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Measurement of thermal neutron capture cross-section and resonance integral for the 165Ho(n,γ)166gHo reaction by the activation method
Accepted Manuscript Measurement of Thermal Neutron Capture Cross-Section and Resonance Inte‐ gral for the 165Ho(n,γ)166gHo Reaction by the Activation Method Samaneh Zolghadri, Hasan Yousefnia, Hosein Afarideh, Ali Bahrami-Samani, Amir Reza Jalilian, Mohammad Ghanadi-Maragheh PII: DOI: Reference:
S0168-583X(12)00736-7 http://dx.doi.org/10.1016/j.nimb.2012.11.013 NIMB 59033
To appear in:
Nucl. Instr. and Meth. in Phys. Res. B
Received Date: Revised Date:
17 April 2012 12 November 2012
Please cite this article as: S. Zolghadri, H. Yousefnia, H. Afarideh, A. Bahrami-Samani, A.R. Jalilian, M. GhanadiMaragheh, Measurement of Thermal Neutron Capture Cross-Section and Resonance Integral for the 165 Ho(n,γ)166gHo Reaction by the Activation Method, Nucl. Instr. and Meth. in Phys. Res. B (2012), doi: http:// dx.doi.org/10.1016/j.nimb.2012.11.013
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Measurement of Thermal Neutron Capture Cross-Section and Resonance Integral for the 165Ho(n,γ)166gHo Reaction by the Activation Method Samaneh Zolghadria, Hasan Yousefnia a, Hosein Afaridehb, Ali BahramiSamania, Amir Reza Jaliliana, Mohammad Ghanadi-Maragheha a
Radiopharmaceutical Research and Development Laboratory (RRDL), Nuclear Sciences
and Technology Research Institute (NSTRI), Tehran, Iran, Postal Code: 14395-836. b
Department of Physics, Amirkabir University of Technology, Tehran, Iran.
Abstract The thermal neutron capture cross-section and resonance integral for the 165
Ho(n,γ)166Ho reaction were measured experimentally by the activation
method. Holmium oxide, manganese oxide and cobalt oxide powders, all dissolved in a mixture of hydrochloric acid and nitric acid, were irradiated within and without cadmium covers in the Tehran Research Reactor. The measured value of the thermal neutron cross-section relative to the 55
Mn(n,γ)56Mn and 59Co(n,γ)60Co monitor reactions (with thermal neutron cross-
section of 13.3 ± 0.1b and 37.18 ± 0.06b) was 58.6 ± 1.8b. The result was in a good agreement with the most previously reported values. Also the resonance integral was determined relative to the
55
Mn(n,γ)56Mn and
59
Co(n,γ)60Co
monitor reactions with the reference value of 14.0 ± 0.3 and 75.9 ± 2.0 respectively. The measured resonance integral of the
165
Ho(n,γ)166Ho reaction
at the cadmium cut-off energy of 0.55eV was 650 ± 31. The result was measured with high precision and compared with other measurements in the literature. Keywords: Activation method ,
165
Ho(n,γ)166Ho, Resonance integral, Thermal
neutron cross-section, corresponding author. Tel: +98 935 969 5292; Fax: +98 21 88221116 email address :[email protected]
1
1. Introduction Nowadays the field of radionuclide therapy is going through an extremely interesting phase and is poised for greater growth and development in the coming years.166Ho is a therapeutic radionuclide which can be produced with a reasonable specific activity using the (n, gamma) reaction [1] . Since this radionuclide has favorable physical characteristics, it is considered as one of the widely needed medical isotopes that have recently been discovered [2]. 166
Ho-radiopharmaceuticals have been developed and used in various disease
and malignancy therapies.
166
Ho-DOTMP is a radio-labeled tetraphosphonate
localized specifically in the skeleton and is used for the treatment of multiple myeloma [3].
166
Ho chitosan is an effective compound for radiation
synovectomy [4] and also for the treatment of liver malignancies [5].
166
Ho-
DTPA complex can be used for endovascular radiation therapy [6]. Nowadays many other 166Ho-radiopharmaceuticals are produced in the research phase. Knowledge of the thermal neutron capture cross-section and resonance integral of the
165
Ho(n,γ)166Ho reaction is important because the related data are used
not only in the production of
166
Ho for activity determination of the produced
radionuclide but also in other applied nuclear fields. However, further studies have been reported in relation to the measurement of thermal neutron capture cross-section and resonance integral of this reaction, large discrepancies are perceived among the reported data [7]. Therefore, it seems that more studies are essential to determine the cross-section data more accurately. This could be achieved by using high purity materials, optimizing the irradiation, decay and counting times and the weight of irradiated element (taking care to minimize neutron self-shielding effects)[8]. In addition to the discrepancies mentioned above, variation of flux can cause significant errors. Unfortunately, even in the latest reported work [9] to evaluate the thermal neutron cross-section and
2
165
Ho(n,γ)166gHo reaction, the variation of flux is still
resonance integral for quite considerable [10].
Due to the large discrepancies found among the reported data and also the error caused by the variation of the flux which could be clearly seen in the previous researches, the measurement of the thermal neutron cross-section and resonance integral of
165
Mn(n,γ)56Mn
55
Ho was performed with great precision. In this work and
59
Co(n,γ)60Co
reactions,
having
favorable
nuclear
characteristics, were selected as neutron monitors. In order to reduce the errors caused by the variation of the flux, the sample and monitors were mixed and irradiated in the same position. For this purpose, MnO2 and Co3O4 powders were mixed with Ho2O3 and dissolved in a mixture of hydrochloric acid and nitric acid (3:1). Then a polystyrene tube was filled with the 50µl of the above solution in which the weight of each element was in the order of a microgram and then the solution was irradiated in the Tehran Research Reactor. By this method the neutron self-shielding factor could be neglected which could help to get the analytical results more accurately. 2. Material and methods 2.1. Sample irradiation Natural holmium oxide (Ho2O3), manganese oxide (MnO2), cobalt oxide (Co3O4) (with chemical purity of more than 99.8%) and all other chemical reagents were purchased from Merck (Darmstadt, Germany). In order to provide a suitable sample, Ho2O3, MnO2 and Co3O4 were weighed on a calibrated balance, mixed and dissolved in the reasonable amount of ultrapure solvent [mixture of hydrochloric acid and nitric acid (3:1)]. Then a polystyrene tube was filled with the 50µl of the above solution. The solution (50µl) contained 0.56, 0.09 and 824.52 µg of Ho2O3, MnO2 and Co3O4 3
respectively. Therefore, the amounts of Ho, Mn and Co were 0.48, 0.05 and 605.33 µg respectively. The polystyrene tube was located in the oven at 80ºC and the solution was dried. Therefore, the elements were deposited homogenously at the bottom of the tube. Due to the small amount of the materials, the thickness was negligible. Another polystyrene tube with the same solution as describe above, was prepared and located in the cadmium shield. Then both of them were placed in an aluminum can, sealed and irradiated in Tehran Research Reactor. The flux in Tehran Research Reactor was monitored by gold foil activation method (with and without cadmium foil shield). The flux at the irradiation position was 2.5 × 1013 ± 5% n/ Cm2.S. The error was in measuring of absolute value of the flux at the irradiation point. Since all the elements were mixed and placed in the same position, this value did not play any role in these measurements. Since the monitors and the element under consideration were all mixed and irradiated at the same position simultaneously, all elements experienced the same flux, therefore, the variation of the flux was negligible. The reason for significant reduction of errors is due to the same flux trend for all irradiated elements. Irradiation was performed with and without a standard cadmium cover (height/diameter =2, wall thickness=1mm) in Tehran Research Reactor for 10 minutes. This experiment was repeated 5 times.
2.2. Activity measurements For the activity measurement, the tube was washed with ultrapure solvent [mixture of hydrochloric acid and nitric acid (3:1)] and a homogeneous solution was prepared. The activity of the samples was measured by a p-type coaxial 4
high-purity germanium (HPGe) detector (model: EGPC 80-200R) coupled with a multichannel analyzer card system. The detection efficiency of the detector was 80% at 1332.501 keV relative to 3 ״diameter × 3 ״length NaI(Tl) detector. The resolution of the detector was 1.8keV for 1332.5keV (60Co) and 0.9 keV for 122 keV (57Co). Various standard reference sources of 85
Sr and
152
241
Am,
133
Ba,
137
Cs, 88Y,
Eu having the same geometry were used for the measurement of
detection efficiency. The geometry of irradiated sample also was the same as the standard reference source. The measurement was based on the γ-ray peaks with the highest intensity in the spectrum of isotope under consideration and after 2-4 hours of irradiation depending on the activity of the samples (this cooling time is necessary for reducing dead time losses). They were counted up at the reference distance of 15-20cm from the detector to minimize the uncertainties caused by the pile-up effects. The counting time was considered between 10-15 minutes based on the activity of each sample. It should be mentioned that the errors due to a decrease of dead time during counting were minimized by keeping the counting time below one tenth of the half life of the measured radionuclide. Dead times were less than 1%.The measured gamma-ray spectrum of the sample is shown in Fig. 1.
3. calculation 3.1. Thermal neutron cross-section determination The reaction rate of each sample is the reaction rate induced by both thermal and epithermal neutrons. For 1/V absorbers such as
165
Ho, the HØgdahl
convention [11] can be used for the reaction rate of the produced radionuclide which is given by
5
(1)
R g Gthφthσ0 φep I0 α Ge
In the above equation, g is the Westcott correction factor which shows the departure from 1/V law, φth and φep are the thermal and epithermal neutron flux, Gth and Ge are the thermal and epithermal neutron self-shielding factors, σ0 is the thermal neutron capture cross-section and I0 is the resonance integral. A sufficient thick cadmium cover absorbs all thermal neutrons, more or less inevitably a small number of the epithermal neutrons in the range between 0.1eV and 0.6eV [12]. Therefore, in this situation the reaction rate is only induced by the epithermal neutrons and determined as (2)
Rcd φep I0 α Ge Fcd
The correction factor Fcd=Ccd/Cep shows the difference between the reaction rate of the cadmium covered isotope and the reaction rate of the bare isotope induced by epithermal neutrons. R and Rcd in equations 1 and 2 are the reaction rates per target nucleus calculated as (3)
R , Rcd
The amounts of parameters needed for radioactivity determination are given in Table 1. Table1 6
Nuclear decay data used for determination of radioactivity.
Radionuclide
56
Mn
Atomic weight
Half life
(g/mol)
(day)
[13]
[14]
54.938049(9)
0.107449(19)
Detected γ-ray energy
Emission probability (%)
(keV)
[14]
[ 15] 846.7638(19)
98.85(3)
1173.22(8) 60
Co
166
Ho
58.933200(9)
1925.23(27)
164.93032(2)
1.1165(13)
1332.492(4)
99.85(3) 99.9826(6)
80.576(2)
6.55(8)
Nabs is the net number of counts under the full-energy peak collected during measuring time tm, w the weight of irradiated element, the saturation factor with λ being the decay constant, tirr the irradiation time, the decay factor with td being the decay time, the measurement factor correcting the decay during the measuring time, tm, M the atomic weight, θ the isotopic abundance, NA the Avogadro’s number, Iγ the absolute gamma-ray emission probability and εp the full-energy peak detection efficiency. From equations 1 and 2, the relationship between the thermal neutron crosssection of the produced radionuclide and the monitor can be derived by the following equation:
The thermal neutron capture cross-section for and
166
Ho relative to 55Mn(n,γ)56Mn
59
Co(n,γ)60Co monitor reaction with the well-known cross-section and
resonance integral (given in Table 2) was determined according to equation 4. The weight of irradiated materials was sufficiently low so that no correction for neutron self-shielding was necessary. 7
3.2. Epithermal neutron spectrum shaping factor, α, determination The knowledge of the epithermal spectrum shape factor α is an essential parameter for the correction of resonance integrals. Various methods have been reported for determination of α-shape factor experimentally [16]. In this study, α-shape factor for the epithermal neutron spectrum was determined by the dualmonitor method using the measured Cd ratios for
55
Mn(n,γ)56Mn and
59
Co(n,γ)60Co reactions according to the following equation:
with
3.3. Resonance integral determination The reference resonance integral I0 is usually defined by the product of the cross-section and a pure 1/E spectrum integrated between cadmium cut off energy Ecd and an arbitrarily chosen upper limit E3: (5) As it can be seen in the above equation, the resonance integral depends on the shape of neutron spectrum in the epithermal range. In general, the epithermal neutron spectrum deviates from the 1/E behavior; hence it can be shown by 1/E1+α, where α is the epithermal neutron spectrum shaping factor. Therefore, the resonance integral is related to α and demonstrated by I0(α).The relationship between I0(α) and I0 is given by (6) 8
with Er the effective resonance energy defined by Ryves [17] while Ecd is the cadmium cut-off energy. For each monitor, I0 was converted to I0(α) by equation 6 and the value of the measured α. Then I0(α) for the
165
Ho(n,γ)166gHo reaction was determined by
equation 7 relative to each monitor reaction and then I0(α) was converted to I0 according to equation 6. (7) The amounts of parameters needed for thermal neutron cross-section and resonance integral determination are given in Table 2.
Table 2 Nuclear data for thermal neutron cross-section and resonance integral determination
Nuclear reaction 55
Mn(n,γ)56Mn
59 165
σ0 (b) [18]
I0 (b) [18]
Fcd
g [18]
Ēr [19]
13.3 ± 0.1
14.0 ± 0.3
1.0 [20]
1.0004
468(51)
60
37.18 ± 0.06
75.9 ± 2.0
0.9909(20) [21]
1.0003
136(7)
166
-
-
0.99 [20]
1.0020
12.3(0.4)
Co(n,γ) Co
Ho(n,γ) Ho
4. Results and discussion The epithermal spectrum shape factor was calculated according to the procedure described earlier. The calculated value was -0.10. The thermal neutron capture cross-section was determined for
165
Ho(n,γ)166gHo reaction
relative to
55
Mn(n,γ)56Mn and 59Co(n,γ)60Co monitor reaction with the cross-section value
of 13.3b and 37.18b respectively. This measurement was carried out five times. For each experiment, the cross-section and resonance integral values and also 9
the uncertainties of them were calculated. These values are shown in Table 3. The final results for the cross-section and resonance integral were the averages for all experiments. The final uncertainty was calculated on the bases of the error propagation formula which can be seen below.
Where
is the uncertainty for each experiment and N is the number of
experiments. The determined average capture cross-section for
165
Ho(n,γ)166gHo reaction was
58.6 ± 1.8b. The thermal neutron capture cross-section was measured with high precision and was in a good agreement with the result of Van Do Nguyen (2011), Rajput (2009), Yucle (2005) and De corte (2003). The epithermal neutron spectrum shaping factor was determined by the dualmonitor cadmium ratio method. Table 3 Thermal neutron capture cross-section and resonance integral of 165Ho(n,γ)166gHo for all samples.
Sample
Thermal neutron
Resonance
No.
capture cross-
integral (b)
section (b) 1
60.1 ± 1.9
667 ± 30
2
59.2 ± 1.7
658± 22
3
58.3 ± 1.8
642± 32
4
57.8 ± 1.6
634 ± 25
5
57.6 ± 1.8
649 ± 42
Also the resonance integral for
165
Ho(n,γ)166gHo reaction relative to
55
Mn(n,γ)56Mn and 59Co(n,γ)60Co monitor reaction with the resonance value of
14.0b and 75.9b was determined .The measured resonance integral agreed 10
within 3% with the result of Van Do Nguyen (2011), Rajput (2009), Yucle (2005), Holden (1999) and De corte (1989). The measured values in this research and the previously reported values are given in Table 4. The experimental uncertainties for the thermal neutron cross-section and resonance integral measurements for a single experiment are given in Table 5. The main source of the uncertainty for the thermal neutron cross-section measurement is the detection efficiency. The main sources of the uncertainties for the resonance integral measurement are α-shape parameter and monitor resonance integral. As it can be seen the measured values of both thermal neutron capture crosssection and resonance integral are in a remarkable consistency with recent measurements. As outlined earlier, the weight of irradiated element should be kept as low as possible to minimize the neutron self-shielding factor; but it is obvious that the accuracy in the amount of element decreases with decreasing the mass of each element. Therefore, a reasonable amount of an element mass was weighed with great accuracy and then dissolved in suitable amount of ultrapure solution. Then a suitable volume of solution having approximately 10-100µg of element was irradiated. Therefore, by this method, the mass of each element is so low that the neutron self-shielding factor can be neglected.
Table 4 Thermal neutron capture cross-section and resonance integral for 165Ho(n,γ)166gHo.
Reference
Thermal neutron
Resonance
Cadmium
Monitor
capture cross-
integral(b)
cut-off
used
section(b) This
58.6 ± 1.8
Year
energy (eV) 650 ± 31
0.55
Mn, Co
2012
work 11
[9]
59.7 ± 2.5
671± 47
0.55
Au
2011
[22]
64.6959
_
_
_
2011
[2]
58.98 ± 2.10
657 ± 36
_
Au, Co,
2009
Zn, Zr [23]
52.8 ± 1.3
_
_
_
2006
[24]
59.2 ± 2.5
667 ± 46
0.55
Mn
2005
[25]
58.5 ± 1.3
_
_
Au
2003
[26]
58
670
0.5
Au
1999
[27]
64.4 ± 2.8
_
_
_
1998
[28]
66.500
752
_
_
1997
[8]
58.1 ± 2.3
636 ± 32
_
Au
1989
[29]
61.4 ± 1.0
718 ± 40
0.5
Au, Sc,
1978
Co, U [30]
61.2 ± 1.1
618 ± 33
0.1
Au, Mn
1974
[31]
63.0 ± 3.3
700 ± 20
0.5
_
1973
[32]
64 ± 6
_
_
Co
1962
Table 5
Experimental uncertainties for the thermal neutron cross-section and resonance integral measurements for one experiment.
Thermal neutron capture
Resonance integral
Cross-section measurement
measurement
Uncertainties due to
Uncertainties(%) 166
Ho
55
Mn
Uncertainties due to
60
Co
Ho
Monitor resonance
Statistical error
0.42 0.37
0.46
Detection Efficiency
1.52 1.63
1.72
Mass
0.01 0.01
0.01
Half life
0.12 0.018 0.014
γ-ray emission probability
1.22 0.036 0.03
Monitor thermal neutron cross-section
-
0.75
Uncertainties(%) 166
Mn
60
Co
2.14
2.63
α-Shape parameter
3.91 4.23
4.16
Cadmium ratio
1.32 1.47
1.25
1.63 0.75
0.16
integral
Reference thermal neutron cross-section
-
55
0.16 12
Total uncertainty
1.99 1.83
1.78
Total uncertainty
4.43 5.01
5.08
It should be mentioned that, by this method, the neutron flux characteristics for the comparator and the element under consideration are identical. Therefore, this evaluation method can yield accurate values under conditions that the experiments are performed with small amount of comparator and element masses and an identical neutron flux for both comparator and element. 5. Conclusions Thermal neutron capture cross-section and resonance integral for 165Ho(n,γ)166gHo reaction were measured by the neutron activation method relative to 55
Mn(n,γ)56Mn and
59
Co(n,γ)60Co monitor reaction. The epithermal neutron
spectrum shaping factor was determined by the dual-monitor cadmium ratio method. The obtained values for thermal neutron capture cross-section and resonance integral were 58.6 ± 1.8 and 650 ± 31 which were in a good agreement with the previous literature. It seems that by the method used in this research, the thermal neutron cross-section can be determined with great precision.
13
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17
Fig 1. HPGe spectrum: gamma-ray spectrum of the sample which contain 166Ho, 56Mn and 60
Co.
S0168-583X(12)00736-7 http://dx.doi.org/10.1016/j.nimb.2012.11.013 NIMB 59033
To appear in:
Nucl. Instr. and Meth. in Phys. Res. B
Received Date: Revised Date:
17 April 2012 12 November 2012
Please cite this article as: S. Zolghadri, H. Yousefnia, H. Afarideh, A. Bahrami-Samani, A.R. Jalilian, M. GhanadiMaragheh, Measurement of Thermal Neutron Capture Cross-Section and Resonance Integral for the 165 Ho(n,γ)166gHo Reaction by the Activation Method, Nucl. Instr. and Meth. in Phys. Res. B (2012), doi: http:// dx.doi.org/10.1016/j.nimb.2012.11.013
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Measurement of Thermal Neutron Capture Cross-Section and Resonance Integral for the 165Ho(n,γ)166gHo Reaction by the Activation Method Samaneh Zolghadria, Hasan Yousefnia a, Hosein Afaridehb, Ali BahramiSamania, Amir Reza Jaliliana, Mohammad Ghanadi-Maragheha a
Radiopharmaceutical Research and Development Laboratory (RRDL), Nuclear Sciences
and Technology Research Institute (NSTRI), Tehran, Iran, Postal Code: 14395-836. b
Department of Physics, Amirkabir University of Technology, Tehran, Iran.
Abstract The thermal neutron capture cross-section and resonance integral for the 165
Ho(n,γ)166Ho reaction were measured experimentally by the activation
method. Holmium oxide, manganese oxide and cobalt oxide powders, all dissolved in a mixture of hydrochloric acid and nitric acid, were irradiated within and without cadmium covers in the Tehran Research Reactor. The measured value of the thermal neutron cross-section relative to the 55
Mn(n,γ)56Mn and 59Co(n,γ)60Co monitor reactions (with thermal neutron cross-
section of 13.3 ± 0.1b and 37.18 ± 0.06b) was 58.6 ± 1.8b. The result was in a good agreement with the most previously reported values. Also the resonance integral was determined relative to the
55
Mn(n,γ)56Mn and
59
Co(n,γ)60Co
monitor reactions with the reference value of 14.0 ± 0.3 and 75.9 ± 2.0 respectively. The measured resonance integral of the
165
Ho(n,γ)166Ho reaction
at the cadmium cut-off energy of 0.55eV was 650 ± 31. The result was measured with high precision and compared with other measurements in the literature. Keywords: Activation method ,
165
Ho(n,γ)166Ho, Resonance integral, Thermal
neutron cross-section, corresponding author. Tel: +98 935 969 5292; Fax: +98 21 88221116 email address :[email protected]
1
1. Introduction Nowadays the field of radionuclide therapy is going through an extremely interesting phase and is poised for greater growth and development in the coming years.166Ho is a therapeutic radionuclide which can be produced with a reasonable specific activity using the (n, gamma) reaction [1] . Since this radionuclide has favorable physical characteristics, it is considered as one of the widely needed medical isotopes that have recently been discovered [2]. 166
Ho-radiopharmaceuticals have been developed and used in various disease
and malignancy therapies.
166
Ho-DOTMP is a radio-labeled tetraphosphonate
localized specifically in the skeleton and is used for the treatment of multiple myeloma [3].
166
Ho chitosan is an effective compound for radiation
synovectomy [4] and also for the treatment of liver malignancies [5].
166
Ho-
DTPA complex can be used for endovascular radiation therapy [6]. Nowadays many other 166Ho-radiopharmaceuticals are produced in the research phase. Knowledge of the thermal neutron capture cross-section and resonance integral of the
165
Ho(n,γ)166Ho reaction is important because the related data are used
not only in the production of
166
Ho for activity determination of the produced
radionuclide but also in other applied nuclear fields. However, further studies have been reported in relation to the measurement of thermal neutron capture cross-section and resonance integral of this reaction, large discrepancies are perceived among the reported data [7]. Therefore, it seems that more studies are essential to determine the cross-section data more accurately. This could be achieved by using high purity materials, optimizing the irradiation, decay and counting times and the weight of irradiated element (taking care to minimize neutron self-shielding effects)[8]. In addition to the discrepancies mentioned above, variation of flux can cause significant errors. Unfortunately, even in the latest reported work [9] to evaluate the thermal neutron cross-section and
2
165
Ho(n,γ)166gHo reaction, the variation of flux is still
resonance integral for quite considerable [10].
Due to the large discrepancies found among the reported data and also the error caused by the variation of the flux which could be clearly seen in the previous researches, the measurement of the thermal neutron cross-section and resonance integral of
165
Mn(n,γ)56Mn
55
Ho was performed with great precision. In this work and
59
Co(n,γ)60Co
reactions,
having
favorable
nuclear
characteristics, were selected as neutron monitors. In order to reduce the errors caused by the variation of the flux, the sample and monitors were mixed and irradiated in the same position. For this purpose, MnO2 and Co3O4 powders were mixed with Ho2O3 and dissolved in a mixture of hydrochloric acid and nitric acid (3:1). Then a polystyrene tube was filled with the 50µl of the above solution in which the weight of each element was in the order of a microgram and then the solution was irradiated in the Tehran Research Reactor. By this method the neutron self-shielding factor could be neglected which could help to get the analytical results more accurately. 2. Material and methods 2.1. Sample irradiation Natural holmium oxide (Ho2O3), manganese oxide (MnO2), cobalt oxide (Co3O4) (with chemical purity of more than 99.8%) and all other chemical reagents were purchased from Merck (Darmstadt, Germany). In order to provide a suitable sample, Ho2O3, MnO2 and Co3O4 were weighed on a calibrated balance, mixed and dissolved in the reasonable amount of ultrapure solvent [mixture of hydrochloric acid and nitric acid (3:1)]. Then a polystyrene tube was filled with the 50µl of the above solution. The solution (50µl) contained 0.56, 0.09 and 824.52 µg of Ho2O3, MnO2 and Co3O4 3
respectively. Therefore, the amounts of Ho, Mn and Co were 0.48, 0.05 and 605.33 µg respectively. The polystyrene tube was located in the oven at 80ºC and the solution was dried. Therefore, the elements were deposited homogenously at the bottom of the tube. Due to the small amount of the materials, the thickness was negligible. Another polystyrene tube with the same solution as describe above, was prepared and located in the cadmium shield. Then both of them were placed in an aluminum can, sealed and irradiated in Tehran Research Reactor. The flux in Tehran Research Reactor was monitored by gold foil activation method (with and without cadmium foil shield). The flux at the irradiation position was 2.5 × 1013 ± 5% n/ Cm2.S. The error was in measuring of absolute value of the flux at the irradiation point. Since all the elements were mixed and placed in the same position, this value did not play any role in these measurements. Since the monitors and the element under consideration were all mixed and irradiated at the same position simultaneously, all elements experienced the same flux, therefore, the variation of the flux was negligible. The reason for significant reduction of errors is due to the same flux trend for all irradiated elements. Irradiation was performed with and without a standard cadmium cover (height/diameter =2, wall thickness=1mm) in Tehran Research Reactor for 10 minutes. This experiment was repeated 5 times.
2.2. Activity measurements For the activity measurement, the tube was washed with ultrapure solvent [mixture of hydrochloric acid and nitric acid (3:1)] and a homogeneous solution was prepared. The activity of the samples was measured by a p-type coaxial 4
high-purity germanium (HPGe) detector (model: EGPC 80-200R) coupled with a multichannel analyzer card system. The detection efficiency of the detector was 80% at 1332.501 keV relative to 3 ״diameter × 3 ״length NaI(Tl) detector. The resolution of the detector was 1.8keV for 1332.5keV (60Co) and 0.9 keV for 122 keV (57Co). Various standard reference sources of 85
Sr and
152
241
Am,
133
Ba,
137
Cs, 88Y,
Eu having the same geometry were used for the measurement of
detection efficiency. The geometry of irradiated sample also was the same as the standard reference source. The measurement was based on the γ-ray peaks with the highest intensity in the spectrum of isotope under consideration and after 2-4 hours of irradiation depending on the activity of the samples (this cooling time is necessary for reducing dead time losses). They were counted up at the reference distance of 15-20cm from the detector to minimize the uncertainties caused by the pile-up effects. The counting time was considered between 10-15 minutes based on the activity of each sample. It should be mentioned that the errors due to a decrease of dead time during counting were minimized by keeping the counting time below one tenth of the half life of the measured radionuclide. Dead times were less than 1%.The measured gamma-ray spectrum of the sample is shown in Fig. 1.
3. calculation 3.1. Thermal neutron cross-section determination The reaction rate of each sample is the reaction rate induced by both thermal and epithermal neutrons. For 1/V absorbers such as
165
Ho, the HØgdahl
convention [11] can be used for the reaction rate of the produced radionuclide which is given by
5
(1)
R g Gthφthσ0 φep I0 α Ge
In the above equation, g is the Westcott correction factor which shows the departure from 1/V law, φth and φep are the thermal and epithermal neutron flux, Gth and Ge are the thermal and epithermal neutron self-shielding factors, σ0 is the thermal neutron capture cross-section and I0 is the resonance integral. A sufficient thick cadmium cover absorbs all thermal neutrons, more or less inevitably a small number of the epithermal neutrons in the range between 0.1eV and 0.6eV [12]. Therefore, in this situation the reaction rate is only induced by the epithermal neutrons and determined as (2)
Rcd φep I0 α Ge Fcd
The correction factor Fcd=Ccd/Cep shows the difference between the reaction rate of the cadmium covered isotope and the reaction rate of the bare isotope induced by epithermal neutrons. R and Rcd in equations 1 and 2 are the reaction rates per target nucleus calculated as (3)
R , Rcd
The amounts of parameters needed for radioactivity determination are given in Table 1. Table1 6
Nuclear decay data used for determination of radioactivity.
Radionuclide
56
Mn
Atomic weight
Half life
(g/mol)
(day)
[13]
[14]
54.938049(9)
0.107449(19)
Detected γ-ray energy
Emission probability (%)
(keV)
[14]
[ 15] 846.7638(19)
98.85(3)
1173.22(8) 60
Co
166
Ho
58.933200(9)
1925.23(27)
164.93032(2)
1.1165(13)
1332.492(4)
99.85(3) 99.9826(6)
80.576(2)
6.55(8)
Nabs is the net number of counts under the full-energy peak collected during measuring time tm, w the weight of irradiated element, the saturation factor with λ being the decay constant, tirr the irradiation time, the decay factor with td being the decay time, the measurement factor correcting the decay during the measuring time, tm, M the atomic weight, θ the isotopic abundance, NA the Avogadro’s number, Iγ the absolute gamma-ray emission probability and εp the full-energy peak detection efficiency. From equations 1 and 2, the relationship between the thermal neutron crosssection of the produced radionuclide and the monitor can be derived by the following equation:
The thermal neutron capture cross-section for and
166
Ho relative to 55Mn(n,γ)56Mn
59
Co(n,γ)60Co monitor reaction with the well-known cross-section and
resonance integral (given in Table 2) was determined according to equation 4. The weight of irradiated materials was sufficiently low so that no correction for neutron self-shielding was necessary. 7
3.2. Epithermal neutron spectrum shaping factor, α, determination The knowledge of the epithermal spectrum shape factor α is an essential parameter for the correction of resonance integrals. Various methods have been reported for determination of α-shape factor experimentally [16]. In this study, α-shape factor for the epithermal neutron spectrum was determined by the dualmonitor method using the measured Cd ratios for
55
Mn(n,γ)56Mn and
59
Co(n,γ)60Co reactions according to the following equation:
with
3.3. Resonance integral determination The reference resonance integral I0 is usually defined by the product of the cross-section and a pure 1/E spectrum integrated between cadmium cut off energy Ecd and an arbitrarily chosen upper limit E3: (5) As it can be seen in the above equation, the resonance integral depends on the shape of neutron spectrum in the epithermal range. In general, the epithermal neutron spectrum deviates from the 1/E behavior; hence it can be shown by 1/E1+α, where α is the epithermal neutron spectrum shaping factor. Therefore, the resonance integral is related to α and demonstrated by I0(α).The relationship between I0(α) and I0 is given by (6) 8
with Er the effective resonance energy defined by Ryves [17] while Ecd is the cadmium cut-off energy. For each monitor, I0 was converted to I0(α) by equation 6 and the value of the measured α. Then I0(α) for the
165
Ho(n,γ)166gHo reaction was determined by
equation 7 relative to each monitor reaction and then I0(α) was converted to I0 according to equation 6. (7) The amounts of parameters needed for thermal neutron cross-section and resonance integral determination are given in Table 2.
Table 2 Nuclear data for thermal neutron cross-section and resonance integral determination
Nuclear reaction 55
Mn(n,γ)56Mn
59 165
σ0 (b) [18]
I0 (b) [18]
Fcd
g [18]
Ēr [19]
13.3 ± 0.1
14.0 ± 0.3
1.0 [20]
1.0004
468(51)
60
37.18 ± 0.06
75.9 ± 2.0
0.9909(20) [21]
1.0003
136(7)
166
-
-
0.99 [20]
1.0020
12.3(0.4)
Co(n,γ) Co
Ho(n,γ) Ho
4. Results and discussion The epithermal spectrum shape factor was calculated according to the procedure described earlier. The calculated value was -0.10. The thermal neutron capture cross-section was determined for
165
Ho(n,γ)166gHo reaction
relative to
55
Mn(n,γ)56Mn and 59Co(n,γ)60Co monitor reaction with the cross-section value
of 13.3b and 37.18b respectively. This measurement was carried out five times. For each experiment, the cross-section and resonance integral values and also 9
the uncertainties of them were calculated. These values are shown in Table 3. The final results for the cross-section and resonance integral were the averages for all experiments. The final uncertainty was calculated on the bases of the error propagation formula which can be seen below.
Where
is the uncertainty for each experiment and N is the number of
experiments. The determined average capture cross-section for
165
Ho(n,γ)166gHo reaction was
58.6 ± 1.8b. The thermal neutron capture cross-section was measured with high precision and was in a good agreement with the result of Van Do Nguyen (2011), Rajput (2009), Yucle (2005) and De corte (2003). The epithermal neutron spectrum shaping factor was determined by the dualmonitor cadmium ratio method. Table 3 Thermal neutron capture cross-section and resonance integral of 165Ho(n,γ)166gHo for all samples.
Sample
Thermal neutron
Resonance
No.
capture cross-
integral (b)
section (b) 1
60.1 ± 1.9
667 ± 30
2
59.2 ± 1.7
658± 22
3
58.3 ± 1.8
642± 32
4
57.8 ± 1.6
634 ± 25
5
57.6 ± 1.8
649 ± 42
Also the resonance integral for
165
Ho(n,γ)166gHo reaction relative to
55
Mn(n,γ)56Mn and 59Co(n,γ)60Co monitor reaction with the resonance value of
14.0b and 75.9b was determined .The measured resonance integral agreed 10
within 3% with the result of Van Do Nguyen (2011), Rajput (2009), Yucle (2005), Holden (1999) and De corte (1989). The measured values in this research and the previously reported values are given in Table 4. The experimental uncertainties for the thermal neutron cross-section and resonance integral measurements for a single experiment are given in Table 5. The main source of the uncertainty for the thermal neutron cross-section measurement is the detection efficiency. The main sources of the uncertainties for the resonance integral measurement are α-shape parameter and monitor resonance integral. As it can be seen the measured values of both thermal neutron capture crosssection and resonance integral are in a remarkable consistency with recent measurements. As outlined earlier, the weight of irradiated element should be kept as low as possible to minimize the neutron self-shielding factor; but it is obvious that the accuracy in the amount of element decreases with decreasing the mass of each element. Therefore, a reasonable amount of an element mass was weighed with great accuracy and then dissolved in suitable amount of ultrapure solution. Then a suitable volume of solution having approximately 10-100µg of element was irradiated. Therefore, by this method, the mass of each element is so low that the neutron self-shielding factor can be neglected.
Table 4 Thermal neutron capture cross-section and resonance integral for 165Ho(n,γ)166gHo.
Reference
Thermal neutron
Resonance
Cadmium
Monitor
capture cross-
integral(b)
cut-off
used
section(b) This
58.6 ± 1.8
Year
energy (eV) 650 ± 31
0.55
Mn, Co
2012
work 11
[9]
59.7 ± 2.5
671± 47
0.55
Au
2011
[22]
64.6959
_
_
_
2011
[2]
58.98 ± 2.10
657 ± 36
_
Au, Co,
2009
Zn, Zr [23]
52.8 ± 1.3
_
_
_
2006
[24]
59.2 ± 2.5
667 ± 46
0.55
Mn
2005
[25]
58.5 ± 1.3
_
_
Au
2003
[26]
58
670
0.5
Au
1999
[27]
64.4 ± 2.8
_
_
_
1998
[28]
66.500
752
_
_
1997
[8]
58.1 ± 2.3
636 ± 32
_
Au
1989
[29]
61.4 ± 1.0
718 ± 40
0.5
Au, Sc,
1978
Co, U [30]
61.2 ± 1.1
618 ± 33
0.1
Au, Mn
1974
[31]
63.0 ± 3.3
700 ± 20
0.5
_
1973
[32]
64 ± 6
_
_
Co
1962
Table 5
Experimental uncertainties for the thermal neutron cross-section and resonance integral measurements for one experiment.
Thermal neutron capture
Resonance integral
Cross-section measurement
measurement
Uncertainties due to
Uncertainties(%) 166
Ho
55
Mn
Uncertainties due to
60
Co
Ho
Monitor resonance
Statistical error
0.42 0.37
0.46
Detection Efficiency
1.52 1.63
1.72
Mass
0.01 0.01
0.01
Half life
0.12 0.018 0.014
γ-ray emission probability
1.22 0.036 0.03
Monitor thermal neutron cross-section
-
0.75
Uncertainties(%) 166
Mn
60
Co
2.14
2.63
α-Shape parameter
3.91 4.23
4.16
Cadmium ratio
1.32 1.47
1.25
1.63 0.75
0.16
integral
Reference thermal neutron cross-section
-
55
0.16 12
Total uncertainty
1.99 1.83
1.78
Total uncertainty
4.43 5.01
5.08
It should be mentioned that, by this method, the neutron flux characteristics for the comparator and the element under consideration are identical. Therefore, this evaluation method can yield accurate values under conditions that the experiments are performed with small amount of comparator and element masses and an identical neutron flux for both comparator and element. 5. Conclusions Thermal neutron capture cross-section and resonance integral for 165Ho(n,γ)166gHo reaction were measured by the neutron activation method relative to 55
Mn(n,γ)56Mn and
59
Co(n,γ)60Co monitor reaction. The epithermal neutron
spectrum shaping factor was determined by the dual-monitor cadmium ratio method. The obtained values for thermal neutron capture cross-section and resonance integral were 58.6 ± 1.8 and 650 ± 31 which were in a good agreement with the previous literature. It seems that by the method used in this research, the thermal neutron cross-section can be determined with great precision.
13
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166
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17
Fig 1. HPGe spectrum: gamma-ray spectrum of the sample which contain 166Ho, 56Mn and 60
Co.