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Determination of the total neutron cross section for natural hafnium in the energy range 2–145 keV
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ScienceDirect Nuclear Physics A 996 (2020) 121693 www.elsevier.com/locate/nuclphysa
Determination of the total neutron cross section for natural hafnium in the energy range 2–145 keV Olena Gritzay ∗ , Anna Grymalo, Volodymyr Pshenychnyi, Vitaliy Venedyktov, Viktor Shachov Institute for Nuclear Research, National Academy of Sciences of Ukraine, prospekt Nauky, 47, Kyiv, 03028, Ukraine Received 19 September 2019; received in revised form 19 December 2019; accepted 30 December 2019 Available online 8 January 2020
Abstract Experimental determination of the total neutron cross section for natural hafnium was carried out at the Kyiv Research Reactor using the neutron filtered beams with the energies 2, 54, 59, and 145 keV. The transmission method was used in these measurements. The results are presented together with the analysis of the previous experimental data and the evaluated nuclear data from the ENDF libraries. © 2020 Elsevier B.V. All rights reserved. Keywords: Total neutron cross section; Natural hafnium; Filtered neutron beam; Transmission method; Kyiv Research Reactor
1. Introduction Hafnium and its alloys are used for control rods in nuclear reactors for energy productions and submarine propulsion, because hafnium is an excellent neutron absorber, corrosion resistant, and it has a very high melting point. As it is known the interpretations of critical experiments with UOx fuel conducted by CEA in the AZUR zero-power reactors has shown systematic underestimation of the reactivity worth that may be attributed to an overestimated natural hafnium capture cross section. Experimental results reported in the literature obtained either from microscopic or integral measurements have pointed * Corresponding author.
E-mail address: [email protected] (O. Gritzay). https://doi.org/10.1016/j.nuclphysa.2020.121693 0375-9474/© 2020 Elsevier B.V. All rights reserved.
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out that all existing evaluated neutron data libraries show deficiencies concerning description of the nuclear properties of the hafnium isotopes. So, a new high precision measurement of the capture cross section for natural hafnium is needed. The development of the filtered neutron beam technique at the Kyiv Research Reactor (KRR) enables to form the fluxes of about 106 to 107 neutrons/cm2 /s at fixed neutron energies in the range 0–160 keV at the horizontal reactor channels. High intensity quasi-mono-energy beam availability and the existing experimental base allow us to perform precise measurements of total neutron cross sections with an accuracy better than 0.1% and of neutron elastic scattering cross sections with an accuracy better than 3%. At neutron energies smaller than 100 keV the hafnium capture cross section may be determined as the difference between total and elastic scattering cross sections. So, the achievement of a 4% uncertainty of the capture cross section for natural hafnium being measured at the KRR filtered beams is possible. The measurements of the total neutron cross section for natural hafnium, results of which are presented here, were the first step to solve this task. 2. Experimental set-up and measurements Experimental investigation of the total neutron cross section for natural hafnium was made on the eighth and ninth horizontal experimental channels (HEC) at the KRR. One (HEC-8) of these channels, having a diameter 60 mm, begins at the Be reflector. Another one (HEC-9), having a diameter of 100 mm, begins at the reactor core. Experimental installations on horizontal reactor channels include the systems of filtered neutron beam forming, neutron detector and registration systems, sample management systems and systems of radiation shielding. The forming system includes the elements of beam collimation and neutron filtering on the way from reactor core to the detector. The preliminary forming of necessary beam geometry is realized with two iron and boron carbide collimators, installed behind the shutter at a distance of 1.5 m from the channel start. General length of the collimators is 600 mm (390 mm – iron, 210 mm – boron carbide). Further beam forming takes place in the first three discs of shutter and in outer collimator. By turns lead, textolite and mixture of paraffin with H3 BO3 are used as material for these collimators. The collimation system provided beam narrowing to 12 mm/m, what corresponded to beam diameter at the sample in 10 mm. The elements of the neutron filtration system take place in the first three disks of shutter and in outer collimator. Scheme of the experimental installation on the 8-th horizontal reactor channels is shown in Fig. 1. The experimental installations for total cross section measurements on the eighth and ninth HEC are similar, discrepancies consist in construction of the devices for sample removing and in construction of the radiation shielding systems. On both horizontal channels the radiation shielding systems are made of two boxes. The first and second boxes are separated by a shielding wall (thickness 40 cm on the 8-th HEC, thickness 70 cm on the 9-th HEC), in which the Pb collimator (internal diameter 2 cm) is placed. The outside collimator with additional elements for beam collimation and neutron filtration and the device for sample removing are placed in the first boxes; detectors, their power supply electronic blocks and monitoring equipment are located in the second boxes. Walls and ceilings of boxes on the both channels were made from metal containers filled by metal scrap, water and 5–7% boric acid. Both boxes on these different channels have different sizes, disposition of entrances and thickness of walls. The detection and neutron registration systems on both HEC include: neutron counter, electronic blocks, personal computer and communication lines about 50 m long between spectro-
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Fig. 1. A scheme of the experimental installation on the HEC-8. 1 – reactor core; 2 – beryllium reflector; 3 – horizontal channel; 4 – preliminary collimators; 5 – elements for forming of the beam; 6 – outside collimator; 7 – shutter disks; 8 – filter components; 9 – biological shielding; 10 – device for sample removing; 11 – Installation for Angle Scattering Distribution (IASD-3); 12 – tube to conduct of beam to neutron catching; 13 – neutron beam catching; 14 – radiation shielding of installation.
metric installation and measuring room. For neutron average energy 2 keV, the helium-3 counter CHM-17 (diameter – 18 mm, length – 500 mm, gas pressure – 7 atm) was used. For neutron average energies 54, 59 and 145 keV, the proportional hydrogen recoil counter LND 281 (Gas Filling – H + CH4 + N2 , diameter – 38.1 mm, length – 254.0 mm, gas pressure – 4.3 atm.) was used. Because the shape of the spectrum from a 3 He proportional counter does not allow us to distinguish contribution from different incident neutron energies, we tried to create the 2 keV filter as more as possible pure (especially in the thermal energy region where efficiency of this counter is very high) to decrease a value of an error connected with existence in the filtered neutron beam additional lines. A value of this error was evaluated by calculation using ENDF/B libraries. The shape of the spectrum from the recoil proton counter has the shape of shelves, where each shelf corresponds to a specific neutron energy (with the exception of the low-energy region, where the shelves actually merge and the effect of gamma rays and the wall effect are manifested). Thus, in order to remove the contribution from additional lines, we have to cut out the spectrum to the left of the investigated energy region and to subtract the values on the shelf to the right of this region. That is why the requirement for the purity of the filter is not so strong when studying in the energy region above 10 keV. To estimate the possible error values connected with the presence of additional lines in the 54, 59 and 145 keV filtered neutron beams, we fulfilled the calculation using the ENDF/B libraries, but they were taken into account experimentally. The total neutron cross sections for natural hafnium at the neutron filtered beams were measured on the horizontal reactor channels at KRR using transmission method. For determination of background counting rate the polyethylene samples with thickness 0.01315–0.02281 nucl/barn were used. To remove the influence of instability factors, the samples at neutron beam were replaced every minute. The natural hafnium samples were made from metal hafnium ingots, purchased at the State Research and Production Enterprise “Zirconium”. According to the passport, the chemical composition was as follows: Hf not less than 99.26%, mass fraction of impurities – 0.74%, including 0.62% zirconium. For measurements, a number of samples with a diameter of 30.4 mm were made. The observed total neutron cross section was calculated by using the following formula: σobs = −(1/n) · lnT , σobs = −(1/n) (dT /T )2 + (σobs dn)2 , (1)
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Table 1 Filter composition with the average energy 2 keV. Element (ENDF)
Sc (JEFF-3.2)
60 Ni
54 Fe
(JEFF-3.2)
S (JEFF-3.2)
Co (JEFF-3.2)
10 B
(JEFF-3.2)
Thickness, g/cm2
110.59
80.2
39.37
55.7
26.7
0.2
(JEFF-3.2)
Fig. 2. Calculated neutron spectrum after the 2 keV filter.
where n-thickness of the transmission.
nat Hf
sample in nucl/barn, < T >-experimental average value of the
2.1. Filter 2 keV The filter component optimization, to receive the highest intensity of the main energy line in the neutron spectrum, was carried out by means of calculation using our code FILTER_7 [1]. The components of this filter and the calculated neutron spectrum after this filter are presented in Table 1 and in Fig. 2. Purity of the filter – 99.6%. Other additions to the main neutron line were negligible: a line with the energy 26.7 keV was about 0.1%, lines 42.8 keV, 49.0 keV and 64.6 keV were about 0.15%, 0.02% and 0.13%, respectively. The evaluated error values to the cross section connected with the presence of additional lines at the 26.7 keV energy is 0.035%, at 42.8 keV, 49.0 keV and 64.6 keV lines are 0.145%, 0.017% and 0.125%, respectively. So, the error to the cross section connected with the presence of all additional lines did not exceed 0.322%. The calculated energy and width of the neutron line (95% response function) after this filter are: 1.91 ±0.69 0.86 keV An experimental investigation of the total neutron cross sections for nat Hf was carried out on the HEC-9 at the KRR. Two series of measurements were fulfilled on the filtered neutron beam with the 2 keV average energy. In each of these series a set of the samples with thickness from
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Table 2 Sample thickness, total neutron cross section obtained on the 2 keV filter. Thickness (n), nucl/barn 0.00236 ± 0.00002 0.00427 ± 0.00003 0.00473 ± 0.00003 0.00785 ± 0.00005 0.01257 ± 0.00008
± σ , barn (σ /σ , %) First series 23.09 ± 0.21 (0.91) 23.15 ± 0.22 (0.95) 21.45 ± 0.15 (0.70)
Second series 23.57 ± 0.41 (1.74) 22.99 ± 0.32 (1.39) 20.52 ± 0.18 (0.88)
Fig. 3. Total neutron cross sections obtained with the 2 keV filtered neutron beam.
0.00236 to 0.01257 nucl/barn was used. The obtained values of the total neutron cross section are presented in Table 2 and in Fig. 3. As shown in Table 2 and in Fig. 3, these observed total neutron cross sections depend on the thickness of the sample. This is due to the presence of resonances in the hafnium total cross section in the energy range 0.39–2.99 keV. For determination of the unshielded total neutron cross section, it is necessary to enter a correction on a self-shielding effect, namely: to divide the eff observed total neutron cross sections σt j into the self-shielding factors: eff
σt unsh. = σt j /kj , j
(2)
where kj – resonance self-shielding factor for the sample with thickness j . The resonance self-shielding factors kj were calculated by using the following formula: kj = σt sh.calc. /σt unsh.calc. , j
(3)
where σt unsh.calc. – the unshielded total neutron cross section, σt sh.calc. – a set of the shielded j sh.calc. neutron cross section σt j for j thicknesses of the investigated samples, calculated using the MCNP 4c code [2]. In these MCNP 4c calculations the simplified geometry of the experiment was used. The calculated spectrum after 2 keV filter (see Fig. 2) was used as a neutron source. The hafnium sample with diameter 30.4 mm was placed at the distance of 2 m from
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Fig. 4. Our experimental results and the calculated total neutron cross section using the MCNP 4c code. Table 3 The parameters of the extrapolation using ENDF/B-VI and CENDL-3.1 libraries. Libraries ENDF/B-VI CENDL-3.1
Coefficients a
b
c
χ2
34.79 ± 0.07 23.72 ± 0,04
−504 ± 19 −447 ± 39
17153 ± 1106 12411 ± 2899
1.0 1.0
the neutron source. The distance from the sample to the neutron detector was 2 m (parameters of the detector: Ø = 38 mm, l = 200 mm). Ten samples were used in the modeling: five of them correspond to the samples from our experiment and another five were thinner samples. The thickness of the thinnest sample was 0.00022 nucl/barn. The MCNP 4c calculations were done using data from two evaluated data libraries:ENDF/B-VI and CENDL-3.1. Just in these libraries the largest differences between the total neutron cross section for natural hafnium are observed. These calculation results and our experimental data (see Table 2) are presented in Fig. 4. The extrapolation to zero thickness (solid line) with using polynomial of the second order σt sh.calc. = a + bM · nj + c · n2j (coefficients a, band c are given in the Table 3) gives a possibility to determine σt unsh.calc. = 34.79 ± 0.07 barn using the ENDF/B-VI library calculations and σt un.calc. = 23.72 ± 0.04 barn using the CENDL-3.1. As we can see in Fig. 4, the unshielded total neutron cross sections determined with using data from ENDF/B-VI and CENDL-3.1 libraries differ more than 30%. The difference between the parameters b is significantly less (the solid lines in Fig. 4 is almost parallel). Such situation can be observed in the case, when the structure of the resonance cross sections is close enough to the investigated energy region. The obtained resonance self-shielding factors kj , calculated with using the calculation results from ENDF/B-VI and CENDL-3.1 and formula (3) are presented in Table 4. The errors kj were calculated using the next formula: 2 2 kj = kj · /σt sh.calc. + σt unsh.calc. /σt unsh.calc. (4) σt sh.calc. j j
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Table 4 Calculated self-shielding factors. Thickness (nj ), nucl/barn
ENDF/B-VI kj
kj
kj
CENDL-3.1 kj
0.00022 0.00044 0.00074 0.00118 0.00175 0.00236* 0.00427* 0.00473* 0.00783* 0.01256*
1.00 0.99 1.00 0.988 0.978 0.970 0.947 0.942 0.918 0.896
0.02 0.01 0.01 0.004 0.003 0.002 0.001 0.001 0.001 0.001
1.00 0.99 0.99 0.98 0.96 0.95 0.920 0.913 0.880 0.846
0.06 0.03 0.02 0.01 0.01 0.01 0.004 0.003 0.002 0.002
* The thickness of the sample which was used in the experiment.
Table 5 The observed (shielded) and unshielded cross sections values. Thickness (n), nucl/barn
0.00236 0.00427 0.00427 0.00473 0.00785 0.01257
Experimental and experimentally-calculated results Observed (shielded) cross section
σjsh. /kENDF/B−VI
σjsh. /kfrom CENDL − 3.1
σjsh. , barn
σjsh.
unsh. , barn σexp
unsh. σexp
unsh. , barn σexp
unsh σexp
23.57 23.00 23.09 23.15 21.45 20.52
0.41 0.32 0.21 0.22 0.15 0.18
24.29 24.29 24.39 24.57 23.36 22.89
0.45 0.36 0.25 0.26 0.18 0.22
24.74 25.01 25.11 25.37 24.38 24.26
0.45 0.36 0.25 0.26 0.18 0.22
The calculated values of the resonance self-shielding factors kj were used for determination of the experimental value σt unsh. (using formula (2)). The calculation results are presented in j Table 5. The errors σt unsh. were calculated using the next formula: j σt unsh. j
= σt unsh. j
·
sh. σt sh. j /σt j
2
2 + kj /kj
(5)
The mean value of the experimental unshielded total cross section obtained from measurement unsh. = 23.75 ± 0.29 barn using the resonance results with six hafnium measurements is σt unsh. = 24.71 ± 0.19 barn with the self-shielding factors calculated with the ENDF/B-VI and σt CENDL-3.1 library. The average value of the experimental unshielded total cross section and its uncertainty were calculated using next formulas: n
n
2 2 < σ >= σi /σi / 1/σi (6) i=1
i=1
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Table 6 Filter composition with the average energy 54 keV. Element (ENDF)
Si (JEFF-3.2)
S (JEFF-3.2)
Mn (JEFF-3.2)
Al (JEFF-3.2)
10 B
Thickness, g/cm2
256.3
76.8
6.26
5.39
0.5
(JEFF-3.2)
Fig. 5. Calculated neutron spectrum after the 54 keV filter.
n 2
< σ >= 1/ 1/σi
(7)
i=1
As expected, the unshielded cross section values are close – the difference is just 1 barn, but what value is the more reliable? Since in absolute value our result agrees better with the data from CENDL-3.1, we consider that the received in this work experimental value of the unshielded total unsh. = 24.71 ± 0.19 barn. cross section is σexp 2.2. Filter 54 keV The composite neutron filter consisting of Si, Al, S, Mn and 10 B was used to obtain the quasi-mono-energy beam with the average energy 54 keV. The filter components (g/cm2 ) are given in Table 6. The calculated spectrum after the 54 keV filter is presented in Fig. 5. Purity of the beam was about 99.6%. Other additions to the main neutron line were negligible: three lines in the energy region 144–146 keV were about 0.4%. The estimated possible error value to the cross section connected with the presence of additional lines does not exceed 0.32%. The limits of 95% response function for the 54 keV filter spectrum were defined as: 53.86 ±0.25 0.29 keV Measurements of the total neutron cross section for natural hafnium at the energy 54 keV were carried out on the 8-th HEC. The sample thickness and the total neutron cross section, obtained on each sample, are presented in Table 7 and in Fig. 6.
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Table 7 Sample thickness and experimental results, obtained with the 54 keV filtered beam. Thickness (n), nucl/barn
σ ± σ , barn
σ /σ , %
0.00491 ± 0.00004 0.00799 ± 0.00003 0.01289 ± 0.00004
8.55 ± 0.29 8.61 ± 0.21 8.65 ± 0.09
3.39 2.44 1.04
Fig. 6. Total neutron cross sections obtained with the 54 keV filtered neutron beam.
As we can see from Table 7 and Fig. 6, the results, obtained on different hafnium samples, coincide within the experimental error and a self-shielding effect is not observed. The average value of the total cross section and its uncertainty were calculated with using formulas (6) and (7). The total neutron cross section averaged on the 3 samples is: 8.65 ± 0.01 barn (0.12%). 2.3. Filter 59 keV The filter with the average neutron energy 59 keV was used in the experimental investigations [3–6]. Now this filter was recalculated and it was complemented by the new components. These calculations were done using the Filter-7 code. The components of this filter are presented in Table 8. The calculated neutron spectrum after this filter is presented in Fig. 7. Purity of the filter – 95.0%. Other additions to the main neutron line were negligible: lines with the energy 36.1 keV, 38.7 keV, and 80.5 keV were 0.01%, 0.01%, 0.02%, respectively, two groups of lines in the energy region 230–280 keV and 325–368 keV were about 0.15% and 0.75%, respectively. A contribution of the lines above 540 keV was about 4%. The estimated possible error value to the cross section connected with the presence of additional lines does not exceed 1.7%. The calculated energy and width of the neutron line (95% response function) after this filter are:
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Table 8 Composition of the filter with the average energy 59 keV. Element (ENDF)
S (JEFF-3.2)
58 Ni
V (JEFF-3.2)
Al (JEFF-3.2)
10 B
(JEFF-3.2)
Thickness, g/cm2
116.53
81.42
24.44
5.4
0.5
(JEFF-3.2)
Fig. 7. Calculated neutron spectrum after the 59 keV filter.
58.5 ±1.9 6.4 keV The experimental investigations of the total neutron cross sections for natHf were carried out on the 8-th HEC at the KRR. Three series of measurements were carried out. In each of the series a set of the metallic hafnium samples with thicknesses from 0.00245 ± 0.00004 to 0.0130 ± 0.0001 nucl/barn were used. Measurement results of the total neutron cross section of the natural hafnium for each of the series are presented in Table 9 and in Fig. 8. As shown in Table 9 and in Fig. 8, the observed total neutron cross sections depend on the thickness of the sample. This is again due to resonances present in the hafnium total cross section in the energy range 58–60 keV. In Fig. 8, there are experimental total neutron cross sections received in each of the series and their extrapolation to zero thickness using the second order polynomial. Unshielded total neutron cross section value received in these measurements is 11.47 ± 0.69 barn, (6.0%). 2.4. Filter 145 keV Measurements of the total neutron cross section for natural hafnium at the energy 145 keV were carried out on the 9-th HEC.A composition of the filter for getting a quasi-mono-energetic line with the average energy 145 keV is presented in Table 10. Spectrum after this filter, calculated by the Filter-7 code, is presented in Fig. 9. Purity of the filter – 98.87%. The contribution of the line 54 keV was about 1.13%. The estimated possible error value to the cross section connected with the presence of additional lines does not exceed 0.95%. Other additions to the main neutron line were negligible. The calculated energy and width of the neutron line (95% response function) after this filter are:
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Table 9 The sample thickness and experimental results. σ ± σ , b (σ/σ , %)
Thickness (n), nucl/barn
First series
0.00245 ± 0.00004 0.00437 ± 0.00004 0.00464 ± 0.00004 0.00709 ± 0.00009 0.00798 ± 0.00004 0.0124 ± 0.0001 0.0130 ± 0.0001
Second series
10.61 ± 0.37 (3.55) 10.33 ± 0.21 (2.01) 10.22 ± 0.15 (1.47)
Third series 11.23 ± 0.60 (5.4)
10.73 ± 0.41 (3.86) 10.35 ± 0.25 (2.38)
10.94 ± 0.33 (3.03) 10.58 ± 0.24 (2.29)
10.37 ± 0.17 (1.67)
Fig. 8. Total neutron cross sections obtained with the 59 keV filtered neutron beam.
Table 10 Composition of the filter with average energy 145 keV. Element (ENDF)
Si (JEFF-3.2)
Ti (JEFF-3.2)
10 B
Thickness, g/cm2
184.07
11.49
0.2
(JEFF-3.2)
144.86 ±3.83 5.03 keV Three series of measurements were carried out. In each of these series a set of the samples of metallic hafnium with thicknesses from 0.00423 ± 0.00001 to 0.07701 ± 0.0007 nucl/barn were used. Measurement results of the total neutron cross section for natural hafnium in each of the series are presented in Table 11 and in Fig. 10. As shown in Fig. 10 in each of these series there is no dependence of the total cross section on the sample thickness. Therefore the average value of the total neutron cross section was calculated using formulas (6), (7) and it equals 8.47 ± 0.01 barn (0.12%).
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Fig. 9. Calculated neutron spectrum after the 145 keV filter. Table 11 Sample thickness and experimental results. Thickness (n), nucl/barn
σ ± σ , barn (σ/σ , %) First series
Second series
0.00423 ± 0.00001 0.01242 ± 0.00004 0.02745 ± 0.00009 0.04193 ± 0.00005 0.07701 ± 0.00007 Average value σ Average value σ over 3 series
8.34 ± 0.06 (0.72) 8.47 ± 0.04 (0.47) 8.40 ± 0.03 (0.36)
8.58 ± 0.09(1.05)
8.41 ± 0.02 (0.24)
8.53 ± 0.02 (0.23) 8.47 ± 0.01 (0.12)
8.55 ± 0.04 (0.47) 8.52 ± 0.03 (0.35)
Third series
8.47 ± 0.02 (0.24) 8.41 ± 0.01 (0.12) 8.42 ± 0.01 (0.12)
Fig. 10. Experimental total neutron cross section received in each of the series.
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Fig. 11. Total neutron cross section from CENDL-3.1 and ENDF/B-VI, experimental data from database EXFOR/CSISRS and our experimental result for the energy 2 keV.
3. Discussion of results The total neutron cross section for the nat Hf is presented in three libraries: ENDF/B-VI, JENDL-3.2 and CENDL-2. In other libraries, there are information for separate isotopes, so for these libraries, the total cross section was calculated by the code PREPRO 2015 (subroutine MIXER) using all 6 hafnium isotopes. The total neutron cross section from the database EXFOR/CSISRS and our experimental results for the energy 2 keV and 54, 59 and 145 keV are presented in Fig. 11 and in Fig. 12. Also, the two most discrepant cross sections, found in CENDL-3.1 and ENDF/B-VI, are presented in Fig. 11, found in JENDL-4.0 and ENDF/B-VI are presented in Fig. 12. Cross sections from all other ENDF/B libraries are placed between these libraries. To compare our experimental results with the evaluated data, the point-wise total neutron cross sections for nat Hf from the ENDF/B libraries were averaged on the calculated spectrum after the 2, 54, 59 and 145 keV filter. The obtained values are presented in Table 12. As shown in Fig. 12 and in Table 12 experimental total cross section for the nat Hf obtained at the energy 54 keV does not coincide with any of the libraries, but it is in good agreement with the results of [7] and slightly higher of the experimental data presented in [8]. Our experimental result at the 59 keV energy is in good agreement with the ENDF/B-VII.1 (JEFF-3.1) library and does not coincide with the results of other authors. Our experimental result at the energy 145 keV is better in agreement with the JENDL-4.0 library and lies slightly below the data presented in [9,10]. We assume (in detail see [6], where our results at the 59 keV filter were published for the first time) that in the energy region above 50 keV there is a resonance or group of resonances. In the future, we plan to conduct measurements using the average energy shift method for filtered neutron beam [11]. This method gives possibility to obtain a set of cross sections at the close energies in the energy region of an assumed resonance. This will allow us to prove or disprove the existence of a resonance in this region.
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Average energy of the filter (keV)
Average region (keV)
Libraries ENDF/B-VII.1 (JEFF-3.1)
JENDL-4.0
ROSFOND-2010
CENDL-3.1
Our exp. result σ ± σ , barn (σ/σ , %)
2 54 59 145
0.39–2.99 38.9–54.8 52.2–60.1 110.45–155.15
26.44 (26.94) 11.32 11.1 8.89
25.66 10.05 9.86 8.39
25.41 10.88 10.65 8.84
23.93 10.44 10.24 8.81
24.71 ± 0.19, (0.77) 8.65 ± 0.01, (0.12) 11.47 ± 0.69, (6.0) 8.47 ± 0.01, (0.12)
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Table 12 Averaged total neutron cross section from the ENDF/B libraries and our experimental results.
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Fig. 12. Total neutron cross section from the ENDF/B libraries, experimental data from database EXFOR/CSISRS and our experimental result at the energy 54, 59 and 145 keV.
4. Conclusions The total neutron cross sections of the nat Hf in the energy range 2–145 keV at the filtered neutron beam were measured. There is no dependence of the total cross section on the sample thickness at the energies 54 keV and 145 keV, which means that a self-shielding effect is not observed. Our experimental results at the energies 54 and 145 keV are in good agreement with the results of other authors. Our experimental data at the energy 54 keV does not coincide with any of the libraries and our data at the energy 145 keV is better in agreement with the JENDL-4.0 library. There is a dependence of the total cross section on the sample thickness at the energies 2 keV and 59 keV. Our experimental data is slightly higher than the results of other authors, this may be due to the fact that these authors did not take into account a self-shielding effect. The unshielded total neutron cross sections at the energies 2 keV and 59 keV are in a good agreement with CENDL-3.1 and ENDF/B-VII.1, respectively. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] O.O. Gritzay, M.M. Vakulenko, in: Proc. of the 4-th Int. Conf. NPAE, Kyiv, Ukraine, 2013, p. 426. [2] J.F. Briesmeister (Ed.), MCNP – A General Monte Carlo N-Particle Transport Code. Version 4C. Report No. LA-13709-M, Los Alamos National Laboratory, NM, USA, March 2000, p. 788. [3] O.O. Gritzay, V.V. Kolotyi, N.A. Klimova, O.I. Kalchenko, M.L. Gnidak, O.I. Korol, P.M. Vorona, in: Proc. of the ND 2004, USA, Santa Fe, 2004. [4] O.O. Gritzay, V.V. Kolotyi, N.A. Klimova, O.I. Kalchenko, P.N. Vorona, M.L. Gnidak, in: Proc. of the ISRD 12, USA, Gatlinburg, 2005.
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[5] V.A. Libman, O.O. Gritzay, V.F. Razbudey, in: Proc. of the 2-nd Int. Conf. “Current Problems of Nuclear Physics and Atomic Energy”, Kyiv, Ukraine, 2008, p. 548. [6] O.O. Gritzay, A.K. Grymalo, V.V. Koloty, V.M. Venedyktov, S.P. Volkovetskyi, V.P. Shachov, Uzhhorod University Scientific Herald, Ser. Phys. 30 (2011) 142 (Ukr). [7] A. Okazaki, S.E. Darden, R.B. Walton, Phys. Rev. B 93 (1954) 461. [8] H.J. Cho, K. Kobayashi, S. Yamamoto, Y. Fujita, Y. Lee, G. Kim, I.S. Ko, M.-H. Cho, W. Namkung, S.K. Ko, Ann. Nucl. Energy 27 (2000) 1259. [9] G.L. Sherwood, A.B. Smith, J.F. Whalen, Nucl. Sci. Eng. 39 (1970) 67. [10] M. Divadeenam, E.G. Bilpuch, H.W. Newson, Prog. Rep.: USAEC Nucl. Cross Sections Advisory Comm. Repts 31 (1970) 218. [11] O.O. Gritzay, A.K. Grymalo, V.A. Pshenychnyi, Nucl. Phys. At. Energy 17 (2016) 411 (Ukr).
ScienceDirect Nuclear Physics A 996 (2020) 121693 www.elsevier.com/locate/nuclphysa
Determination of the total neutron cross section for natural hafnium in the energy range 2–145 keV Olena Gritzay ∗ , Anna Grymalo, Volodymyr Pshenychnyi, Vitaliy Venedyktov, Viktor Shachov Institute for Nuclear Research, National Academy of Sciences of Ukraine, prospekt Nauky, 47, Kyiv, 03028, Ukraine Received 19 September 2019; received in revised form 19 December 2019; accepted 30 December 2019 Available online 8 January 2020
Abstract Experimental determination of the total neutron cross section for natural hafnium was carried out at the Kyiv Research Reactor using the neutron filtered beams with the energies 2, 54, 59, and 145 keV. The transmission method was used in these measurements. The results are presented together with the analysis of the previous experimental data and the evaluated nuclear data from the ENDF libraries. © 2020 Elsevier B.V. All rights reserved. Keywords: Total neutron cross section; Natural hafnium; Filtered neutron beam; Transmission method; Kyiv Research Reactor
1. Introduction Hafnium and its alloys are used for control rods in nuclear reactors for energy productions and submarine propulsion, because hafnium is an excellent neutron absorber, corrosion resistant, and it has a very high melting point. As it is known the interpretations of critical experiments with UOx fuel conducted by CEA in the AZUR zero-power reactors has shown systematic underestimation of the reactivity worth that may be attributed to an overestimated natural hafnium capture cross section. Experimental results reported in the literature obtained either from microscopic or integral measurements have pointed * Corresponding author.
E-mail address: [email protected] (O. Gritzay). https://doi.org/10.1016/j.nuclphysa.2020.121693 0375-9474/© 2020 Elsevier B.V. All rights reserved.
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out that all existing evaluated neutron data libraries show deficiencies concerning description of the nuclear properties of the hafnium isotopes. So, a new high precision measurement of the capture cross section for natural hafnium is needed. The development of the filtered neutron beam technique at the Kyiv Research Reactor (KRR) enables to form the fluxes of about 106 to 107 neutrons/cm2 /s at fixed neutron energies in the range 0–160 keV at the horizontal reactor channels. High intensity quasi-mono-energy beam availability and the existing experimental base allow us to perform precise measurements of total neutron cross sections with an accuracy better than 0.1% and of neutron elastic scattering cross sections with an accuracy better than 3%. At neutron energies smaller than 100 keV the hafnium capture cross section may be determined as the difference between total and elastic scattering cross sections. So, the achievement of a 4% uncertainty of the capture cross section for natural hafnium being measured at the KRR filtered beams is possible. The measurements of the total neutron cross section for natural hafnium, results of which are presented here, were the first step to solve this task. 2. Experimental set-up and measurements Experimental investigation of the total neutron cross section for natural hafnium was made on the eighth and ninth horizontal experimental channels (HEC) at the KRR. One (HEC-8) of these channels, having a diameter 60 mm, begins at the Be reflector. Another one (HEC-9), having a diameter of 100 mm, begins at the reactor core. Experimental installations on horizontal reactor channels include the systems of filtered neutron beam forming, neutron detector and registration systems, sample management systems and systems of radiation shielding. The forming system includes the elements of beam collimation and neutron filtering on the way from reactor core to the detector. The preliminary forming of necessary beam geometry is realized with two iron and boron carbide collimators, installed behind the shutter at a distance of 1.5 m from the channel start. General length of the collimators is 600 mm (390 mm – iron, 210 mm – boron carbide). Further beam forming takes place in the first three discs of shutter and in outer collimator. By turns lead, textolite and mixture of paraffin with H3 BO3 are used as material for these collimators. The collimation system provided beam narrowing to 12 mm/m, what corresponded to beam diameter at the sample in 10 mm. The elements of the neutron filtration system take place in the first three disks of shutter and in outer collimator. Scheme of the experimental installation on the 8-th horizontal reactor channels is shown in Fig. 1. The experimental installations for total cross section measurements on the eighth and ninth HEC are similar, discrepancies consist in construction of the devices for sample removing and in construction of the radiation shielding systems. On both horizontal channels the radiation shielding systems are made of two boxes. The first and second boxes are separated by a shielding wall (thickness 40 cm on the 8-th HEC, thickness 70 cm on the 9-th HEC), in which the Pb collimator (internal diameter 2 cm) is placed. The outside collimator with additional elements for beam collimation and neutron filtration and the device for sample removing are placed in the first boxes; detectors, their power supply electronic blocks and monitoring equipment are located in the second boxes. Walls and ceilings of boxes on the both channels were made from metal containers filled by metal scrap, water and 5–7% boric acid. Both boxes on these different channels have different sizes, disposition of entrances and thickness of walls. The detection and neutron registration systems on both HEC include: neutron counter, electronic blocks, personal computer and communication lines about 50 m long between spectro-
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Fig. 1. A scheme of the experimental installation on the HEC-8. 1 – reactor core; 2 – beryllium reflector; 3 – horizontal channel; 4 – preliminary collimators; 5 – elements for forming of the beam; 6 – outside collimator; 7 – shutter disks; 8 – filter components; 9 – biological shielding; 10 – device for sample removing; 11 – Installation for Angle Scattering Distribution (IASD-3); 12 – tube to conduct of beam to neutron catching; 13 – neutron beam catching; 14 – radiation shielding of installation.
metric installation and measuring room. For neutron average energy 2 keV, the helium-3 counter CHM-17 (diameter – 18 mm, length – 500 mm, gas pressure – 7 atm) was used. For neutron average energies 54, 59 and 145 keV, the proportional hydrogen recoil counter LND 281 (Gas Filling – H + CH4 + N2 , diameter – 38.1 mm, length – 254.0 mm, gas pressure – 4.3 atm.) was used. Because the shape of the spectrum from a 3 He proportional counter does not allow us to distinguish contribution from different incident neutron energies, we tried to create the 2 keV filter as more as possible pure (especially in the thermal energy region where efficiency of this counter is very high) to decrease a value of an error connected with existence in the filtered neutron beam additional lines. A value of this error was evaluated by calculation using ENDF/B libraries. The shape of the spectrum from the recoil proton counter has the shape of shelves, where each shelf corresponds to a specific neutron energy (with the exception of the low-energy region, where the shelves actually merge and the effect of gamma rays and the wall effect are manifested). Thus, in order to remove the contribution from additional lines, we have to cut out the spectrum to the left of the investigated energy region and to subtract the values on the shelf to the right of this region. That is why the requirement for the purity of the filter is not so strong when studying in the energy region above 10 keV. To estimate the possible error values connected with the presence of additional lines in the 54, 59 and 145 keV filtered neutron beams, we fulfilled the calculation using the ENDF/B libraries, but they were taken into account experimentally. The total neutron cross sections for natural hafnium at the neutron filtered beams were measured on the horizontal reactor channels at KRR using transmission method. For determination of background counting rate the polyethylene samples with thickness 0.01315–0.02281 nucl/barn were used. To remove the influence of instability factors, the samples at neutron beam were replaced every minute. The natural hafnium samples were made from metal hafnium ingots, purchased at the State Research and Production Enterprise “Zirconium”. According to the passport, the chemical composition was as follows: Hf not less than 99.26%, mass fraction of impurities – 0.74%, including 0.62% zirconium. For measurements, a number of samples with a diameter of 30.4 mm were made. The observed total neutron cross section was calculated by using the following formula: σobs = −(1/n) · lnT , σobs = −(1/n) (dT /T )2 + (σobs dn)2 , (1)
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Table 1 Filter composition with the average energy 2 keV. Element (ENDF)
Sc (JEFF-3.2)
60 Ni
54 Fe
(JEFF-3.2)
S (JEFF-3.2)
Co (JEFF-3.2)
10 B
(JEFF-3.2)
Thickness, g/cm2
110.59
80.2
39.37
55.7
26.7
0.2
(JEFF-3.2)
Fig. 2. Calculated neutron spectrum after the 2 keV filter.
where n-thickness of the transmission.
nat Hf
sample in nucl/barn, < T >-experimental average value of the
2.1. Filter 2 keV The filter component optimization, to receive the highest intensity of the main energy line in the neutron spectrum, was carried out by means of calculation using our code FILTER_7 [1]. The components of this filter and the calculated neutron spectrum after this filter are presented in Table 1 and in Fig. 2. Purity of the filter – 99.6%. Other additions to the main neutron line were negligible: a line with the energy 26.7 keV was about 0.1%, lines 42.8 keV, 49.0 keV and 64.6 keV were about 0.15%, 0.02% and 0.13%, respectively. The evaluated error values to the cross section connected with the presence of additional lines at the 26.7 keV energy is 0.035%, at 42.8 keV, 49.0 keV and 64.6 keV lines are 0.145%, 0.017% and 0.125%, respectively. So, the error to the cross section connected with the presence of all additional lines did not exceed 0.322%. The calculated energy and width of the neutron line (95% response function) after this filter are: 1.91 ±0.69 0.86 keV An experimental investigation of the total neutron cross sections for nat Hf was carried out on the HEC-9 at the KRR. Two series of measurements were fulfilled on the filtered neutron beam with the 2 keV average energy. In each of these series a set of the samples with thickness from
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Table 2 Sample thickness, total neutron cross section obtained on the 2 keV filter. Thickness (n), nucl/barn 0.00236 ± 0.00002 0.00427 ± 0.00003 0.00473 ± 0.00003 0.00785 ± 0.00005 0.01257 ± 0.00008
± σ , barn (σ /σ , %) First series 23.09 ± 0.21 (0.91) 23.15 ± 0.22 (0.95) 21.45 ± 0.15 (0.70)
Second series 23.57 ± 0.41 (1.74) 22.99 ± 0.32 (1.39) 20.52 ± 0.18 (0.88)
Fig. 3. Total neutron cross sections obtained with the 2 keV filtered neutron beam.
0.00236 to 0.01257 nucl/barn was used. The obtained values of the total neutron cross section are presented in Table 2 and in Fig. 3. As shown in Table 2 and in Fig. 3, these observed total neutron cross sections depend on the thickness of the sample. This is due to the presence of resonances in the hafnium total cross section in the energy range 0.39–2.99 keV. For determination of the unshielded total neutron cross section, it is necessary to enter a correction on a self-shielding effect, namely: to divide the eff observed total neutron cross sections σt j into the self-shielding factors: eff
σt unsh. = σt j /kj , j
(2)
where kj – resonance self-shielding factor for the sample with thickness j . The resonance self-shielding factors kj were calculated by using the following formula: kj = σt sh.calc. /σt unsh.calc. , j
(3)
where σt unsh.calc. – the unshielded total neutron cross section, σt sh.calc. – a set of the shielded j sh.calc. neutron cross section σt j for j thicknesses of the investigated samples, calculated using the MCNP 4c code [2]. In these MCNP 4c calculations the simplified geometry of the experiment was used. The calculated spectrum after 2 keV filter (see Fig. 2) was used as a neutron source. The hafnium sample with diameter 30.4 mm was placed at the distance of 2 m from
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Fig. 4. Our experimental results and the calculated total neutron cross section using the MCNP 4c code. Table 3 The parameters of the extrapolation using ENDF/B-VI and CENDL-3.1 libraries. Libraries ENDF/B-VI CENDL-3.1
Coefficients a
b
c
χ2
34.79 ± 0.07 23.72 ± 0,04
−504 ± 19 −447 ± 39
17153 ± 1106 12411 ± 2899
1.0 1.0
the neutron source. The distance from the sample to the neutron detector was 2 m (parameters of the detector: Ø = 38 mm, l = 200 mm). Ten samples were used in the modeling: five of them correspond to the samples from our experiment and another five were thinner samples. The thickness of the thinnest sample was 0.00022 nucl/barn. The MCNP 4c calculations were done using data from two evaluated data libraries:ENDF/B-VI and CENDL-3.1. Just in these libraries the largest differences between the total neutron cross section for natural hafnium are observed. These calculation results and our experimental data (see Table 2) are presented in Fig. 4. The extrapolation to zero thickness (solid line) with using polynomial of the second order σt sh.calc. = a + bM · nj + c · n2j (coefficients a, band c are given in the Table 3) gives a possibility to determine σt unsh.calc. = 34.79 ± 0.07 barn using the ENDF/B-VI library calculations and σt un.calc. = 23.72 ± 0.04 barn using the CENDL-3.1. As we can see in Fig. 4, the unshielded total neutron cross sections determined with using data from ENDF/B-VI and CENDL-3.1 libraries differ more than 30%. The difference between the parameters b is significantly less (the solid lines in Fig. 4 is almost parallel). Such situation can be observed in the case, when the structure of the resonance cross sections is close enough to the investigated energy region. The obtained resonance self-shielding factors kj , calculated with using the calculation results from ENDF/B-VI and CENDL-3.1 and formula (3) are presented in Table 4. The errors kj were calculated using the next formula: 2 2 kj = kj · /σt sh.calc. + σt unsh.calc. /σt unsh.calc. (4) σt sh.calc. j j
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Table 4 Calculated self-shielding factors. Thickness (nj ), nucl/barn
ENDF/B-VI kj
kj
kj
CENDL-3.1 kj
0.00022 0.00044 0.00074 0.00118 0.00175 0.00236* 0.00427* 0.00473* 0.00783* 0.01256*
1.00 0.99 1.00 0.988 0.978 0.970 0.947 0.942 0.918 0.896
0.02 0.01 0.01 0.004 0.003 0.002 0.001 0.001 0.001 0.001
1.00 0.99 0.99 0.98 0.96 0.95 0.920 0.913 0.880 0.846
0.06 0.03 0.02 0.01 0.01 0.01 0.004 0.003 0.002 0.002
* The thickness of the sample which was used in the experiment.
Table 5 The observed (shielded) and unshielded cross sections values. Thickness (n), nucl/barn
0.00236 0.00427 0.00427 0.00473 0.00785 0.01257
Experimental and experimentally-calculated results Observed (shielded) cross section
σjsh. /kENDF/B−VI
σjsh. /kfrom CENDL − 3.1
σjsh. , barn
σjsh.
unsh. , barn σexp
unsh. σexp
unsh. , barn σexp
unsh σexp
23.57 23.00 23.09 23.15 21.45 20.52
0.41 0.32 0.21 0.22 0.15 0.18
24.29 24.29 24.39 24.57 23.36 22.89
0.45 0.36 0.25 0.26 0.18 0.22
24.74 25.01 25.11 25.37 24.38 24.26
0.45 0.36 0.25 0.26 0.18 0.22
The calculated values of the resonance self-shielding factors kj were used for determination of the experimental value σt unsh. (using formula (2)). The calculation results are presented in j Table 5. The errors σt unsh. were calculated using the next formula: j σt unsh. j
= σt unsh. j
·
sh. σt sh. j /σt j
2
2 + kj /kj
(5)
The mean value of the experimental unshielded total cross section obtained from measurement unsh. = 23.75 ± 0.29 barn using the resonance results with six hafnium measurements is σt unsh. = 24.71 ± 0.19 barn with the self-shielding factors calculated with the ENDF/B-VI and σt CENDL-3.1 library. The average value of the experimental unshielded total cross section and its uncertainty were calculated using next formulas: n
n
2 2 < σ >= σi /σi / 1/σi (6) i=1
i=1
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Table 6 Filter composition with the average energy 54 keV. Element (ENDF)
Si (JEFF-3.2)
S (JEFF-3.2)
Mn (JEFF-3.2)
Al (JEFF-3.2)
10 B
Thickness, g/cm2
256.3
76.8
6.26
5.39
0.5
(JEFF-3.2)
Fig. 5. Calculated neutron spectrum after the 54 keV filter.
n 2
< σ >= 1/ 1/σi
(7)
i=1
As expected, the unshielded cross section values are close – the difference is just 1 barn, but what value is the more reliable? Since in absolute value our result agrees better with the data from CENDL-3.1, we consider that the received in this work experimental value of the unshielded total unsh. = 24.71 ± 0.19 barn. cross section is σexp 2.2. Filter 54 keV The composite neutron filter consisting of Si, Al, S, Mn and 10 B was used to obtain the quasi-mono-energy beam with the average energy 54 keV. The filter components (g/cm2 ) are given in Table 6. The calculated spectrum after the 54 keV filter is presented in Fig. 5. Purity of the beam was about 99.6%. Other additions to the main neutron line were negligible: three lines in the energy region 144–146 keV were about 0.4%. The estimated possible error value to the cross section connected with the presence of additional lines does not exceed 0.32%. The limits of 95% response function for the 54 keV filter spectrum were defined as: 53.86 ±0.25 0.29 keV Measurements of the total neutron cross section for natural hafnium at the energy 54 keV were carried out on the 8-th HEC. The sample thickness and the total neutron cross section, obtained on each sample, are presented in Table 7 and in Fig. 6.
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Table 7 Sample thickness and experimental results, obtained with the 54 keV filtered beam. Thickness (n), nucl/barn
σ ± σ , barn
σ /σ , %
0.00491 ± 0.00004 0.00799 ± 0.00003 0.01289 ± 0.00004
8.55 ± 0.29 8.61 ± 0.21 8.65 ± 0.09
3.39 2.44 1.04
Fig. 6. Total neutron cross sections obtained with the 54 keV filtered neutron beam.
As we can see from Table 7 and Fig. 6, the results, obtained on different hafnium samples, coincide within the experimental error and a self-shielding effect is not observed. The average value of the total cross section and its uncertainty were calculated with using formulas (6) and (7). The total neutron cross section averaged on the 3 samples is: 8.65 ± 0.01 barn (0.12%). 2.3. Filter 59 keV The filter with the average neutron energy 59 keV was used in the experimental investigations [3–6]. Now this filter was recalculated and it was complemented by the new components. These calculations were done using the Filter-7 code. The components of this filter are presented in Table 8. The calculated neutron spectrum after this filter is presented in Fig. 7. Purity of the filter – 95.0%. Other additions to the main neutron line were negligible: lines with the energy 36.1 keV, 38.7 keV, and 80.5 keV were 0.01%, 0.01%, 0.02%, respectively, two groups of lines in the energy region 230–280 keV and 325–368 keV were about 0.15% and 0.75%, respectively. A contribution of the lines above 540 keV was about 4%. The estimated possible error value to the cross section connected with the presence of additional lines does not exceed 1.7%. The calculated energy and width of the neutron line (95% response function) after this filter are:
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Table 8 Composition of the filter with the average energy 59 keV. Element (ENDF)
S (JEFF-3.2)
58 Ni
V (JEFF-3.2)
Al (JEFF-3.2)
10 B
(JEFF-3.2)
Thickness, g/cm2
116.53
81.42
24.44
5.4
0.5
(JEFF-3.2)
Fig. 7. Calculated neutron spectrum after the 59 keV filter.
58.5 ±1.9 6.4 keV The experimental investigations of the total neutron cross sections for natHf were carried out on the 8-th HEC at the KRR. Three series of measurements were carried out. In each of the series a set of the metallic hafnium samples with thicknesses from 0.00245 ± 0.00004 to 0.0130 ± 0.0001 nucl/barn were used. Measurement results of the total neutron cross section of the natural hafnium for each of the series are presented in Table 9 and in Fig. 8. As shown in Table 9 and in Fig. 8, the observed total neutron cross sections depend on the thickness of the sample. This is again due to resonances present in the hafnium total cross section in the energy range 58–60 keV. In Fig. 8, there are experimental total neutron cross sections received in each of the series and their extrapolation to zero thickness using the second order polynomial. Unshielded total neutron cross section value received in these measurements is 11.47 ± 0.69 barn, (6.0%). 2.4. Filter 145 keV Measurements of the total neutron cross section for natural hafnium at the energy 145 keV were carried out on the 9-th HEC.A composition of the filter for getting a quasi-mono-energetic line with the average energy 145 keV is presented in Table 10. Spectrum after this filter, calculated by the Filter-7 code, is presented in Fig. 9. Purity of the filter – 98.87%. The contribution of the line 54 keV was about 1.13%. The estimated possible error value to the cross section connected with the presence of additional lines does not exceed 0.95%. Other additions to the main neutron line were negligible. The calculated energy and width of the neutron line (95% response function) after this filter are:
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Table 9 The sample thickness and experimental results. σ ± σ , b (σ/σ , %)
Thickness (n), nucl/barn
First series
0.00245 ± 0.00004 0.00437 ± 0.00004 0.00464 ± 0.00004 0.00709 ± 0.00009 0.00798 ± 0.00004 0.0124 ± 0.0001 0.0130 ± 0.0001
Second series
10.61 ± 0.37 (3.55) 10.33 ± 0.21 (2.01) 10.22 ± 0.15 (1.47)
Third series 11.23 ± 0.60 (5.4)
10.73 ± 0.41 (3.86) 10.35 ± 0.25 (2.38)
10.94 ± 0.33 (3.03) 10.58 ± 0.24 (2.29)
10.37 ± 0.17 (1.67)
Fig. 8. Total neutron cross sections obtained with the 59 keV filtered neutron beam.
Table 10 Composition of the filter with average energy 145 keV. Element (ENDF)
Si (JEFF-3.2)
Ti (JEFF-3.2)
10 B
Thickness, g/cm2
184.07
11.49
0.2
(JEFF-3.2)
144.86 ±3.83 5.03 keV Three series of measurements were carried out. In each of these series a set of the samples of metallic hafnium with thicknesses from 0.00423 ± 0.00001 to 0.07701 ± 0.0007 nucl/barn were used. Measurement results of the total neutron cross section for natural hafnium in each of the series are presented in Table 11 and in Fig. 10. As shown in Fig. 10 in each of these series there is no dependence of the total cross section on the sample thickness. Therefore the average value of the total neutron cross section was calculated using formulas (6), (7) and it equals 8.47 ± 0.01 barn (0.12%).
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Fig. 9. Calculated neutron spectrum after the 145 keV filter. Table 11 Sample thickness and experimental results. Thickness (n), nucl/barn
σ ± σ , barn (σ/σ , %) First series
Second series
0.00423 ± 0.00001 0.01242 ± 0.00004 0.02745 ± 0.00009 0.04193 ± 0.00005 0.07701 ± 0.00007 Average value σ Average value σ over 3 series
8.34 ± 0.06 (0.72) 8.47 ± 0.04 (0.47) 8.40 ± 0.03 (0.36)
8.58 ± 0.09(1.05)
8.41 ± 0.02 (0.24)
8.53 ± 0.02 (0.23) 8.47 ± 0.01 (0.12)
8.55 ± 0.04 (0.47) 8.52 ± 0.03 (0.35)
Third series
8.47 ± 0.02 (0.24) 8.41 ± 0.01 (0.12) 8.42 ± 0.01 (0.12)
Fig. 10. Experimental total neutron cross section received in each of the series.
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Fig. 11. Total neutron cross section from CENDL-3.1 and ENDF/B-VI, experimental data from database EXFOR/CSISRS and our experimental result for the energy 2 keV.
3. Discussion of results The total neutron cross section for the nat Hf is presented in three libraries: ENDF/B-VI, JENDL-3.2 and CENDL-2. In other libraries, there are information for separate isotopes, so for these libraries, the total cross section was calculated by the code PREPRO 2015 (subroutine MIXER) using all 6 hafnium isotopes. The total neutron cross section from the database EXFOR/CSISRS and our experimental results for the energy 2 keV and 54, 59 and 145 keV are presented in Fig. 11 and in Fig. 12. Also, the two most discrepant cross sections, found in CENDL-3.1 and ENDF/B-VI, are presented in Fig. 11, found in JENDL-4.0 and ENDF/B-VI are presented in Fig. 12. Cross sections from all other ENDF/B libraries are placed between these libraries. To compare our experimental results with the evaluated data, the point-wise total neutron cross sections for nat Hf from the ENDF/B libraries were averaged on the calculated spectrum after the 2, 54, 59 and 145 keV filter. The obtained values are presented in Table 12. As shown in Fig. 12 and in Table 12 experimental total cross section for the nat Hf obtained at the energy 54 keV does not coincide with any of the libraries, but it is in good agreement with the results of [7] and slightly higher of the experimental data presented in [8]. Our experimental result at the 59 keV energy is in good agreement with the ENDF/B-VII.1 (JEFF-3.1) library and does not coincide with the results of other authors. Our experimental result at the energy 145 keV is better in agreement with the JENDL-4.0 library and lies slightly below the data presented in [9,10]. We assume (in detail see [6], where our results at the 59 keV filter were published for the first time) that in the energy region above 50 keV there is a resonance or group of resonances. In the future, we plan to conduct measurements using the average energy shift method for filtered neutron beam [11]. This method gives possibility to obtain a set of cross sections at the close energies in the energy region of an assumed resonance. This will allow us to prove or disprove the existence of a resonance in this region.
14
Average energy of the filter (keV)
Average region (keV)
Libraries ENDF/B-VII.1 (JEFF-3.1)
JENDL-4.0
ROSFOND-2010
CENDL-3.1
Our exp. result σ ± σ , barn (σ/σ , %)
2 54 59 145
0.39–2.99 38.9–54.8 52.2–60.1 110.45–155.15
26.44 (26.94) 11.32 11.1 8.89
25.66 10.05 9.86 8.39
25.41 10.88 10.65 8.84
23.93 10.44 10.24 8.81
24.71 ± 0.19, (0.77) 8.65 ± 0.01, (0.12) 11.47 ± 0.69, (6.0) 8.47 ± 0.01, (0.12)
O. Gritzay et al. / Nuclear Physics A 996 (2020) 121693
Table 12 Averaged total neutron cross section from the ENDF/B libraries and our experimental results.
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Fig. 12. Total neutron cross section from the ENDF/B libraries, experimental data from database EXFOR/CSISRS and our experimental result at the energy 54, 59 and 145 keV.
4. Conclusions The total neutron cross sections of the nat Hf in the energy range 2–145 keV at the filtered neutron beam were measured. There is no dependence of the total cross section on the sample thickness at the energies 54 keV and 145 keV, which means that a self-shielding effect is not observed. Our experimental results at the energies 54 and 145 keV are in good agreement with the results of other authors. Our experimental data at the energy 54 keV does not coincide with any of the libraries and our data at the energy 145 keV is better in agreement with the JENDL-4.0 library. There is a dependence of the total cross section on the sample thickness at the energies 2 keV and 59 keV. Our experimental data is slightly higher than the results of other authors, this may be due to the fact that these authors did not take into account a self-shielding effect. The unshielded total neutron cross sections at the energies 2 keV and 59 keV are in a good agreement with CENDL-3.1 and ENDF/B-VII.1, respectively. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] O.O. Gritzay, M.M. Vakulenko, in: Proc. of the 4-th Int. Conf. NPAE, Kyiv, Ukraine, 2013, p. 426. [2] J.F. Briesmeister (Ed.), MCNP – A General Monte Carlo N-Particle Transport Code. Version 4C. Report No. LA-13709-M, Los Alamos National Laboratory, NM, USA, March 2000, p. 788. [3] O.O. Gritzay, V.V. Kolotyi, N.A. Klimova, O.I. Kalchenko, M.L. Gnidak, O.I. Korol, P.M. Vorona, in: Proc. of the ND 2004, USA, Santa Fe, 2004. [4] O.O. Gritzay, V.V. Kolotyi, N.A. Klimova, O.I. Kalchenko, P.N. Vorona, M.L. Gnidak, in: Proc. of the ISRD 12, USA, Gatlinburg, 2005.
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