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Measurement of thermal neutron cross-section and resonance integral for the 165Ho(n,γ)166gHo reaction using electron linac-based neutron source
Nuclear Instruments and Methods in Physics Research B 269 (2011) 159–166
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Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Measurement of thermal neutron cross-section and resonance integral for the 165Ho(n,c)166gHo reaction using electron linac-based neutron source Van Do Nguyen a, Duc Khue Pham a, Tien Thanh Kim a, Guinyun Kim b,⇑, Manwoo Lee b, Kyung Sook Kim b, Heung-Sik Kang c, Moo-Hyun Cho c, In Soo Ko c, Won Namkung c a b c
Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Hanoi, Viet Nam Department of Physics, Kyungpook National University, Daegu 702-701, Republic of Korea Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
a r t i c l e
i n f o
Article history: Received 25 August 2010 Received in revised form 1 November 2010 Available online 9 November 2010 Keywords: Thermal neutron cross-section Resonance integral 165 Ho(n,c)166gHo 197 Au(n,c)198Au 65 MeV electron linac Activation method
a b s t r a c t The thermal neutron cross-section and the resonance integral of the 165Ho(n,c)166gHo reaction have been measured by the activation method using a 197Au(n,c)198Au monitor reaction as a single comparator. The high-purity natural Ho and Au foils with and without a cadmium shield case of 0.5 mm thickness were irradiated in a neutron field of the Pohang neutron facility. The induced activities in the activated foils were measured with a calibrated p-type high-purity Ge detector. The correction factors for the c-ray attenuation (Fg), the thermal neutron self-shielding (Gth), the resonance neutron self-shielding (Gepi) effects, and the epithermal neutron spectrum shape factor (a) were taken into account. The thermal neutron cross-section for the 165Ho(n,c)166gHo reaction has been determined to be 59.7 ± 2.5 barn, relative to the reference value of 98.65 ± 0.09 barn for the 197Au(n,c)198Au reaction. By assuming the cadmium cutoff energy of 0.55 eV, the resonance integral for the 165Ho(n,c)166gHo reaction is 671 ± 47 barn, which is determined relative to the reference value of 1550 ± 28 barn for the 197Au(n,c)198Au reaction. The present results are, in general, good agreement with most of the previously reported data within uncertainty limits. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The stable isotope 165Ho has 100% natural abundance. This rare earth element can be used in nuclear reactors for nuclear control rods due to the thermal neutron cross-section and epithermal resonance integral for the 165Ho(n,c)166gHo reaction are rather high. In addition, 166gHo is one of the preferred radionuclides for nuclear medicine applications [1] because of its physical properties, which include high-energy b radiation (Eb1 = 1855 keV (51%), Eb2 = 1776 keV (48%), and Ebav = 666 keV), a short half-life (26.76 h), and decay to a stable daughter. It also emits low-intensity and low-energy c-rays (80.57 keV, 6.56%) which are suitable for imaging by a gamma camera. The 166gHo can be produced by either direct neutron capture of 165Ho or by indirect nuclear reaction 164Dy(n,c)165Dy(n,c)166Dy(b–)166gHo [1,2]. However, in practical applications, the production of 166gHo through 165Ho(n,c)166gHo reaction was widely used. Therefore, the knowledge of thermal neutron cross-section and resonance integral of the 165Ho(n,c)166gHo reaction would become important because the neutron activation cross-section data are ⇑ Corresponding author. Tel.: + 82 53 950 5320; fax: +82 53 955 5356. E-mail address: [email protected] (G. Kim). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.11.013
needed for the production of 166gHo and may also used in other studies related to the interaction of neutrons with matters. There are about 30 measurements and evaluations on the thermal neutron capture cross-sections and the resonance integrals for the 165Ho(n,c)166gHo reaction in the literature [3–31] from 1947 to 2009. However, the measured thermal neutron cross-sections for the 165Ho(n,c)166gHo reaction are varied from 58 [8] to 67 barn [27]. This fact shows that, there are still large deviations (15.5%) among the experimental results. The measured resonance integrals for the 165Ho(n,c)166gHo reaction are varied from 600 [25] to 830 barn [23]. The difference between the lowest and the highest values of the resonance integral found in literature is 33.8%. Therefore, it is necessary to measure more new data for better comparison and evaluation. We measured the thermal neutron cross-section and resonance integral of the 165Ho(n,c)166gHo reaction by using the well known activation method at the Pohang Neutron Facility (PNF) based on the 65-MeV electron linear accelerator (linac). There are few measurements similar to this work done at PNF [32]. The thermal neutron cross-section and the resonance integral for the 165 Ho(n,c)166gHo reaction were determined relative to the reference values of the 197Au(n,c)198Au reaction. In this experiment the necessary correction factors for c-ray attenuation (Fg), thermal
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neutron self-shielding (Gth), and resonance neutron self-shielding (Gepi) effects were taken into account. In addition, the neutron field used in sample activations, in general, approximately follow a 1/E1 + a distribution, thus giving rise to the remarkable effect in the final result due to the magnitude of the spectrum shape factor (a). Therefore, in order to improve the accuracy of the resonance integral result, the effect of the spectrum shape factor (a) in epithermal neutron spectrum was also taken into account. The present results are compared with the existing experimental data and the evaluated values.
Table 1 Characteristics of the activation foils: Ho, Au and In. Foils
Size (mm)
Thickness (mm)
Weight (g)
Purity (%)
Ho1 Ho2 AuC AuD In13 In14 In15 In43 In44 In45
10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0
0.025 0.025 0.03 0.03 0.05 0.05 0.05 0.05 0.05 0.05
0.0206 0.0207 0.0467 0.0463 0.0316 0.0314 0.0327 0.0318 0.0326 0.0323
99.9 99.9 99.95 99.95 99.95 99.95 99.95 99.95 99.95 99.95
2. Experimental procedure 2.1. Neutron source Neutrons used in this experiment were produced from the Pohang Neutron Facility (PNF) based on the pulsed electron linac of the Pohang Accelerator Laboratory (PAL), Korea [33]. The characteristics of the PNF are described elsewhere [34–38], so only a general description is given here. It consists of an electron linac, a photo-neutron target, and a 12-m long time-of-flight (TOF) path. The photo-neutron target was composed of ten Ta plates with a diameter of 4.9 cm and an effective thickness of 7.4 cm. There was a 0.15 cm water gap between Ta plates in order to cool the target effectively. The housing of the target was made of titanium. The photo-neutron target was set in the center of a cylindrical water moderator. The water moderator made by an aluminum cylinder with a thickness of 0.5 cm, a diameter of 30 cm, and a height of 30 cm. The distributions of neutrons with and without water moderator were described elsewhere [39,40]. The photo-neutrons produced in the giant dipole resonance region consist of a large portion of evaporated neutrons and a small fraction of directly emitted neutrons which dominated at high energies. The neutrons produced in the Ta target without water moderator have a Maxwellian energy distribution with a nuclear temperature of 0.45 MeV. The estimated neutron yield per kW of beam power for electron energies above 50 MeV at the Ta target is about 1.9 1012 n/s [39], which is consistent with the calculated value based on Swanson’s formula, 1.2 1011 Z0.66, where Z is the atomic number of the target material [41]. The total neutron yield per kW of beam power was also measured by using the multiple-foil technique and found (2.30 ± 0.28) 1012 n/s [40]. The neutron energy spectrum with the water moderator is shifted to lower energy region because of the effect of moderation by water. To increase the thermal neutrons in this facility, we have used water to a level of 3–5 cm above the Ta target surface [39]. In this experiment the water level was 5 cm above the target surface. 2.2. Sample irradiation High-purity (99.9%) natural Holmium foils, 10 10 mm rectangular shape and 0.025 mm in thickness, were used as the activation samples. The Au and In metallic foils were used as the comparator reactions and the neutron flux monitors, respectively. The characteristics of Ho, Au, and In foils are given in Table 1. In order to measure the thermal neutron cross-section and the resonance integral for the 165Ho(n,c)166gHo reaction by activation method relative to the 197Au(n,c)198Au reaction, the natural Ho and Au foils were irradiated with and without a Cd cover with a thickness of 0.5 mm. The neutron fluxes exposed to each sample during the irradiation were determined from activities of In monitors stacked alternatively between Ho and Au foils. The Ho, Au, and In foils were stacked on the sample holder, and the sample holder was placed on the upper surface of the water moderator
as shown in Fig. 1, where Ho(Cd) and Au(Cd) denote the activation foil covered with a 0.5-mm thick Cd. The neutron flux exposed to each sample was extrapolated from the measured activities of In foils irradiated simultaneously with the foil samples. The cadmium ratio is defined by CR = (R/Rcd), where R and Rcd are reaction rates per atom for bare and Cd-covered isotope irradiation, respectively. The measured cadmium ratio for 197Au was 2.76 ± 0.04, and that for 165Ho was 2.18 ± 0.03, respectively. In this study, the irradiation time was 180 min. The main nuclear data together with their uncertainties given in parenthesis for the nuclear reactions considered such as 165Ho(n,c)166gHo, 197 Au(n,c)198Au, and 115In(n,c)116mIn are listed in Table 2 based on the table of isotopes [42]. 2.3. Measurement of activity After an irradiation and an appropriate waiting time, the irradiated foils were taken off, and the activities of 166gHo, 198Au, and 116m In were measured by using a high-resolution c-ray spectrometer. The c-ray spectrometer was a p-type coaxial CANBERRA high-purity germanium (HPGe) detector with a diameter of 59.2 mm and a thickness of 30 mm. The HPGe-detector was coupled to a computer based multi-channel analyzer card system, which can determine the photo-peak-area of c-ray spectra by using the GENIE2000 computer program. The energy resolution of the detector was 1.80 keV full width at half maximum (FWHM) at the 1332.501 keV peak of 60Co. The detection efficiency is 20% at 1332.501 keV relative to a 300 diameter 300 length NaI(Tl) detector. The detection efficiency for the c-ray spectrometer was calibrated with a set of standard c-ray sources such as 241Am (59.541 keV), 137 Cs (661.657 keV), 54Mn (834.848 keV), 60Co (1173.237 keV and 1332.501 keV), and 133Ba (80.997 keV; 276.398 keV; 302.853 keV 356.017 and 383.815 keV). The measured detection efficiencies were fitted by the following function:
ln e ¼
5 X
an ðln ðE=E0 ÞÞn
ð1Þ
n¼0
where e is the detection efficiency, an represents the fitting parameters, and E is the energy of the photopeak, and E0 = 1 keV. The detection efficiencies as a function of the photon energy measured at different distances between the gamma source and the surface of the detector were illustrated in Ref. [32]. The waiting and the measuring times were chosen based on the activity and the half-life of each radioactive isotope. In order to minimize the uncertainties caused by random coincidence and pile-up effects, we have chosen the appropriate distance between the sample and the detector for each measurement. Generally, the dead times were kept below 2% for all measurements. For this purpose, the measured foil was attached on plastic holder and can be set at a distance from 5 to 105 mm from the surface of the HPGe detector.
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Fig. 1. Configuration of the neutron source based on the Ta target and water moderator system and the experimental arrangement of the activation samples. The numbers in this figure refer to dimension in cm.
Table 2 Nuclear decay data and their uncertainties given in parenthesis are used for the determination of the radioactivities [42]. Nuclear reaction
165
Ho(n,c)166gHo
197
Au(n,c)198Au
115
In(n,c)116mIn
Half-life, T1/2
26.824 h (12)
2.69517 days (21) 54.41 min (17)
Main gamma-rays Intensity (%)
80.576(2) 1379.437(6) 1581.834(7) 1662.439(6)
6.56(13) 0.922 0.182(3) 0.1191(20)
411.80205 (17) 675.8836 (7)
3. Data analysis 3.1. Thermal neutron cross-section The thermal neutron cross-section for the 165Ho(n,c)166gHo reaction, r0,Ho has been determined relative to that for the 197 Au(n,c)198Au reaction as follows [43]:
RHo F Ho;Cd RHo;Cd Gth;Au g Au RAu F Au;Cd RAu;Cd Gth;Ho g Ho
95.58 0.084 (3)
416.86 (3) 1097.3 (2) 1293.54 (15)
To measure the activities of the reaction products formed via the 165Ho(n,c)166gHo, 197Au(n,c)198Au and 115In(n,c)116mIn reactions, we have chosen the c-ray peaks with high intensity, well separated, and relatively low background. The activity of the 166g Ho was determined by using the c-ray of 80.576 keV (6.56%). The activity of the 198Au was determined by using the 411.80 keV (95.58%) c-ray peak. In case of the 116mIn, the activity was measured using the 1293.54 keV (84.4%) c-ray peak. The measuring times were varied from several ten minutes to several hours depending on the statistics of the c-ray peaks. A typical gamma spectrum of the activated Ho sample is shown in Fig. 2.
r0;Ho ¼ r0;Au
Isotopic abundance (%)
Energy (keV)
ð2Þ
where r0,Au is the thermal neutron cross-section of the 197 Au(n,c)198Au reaction, Rx and Rx,Cd are reaction rates per atom for bare and Cd-covered x (Ho or Au) isotope irradiation, respectively. The cadmium correction factor, Fx,cd accounts for the difference in count rate for Cd covered and bare samples, and Gth,x is the thermal neutron self-shielding factor for x samples. The Westcott factor gx, correction for departure from 1/v cross-section behav-
27.7 (12) 56.2 (11) 84.4 (17)
100
100 95.7 (2)
ior, for the 165Ho(n,c)166gHo reaction is 1.002 [7], and that for the Au(n,c)198Au reaction is 1.0054 [7]. The details of some other correction factors for the relevant nuclear reactions will be given in Section 3.3. After bare and Cd-covered sample irradiations, the reaction rates Rx and Rx,Cd for Ho and Au samples are determined by [40]. 197
Rx or Rx;Cd ¼
no eIc ð1
Nobs kð1 ektcp Þ k e s Þð1 ekti Þektw ð1
ektc Þ
;
ð3Þ
where Nobs is the net number of counts under the full-energy peak collected during the measuring time tc, no is the number of target nuclei, e is the detector efficiency, Ic is the intensity of the c-ray, k is the decay constant, ti is the irradiation time, tw is the waiting time, s is the pulse width, and tcp is the cycle period. 3.2. Resonance integral The resonance integral for the (n,c) reaction in an ideal 1/E epithermal neutron spectrum is defined by the following relation:
I0 ¼
Z
1
Ecd
rðEÞ E
dE
ð4Þ
where r(E) is the cross-section as a function of neutron energy E, and Ecd is the cadmium cut-off energy, which is usually defined as 0.55 eV. However, the resonance integral defined in Eq. (4) is not valid in a non-ideal, real epithermal neutron spectrum [44]. The resonance integral, I0(a)for a 1=E1þa real epithermal neutron spectrum is defined as follows [44,45]:
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Fig. 2. A typical gamma spectrum from the Ho foil irradiated by thermal neutrons with irradiation time 180 min, waiting time 1055 min, and measuring time 30 min.
Table 3 Nuclear data used for a determination. Nuclear reaction
CR
Er ; eV[6]
Q0 [6]
G
Fcd [50]
g [7]
197
2.76 ± 0.04 2.88 ± 0.05
5.65 20.5
15.7 13.7
0.302 ± 0.006 0.415 ± 0.008
1.009 1.101
1.0054 1.0018
Au(n,c)198Au 186 W(n,c)187W
I0 ðaÞ ¼
Z
1 ECd
rðEÞ ð1eVÞa E1þa
dE;
ð5Þ
where a is an epithermal neutron spectrum shaping factor, which is energy independent. The relationship between I0 and I0(a) is given by [44]:
I0 0:426g r0 0:426g r0 ; I0 ðaÞ ¼ ð1 eVÞa þ a a r Þ ð2a þ 1ÞðECd Þ ðE
ð6Þ
r effective resonance energy (eV), as defined by Ryves where E [46,47], the term (I0 0.426gr0) represents the reduced resonance r integral, i.e. with the 1/v tail subtracted. The literature values of E are 5.65 eV for 197Au [6] and 12.3 eV for 166Ho [6], respectively. The epithermal neutron spectrum shape factor, a at the sample irradiation position was experimentally determined by using the dual monitor method using the measured Cd ratios for the 197Au(n,c)198Au and the 186W(n,c)187W reactions. The half-life of the 187W is 23.72 h, and the main c-ray energies and intensities (%) of 187W used in the calculation are: 479.53 keV (21.8%) and 685.77 keV (27.30%). After having the Cd ratios for the 197Au(n,c)198Au and the 186W(n,c)187W reactions with the Cd cover thickness of 0.5 mm, the a-shape factor was derived from the following equation [45,48,49]:
ðCR 1ÞAu fðQ 0 0:4264ÞGgW ðEr;W Þa þ C a ¼ ; ðCR 1ÞW fðQ 0 0:4264ÞGgAu ðEr;Au Þa þ C a
ð7Þ
I0 where CR* = CR/Fcd, C a ¼ ð20:4264 aþ1ÞEaCd ; Q 0 ¼ g r0 , G is the ratio of the epithermal neutron self-shielding factor Gepi to the thermal neutron self-shielding factor Gth given in Table 3 for Au and W foils. By using the nuclear data given in Table 3, the a-shape factor has been found to be 0.068 ± 0.005. The measured resonance integral I0(a) for the 165Ho(n,c)166gHo reaction has been determined relative to that for the 197Au(n,c)198Au reaction as a standard by the following relation [43]:
I0;Ho ðaÞ ¼ I0;Au ðaÞ
g Ho r0;Ho CRAu F Au;Cd Gepi;Au Gth;Ho g Au r0;Au CRHo F Ho;Cd Gth;Au Gepi;Ho
ð8Þ
where Gth,x and Gepi,x are the thermal and the epithermal neutron self-shielding factor for Ho (or Au) sample, respectively.
In the determination of the resonance integral from Eq. (8), the thermal and epithermal self-shielding factors, Gth and Gepi were calculated according to the Section 3.3. Then, the obtained I0,Ho(a) value was converted to I0,Ho by using Eq. (6). 3.3. Correction factors In order to improve the accuracy of the experimental results, the following correction factors such as the neutron self-shielding, the gamma attenuation, the cadmium correction, and the g-factors were considered. The thermal neutron self-shielding correction factor for thin slabs was calculated as follows [51]:
Gth ¼
ð1 en Þ ; n
ð9Þ
pffiffiffiffi where n ¼ 2= pR0 t, R0 is the macroscopic capture cross-section for thermal neutrons (En = 0.0253 eV), and t is the foil thickness. The epithermal neutron self-shielding factor was calculated as follows [52]:
Gepi ¼
0:94 1 þ ðz=2:70Þ0:82
þ 0:06;
ð10Þ
P where a dimensionless variable z ¼ tot ðEres Þ 1:5t ðCc =CÞ1=2 , which converts the dependence of Gepi on the dimension and physical and nuclear parameters into a unique curve [53] and P qN A tot ðEres Þ ¼ M rEres is the macroscopic cross-section at the resonance peak (Eres) (where q is the density; NA is the Avogadro’s number; M is the atomic weight; rEres is the microscopic cross-section at Eres), t is the foil thickness, and C is the total resonance width (C = Cc + Cn, where Cc and Cn are resonance widths for (n,c) and (n,n0 ) reactions). The correction factor for a c-ray attenuation, Fg, in the activation foil at a given c-ray energy was approximated as follows [49]:
Fg ¼
lt ; 1 elt
ð11Þ
where l is the linear attenuation coefficient (cm1), and t is the sample thickness in cm. The correction factor for a c -ray attenua-
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Table 5 Uncertainties for the thermal neutron cross-section and the resonance integral measurements. Uncertainties due to
Uncertainties (%) 197
Fig. 3. The simplified decay scheme of
166
Ho.
tion for the 80.576 keV c-ray from 166gHo and 411.80 keV c-ray from 198Au are 0.97 and 0.99, respectively. The measured activity can be corrected to zero attenuation by dividing with factor Fg. From Fig. 3 we can recognize that the 80.57 keV c-ray is in coincidence with the 705.33 keV (0.0137%); 1379.44 keV (0.922%); 1581.83 keV (0.182%) and 1749.84 keV (0.0262%) c-rays. The true coincidence summing factor was calculated based on the measured total and absolute photopeak efficiencies and the formulae for complex decay schemes [54,55]. The true coincidence summing factor obtained at 5 cm distance between the sample and the surface of the HPGe detector is very small (61.005). The cadmium correction factor, FCd, accounts for the fact that the specific count rate of a cadmium covered isotope is significantly differ from the specific count rate of the bare isotope induced by epithermal neutrons, usually does not significantly differ from unity. However, FCd can be higher than unity when the resonance of Cd and that of the Cd-covered isotope partially overlap. The cadmium correction factor for the 165Ho(n,c)166gHo reaction and the 197Au(n,c)198Au are 1.010 and 1.009 [50], respectively. The main correction factors used for the determination of thermal neutron capture cross-sections and resonance integrals of the investigated nuclear reactions: 165Ho(n,c)166gHo and 197 Au(n,c)198Au are listed in Table 4.
4. Results and discussion The thermal neutron cross-section and the resonance integral for the 165Ho(n,c)166gHo reaction have been measured relative to the reference values of r0 = 98.65 ± 0.09 barn and I0 = 1550 ± 28 barn for the 197Au(n,c)198Au reaction [14]. The main sources of the experimental uncertainties for the present measurements are given in Table 5. We can see from Table 5 that the main sources of the uncertainties for the thermal neutron cross-section measurement are due to the detection efficiency (2.5%), the c-ray intensity (1.98%), and the statistical error (0.8%). The main sources of the uncertainties for the resonance integral measurement are due to the a-shape factor (4.25%), the reference thermal neutron cross-section (1.85%), the reference resonance integral (1.81%), and the epithermal neutron self-shielding factor (1.70%). The total
Au
0.50 0.50 2.40 0.20 0.008 0.10 0.70
0.80 0.50 2.50 0.20 0.045 1.98 0.50
Resonance integral measurements Epithermal neutron self-shielding factor Thermal neutron self-shielding factor Reference thermal neutron cross-section Reference resonance integral Cadmium ratio a-shape factor Total experimental uncertainty
1.70 0.70 0.09 1.81 1.50 4.25 5.19
1.50 0.50 1.85 – 1.35 3.70 4.63
uncertainties for the thermal neutron cross-section and the resonance integral for the 165Ho(n,c)166gHo reaction have been estimated to be 4.2% and 7.0%, respectively by combining the uncertainties for 165Ho and 197Au listed in Table 5. The present thermal neutron cross-section of the 165Ho(n,166g c) Ho reaction is 59.7 ± 2.5 barn and is compared with the existing experimental and evaluated data in Table 6 and in Fig. 4. The weighted average and error in Table 6 was calculated for the experimental data only by assuming that measurements of a given quantity are uncorrelated. As seen in Table 6, the experimental and the evaluated values for the thermal neutron cross-section of the 165 Ho(n,c)166gHo reaction are varied from 58 [8] to 67 barn [23,27]. The present result of 59.7 ± 2.5 barn is in good agreement within 4.2% (1r) with the experimental data obtained by Rajput et al. [3], Yucel et al. [5], De Corte [6], Holden [8], Kafala et al. [10], De Corte and Simonits [12], Gryntakis et al. [13], Mughabghab [14], Simonits et al. [15], Heft [16], Ryves and Zieba [20], Zimmerman et el., [26] and Seren et al., [31]. However, the present result differs from the evaluated results of ENDF/B-VII.0 [4], Mughabghab [7], JFF2.2 [11], and also some experimental data of Danon et al. [9], Erdtmann [17], Steinnes [21], Walker [22], Scoville and Rogers [23], THAI-AEC-10 [25], Stephenson [27], Keisch and Faler [29], and Pomerance [30] by 5.5–12.2%. The weighted average of the thermal neutron cross-section for the experimental values included the present result is 61.38 ± 0.36 barn. This is lower than the evaluated vales of ENDF/B-VII.0 [4] and Mughabghab [7] by about 5% and of JFF2.2 [11] by about 8%. The present resonance integral for the 165Ho(n,c)166Ho reaction is 671 ± 47 barn by assuming the cadmium cut-off energy of 0.55 eV and is compared with the existing experimental and evaluated data in Table 6 and in Fig. 5. As seen from Table 6 and Fig. 5, the experimental and the evaluated values for the resonance integral of the 165Ho(n,c)166Ho reaction are valued from 600 [25] to 830 barn [23]. The maximum deviation between these two values is 38.3%. The present resonance integral value 671 ± 47 barn is in good agreement within 7.0% (1r) with almost all the existing resonance integral data. However, it disagrees with the measure-
Nuclear reaction
Er ; eV[6]
Q0 [6]
Gth
Gepi
FCd [50]
g [7]
165
12.3 5.65
10.9(2.4) 15.7
0.997 ± 0.005 0.990 ± 0.007
0.650 ± 0.008 0.299 ± 0.005
1.010 1.009
1.002 1.0054
197
Ho(n,c) Ho Au(n,c)198Au
Ho
Thermal neutron cross-section measurements Statistical error Geometry Detection efficiency Mass (foil weight) Half-life c-ray intensity Thermal neutron self-shielding factor
Table 4 Correction factors used for the calculation of thermal neutron capture cross-section and resonance integral.
166
165
164
V.D. Nguyen et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 159–166
Table 6 Thermal neutron cross-section and resonance integral for the
165
Ho(n,c)166gHo reaction.
Year
Authors
r0 (barn)
% Diff. in r0
I0 (barn)
2010 2009 2006 2005 2003 2003 1999 1998 1997 1994 1989 1987 1984 1984 1978 1976 1975 1974 1974 1972 1969 1968 1967 1967 1967 1967 1966 1962 1951 1947 Average
This work Rajput et al. ENDF/B-VII.0 Yucel et al. De Corte Mughabghab Holden Danon et al. Kafala et al. JFF2.2 De Corte and Simonits Gryntakis et al. Mughabghab Simonits et al. Heft Erdtmann Steinnes Van Der Linden et al. Ryves and Zieba Steinnes Walker Scoville and Rogers Hayodom et al. THAI-AEC-10 Zimmerman et al. Stephenson Le Sage and Sher Keisch and Faler Pomerance Seren et al. Experimental Data
59.7 ± 2.5 58.98 ± 2.1 64.67 59.2 ± 2.5 58.5 ± 1.3 64.7 ± 1.2 58 64.4 ± 2.8 61.2 ± 0.8 66.59 58.1 ± 2.3 61.2 ± 1.1 61.2 ± 1.1 61.2 ± 3 61.4 ± 1.0 63 ± 3.3 – – 61.2 ± 1.1 65 ± 2 63 67 – 64 60 ± 2 67 – 64 ± 6 64 ± 3 59.6 ± 12 61.38 ± 0.36
– 1.21 8.32 0.837 2.01 8.37 2.85 7.87 2.51 11.54 2.68 2.51 2.51 2.51 2.51 5.53
671 ± 47 657 ± 36 682 667 ± 46 – 665 ± 22 670 671 ± 8 761.4 636 ± 32 660 ± 35 650 ± 22 670 ± 37 718 ± 40 660 ± 30 660 ± 30 626 ± 93 618 ± 33 710 ± 30 685 ± 30 830 ± 25 628 600 ± 110 – 674 696 ± 45 – – – 675.7 ± 5.7
2.51 8.88 5.53 12.23 7.2 0.50 12.23 7.2 7.2 0.167 2.81
% Diff. in I0 – –2.09 –1.64 0.596 0.894 0.147 0.0 13.47 5.22 1.64 3.13 0.149 7.00 1.64 1.64 6.71 7.90 5.81 2.09 23.70 6.41 10.58
Cd cut-off energy (eV)
Monitor
0.55 0.55 – 0.55 – 0.50 0.50 – 0.55 – 0.55 0.50 0.50 0.55 0.50 0.50 0.50 0.55 0.10 0.50
Au Au Evaluation Mn Au Evaluation Au TOF Au Evaluation Au Compilation Au Au Sc, Co, Au, U Au Au Au Au, Mn Au Calculated Exp Au Exp Abs. meas. Calculated Au Co Au Au
0.50 –
0.447 3.73 – – 0.745
0.50 – – –
% Diff. means that the percentage difference = 100 (1 literature value/present value).
Fig. 4. Comparison of the evaluation and the experimental values for the thermal neutron cross-section of the value for the experimental values included the present result.
ments of Ryves and Zieba [20] by 7.9%, of THAI-AEC-10 [25] by 10.6%, and of Scoville and Rogers [23] by 23.7%. The present resonance integral is also differ from the evaluation data of JFF2.2 [11] by 13.5%. The weighted average value for the experimental values included the present result is 675.7 ± 5.7 barn. The difference between this average value and the present resonance integral result for the 165Ho(n,c)166gHo reaction is only 0.7%. The weighted average value is in general good agreement with the evaluated values
165
Ho(n,c)166gHo reaction. The line is the weighted average
of ENDF/B-VII.0 [4] and Mughabghab [7] but different from JFF2.2 [11] by about 13%.
5. Conclusion The thermal neutron cross-section and the resonance integral for the 165Ho(n,c)166gHo reaction have been measured relative to
V.D. Nguyen et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 159–166
Fig. 5. Comparison of the evaluation and the experimental values for the resonance integral of the experimental values included the present result.
the reference reaction 197Au(n,c)198Au by the activation method at the Pohang neutron facility based on the electron linac. In order to improve the accuracy of the experimental results, the necessary corrections including the a-shape factor in the 1/E1+a epithermal neutron-spectrum were made. The results obtained for the thermal neutron cross-section and the resonance integral of the 165 Ho(n,c)166gHo reaction are 59.7 ± 2.5 barn and 671 ± 47 barn, respectively. The wide variation in the existing thermal neutron cross-section and resonance integral for the 165Ho(n,c)166gHo reaction given in Table 6 indicated that there is still a consistency problem among those measured and evaluated ones. The weighted average of the thermal neutron cross-section for the experimental data including the present result is 61.38 ± 0.36 barn. This is lower than the evaluated values of ENDF/BVII.0 [4] and Mughabghab [7] by about 5% and of JFF2.2 [11] by about 8%. The weighted average of the experimental resonance integral values included the present result is 675.7 ± 5.7 barn. This is in general good agreement with the evaluated values of ENDF/BVII.0 [4] and Mughabghab [7] but different from JFF2.2 [11] by about 13%. Acknowledgements The authors would like to express their sincere thanks to the staffs of Pohang Accelerator Laboratory for excellent operation of the electron linac and their strong support. This work was supported by the National Research Foundation of Korea (NRF) through a Grant provided by the Korean Ministry of Education, Science and Technology (MEST) in 2010 (Project No. 2010-0018498 and 2010-0021375), by the Institutional Activity Program of Korea Atomic Energy Research Institute, and by the Vietnam National Foundation for Science and Technology Development (NAFOSTED). References [1] IAEA-TECDOC-1228, Therapeutic applications of radiophamaceuticals, IAEA, 2001. [2] S. Lahiri, K.J. Volkers, B. Wierczinski, Appl. Radiat. Isot. 61 (2004) 1157. [3] M.U. Rajput, N.L. Maidana, V.R. Vanin, M.S. Dias, M.F. Koskinas, Radiochim. Acta 97 (2009) 63. [4] M.B. Chadwick et al., ENDF/B-VII.0: next generation evaluated nuclear data library for nuclear science and technology, Nucl. Data Sheets 107 (2006) 2931. [5] H. Yucel, M. Karadag, Ann. Nucl. Energy 32 (2005) 1.
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165
Ho(n,c)166gHo reaction. The line is the weighted average value for the
[6] F. De Corte, A. Simonits, Recommended nuclear data for use in the k0 standardization of neutron activation analysis, Atom. Data Nucl. Tables 85 (2003) 47. [7] S.F. Mughabghab, Thermal Neutron Capture Cross Section, Resonance Integrals and g Factor, INDC(NDS)-440, IAEA 2003. [8] N.E. Holden, Neutron Scattering and Absorption Properties, CRC Handbook of Chemistry and Physics, 79th ed., CRC Press, New York, 1998. [9] Y. Danon, C.J. Werner, G. Youk, R.C. Block, R.E. Slovacek, N.C. Francis, J.A. Burke, N.J. Drindak, F. Feiner, J.A. Helm, Nucl. Sci. Eng. 128 (1998) 61. [10] S.I. Kafala, T.D. MacMahon, S.B. Borzakov, J. Radioanal. Nucl. Chem. 215 (1997) 193. [11] JFF Report 14, Table of Simple Integral Neutron Cross Section Data from JEFF2.2, ENDF/B-VI, JENDL-3.2, BROND-2 and CENDL-2, OECD, 1994. [12] F. De Corte, A. Simonits, J. Radioanal. Nucl. Chem. 133 (1989) 43. [13] E. Gryntakis, D.E. Cullen, G. Mundy, Handbook on Nuclear Activation Data, IAEA Technical Reports Series 273, Viena, 1987. [14] S.F. Mughabghab, Neutron Cross Section, vol. 1. Academic Press, Inc., Sandiego, New York, Boston, London, Sydny, Tokyo, Toronto, 1984. [15] A. Simonits, F. De Corte, L. Moens, J. Hoste, J. Radioanal. Nucl. Chem. 81 (1984) 369. [16] R.E. Heft, A consistent set of nuclear parameter values for absolute INAA, in: Conference on Computers in Activation Analysis and Gamma-Ray Spectroscopy, Mayaguez, Puerto Rico, 30 April–4 May 1978, p. 495. [17] G. Erdtmann, Neutron Activation Table, Verlag Chemie, Weiheim, 1976. [18] E. Steinnes, J. Inorg. Nucl. Chem. 37 (1975) 1591. [19] R. Van der Linden, F. De Corte, J. Hoste, J. Radioanal. Nucl. Chem. 20 (1974) 695. [20] T.B. Ryves, K.J. Zieba, J. Phys. A 7 (1974) 2318. [21] E. Steinnes, J. Inorg. Nucl. Chem. 34 (1972) 2699. [22] W.H. Walker, Atomic Energy of Canada Ltd., Report AECL-3037 Part 1, 1969. [23] J.J. Scoville, J.W. Roger, Report IN-1195, 1968. [24] V. Hayodom, W. Boonkong, S. Mahapanyawong, C. Chaimonkon. Progress Report, Thailand, EXFOR Data Bank, available from: http://www.nndc.bnl.gov/ exfor/exfor00.htm., 1967 [25] Office of Atomic Energy of Peace, Bangkok, Certain Accounts on the Utilization of the Thai Research Reactor, Bangkok Conference Report THAI-AEC-10, 1967. [26] R.L. Zimmerman, L.Q. Amaral, R. Fulfaro, M.C. Mattos, M. Abreu, R. Stasiulevicius, Nucl. Phys. A 95 (1967) 683. [27] T.E. Stephenson, Neutron Cross Section and Resonance Integrals of Holmium, BNL-12269, 1967. [28] L. Le Sage, R. Sher, A measurement of the infinite dilution capture resonance integrals with a moxon-rae detector, in: Reactor Physics Conference, San Diego, 2, 1966, p. 175. [29] B. Keisch, K.T. Faler, Half-life determination of long-lived 166Ho, Washington AEC Office Reports, 1041, 1962, p. 36. [30] H. Pomerance, Phys. Rev. 83 (1951) 641. [31] L. Seren, H.N. Friedlander, S.H. Turkel, Phys. Rev. 72 (1947) 888. [32] V.D. Nguyen, D.K. Pham, T.T. Kim, T.S. Le, Y.S. Lee, G.N. Kim, Y. Oh, H.S. Lee, M.H. Cho, I.S. Ko, W. Namkung, Nucl. Instr. Meth. B 266 (2008) 21; V.D. Nguyen, D.K. Pham, T.T. Kim, T.S. Le, Y.S. Lee, G.N. Kim, Y.S. Lee, Y. Oh, H.S. Lee, M.H. Cho, I.S. Ko, W. Namkung, Nucl. Instr. Meth. B 266 (2008) 863; V.D. Nguyen, D.K. Pham, T.T. Kim, T.S. Le, Y.S. Lee, G.N. Kim, Y. Oh, H.S. Lee, M.H. Cho, I.S. Ko, W. Namkung, Nucl. Instr. Meth. B 267 (2009) 462. [33] G.N. Kim et al., in: G. Reffo, A. Ventura, C. Grandi (Eds.), Proceedings of the International Conference on Nuclear Data for Science and Technology, Trieste, 1997, p. 556.
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Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Measurement of thermal neutron cross-section and resonance integral for the 165Ho(n,c)166gHo reaction using electron linac-based neutron source Van Do Nguyen a, Duc Khue Pham a, Tien Thanh Kim a, Guinyun Kim b,⇑, Manwoo Lee b, Kyung Sook Kim b, Heung-Sik Kang c, Moo-Hyun Cho c, In Soo Ko c, Won Namkung c a b c
Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Hanoi, Viet Nam Department of Physics, Kyungpook National University, Daegu 702-701, Republic of Korea Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea
a r t i c l e
i n f o
Article history: Received 25 August 2010 Received in revised form 1 November 2010 Available online 9 November 2010 Keywords: Thermal neutron cross-section Resonance integral 165 Ho(n,c)166gHo 197 Au(n,c)198Au 65 MeV electron linac Activation method
a b s t r a c t The thermal neutron cross-section and the resonance integral of the 165Ho(n,c)166gHo reaction have been measured by the activation method using a 197Au(n,c)198Au monitor reaction as a single comparator. The high-purity natural Ho and Au foils with and without a cadmium shield case of 0.5 mm thickness were irradiated in a neutron field of the Pohang neutron facility. The induced activities in the activated foils were measured with a calibrated p-type high-purity Ge detector. The correction factors for the c-ray attenuation (Fg), the thermal neutron self-shielding (Gth), the resonance neutron self-shielding (Gepi) effects, and the epithermal neutron spectrum shape factor (a) were taken into account. The thermal neutron cross-section for the 165Ho(n,c)166gHo reaction has been determined to be 59.7 ± 2.5 barn, relative to the reference value of 98.65 ± 0.09 barn for the 197Au(n,c)198Au reaction. By assuming the cadmium cutoff energy of 0.55 eV, the resonance integral for the 165Ho(n,c)166gHo reaction is 671 ± 47 barn, which is determined relative to the reference value of 1550 ± 28 barn for the 197Au(n,c)198Au reaction. The present results are, in general, good agreement with most of the previously reported data within uncertainty limits. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction The stable isotope 165Ho has 100% natural abundance. This rare earth element can be used in nuclear reactors for nuclear control rods due to the thermal neutron cross-section and epithermal resonance integral for the 165Ho(n,c)166gHo reaction are rather high. In addition, 166gHo is one of the preferred radionuclides for nuclear medicine applications [1] because of its physical properties, which include high-energy b radiation (Eb1 = 1855 keV (51%), Eb2 = 1776 keV (48%), and Ebav = 666 keV), a short half-life (26.76 h), and decay to a stable daughter. It also emits low-intensity and low-energy c-rays (80.57 keV, 6.56%) which are suitable for imaging by a gamma camera. The 166gHo can be produced by either direct neutron capture of 165Ho or by indirect nuclear reaction 164Dy(n,c)165Dy(n,c)166Dy(b–)166gHo [1,2]. However, in practical applications, the production of 166gHo through 165Ho(n,c)166gHo reaction was widely used. Therefore, the knowledge of thermal neutron cross-section and resonance integral of the 165Ho(n,c)166gHo reaction would become important because the neutron activation cross-section data are ⇑ Corresponding author. Tel.: + 82 53 950 5320; fax: +82 53 955 5356. E-mail address: [email protected] (G. Kim). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.11.013
needed for the production of 166gHo and may also used in other studies related to the interaction of neutrons with matters. There are about 30 measurements and evaluations on the thermal neutron capture cross-sections and the resonance integrals for the 165Ho(n,c)166gHo reaction in the literature [3–31] from 1947 to 2009. However, the measured thermal neutron cross-sections for the 165Ho(n,c)166gHo reaction are varied from 58 [8] to 67 barn [27]. This fact shows that, there are still large deviations (15.5%) among the experimental results. The measured resonance integrals for the 165Ho(n,c)166gHo reaction are varied from 600 [25] to 830 barn [23]. The difference between the lowest and the highest values of the resonance integral found in literature is 33.8%. Therefore, it is necessary to measure more new data for better comparison and evaluation. We measured the thermal neutron cross-section and resonance integral of the 165Ho(n,c)166gHo reaction by using the well known activation method at the Pohang Neutron Facility (PNF) based on the 65-MeV electron linear accelerator (linac). There are few measurements similar to this work done at PNF [32]. The thermal neutron cross-section and the resonance integral for the 165 Ho(n,c)166gHo reaction were determined relative to the reference values of the 197Au(n,c)198Au reaction. In this experiment the necessary correction factors for c-ray attenuation (Fg), thermal
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neutron self-shielding (Gth), and resonance neutron self-shielding (Gepi) effects were taken into account. In addition, the neutron field used in sample activations, in general, approximately follow a 1/E1 + a distribution, thus giving rise to the remarkable effect in the final result due to the magnitude of the spectrum shape factor (a). Therefore, in order to improve the accuracy of the resonance integral result, the effect of the spectrum shape factor (a) in epithermal neutron spectrum was also taken into account. The present results are compared with the existing experimental data and the evaluated values.
Table 1 Characteristics of the activation foils: Ho, Au and In. Foils
Size (mm)
Thickness (mm)
Weight (g)
Purity (%)
Ho1 Ho2 AuC AuD In13 In14 In15 In43 In44 In45
10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0
0.025 0.025 0.03 0.03 0.05 0.05 0.05 0.05 0.05 0.05
0.0206 0.0207 0.0467 0.0463 0.0316 0.0314 0.0327 0.0318 0.0326 0.0323
99.9 99.9 99.95 99.95 99.95 99.95 99.95 99.95 99.95 99.95
2. Experimental procedure 2.1. Neutron source Neutrons used in this experiment were produced from the Pohang Neutron Facility (PNF) based on the pulsed electron linac of the Pohang Accelerator Laboratory (PAL), Korea [33]. The characteristics of the PNF are described elsewhere [34–38], so only a general description is given here. It consists of an electron linac, a photo-neutron target, and a 12-m long time-of-flight (TOF) path. The photo-neutron target was composed of ten Ta plates with a diameter of 4.9 cm and an effective thickness of 7.4 cm. There was a 0.15 cm water gap between Ta plates in order to cool the target effectively. The housing of the target was made of titanium. The photo-neutron target was set in the center of a cylindrical water moderator. The water moderator made by an aluminum cylinder with a thickness of 0.5 cm, a diameter of 30 cm, and a height of 30 cm. The distributions of neutrons with and without water moderator were described elsewhere [39,40]. The photo-neutrons produced in the giant dipole resonance region consist of a large portion of evaporated neutrons and a small fraction of directly emitted neutrons which dominated at high energies. The neutrons produced in the Ta target without water moderator have a Maxwellian energy distribution with a nuclear temperature of 0.45 MeV. The estimated neutron yield per kW of beam power for electron energies above 50 MeV at the Ta target is about 1.9 1012 n/s [39], which is consistent with the calculated value based on Swanson’s formula, 1.2 1011 Z0.66, where Z is the atomic number of the target material [41]. The total neutron yield per kW of beam power was also measured by using the multiple-foil technique and found (2.30 ± 0.28) 1012 n/s [40]. The neutron energy spectrum with the water moderator is shifted to lower energy region because of the effect of moderation by water. To increase the thermal neutrons in this facility, we have used water to a level of 3–5 cm above the Ta target surface [39]. In this experiment the water level was 5 cm above the target surface. 2.2. Sample irradiation High-purity (99.9%) natural Holmium foils, 10 10 mm rectangular shape and 0.025 mm in thickness, were used as the activation samples. The Au and In metallic foils were used as the comparator reactions and the neutron flux monitors, respectively. The characteristics of Ho, Au, and In foils are given in Table 1. In order to measure the thermal neutron cross-section and the resonance integral for the 165Ho(n,c)166gHo reaction by activation method relative to the 197Au(n,c)198Au reaction, the natural Ho and Au foils were irradiated with and without a Cd cover with a thickness of 0.5 mm. The neutron fluxes exposed to each sample during the irradiation were determined from activities of In monitors stacked alternatively between Ho and Au foils. The Ho, Au, and In foils were stacked on the sample holder, and the sample holder was placed on the upper surface of the water moderator
as shown in Fig. 1, where Ho(Cd) and Au(Cd) denote the activation foil covered with a 0.5-mm thick Cd. The neutron flux exposed to each sample was extrapolated from the measured activities of In foils irradiated simultaneously with the foil samples. The cadmium ratio is defined by CR = (R/Rcd), where R and Rcd are reaction rates per atom for bare and Cd-covered isotope irradiation, respectively. The measured cadmium ratio for 197Au was 2.76 ± 0.04, and that for 165Ho was 2.18 ± 0.03, respectively. In this study, the irradiation time was 180 min. The main nuclear data together with their uncertainties given in parenthesis for the nuclear reactions considered such as 165Ho(n,c)166gHo, 197 Au(n,c)198Au, and 115In(n,c)116mIn are listed in Table 2 based on the table of isotopes [42]. 2.3. Measurement of activity After an irradiation and an appropriate waiting time, the irradiated foils were taken off, and the activities of 166gHo, 198Au, and 116m In were measured by using a high-resolution c-ray spectrometer. The c-ray spectrometer was a p-type coaxial CANBERRA high-purity germanium (HPGe) detector with a diameter of 59.2 mm and a thickness of 30 mm. The HPGe-detector was coupled to a computer based multi-channel analyzer card system, which can determine the photo-peak-area of c-ray spectra by using the GENIE2000 computer program. The energy resolution of the detector was 1.80 keV full width at half maximum (FWHM) at the 1332.501 keV peak of 60Co. The detection efficiency is 20% at 1332.501 keV relative to a 300 diameter 300 length NaI(Tl) detector. The detection efficiency for the c-ray spectrometer was calibrated with a set of standard c-ray sources such as 241Am (59.541 keV), 137 Cs (661.657 keV), 54Mn (834.848 keV), 60Co (1173.237 keV and 1332.501 keV), and 133Ba (80.997 keV; 276.398 keV; 302.853 keV 356.017 and 383.815 keV). The measured detection efficiencies were fitted by the following function:
ln e ¼
5 X
an ðln ðE=E0 ÞÞn
ð1Þ
n¼0
where e is the detection efficiency, an represents the fitting parameters, and E is the energy of the photopeak, and E0 = 1 keV. The detection efficiencies as a function of the photon energy measured at different distances between the gamma source and the surface of the detector were illustrated in Ref. [32]. The waiting and the measuring times were chosen based on the activity and the half-life of each radioactive isotope. In order to minimize the uncertainties caused by random coincidence and pile-up effects, we have chosen the appropriate distance between the sample and the detector for each measurement. Generally, the dead times were kept below 2% for all measurements. For this purpose, the measured foil was attached on plastic holder and can be set at a distance from 5 to 105 mm from the surface of the HPGe detector.
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Fig. 1. Configuration of the neutron source based on the Ta target and water moderator system and the experimental arrangement of the activation samples. The numbers in this figure refer to dimension in cm.
Table 2 Nuclear decay data and their uncertainties given in parenthesis are used for the determination of the radioactivities [42]. Nuclear reaction
165
Ho(n,c)166gHo
197
Au(n,c)198Au
115
In(n,c)116mIn
Half-life, T1/2
26.824 h (12)
2.69517 days (21) 54.41 min (17)
Main gamma-rays Intensity (%)
80.576(2) 1379.437(6) 1581.834(7) 1662.439(6)
6.56(13) 0.922 0.182(3) 0.1191(20)
411.80205 (17) 675.8836 (7)
3. Data analysis 3.1. Thermal neutron cross-section The thermal neutron cross-section for the 165Ho(n,c)166gHo reaction, r0,Ho has been determined relative to that for the 197 Au(n,c)198Au reaction as follows [43]:
RHo F Ho;Cd RHo;Cd Gth;Au g Au RAu F Au;Cd RAu;Cd Gth;Ho g Ho
95.58 0.084 (3)
416.86 (3) 1097.3 (2) 1293.54 (15)
To measure the activities of the reaction products formed via the 165Ho(n,c)166gHo, 197Au(n,c)198Au and 115In(n,c)116mIn reactions, we have chosen the c-ray peaks with high intensity, well separated, and relatively low background. The activity of the 166g Ho was determined by using the c-ray of 80.576 keV (6.56%). The activity of the 198Au was determined by using the 411.80 keV (95.58%) c-ray peak. In case of the 116mIn, the activity was measured using the 1293.54 keV (84.4%) c-ray peak. The measuring times were varied from several ten minutes to several hours depending on the statistics of the c-ray peaks. A typical gamma spectrum of the activated Ho sample is shown in Fig. 2.
r0;Ho ¼ r0;Au
Isotopic abundance (%)
Energy (keV)
ð2Þ
where r0,Au is the thermal neutron cross-section of the 197 Au(n,c)198Au reaction, Rx and Rx,Cd are reaction rates per atom for bare and Cd-covered x (Ho or Au) isotope irradiation, respectively. The cadmium correction factor, Fx,cd accounts for the difference in count rate for Cd covered and bare samples, and Gth,x is the thermal neutron self-shielding factor for x samples. The Westcott factor gx, correction for departure from 1/v cross-section behav-
27.7 (12) 56.2 (11) 84.4 (17)
100
100 95.7 (2)
ior, for the 165Ho(n,c)166gHo reaction is 1.002 [7], and that for the Au(n,c)198Au reaction is 1.0054 [7]. The details of some other correction factors for the relevant nuclear reactions will be given in Section 3.3. After bare and Cd-covered sample irradiations, the reaction rates Rx and Rx,Cd for Ho and Au samples are determined by [40]. 197
Rx or Rx;Cd ¼
no eIc ð1
Nobs kð1 ektcp Þ k e s Þð1 ekti Þektw ð1
ektc Þ
;
ð3Þ
where Nobs is the net number of counts under the full-energy peak collected during the measuring time tc, no is the number of target nuclei, e is the detector efficiency, Ic is the intensity of the c-ray, k is the decay constant, ti is the irradiation time, tw is the waiting time, s is the pulse width, and tcp is the cycle period. 3.2. Resonance integral The resonance integral for the (n,c) reaction in an ideal 1/E epithermal neutron spectrum is defined by the following relation:
I0 ¼
Z
1
Ecd
rðEÞ E
dE
ð4Þ
where r(E) is the cross-section as a function of neutron energy E, and Ecd is the cadmium cut-off energy, which is usually defined as 0.55 eV. However, the resonance integral defined in Eq. (4) is not valid in a non-ideal, real epithermal neutron spectrum [44]. The resonance integral, I0(a)for a 1=E1þa real epithermal neutron spectrum is defined as follows [44,45]:
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Fig. 2. A typical gamma spectrum from the Ho foil irradiated by thermal neutrons with irradiation time 180 min, waiting time 1055 min, and measuring time 30 min.
Table 3 Nuclear data used for a determination. Nuclear reaction
CR
Er ; eV[6]
Q0 [6]
G
Fcd [50]
g [7]
197
2.76 ± 0.04 2.88 ± 0.05
5.65 20.5
15.7 13.7
0.302 ± 0.006 0.415 ± 0.008
1.009 1.101
1.0054 1.0018
Au(n,c)198Au 186 W(n,c)187W
I0 ðaÞ ¼
Z
1 ECd
rðEÞ ð1eVÞa E1þa
dE;
ð5Þ
where a is an epithermal neutron spectrum shaping factor, which is energy independent. The relationship between I0 and I0(a) is given by [44]:
I0 0:426g r0 0:426g r0 ; I0 ðaÞ ¼ ð1 eVÞa þ a a r Þ ð2a þ 1ÞðECd Þ ðE
ð6Þ
r effective resonance energy (eV), as defined by Ryves where E [46,47], the term (I0 0.426gr0) represents the reduced resonance r integral, i.e. with the 1/v tail subtracted. The literature values of E are 5.65 eV for 197Au [6] and 12.3 eV for 166Ho [6], respectively. The epithermal neutron spectrum shape factor, a at the sample irradiation position was experimentally determined by using the dual monitor method using the measured Cd ratios for the 197Au(n,c)198Au and the 186W(n,c)187W reactions. The half-life of the 187W is 23.72 h, and the main c-ray energies and intensities (%) of 187W used in the calculation are: 479.53 keV (21.8%) and 685.77 keV (27.30%). After having the Cd ratios for the 197Au(n,c)198Au and the 186W(n,c)187W reactions with the Cd cover thickness of 0.5 mm, the a-shape factor was derived from the following equation [45,48,49]:
ðCR 1ÞAu fðQ 0 0:4264ÞGgW ðEr;W Þa þ C a ¼ ; ðCR 1ÞW fðQ 0 0:4264ÞGgAu ðEr;Au Þa þ C a
ð7Þ
I0 where CR* = CR/Fcd, C a ¼ ð20:4264 aþ1ÞEaCd ; Q 0 ¼ g r0 , G is the ratio of the epithermal neutron self-shielding factor Gepi to the thermal neutron self-shielding factor Gth given in Table 3 for Au and W foils. By using the nuclear data given in Table 3, the a-shape factor has been found to be 0.068 ± 0.005. The measured resonance integral I0(a) for the 165Ho(n,c)166gHo reaction has been determined relative to that for the 197Au(n,c)198Au reaction as a standard by the following relation [43]:
I0;Ho ðaÞ ¼ I0;Au ðaÞ
g Ho r0;Ho CRAu F Au;Cd Gepi;Au Gth;Ho g Au r0;Au CRHo F Ho;Cd Gth;Au Gepi;Ho
ð8Þ
where Gth,x and Gepi,x are the thermal and the epithermal neutron self-shielding factor for Ho (or Au) sample, respectively.
In the determination of the resonance integral from Eq. (8), the thermal and epithermal self-shielding factors, Gth and Gepi were calculated according to the Section 3.3. Then, the obtained I0,Ho(a) value was converted to I0,Ho by using Eq. (6). 3.3. Correction factors In order to improve the accuracy of the experimental results, the following correction factors such as the neutron self-shielding, the gamma attenuation, the cadmium correction, and the g-factors were considered. The thermal neutron self-shielding correction factor for thin slabs was calculated as follows [51]:
Gth ¼
ð1 en Þ ; n
ð9Þ
pffiffiffiffi where n ¼ 2= pR0 t, R0 is the macroscopic capture cross-section for thermal neutrons (En = 0.0253 eV), and t is the foil thickness. The epithermal neutron self-shielding factor was calculated as follows [52]:
Gepi ¼
0:94 1 þ ðz=2:70Þ0:82
þ 0:06;
ð10Þ
P where a dimensionless variable z ¼ tot ðEres Þ 1:5t ðCc =CÞ1=2 , which converts the dependence of Gepi on the dimension and physical and nuclear parameters into a unique curve [53] and P qN A tot ðEres Þ ¼ M rEres is the macroscopic cross-section at the resonance peak (Eres) (where q is the density; NA is the Avogadro’s number; M is the atomic weight; rEres is the microscopic cross-section at Eres), t is the foil thickness, and C is the total resonance width (C = Cc + Cn, where Cc and Cn are resonance widths for (n,c) and (n,n0 ) reactions). The correction factor for a c-ray attenuation, Fg, in the activation foil at a given c-ray energy was approximated as follows [49]:
Fg ¼
lt ; 1 elt
ð11Þ
where l is the linear attenuation coefficient (cm1), and t is the sample thickness in cm. The correction factor for a c -ray attenua-
163
V.D. Nguyen et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 159–166
Table 5 Uncertainties for the thermal neutron cross-section and the resonance integral measurements. Uncertainties due to
Uncertainties (%) 197
Fig. 3. The simplified decay scheme of
166
Ho.
tion for the 80.576 keV c-ray from 166gHo and 411.80 keV c-ray from 198Au are 0.97 and 0.99, respectively. The measured activity can be corrected to zero attenuation by dividing with factor Fg. From Fig. 3 we can recognize that the 80.57 keV c-ray is in coincidence with the 705.33 keV (0.0137%); 1379.44 keV (0.922%); 1581.83 keV (0.182%) and 1749.84 keV (0.0262%) c-rays. The true coincidence summing factor was calculated based on the measured total and absolute photopeak efficiencies and the formulae for complex decay schemes [54,55]. The true coincidence summing factor obtained at 5 cm distance between the sample and the surface of the HPGe detector is very small (61.005). The cadmium correction factor, FCd, accounts for the fact that the specific count rate of a cadmium covered isotope is significantly differ from the specific count rate of the bare isotope induced by epithermal neutrons, usually does not significantly differ from unity. However, FCd can be higher than unity when the resonance of Cd and that of the Cd-covered isotope partially overlap. The cadmium correction factor for the 165Ho(n,c)166gHo reaction and the 197Au(n,c)198Au are 1.010 and 1.009 [50], respectively. The main correction factors used for the determination of thermal neutron capture cross-sections and resonance integrals of the investigated nuclear reactions: 165Ho(n,c)166gHo and 197 Au(n,c)198Au are listed in Table 4.
4. Results and discussion The thermal neutron cross-section and the resonance integral for the 165Ho(n,c)166gHo reaction have been measured relative to the reference values of r0 = 98.65 ± 0.09 barn and I0 = 1550 ± 28 barn for the 197Au(n,c)198Au reaction [14]. The main sources of the experimental uncertainties for the present measurements are given in Table 5. We can see from Table 5 that the main sources of the uncertainties for the thermal neutron cross-section measurement are due to the detection efficiency (2.5%), the c-ray intensity (1.98%), and the statistical error (0.8%). The main sources of the uncertainties for the resonance integral measurement are due to the a-shape factor (4.25%), the reference thermal neutron cross-section (1.85%), the reference resonance integral (1.81%), and the epithermal neutron self-shielding factor (1.70%). The total
Au
0.50 0.50 2.40 0.20 0.008 0.10 0.70
0.80 0.50 2.50 0.20 0.045 1.98 0.50
Resonance integral measurements Epithermal neutron self-shielding factor Thermal neutron self-shielding factor Reference thermal neutron cross-section Reference resonance integral Cadmium ratio a-shape factor Total experimental uncertainty
1.70 0.70 0.09 1.81 1.50 4.25 5.19
1.50 0.50 1.85 – 1.35 3.70 4.63
uncertainties for the thermal neutron cross-section and the resonance integral for the 165Ho(n,c)166gHo reaction have been estimated to be 4.2% and 7.0%, respectively by combining the uncertainties for 165Ho and 197Au listed in Table 5. The present thermal neutron cross-section of the 165Ho(n,166g c) Ho reaction is 59.7 ± 2.5 barn and is compared with the existing experimental and evaluated data in Table 6 and in Fig. 4. The weighted average and error in Table 6 was calculated for the experimental data only by assuming that measurements of a given quantity are uncorrelated. As seen in Table 6, the experimental and the evaluated values for the thermal neutron cross-section of the 165 Ho(n,c)166gHo reaction are varied from 58 [8] to 67 barn [23,27]. The present result of 59.7 ± 2.5 barn is in good agreement within 4.2% (1r) with the experimental data obtained by Rajput et al. [3], Yucel et al. [5], De Corte [6], Holden [8], Kafala et al. [10], De Corte and Simonits [12], Gryntakis et al. [13], Mughabghab [14], Simonits et al. [15], Heft [16], Ryves and Zieba [20], Zimmerman et el., [26] and Seren et al., [31]. However, the present result differs from the evaluated results of ENDF/B-VII.0 [4], Mughabghab [7], JFF2.2 [11], and also some experimental data of Danon et al. [9], Erdtmann [17], Steinnes [21], Walker [22], Scoville and Rogers [23], THAI-AEC-10 [25], Stephenson [27], Keisch and Faler [29], and Pomerance [30] by 5.5–12.2%. The weighted average of the thermal neutron cross-section for the experimental values included the present result is 61.38 ± 0.36 barn. This is lower than the evaluated vales of ENDF/B-VII.0 [4] and Mughabghab [7] by about 5% and of JFF2.2 [11] by about 8%. The present resonance integral for the 165Ho(n,c)166Ho reaction is 671 ± 47 barn by assuming the cadmium cut-off energy of 0.55 eV and is compared with the existing experimental and evaluated data in Table 6 and in Fig. 5. As seen from Table 6 and Fig. 5, the experimental and the evaluated values for the resonance integral of the 165Ho(n,c)166Ho reaction are valued from 600 [25] to 830 barn [23]. The maximum deviation between these two values is 38.3%. The present resonance integral value 671 ± 47 barn is in good agreement within 7.0% (1r) with almost all the existing resonance integral data. However, it disagrees with the measure-
Nuclear reaction
Er ; eV[6]
Q0 [6]
Gth
Gepi
FCd [50]
g [7]
165
12.3 5.65
10.9(2.4) 15.7
0.997 ± 0.005 0.990 ± 0.007
0.650 ± 0.008 0.299 ± 0.005
1.010 1.009
1.002 1.0054
197
Ho(n,c) Ho Au(n,c)198Au
Ho
Thermal neutron cross-section measurements Statistical error Geometry Detection efficiency Mass (foil weight) Half-life c-ray intensity Thermal neutron self-shielding factor
Table 4 Correction factors used for the calculation of thermal neutron capture cross-section and resonance integral.
166
165
164
V.D. Nguyen et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 159–166
Table 6 Thermal neutron cross-section and resonance integral for the
165
Ho(n,c)166gHo reaction.
Year
Authors
r0 (barn)
% Diff. in r0
I0 (barn)
2010 2009 2006 2005 2003 2003 1999 1998 1997 1994 1989 1987 1984 1984 1978 1976 1975 1974 1974 1972 1969 1968 1967 1967 1967 1967 1966 1962 1951 1947 Average
This work Rajput et al. ENDF/B-VII.0 Yucel et al. De Corte Mughabghab Holden Danon et al. Kafala et al. JFF2.2 De Corte and Simonits Gryntakis et al. Mughabghab Simonits et al. Heft Erdtmann Steinnes Van Der Linden et al. Ryves and Zieba Steinnes Walker Scoville and Rogers Hayodom et al. THAI-AEC-10 Zimmerman et al. Stephenson Le Sage and Sher Keisch and Faler Pomerance Seren et al. Experimental Data
59.7 ± 2.5 58.98 ± 2.1 64.67 59.2 ± 2.5 58.5 ± 1.3 64.7 ± 1.2 58 64.4 ± 2.8 61.2 ± 0.8 66.59 58.1 ± 2.3 61.2 ± 1.1 61.2 ± 1.1 61.2 ± 3 61.4 ± 1.0 63 ± 3.3 – – 61.2 ± 1.1 65 ± 2 63 67 – 64 60 ± 2 67 – 64 ± 6 64 ± 3 59.6 ± 12 61.38 ± 0.36
– 1.21 8.32 0.837 2.01 8.37 2.85 7.87 2.51 11.54 2.68 2.51 2.51 2.51 2.51 5.53
671 ± 47 657 ± 36 682 667 ± 46 – 665 ± 22 670 671 ± 8 761.4 636 ± 32 660 ± 35 650 ± 22 670 ± 37 718 ± 40 660 ± 30 660 ± 30 626 ± 93 618 ± 33 710 ± 30 685 ± 30 830 ± 25 628 600 ± 110 – 674 696 ± 45 – – – 675.7 ± 5.7
2.51 8.88 5.53 12.23 7.2 0.50 12.23 7.2 7.2 0.167 2.81
% Diff. in I0 – –2.09 –1.64 0.596 0.894 0.147 0.0 13.47 5.22 1.64 3.13 0.149 7.00 1.64 1.64 6.71 7.90 5.81 2.09 23.70 6.41 10.58
Cd cut-off energy (eV)
Monitor
0.55 0.55 – 0.55 – 0.50 0.50 – 0.55 – 0.55 0.50 0.50 0.55 0.50 0.50 0.50 0.55 0.10 0.50
Au Au Evaluation Mn Au Evaluation Au TOF Au Evaluation Au Compilation Au Au Sc, Co, Au, U Au Au Au Au, Mn Au Calculated Exp Au Exp Abs. meas. Calculated Au Co Au Au
0.50 –
0.447 3.73 – – 0.745
0.50 – – –
% Diff. means that the percentage difference = 100 (1 literature value/present value).
Fig. 4. Comparison of the evaluation and the experimental values for the thermal neutron cross-section of the value for the experimental values included the present result.
ments of Ryves and Zieba [20] by 7.9%, of THAI-AEC-10 [25] by 10.6%, and of Scoville and Rogers [23] by 23.7%. The present resonance integral is also differ from the evaluation data of JFF2.2 [11] by 13.5%. The weighted average value for the experimental values included the present result is 675.7 ± 5.7 barn. The difference between this average value and the present resonance integral result for the 165Ho(n,c)166gHo reaction is only 0.7%. The weighted average value is in general good agreement with the evaluated values
165
Ho(n,c)166gHo reaction. The line is the weighted average
of ENDF/B-VII.0 [4] and Mughabghab [7] but different from JFF2.2 [11] by about 13%.
5. Conclusion The thermal neutron cross-section and the resonance integral for the 165Ho(n,c)166gHo reaction have been measured relative to
V.D. Nguyen et al. / Nuclear Instruments and Methods in Physics Research B 269 (2011) 159–166
Fig. 5. Comparison of the evaluation and the experimental values for the resonance integral of the experimental values included the present result.
the reference reaction 197Au(n,c)198Au by the activation method at the Pohang neutron facility based on the electron linac. In order to improve the accuracy of the experimental results, the necessary corrections including the a-shape factor in the 1/E1+a epithermal neutron-spectrum were made. The results obtained for the thermal neutron cross-section and the resonance integral of the 165 Ho(n,c)166gHo reaction are 59.7 ± 2.5 barn and 671 ± 47 barn, respectively. The wide variation in the existing thermal neutron cross-section and resonance integral for the 165Ho(n,c)166gHo reaction given in Table 6 indicated that there is still a consistency problem among those measured and evaluated ones. The weighted average of the thermal neutron cross-section for the experimental data including the present result is 61.38 ± 0.36 barn. This is lower than the evaluated values of ENDF/BVII.0 [4] and Mughabghab [7] by about 5% and of JFF2.2 [11] by about 8%. The weighted average of the experimental resonance integral values included the present result is 675.7 ± 5.7 barn. This is in general good agreement with the evaluated values of ENDF/BVII.0 [4] and Mughabghab [7] but different from JFF2.2 [11] by about 13%. Acknowledgements The authors would like to express their sincere thanks to the staffs of Pohang Accelerator Laboratory for excellent operation of the electron linac and their strong support. This work was supported by the National Research Foundation of Korea (NRF) through a Grant provided by the Korean Ministry of Education, Science and Technology (MEST) in 2010 (Project No. 2010-0018498 and 2010-0021375), by the Institutional Activity Program of Korea Atomic Energy Research Institute, and by the Vietnam National Foundation for Science and Technology Development (NAFOSTED). References [1] IAEA-TECDOC-1228, Therapeutic applications of radiophamaceuticals, IAEA, 2001. [2] S. Lahiri, K.J. Volkers, B. Wierczinski, Appl. Radiat. Isot. 61 (2004) 1157. [3] M.U. Rajput, N.L. Maidana, V.R. Vanin, M.S. Dias, M.F. Koskinas, Radiochim. Acta 97 (2009) 63. [4] M.B. Chadwick et al., ENDF/B-VII.0: next generation evaluated nuclear data library for nuclear science and technology, Nucl. Data Sheets 107 (2006) 2931. [5] H. Yucel, M. Karadag, Ann. Nucl. Energy 32 (2005) 1.
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