Mo for each isotope being measured is found. This yields to more accurate results when the cadmium ratio method is used. It is therefore that two different monitors with the sufficiently well known cross sections are used to check for the possible differences in the measured results. The main sources of uncertainty in the experimentally determined Er -values given Tables 4 and 5 are mainly due to the a-shape factor (19–21%), 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%). In this work all uncertainties are given with in ±1r confidence interval (68% confidence level). 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 in the overall uncertainty estimation. However, they are introduced in the overall uncertainty budget. On the other hand, 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. (2). In addition, it was noted by Simonits et al. [11] 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). Since other experimentally determined Er -values for the 152Sm and 165Ho isotopes do not appear in literature at all; the present experimental results are compared only with the present and earlier calculated values by two different approaches described in Section 3.2. Therefore, the present experimental results for the Er -values are given in Table 5, together with the present theoretically calculated values and old theoretical ones. In general, the present experimental values agree with the calculated ones when using the newest resonance data within limits of the estimated uncertainty. However, it implies that when the first approach (Moens’ approach) based on Eq. (4) was used to calculate theoretically the Er -values, the results are not satisfactorily accurate even if currently available most accurate neutron resonance data appeared in literature are used. Because this Moens’ approach was used in past, neglecting neutron widths, Cn. Whereas the Cn widths of the resonances vary in the range 98
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M.G. Budak et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2578–2584 Table 5 Effective resonance energy Er -values for Reaction
152 165 a b c d e f
Sm(n,c)153Sm Ho(n,c)166gHo
152
Sm(n,c)153gSm and
165
Ho(n,c)166gHo reactions.
Experimental effective resonance energy value
Theoretically calculated effective resonance energy values
This work
This workc
Er (eV)
Er (eV) [from Eq. (4)]a
Deviation%b
Er (eV) [from Eq. (5)]d
Deviation%b
Er (eV) [from Eq. (4)]e
Deviation%b
Er (eV) [from Eq. (5)]f
Deviation%b
8.65 ± 1.80 12.90 ± 2.69
8.34 8.63
3.6 33.1
8.59 12.95
0.69 0.39
8.33 9.73
3.70 24.57
8.53 ± 0.09 12.3 ± 0.4
1.39 4.65
Literature
Calculated by Eq. (4) based on first approach [12] using recent resonance data taken from JENDL 3.3 and JEFF 3.1 data libraries. The percentage deviation means = 100 (C/E-1) where C is theoretically calculated value and E is experimentally determined value. Uncertainties are not given due to no uncertainty quoted in the used data. Calculated by the second approach [14] based on Eq. (5), using recent resonance data taken from JENDL 3.3 and JEFF 3.1 data libraries. The first approach Eq. (4) suggested by Moens et al. (1979) [12]. The second approach Eq. (5) suggested by Jovanovic et al. (1987) [14].
of 103–10 eV, and they should be considered in Er -value calculation although at first sight the Cn widths are considerably even for resonances of the same isotope. On the other hand, the radiative widths, Cc are taken into account in Eq. (4) whereas they vary within the range of 0.1–1 eV, and they are fairly constant, within one isotope, because of many c-ray exit channels [47]. Additionally, since there is no evidence that the Er -value is dependent on a the a-shape factor over the resonances [30], the expanding of E r 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. [12] in the first approach. Theoretically calculated Er -values are estimated to be 8.34 eV and 8.53 eV for 152Sm and they are, in general, much smaller than those experimental ones above by 1.4–3.6% for 152Sm when two different theoretical approaches are used. In case of 165Ho isotope, the theoretically calculated Er -value of 8.63 eV from the first approach (Moens’ approach) deviates substantially from the measured value by about 33%, whereas the theoretical Er -value of 12.95 eV from second approach (Jovanovic’s approach) agrees very well with the experimentally determined value. The present experimental Er -values agree with the theoretical ones calculated from the Jovanovic’ approach based on Eq. (5) within limits of the estimated uncertainty. However, it is noting that the results for Er calculated from the first approach are not satisfactorily accurate even if the recent resonance data are used in this approach. Because this Moens’ approach do not take into account the neutron widths at all. This implies that the experimentally determined Er -values might be preferred in the analyses, for example, introduced in k0-NAA method rather than the use of their theoretically determined Er -values. 5. Conclusion It is concluded from this study that, for more accurate Er -values for the isotopes, the new experimentally determined Er -values must be obtained rather than the use of the available theoretical ones. On the other hand, this is important because the quantity and quality of the available resonance parameter data continuously improve in recent databases. For theoretical calculations of Er -values, it is considered that discrepancies between the old calculated Er -values and the recent ones are due to mostly older resonance data. Acknowledgments The experiments in this study were performed in ex-Ankara Nuclear Research and Training Center (ANRTC). Authors are gratefully thanks for the directorate of ex-ANRTC of Turkish Atomic Energy Authority allowing us to use their experimental facilities.
References [1] Y.D. Hong, S.J. Choi, K.H. Kim, B.C. Shin, W.W. Park, S.H. Park, K.B. Park, 166Hocoated balloon for vascular brachytherapy, Applied Radiation and Isotopes 58 (4) (2003) 455–462. [2] E. Dadachova, S. Mirzadeh, S.V. Smith, J. Knapp, F.F. Russ, E.L. Hetherington, Radiolabeling antibodies with Holmium-166, Applied Radiation and Isotopes 48 (4) (1997) 477–481. [3] M.A. Majali, M.C. Debnath, S.K. Saxena, S.H. Joshi, Preparation and evaluation of [166Ho] Holmium-dimethyl diethylenetriaminepentaaceticacid (DMDTPA) as potential radiopharmaceutical for endovascular radiation therapy (EVRT), Applied Radiation and Isotopes 56 (6) (2002) 863–869. [4] S.Y.F. Chu, L.P. Ekström, R.B. Firestone, Table of Radioactive Isotopes, The Lund/ LBNL Nuclear Data Search Version 2.0, February 1999 Web page:
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[20] 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). [21] NuDat, Nuclear Data Retrieval Program (
[34] S. Jovanovic, F. De Corte, A. Simonits, J. Hoste, The Er – comparator technique for the experimental determination of effective resonance energies, Journal of Radioanalytical and Nuclear Chemistry 92 (1985) 399–406. [35] T. El Nimr, F. De Corte, L. Moens, A. Simonits, J. Hoste, Epicadmium neutron activation analysis (ENAA) based on the k0 -comparator method, Journal of Radioanalytical Chemistry 67 (2) (1981) 421–435. [36] V.P. Kolotov, F. De Corte, An electronic database with a compilation of k0 and related data for NAA, Journal of Radioanalytical and Nuclear Chemistry 257 (3) (2003) 501–508. [37] A. Simonits, L. Moens, F. De Corte, A. De Wispelaere, J. Hoste, Absolute intensity of the 140.5 keV gamma-ray of 99Mo, Journal of Radioanalytical and Nuclear Chemistry 67 (1) (1981) 61–74. [38] T. El Nimr, F.M. Ela Assaly, Determination of the attenuation of epicadmium neutrons using the method of varying Cd-thickness, Journal of Radioanalitycal and Nuclear Chemistry 109 (1) (1987) 3–9. [39] F. De Corte, A. Simonits, k0-Measurements and related nuclear data compilation for (n,c) reactor neutron activation analysis, Journal of Radioanalytical and Nuclear Chemistry 133 (1) (1989) 43–130. [40] NIST The National Institute of Standards and Technology Standard Reference Database 126 (XCOM) tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients from 1 keV to 20 MeV for elements Z = 1 to 92 Web Page: (01.07.2009). [41] JEFF-3.1, 2005. Evaluated data library (updated on May, 2005). OECD Nuclear Energy Agency. . [44] ENDF-VII Point wise library. 62-Sm-152 BNL, KAERI, Evaluation, February 2006 by Kim, Mughabghab, Herman, Oblozinsky and 67-Ho-165 LANL, BNL evaluation January 2005 P.G. Young, Mughabghab. . [45] S.F. Mughabghab, fifth ed., Atlas of Neutron Resonances, Resonance Parameters and Thermal Cross Sections Z=1–100, Elsevier, 2006. [46] S.F. Mughabghab, Neutron Cross Sections, vol. 1, Part B, Z = 61–100, NNDC, BNL, Academic Press Inc., Uptown, New York, 1984. [47] H. Postma, M. Blaauw, P. Bode, P. Mutti, F. Corvi, P. Siegler, Neutron-resonance captures analysis of materials, Journal of Radioanalytical and Nuclear Chemistry 248 (1) (2001) 115–120.
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Determination of effective resonance energies for the (n,c) reactions of 152Sm and 165Ho by using dual monitors M.G. Budak a,1, M. Karadag a, H. Yücel b,* a b
Gazi University, Gazi Education Faculty, 06500 Teknikokullar-Ankara, Turkey Ankara University, Institute of Nuclear Sciences, 06100 Tandogan-Ankara, Turkey
a r t i c l e
i n f o
Article history: Received 26 May 2010 Received in revised form 29 June 2010 Available online 7 July 2010 Keywords: Effective resonance energy Thermal neutron Cross section 152 Sm 165 Ho Monitor Activation
a b s t r a c t The effective resonance energies Er for the (n,c) reactions of 152Sm and 165Ho isotopes were determined by using dual monitors (55Mn–98Mo) due to their favourable resonance properties. The samples were irradiated in an isotropic neutron field obtained from 241Am–Be neutron sources. The induced activities were measured with a high efficient, p-type Ge detector. The necessary correction factors for thermal neutron self-shielding (Gth), resonance neutron self-shielding (Gepi), self absorption (Fs) and true coincidence summing (Fcoi) effects for the measured c-rays were taken into account. Thus, the experimental Er values for above (n,c) reactions are found to be 8.65 ± 1.80 eV for 152Sm and 12.90 ± 2.69 eV for 165Ho isotopes, respectively. The Er -values for both 152Sm and 165Ho isotopes were also theoretically calculated from the newest resonance data in the literature. Theoretically calculated Er -values are estimated to be 8.34 eV and 8.53 eV for 152Sm by two different approaches, which are generally, much smaller than that the present experimental value by 1.4–3.6% for 152Sm. In case of 165Ho isotope, the theoretically calculated Er -value of 8.63 eV from the first approach deviates substantially from the measured value by about 33%, whereas the theoretical Er -value of 12.95 eV from the second approach agrees very well with our experimentally determined Er -value. The results show that the present experimental Er -values for 152 Sm and 165Ho isotopes agree with the calculated ones from the second approach within limits of the estimated uncertainty if the recently evaluated resonance data are used. However, it is worth noting that the results for Er -value calculated from the first approach are not satisfactorily accurate because of neglecting the neutron widths in that approach. Therefore, this study implies that it be regarded to the experimentally determined Er -value introduced in k0–NAA method for the determination of any analytical result rather than its theoretical value. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction In recent years, Holmium (Ho) and Samarium (Sm) are commonly used rare-earth elements that are attractive for therapeutic radionuclide production. For instance, 166mHo (1.21 103 years) and 166gHo (26.83 h) could be produced from the neutron capture reaction of 165Ho (100%) stable isotope. The first one is the longlived isotope which is generally used in laboratory calibration source. But the latter one is mostly used in radiotherapy due to its good decay properties such as high beta energies 1.773 MeV (48.7%) and 1.854 MeV (50.0%) and its prominent c-ray energy 80.574 keV (6.71%) [1,2]. It is reported that 166gHo due to favourable decay characteristics could be used in endovascular
* Corresponding author. Tel.: +90 3122128577; fax: +90 3122153307. E-mail addresses: [email protected] (M.G. Budak), [email protected], [email protected] (H. Yücel). 1 Tel.:+903122028275. 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.06.037
radionuclide therapy technique in liquid filled low pressure balloon angioplasty, which is a well known standard treatment for atherosclerotic coronary artery disease [3]. On the other hand, Sm is also mostly used in nuclear reactors as an absorber material because of high thermal and epithermal neutron cross sections. Apart from this, some Samarium isotopes have also a great importance in nuclear medicine for therapeutic purposes. For example, the radioactive isotope 153Sm, which is produced from 152Sm(n,c) reaction, is used as one of the b emitting therapeutic radioisotope in nuclear medicine for tumour therapy and bone pain palliation due to its high local beta dose per disintegration and suitable half-life (46.284 h) with beta energies 0.635 MeV (32.2%) and 0.705 MeV (49.6%), Because 153Sm disintegrates beta transitions to excited levels and to the ground state of 153Eu by emission of the prominent c-rays with 69.67 keV (4.85%) and 103.18 keV (30%) energy, while other c-ray emissions with energy up to 763.8 keV are relatively weak [4]. Additionally, it is reported that 153Sm has been tested and used in insect ecology (insects
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behaviors, such as dispersal) as ingested marker of some insects and detected to using neutron activation analysis (NAA) because the sensitivity of its detection by NAA is high [5]. The motivation for the present measurements for the reactions 165 Ho(n,c)166gHo and 152Sm(n,c)153gSm was the discrepancies among effective resonance energies. Because the effective resonance energies as well as thermal neutron and resonance integral cross sections are important in NAA analysis, e.g. in k0–NAA method. Additionally neutron activation cross section data are also commonly used in other studies related to the interaction of neutrons with matter [6–8]. On the other hand, since the launching of the NAA k0-standardization concept [9], great efforts have been made to perform NAA technique in absolute or single-comparator standardization mode for the neutron capture (n,c) activation analysis of any analyte. However, single comparator and absolute standardizations suffer from two important drawbacks [10]. 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 latter one, i.e., absolute standardization 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–NAA method) uses the concept of effective energy Er to correct for the effect of non-ideality 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-ideality of epithermal spectrum shape (deviation from ideal 1/E behaviour) 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 [11]. As well as the epithermal spectrum shape factor (a), the effective resonance energy (Er ) parameter of the nuclide to be activated is also another 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 [12,13]. Therefore, the inaccurate of effective resonance energy ðEr Þvalue can also give rise to more serious error on the analytical result because it is directly related to the 1/(Ear ) in the I0(a) definition [11,14]. From point of view of accurate NAA analysis, the question arises whether the used Er -values used are susceptible to updates of experimental resonance data due to their dependencies on individual resonance energies and resonance widths. 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 [15]. In addition, it is reported that, in some cases when the theoretical resonance data for Er -values are still incomplete, obsolete, inaccurate or even not known at all. Hence, the experimental determination of the Er -value for an isotope should be carried out [11]. It is therefore that in the present study it is aimed to determine the new experimental Er -values for the particular (n,c) reactions of 165 Ho and 152Sm target isotopes by using two different monitors 55 ( Mn–98Mo). The determination ofEr -values is based on the well-reliable cadmium ratio (Cd-ratio) measurements of the isotope being investigated since the Cd-ratio method greatly allows to obtain the reproducible results and thus eliminate the possible differences in the neutron spectrum between the thermal and epithermal activation on the condition that same irradiation and counting conditions is applied to each measurement. On the other hand, since the experimentally determined Er values for 165Ho and 152Sm isotopes do not appear at all in surveying literature, those Er -values theoretically calculated for the above isotopes using the recent resonance parameter data could also be compared with each other. It is thought that this would be helpful in determination of Er -values since the quantity
and quality of the available resonance parameters’ data in the present literature improve continuously. 2. Experimental Each of the samples was separately mixed with a sufficient amount of Al2O3 powder to reduce to some degree the neutron self shielding effects. Then, the samples (Al2O3 + Ho2O3 and Al2O3 + Sm2O3) were filled in the 1 mm thick polystyrene tubes (6.5 mm radius and 6.25 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 to obtain Cd-ratio values. 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 as given in Table 1, together with the percentage dilution, and their neutron self-shielding factors. The thermal and epithermal self-shielding factors (Gth and Gepi) for the powder mixtures filled in the polystyrene sample tubes were calculated using the procedures for the case of the irradiations in an isotopic neutron field [6,16–18]. But those factors for the case of Au and Mo-foils exposed to the same neutron field were calculated by the Nisle’ approximation [19]. The required nuclear data (e.g. resonance parameters, absorption, scattering, total microscopic cross-sections, etc.) were taken from JENDL-3.3 [20] and NUDAT [21] online data libraries. A set of five samples was prepared for each element for obtaining Cd covered-irradiation data. The remaining a set of five samples for each element was then used for obtaining bare irradiation data. In addition, the thin foils of Au and Mo were also irradiated as monitor isotopes. The irradiations were performed in an isotropic neutron field obtained from 241Am–Be neutron sources with total activity 3 592 GBq. The sources were immersed in a paraffin moderator and shielded with 1 mm thick Cd sheet and lead bricks, which was installed at ex-Ankara Nuclear Research and Training Center (ANRTC). The detailed geometrical configuration of this neutron irradiator has been previously described, elsewhere [7,16,22]. The irradiated samples were measured by using a c-ray spectrometer with a p-type, coaxial high pure Ge detector (Canberra Model 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. The Ge crystal has 82 mm diameter and 85.5 mm length mounted in a 101.6 mm diameter Al-end cap. The detector was installed in a 10 cm thick Pb shield lined with a 1 mm thick Sn and 1.5 mm Cu thick (Canberra Model 767) for reducing Pb X-rays in the 72–88 keV. The lead shield was also jacketed by a 9.5 mm steel outer housing. The detector was interfaced to a digital spectrum analyzer (Canberra DSA-1000) with a full featured 16 K ADC/MCA analyzer, based on digital signal pro-
Table 1 The calculated neutron self-shielding factors for the used samples. Irradiated samples
Target isotope
Thermal neutron self shielding factor including scattering, Gth
Epithermal neutron self shielding factor, Gepi
Al2O3-3.4% MnO2 Al2O3-1.05% Sm2O3 Al2O3-1.2% Ho2O3 Mo 0.025 mm-foil Au 0.0005 mm-foil
55
0.997 0.913 0.997 0.999a 1.000a
0.903 0.812 0.890 0.992b 0.925c
Mn Sm 165 Ho 98 Mo 197 Au 152
a Calculated by Nisle approximation, including scattering effect, given in Gilat and Gurfinkel (1963) [19]. b Calculated by approximation given in Beckurtz and Wirtz (1964) [23]. c IAEA (1970) [24].
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Table 2 Measured and calculated efficiencies for a small cylinder tube placed at a 10 cm distance far from a 120.8% relative efficient Ge detector. Nuclide
241
Am Cd Co 123m Te 113 Sn 137 Cs 88 Y 60 Co 60 Co 88 Y 109 57
Gamma ray energy (keV)
59.54120 88.03360 122.0606 159.000 391.698 661.657 898.0420 1173.228 1332.492 1836.063
Full-energy peak efficiency, ep Experimental*
Fitted**
MCNP calculated***
0.0110 ± 0.0005 0.0193 ± 0.0007 0.0207 ± 0.0007 0.0187 ± 0.0006 0.0119 ± 0.0004 0.0087 ± 0.0003 0.0072 ± 0.0002 0.0059 ± 0.0002 0.0056 ± 0.0002 0.0046 ± 0.0001
0.0122 0.0214 0.0206 0.0187 0.0119 0.0087 0.0071 0.0060 0.0056 0.0046
0.0110 0.0184 0.0200 0.0191 0.0118 0.0085 0.0072 0.0062 0.0057 0.0046
True coincidence summing Factor**** Fcoi
Self attenuation factor***** Fs
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9811 0.9808 0.9799 0.9801
1.123 1.090 1.078 1.071 1.050 1.041 1.035 1.031 1.029 1.025
*
The main uncertainty sources are 1.5–2% due to source activities, 0.1–1.2% due to counting statistics, and <1% due to systematic ones. 2 Efficiency data were fitted to a logarithmic polynomial function in the form: ep ¼ expða þ b:ln E þ c:ln E þ d:ln 3 EÞ, where a = 1.918828, b = 5.037222, c = 3.444946, d = 0.698902 in the low energy region of 59–159 keV, and a = 5.010486, b = 0.636695, c = 0.000219, d = 0.022974 in the high energy region of 159–1836 keV. *** The MCNP calculated efficiency data were obtained from GESPECOR Ver. 4.2 program in which both Fcoi and Fs factors were taken into account. **** Fcoi factors calculated for a 1 mm-thick polystyrene cylinder tube of 13 mm diameter and 6.25 mm height, placed at a 10 cm distance far from the 120.8% relative efficient Ge detector. ***** Fs factors were estimated for the same tube geometry but containing SiO2 matrix spiked with nuclides. **
cessing operating through a Genie-2000 gamma spectroscopy software. Each spectrum was collected in 4096 channels memory with an amplifier gain of 0.52 keV/channel, thus covering up to about 2.2 MeV c-ray energy. The net peak areas under the full-energy peaks were evaluated both manually and the interactive peak fitting module of the Genie-2000 software in which the observed counts can be fitted to a normal Gaussian peak without tail, and subtracted either a linear or a stepwise background continuum. The samples were counted at a distance of 10 cm from the detector in order to keep possible true coincidence (TCS) effects at a reasonably low level although the Cd-ratios cancel out the true coincidence effects on the peak areas resulting in specific activities [25]. The chosen 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 not also the dead time and pile-up losses and but for eliminating the possible contributions from the interfering 843.74 keV (71.8%) c-ray emitted from 27Mg (9.458 min) to the 846.77 keV (98.9%) analytical peak of 56Mn (2.5785 h). For the characterization of thermal flux, thermal to epithermal ratio factor (f) of the neutron irradiator unit, it was required to obtain a full-energy efficiency calibration of the Ge detector as a function of energy. To do this, the multi-nuclide standard containing 241 Am, 109Cd, 57Co, 123mTe, 51Cr, 113Sn, 85Sr, 137Cs, 60Co and 88Y radio nuclides spiked in sand matrix (SiO2, density:1.7 ± 0.1 g cm3) purchased from Isotope Products Laboratories Inc traceable to NIST was used. Full-energy peak efficiencies, TCS correction factors (Fcoi) are given in Table 2 together with self absorption (Fs) coefficients for the c-rays of interest. 3. Effective resonance energy determination By a definition, 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 has an importance because it replaces all the resonance energies lying in epithermal region, which is described by a modified 1/E1+a behaviour in Høgdahl formalism [13]. It should be noted that the-value is very sensitive to the accuracy of the Q0(a) value for the monitor used, while applying the single comparator method in the thermal activation analysis [26]. In Høgdahl formal-
ism, the neutron spectrum is divided into two parts, i.e., the thermal and the epithermal region in which the (n,c) activation due to fast neutrons could generally be neglected. Moreover, the division between the thermal and epithermal part of the spectrum is definitely arbitrary and the so-called Cd cut-off energy for a 1 mm thick Cd cover, which is internationally accepted as ECd = 0.55 eV in Høgdahl convention in which for a small sample in a 1 mm thick Cd box. ECd = 0.55 eV value is the lower limit of the resonance integral cross section valid in a non-ideal 1/E1+a epithermal distribution. Although it is not possible to avoid the error in the Er -value to be measured for the isotope due to an uncertainty in the Q0(a) value of the monitor. This can be adjusted in the determination of Er -values by choosing the appropriate Er;c monitor isotopes whose Q0(a) values and other parameters are more accurate and close to those of the isotopes being measured. Accordingly, 55Mn and 98Mo target isotopes having favourable nuclear properties were chosen as the Er;c monitor in the present work. As previously described in detail [15,25], these monitor isotopes 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, especially in high flux irradiations. In addition, most of the resonance captures of 55 Mn and 98Mo occurs at a relatively higher neutron energy region, for example, the first principal resonance of 55Mn is seen at 337 eV and that of 98Mo is at 468 eV [20], which are quite far from 1/v region, thus making their well-established effective resonance energies, as given in Table 3. In following sections of the paper, experimental and theoretical bases of the Er -value determination is briefly given, for the description of data analysis is required to determine effective resonance energy concept for the (n,c) reactions of the target isotopes by the activation method when using Cd-ratios of the isotopes being investigated relative to those of Cd-ratios of monitors such as 55Mn and 98Mo. 3.1. Data analysis for experimentally determined Er -value As is known, the ideal 1/E epithermal neutron spectrum, the resonance integral cross section, I0, including 1/v tail of thermal neutron spectrum defined in the literature [27] is not valid in a non-ideal, real epithermal neutron spectrum and that such a deviating epithermal neutron fluence distribution can be approximated by U(E) = 1/E1+a. Accordingly, a resonance integral I0(a) for a real epithermal neutron spectrum characterized by a-shape factor
Ho (t1/2 = 1200 y, ra = 3.4 b) gives no IT to 166Hof
ln
a
b
El Nimr et al. (1981) [35]. Kolotov and De Corte (2003) [36]. c NUDAT (Sonzogni et al., 2005)[21]. d Simonits et al. (1981)[37]. e El Nimr, T. and Ela-Assaly, F.M. (1987) [38]. f De Corte et al. (1989; 2003) [10,39]. * Self attenuation calculated using mass attenuation coefficients taken from NIST [40] and KORDATEN databases, respectively. ** True coincidence summing correction factors calculated by using GESPECOR Ver 4.2 software with a MCNP modelling for the present detector-source geometry.
165m
26.824(12) h 10.9(2.4%) – 0.99 Ho(n,c)166gHo 165165
2581
[28]. The effective resonance energy, Er -value as the basis firstly defined by Ryves [29] can be estimated by the following equation [11,28,30].
Monitor Investigated isotope Investigated isotope 0.9998 0.9878 0.9973 0.9996 0.9951 0.9950 1.0041 1.0019 1.0973 1.0666 1.0602 1.0133 1.0124 1.0121 95.58 4.73(5) 29.25 6.71(8) 0.92 0.182(3) 0119(20) 411.802(17) 69.67300(13) 103.1801(17) 80.574(8) 1379.437(6) 1581.834(7) 1662.439(6) 2.695(21) days 46.50(21) h 15.7(1.8%) 14.4(2.1%) 0.991 0.982 152
197
Au(n,c)198Au Sm(n,c)153Sm
5.65 ± 0.40 –
1.053(2.6%) 53.1(6.3%) 468 ± 51 241 ± 48 1.00 1.00 Mn(n,c)56Mn Mo(n,c)99Mo(b)99mTc 98
55
energy, Er (eV)b
1.0001 1.0531 1.0358 1.0042 1.0052 1.0053 1.0053
0.9921 0.9988 1.0140 98.9(3) 4.52(24) 2.5789(1) h 65.94(1) h
846.754(20) 140.511(1)
1.0104 1.0062
Fcoi Fs (from GESPECOR) Fs (from NIST) Emission probability,c (%) Energy (keV)
The measured gamma-rayc Half-lifec Q0 (=I0/r0)b s(%) Effective resonance
Cadmium transmission factor, FCda,e Nuclear reaction
Table 3 Nuclear data for the isotopes, self attenuation and true coincidence summing correction factors for the measured gamma-rays.
Self attenuation factor*
True coincidence summing**
Notes
Asp(Mo)/Asp(Mo + Tc),=0.05992d, where Asp is specific activities of isotope investigated.
Monitor Monitor
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Q 0 0:429 f Gth ð2a0:429 Gepi ðF cd Rcd 1Þ þ1ÞEaCd
¼ a ln Er
ð1Þ
In Eq. (1), the a parameter exists in both sides of the equation. It can therefore be initially set to zero, followed by an iterative procedure until it converges to a constant value [31,32]. In this work, the a parameter determined by using the measured Cd-ratios of monitor isotopes 55Mn and 98Mo, because their Q0(a), Er -values and other essential parameters are known more accurately. The presently used iterative procedure is required to fit the experimental data, when plotting left hand term of the Eq. (1) versus ‘‘ln Er ” for each monitor. Thus from the expected straight line, a-shape factor is derived from the slope of the obtained straight line as shown in Fig. 1. Thus, in this work, the extent of non-ideality of epithermal flux shape, i.e., the a-shape factor at the sample irradiation position was determined to be 0.0828 ± 0.0097 for all irradiations. For the effective resonance energy, Eq. (1) can also be re-written for the investigated (Er ) and the monitor isotopes (Er;c ) as follows [33,34]:
1=a Er ¼ ðQ o 0:429Þ= ð½f Gth =½ðF Cd RCd 1ÞGepi Þ C a
ð2Þ
where pffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C a ¼ 0:429=½ð2a þ 1ÞEaCd and 0:429 ¼ 2 E0 =ECd ¼ 2 0:0253=0:55. Thus, the effective resonance energy of the investigated isotope from the ratio of (Er =Er;c ) can easily be determined by taking into account the necessary factors such as neutron self-shielding factors, Gth and Gepi for both monitor (c) and investigated isotope [15,34]. þ The Cd-ratio RCd ¼ A sp =Asp can easily be calculated from the measured specific activities of the isotope, as follows:
Asp ¼ fNp =ðwSDCtm Þgbare and Aþsp ¼ fNp =ðwSDCtm ÞgCd
ð3Þ
þ where A sp and Asp are specific activities obtained after a bare and Cdcovered isotope irradiation; Np is net number of counts under the full-energy peak collected during measuring (live) time, tm; w is mass of irradiated element; S ¼ 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=kt r 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 [35]. Nuclear data used for the investigated isotopes, self attenuation and true coincidence summing correction factors for the measured gamma-rays are given in Table 3. The equivalent 2200 m s1 thermal and epithermal neutron fluxes at the sample irradiation position of the 241Am–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 [22].
3.2. Theoretically calculation of Er -value 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 of an isotope, it can usually be
M.G. Budak et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2578–2584
-
-
-
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ln Fig. 1. Experimental determination of a-shape factor in the irradiation position in the used Am–Be source geometry.
utilized by the following approximate expressions. As the first approach, one can use:
ln Er ¼
X
X
ri Cc;i ln Er;i =Er;i =
i
ri Cc;i =Er;i
ð4Þ
i
where ri is partial capture cross-section, Eri is the i-th resonance energy and Cc,i is the radiative width at the maximum of the i-th resonance energy. It is assumed in Eq. (4) that resonance self-shielding is negligible, which is the case when using sufficiently diluted samples. The newest resonance data is taken from JENDL 3.3. [20] and JEFF 3.1. [41], General Purpose Neutron File OECD-NEA Evaluated Data Library is used in this study. The Er -values resulted from Eq. (4) are also given in Table 5. This approximation was first used by Moens et al. [12], in which neutron widths, Cn are neglected. The second approach suggested by Jovanovic et al. [14] 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.
ln Er ¼
X
wi ln Er;i =
i
X
wi
ð5Þ
i
where the weighting factor wi is given by
wi ¼ ðg Cc Cn =CÞi ð1=E2r;i Þ
ð6Þ
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. For the evaluation of Eq. (5) for the Er -values, the newest resonance data are taken from the available recent literature [20,41–46]. 4. Results and Discussion The Er -values for the isotopes of interest were obtained by Eq. (2) using experimentally determined Cd-ratios and the relevant nuclear data given in Table 3, respectively. The results for Er -values Table 4 The measured effective resonance energy values obtained by dual monitors. Reaction
152 165
Sm(n,c)153gSm Ho(n,c)166gHo
Experimental effective resonance energy value, Er (eV) Using 55Mn monitor
Using 98Mo monitor
Weighted average
8.59 ± 2.34 12.82 ± 3.49
8.72 ± 2.83 13.01 ± 4.22
8.65 ± 1.80 12.90 ± 2.69
obtained by using dual monitor are given in Table 4. The 55Mn and Mo monitors used in the present experiment have intermediate Er -values that cover the range of Er -values for the isotopes of interest, thus allowing being appropriate range for the resonance energy regions (approximately 50–10,000 eV) of some isotopes. As can be seen in Table 4, a consistency between the results obtained by 55Mn and those obtained by 98Mo for each isotope being measured is found. This yields to more accurate results when the cadmium ratio method is used. It is therefore that two different monitors with the sufficiently well known cross sections are used to check for the possible differences in the measured results. The main sources of uncertainty in the experimentally determined Er -values given Tables 4 and 5 are mainly due to the a-shape factor (19–21%), 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%). In this work all uncertainties are given with in ±1r confidence interval (68% confidence level). 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 in the overall uncertainty estimation. However, they are introduced in the overall uncertainty budget. On the other hand, 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. (2). In addition, it was noted by Simonits et al. [11] 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). Since other experimentally determined Er -values for the 152Sm and 165Ho isotopes do not appear in literature at all; the present experimental results are compared only with the present and earlier calculated values by two different approaches described in Section 3.2. Therefore, the present experimental results for the Er -values are given in Table 5, together with the present theoretically calculated values and old theoretical ones. In general, the present experimental values agree with the calculated ones when using the newest resonance data within limits of the estimated uncertainty. However, it implies that when the first approach (Moens’ approach) based on Eq. (4) was used to calculate theoretically the Er -values, the results are not satisfactorily accurate even if currently available most accurate neutron resonance data appeared in literature are used. Because this Moens’ approach was used in past, neglecting neutron widths, Cn. Whereas the Cn widths of the resonances vary in the range 98
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M.G. Budak et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2578–2584 Table 5 Effective resonance energy Er -values for Reaction
152 165 a b c d e f
Sm(n,c)153Sm Ho(n,c)166gHo
152
Sm(n,c)153gSm and
165
Ho(n,c)166gHo reactions.
Experimental effective resonance energy value
Theoretically calculated effective resonance energy values
This work
This workc
Er (eV)
Er (eV) [from Eq. (4)]a
Deviation%b
Er (eV) [from Eq. (5)]d
Deviation%b
Er (eV) [from Eq. (4)]e
Deviation%b
Er (eV) [from Eq. (5)]f
Deviation%b
8.65 ± 1.80 12.90 ± 2.69
8.34 8.63
3.6 33.1
8.59 12.95
0.69 0.39
8.33 9.73
3.70 24.57
8.53 ± 0.09 12.3 ± 0.4
1.39 4.65
Literature
Calculated by Eq. (4) based on first approach [12] using recent resonance data taken from JENDL 3.3 and JEFF 3.1 data libraries. The percentage deviation means = 100 (C/E-1) where C is theoretically calculated value and E is experimentally determined value. Uncertainties are not given due to no uncertainty quoted in the used data. Calculated by the second approach [14] based on Eq. (5), using recent resonance data taken from JENDL 3.3 and JEFF 3.1 data libraries. The first approach Eq. (4) suggested by Moens et al. (1979) [12]. The second approach Eq. (5) suggested by Jovanovic et al. (1987) [14].
of 103–10 eV, and they should be considered in Er -value calculation although at first sight the Cn widths are considerably even for resonances of the same isotope. On the other hand, the radiative widths, Cc are taken into account in Eq. (4) whereas they vary within the range of 0.1–1 eV, and they are fairly constant, within one isotope, because of many c-ray exit channels [47]. Additionally, since there is no evidence that the Er -value is dependent on a the a-shape factor over the resonances [30], the expanding of E r 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. [12] in the first approach. Theoretically calculated Er -values are estimated to be 8.34 eV and 8.53 eV for 152Sm and they are, in general, much smaller than those experimental ones above by 1.4–3.6% for 152Sm when two different theoretical approaches are used. In case of 165Ho isotope, the theoretically calculated Er -value of 8.63 eV from the first approach (Moens’ approach) deviates substantially from the measured value by about 33%, whereas the theoretical Er -value of 12.95 eV from second approach (Jovanovic’s approach) agrees very well with the experimentally determined value. The present experimental Er -values agree with the theoretical ones calculated from the Jovanovic’ approach based on Eq. (5) within limits of the estimated uncertainty. However, it is noting that the results for Er calculated from the first approach are not satisfactorily accurate even if the recent resonance data are used in this approach. Because this Moens’ approach do not take into account the neutron widths at all. This implies that the experimentally determined Er -values might be preferred in the analyses, for example, introduced in k0-NAA method rather than the use of their theoretically determined Er -values. 5. Conclusion It is concluded from this study that, for more accurate Er -values for the isotopes, the new experimentally determined Er -values must be obtained rather than the use of the available theoretical ones. On the other hand, this is important because the quantity and quality of the available resonance parameter data continuously improve in recent databases. For theoretical calculations of Er -values, it is considered that discrepancies between the old calculated Er -values and the recent ones are due to mostly older resonance data. Acknowledgments The experiments in this study were performed in ex-Ankara Nuclear Research and Training Center (ANRTC). Authors are gratefully thanks for the directorate of ex-ANRTC of Turkish Atomic Energy Authority allowing us to use their experimental facilities.
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[20] JENDL-3.3, K. Shibata, et al., 2002. Japanese evaluated nuclear data library version 3 Revision-3: Program for nuclear data on the web (
[34] S. Jovanovic, F. De Corte, A. Simonits, J. Hoste, The Er – comparator technique for the experimental determination of effective resonance energies, Journal of Radioanalytical and Nuclear Chemistry 92 (1985) 399–406. [35] T. El Nimr, F. De Corte, L. Moens, A. Simonits, J. Hoste, Epicadmium neutron activation analysis (ENAA) based on the k0 -comparator method, Journal of Radioanalytical Chemistry 67 (2) (1981) 421–435. [36] V.P. Kolotov, F. De Corte, An electronic database with a compilation of k0 and related data for NAA, Journal of Radioanalytical and Nuclear Chemistry 257 (3) (2003) 501–508. [37] A. Simonits, L. Moens, F. De Corte, A. De Wispelaere, J. Hoste, Absolute intensity of the 140.5 keV gamma-ray of 99Mo, Journal of Radioanalytical and Nuclear Chemistry 67 (1) (1981) 61–74. [38] T. El Nimr, F.M. Ela Assaly, Determination of the attenuation of epicadmium neutrons using the method of varying Cd-thickness, Journal of Radioanalitycal and Nuclear Chemistry 109 (1) (1987) 3–9. [39] F. De Corte, A. Simonits, k0-Measurements and related nuclear data compilation for (n,c) reactor neutron activation analysis, Journal of Radioanalytical and Nuclear Chemistry 133 (1) (1989) 43–130. [40] NIST The National Institute of Standards and Technology Standard Reference Database 126 (XCOM) tables of X-ray mass attenuation coefficients and mass energy-absorption coefficients from 1 keV to 20 MeV for elements Z = 1 to 92 Web Page: