Fission cross-section measurements of ²³⁷Np, ^242mAm, and ²⁴⁵Cm with lead slowing-down neutron spectrometer

Abstract

The cross sections for neutron-induced fission of ²³⁷Np, Am, and ²⁴⁵Cm have been measured in the energy range from 0.1 eV to 2 keV using the lead slowing-down neutron spectrometer at the Research Reactor Institute, Kyoto University. The fission cross sections were deduced relative to those for ²³⁵U(n,f) and ¹⁰B(n,a). The cross section for ²³⁷Np(n,f) was obtained with the experimental uncertainty of about 20% in the energy region below 25 eV and typically 13% above this energy. The experimental uncertainties for ^242m Am and ²⁴⁵Cm were, respectively, of the order of 14% and 9% in the entire energy region.

Keywords:

• neutron-induced fission
• 0.1 eV to 2 keV
• ²³⁷Np
• ^242mAm
• ²⁴⁵Cm
• minor actinide
• lead slowing-down neutron spectrometer
• parallel plate avalanche chamber

1. Introduction

The management of minor actinides (MAs) is one of the most important issues for the use of nuclear power because of their long-term radiotoxicities. Several ideas have been proposed such as the transmutation and/or incineration of MAs in fast reactors or accelerator-driven subcritical systems. If these are realized, MAs can be reduced and also used as an energy resource. In order to evaluate the feasibility of these techniques, precise nuclear data on neutron-induced reactions, i.e. neutron capture and neutron-induced fission cross sections, are indispensable.

Neptunium-237 is the most abundant MA in high-level radioactive wastes (HLW), and its cross sections of neutron capture and fission are therefore of importance for the investigation of its burn-up characteristics. Although there are many measurements of the cross section for ²³⁷Np(n,f) in a wide energy range, experimental data below 10 eV are still scarce. In this energy region, Yamanaka et al. [1] and Gerasimov et al. [2] obtained the cross section for ²³⁷Np(n,f) using lead slowing-down neutron spectrometers. Carlson et al. [3] and Tovesson and Hill [4] obtained that by the time-of-flight (TOF) method. There are some differences between their data around 10 eV; the cross section is about 30 mb at 10 eV by Yamanaka et al. and Carlson et al., whereas the data of Gerasimov et al. and Tovesson and Hill show smaller values by a factor of two or three.

Americium-242m is less abundant in HLW but has a larger fission cross section when compared with the other americium isotopes such as ^241,243Am. The fission cross section of ^242m Am has been obtained by many researchers. Bowman et al. [5], Dabbs et al. [6], and Browne et al. [7] have obtained the cross section by the TOF method in a wide energy range from the thermal energy region to over 100 keV. Gerasimov et al. [2], Kai et al. [8], and Alekseev et al. [9] have obtained the cross section using lead slowing-down neutron spectrometers.

Curium isotopes are the third abundant MA in HLW after neptunium and americium isotopes. Among the curium isotopes, ^244,245Cm are produced in relatively large amounts. Since the atomic number of curium is 96, the curium isotopes of odd mass number have large cross sections for the neutron-induced fission below few hundreds keV. So far, there are some experimental data for ²⁴⁵Cm(n,f) measured in a wide energy range. Browne et al. [10] and White et al. [11] have obtained the cross section by the TOF method from 10.1 meV to 34.1 eV and 21.2 meV to 63.1 eV, respectively. Block et al. [12] and Gerasimov et al. [2] have obtained the cross section using lead slowing-down neutron spectrometers from 1.10 eV to 91.5 keV and from 25.4 meV to 41.2 keV, respectively. In the energy region below 2 eV, the cross sections obtained by the TOF method and the lead slowing-down neutron spectrometer show different energy dependences each other. Recently, Alekseev et al. [9] have measured the cross section in the energy range from 28.1 meV to 20.6 keV using a lead slowing-down neutron spectrometer, where the resulting cross section shows a similar energy dependence to the data obtained by the TOF method in the energy region below 2 eV.

In the present study, the cross sections for neutron-induced fission of ²³⁷Np, ^242m Am, and ²⁴⁵Cm have been measured in the neutron-energy range from 0.1 eV to 2 keV using the lead slowing-down neutron spectrometer at the Research Reactor Institute, Kyoto University (KURRI). Measuring the cross sections for different nuclides using the same experimental setup will also be a consistency check for the data analysis.

2. Experimental procedure

2.1. Lead slowing-down neutron spectrometer

The experiment was carried out using the lead slowing-down neutron spectrometer (KULS) [13] coupled to the electron linear accelerator at KURRI. A schematic layout of KULS is shown in Figure 1. KULS is a lead cube of 1.5×1.5 × 1.5 m³ assembled by 1600 lead blocks of cm³. There are eight experimental holes provided for parallel measurements (in the figure, only four experimental holes are depicted). The size of each experimental hole was 10 × 10 cm² and 45 cm in depth. One of the experimental holes is surrounded by a bismuth layer of 10–15 cm in thickness in order to reduce a background due to high-energy γ rays (6–7 MeV) from neutron captures of lead. All sides of the spectrometer, except for the experimental hole, were covered with 0.5-mm-thick cadmium sheets to prevent low-energy neutrons from scattering in/out the spectrometer.

Figure 1. Top view of KULS. Photo-neutrons produced in the tantalum target are slowed down in the lead material. Fission fragments are detected with MLPPAC (multi-layered parallel-plate avalanche chamber) placed in one of the experimental holes provided to KULS.

A tantalum target placed in the center of KULS is used for the production of Bremsstrahlung photons and subsequent neutrons by (γ,n) reactions. The neutrons are asymptotically slowed down by successive inelastic and elastic scatterings in KULS. The energy of the neutrons (E_n ) at the time-of-“travel” (t) in the lead material was deduced from a relation E _n  = K/(t−t ₀)². The slowing-down parameters keV μs² and  μs were obtained from a calibration measurement using resonance filters [13], In (1.46 eV), Au (4.91 eV), Co (132 eV), and Cu (230 and 579 eV). In the calibration measurement, slowing-down time spectra were measured using Ar or BF₃ proportional counters which were surrounded by these resonance filters. Peaks due to the capture rays were observed at the resonances in the case of the Ar counter, and dips due to the neutron absorption were observed at the resonances in the case of BF₃ counter.

In the experiments using the lead slowing-down neutron spectrometer, it is difficult to count a number of incident neutrons on a sample. Therefore, a reference-source method was used in the present study in order to deduce the fission cross section. In this method, fission fragments emitted from a sample of interest are detected relative to those from a reference sample such as ²³⁵U whose fission cross section is well known. Under the assumption of the same numbers of incident neutrons on both samples, the fission cross section for the sample of interest can be obtained using the reference cross section.

2.2. Sample preparation

In the original sample of neptunium solution, impurities of Pu and ²⁴⁰Pu have been found by mass spectrometry. Each ratio of the number of atoms of these impurities to that of ²³⁷Np has been determined to be % (²³⁸Pu), % (²³⁹Pu), and % (²⁴⁰Pu). A serious background would be caused by the impurity of ²³⁹Pu in the neutron-induced fission because of its large cross section, i.e. about times larger than that of ²³⁷Np at 25.3 meV [14]. In order to reduce these impurities, a chemical separation was performed by an anion-exchange method. Events of the decay from the small amounts of ²³⁹Pu could not be observed because of its long half-life ( y). Therefore, the activity of ²³⁹Pu was deduced from that of ²³⁸Pu which has much shorter half-life (87.7 y). Since the impurity of ²³⁸Pu was reduced by a factor of 12.5 after the chemical separation, the ratio ²³⁹PuNp was also reduced by the same factor and estimated to be %. The ²³⁷Np sample was deposited on an alumina-membrane filter (Whatman Anodisc) by a filtration method [15, 16]. The deposited area is 20 mm in diameter.

The Am sample was electrodeposited on a stainless steel plate with an active spot of 20 mm in diameter. Impurities of Am and ²⁴²Cm were estimated to be , and relative to the number of the Am atoms, respectively, by spectrometry. In spite of the large amounts of these impurities, the backgrounds are almost negligible because of their small cross sections when compared with that of Am and estimated to be less than 0.6% in the fission yield using the JENDL-4.0 evaluation [14]. The background from the spontaneous fission of ²⁴²Cm, the decay daughter of Am, was measured in an off-beam run and estimated to be at most 0.12% at the neutron energy of 0.1 eV.

The ²⁴⁵Cm sample was obtained from Oak Ridge National Laboratory, USA. Curium-245, the second decay daughter of ²⁴⁹Bk ( = 320 d), was separated from ²⁴⁹Cf ( = 351 d) by a cation-exchange method. After the separation, the sample was electrodeposited on a stainless steel plate with an active spot of 12.7 mm in diameter. Amounts of the impurities contained in the sample were estimated by and spectrometry. The ratios of the impurities were determined to be ²⁴⁴CmCm % and ²⁴⁹CfCm %. Since their fission cross sections are much smaller than that for ²⁴⁵Cm [14], the background from these impurities were not taken into account.

Three ²³⁵U samples were used as the reference. The reference sample used in the measurement of ²³⁷Np was electrodeposited on a stainless steel plate with an active spot of 20 mm in diameter. Although the impurities of ²³⁴U (), ²⁴¹Am (), ²⁴³Am (), and ²⁴²Cm () were found in the sample, they have almost no effect on the reaction because of their small cross sections when compared with that of ²³⁵U. The other ²³⁵U samples, the references for Am and ²⁴⁵Cm, were prepared by the filtration method as mentioned before. A small amount of the ²³⁴U impurity, less than 0.1%, was found in each reference sample by spectrometry.

The number of atoms in each sample and their references are listed in Table 1. The errors are the statistics in the counting. The cross section for ²⁴⁵Cm was measured two times using different reference samples of ²³⁵U(A) and (B).

Table 1. The number of atoms in each sample.

	MA sample	^235U reference
^237Np
Am		(A)
^245Cm		(A)
		(B)
Note: The errors are the statistics in the counting.

2.3. Fragment detector and data acquisition system

Each sample pair of the MA and the ²³⁵U reference was placed back-to-back in the multi-layered parallel-plate avalanche chamber (MLPPAC) [17]. As shown in Figure 2, MLPPAC has two sets of multi-layered electrodes on both sides of the sample pair. Each electrode consists of four aluminized-polyester foils located in 2 mm steps. One fission fragment is then detected by the two layers of PPAC and another fission fragment is stopped by the sample backing. MLPPAC was operated under the condition of 10 Torr iso-butane gas and the biases of –500 V on each cathode. The anode signals from preamplifiers (CANBERRA Model2006) were fed to a 16-channel spectroscopy amplifier (CAEN N568B) for further amplifying and shaping.

Figure 2. MLPPAC has two sets multi-layered electrode. Each consists of four foils of aluminized polyester. Two samples are located between them.

A VME module of LIST&PHA (IWATSU A3100) was employed for the pulse-height and the timing measurement. This module records the pulse heights of input signals as well as their time intervals from the start signal, i.e. neutron time-of-“travel” in KULS. The data acquisition was required for every anode signal. The fractions of dead time to the total run time were and for the measurement of Am and ²⁴⁵Cm, respectively, whereas that for the measurement of ²³⁷Np was much smaller.

3. Data analysis

3.1. Fission event selection

The fission fragments were discriminated from particles by the correlation between the pulse heights of the first and the second anode signals of MLPPAC. An example of the pulse-height correlation observed in the measurement of ²⁴⁵Cm is shown in Figure 3. The distribution due to the light and heavy fragments can be seen and clearly separated from particles lying in the low pulse-height region. Except for the reference sample of ²³⁵U(A), the fission fragments of the other samples are selected in the same manner as this figure. In practice, the selection cut for the fission fragments was applied to the sum spectrum of the first and the second anodes. By fitting the region between the particles and the fission fragments with two exponential functions, the loss of the fission events and the contamination of the particle were estimated to be negligibly small (%).

Figure 3. The correlation between the pulse heights of the first and the second anode signals observed in the measurement of ²⁴⁵Cm. The fission fragments are clearly separated from particles.

However, in the case of the reference sample of ²³⁵U(A), the fission events were not clearly selected. The thick and the thin solid lines in Figure 4 show the pulse-height spectra of the first anode signals when ²³⁵U(A) was used as a reference sample for Am and ²⁴⁵Cm, respectively. For comparison, the pulse-height spectrum for ²³⁵U(B) is also shown by the dashed line. In these spectra, the position and the height of the peak of the fission events were normalized to unity. The discrepancy in the low pulse-height region arises from the difference in electrical noises occurring at the electron-beam injection. As can be seen from this figure, the fission events for ²³⁵U(A) cannot be clearly selected in contrast to ²³⁵U(B), since the valley around the pulse height of 0.5 is filled with the tail of fission events. It seems that this was caused by self-absorption of the fission fragment in the sample. Therefore, the events with the pulse height larger than 0.7, indicated by the dashed vertical line, were selected as the fission events for ²³⁵U(A).

Figure 4. The thick and the thin solid lines show the pulse-height spectra for the reference sample of ²³⁵U(A) used in the measurements of Am and ²⁴⁵Cm, respectively. The dashed line shows that of ²³⁵U(B).

In order to obtain the absolute cross section, the efficiency for the fission-event selection should be estimated. The cross section for ²⁴⁵Cm was separately measured relative to two reference samples, ²³⁵U(A) and ²³⁵U(B). In the pulse-height spectrum for the second reference sample, the fission fragments were clearly discriminated with almost full selection efficiency as shown by the dashed line in Figure 4. Therefore, the selection efficiency of the fission events for ²³⁵U(A) was deduced by comparing the fission-yield ratio ²⁴⁵CmU obtained using these two ²³⁵U samples and estimated to be % when the pulse-height discrimination of 0.7 was applied. Using this value, we obtained the cross section for Am where the reference sample of ²³⁵U(A) was used.

3.2. Cross-section derivation

Using the reference-source method, the cross section is given by

where Y is the yield of fission events, N is the number of atoms, and is the solid angle for the fission fragments. The subscripts of MA and U mean the values for the sample of interest and the reference sample of ²³⁵U, respectively. The reference cross section is usually taken from an evaluated library.

However, the ratio of the energy-dependent fission yield of the MA to that of ²³⁵U is actually distorted because of the resonance peaks in their fission cross sections. Thus, Equation (1) cannot be used directly. In the present study, the energy dependence of the fission cross section was firstly derived using the neutron spectrum which was separately measured with a BF₃ proportional counter. To keep the perturbation of the neutron spectrum as low as possible, the small size counter (50 mm in effective length and 12 mm in diameter) was used. The correction factor for the self-shielding was calculated to be 5% at 0.1 eV, 1.6% at 1 eV, and less than 0.5% above 10 eV. Since the cross section for ¹⁰B shows a simple dependence, the ratio of the fission yield of the MA to that of ¹⁰B is not distorted.

Secondly, the relative cross section was normalized to its absolute cross section. To put in a formula, it is expressed as follows:

where and are the yields of the and the events, respectively. is the normalization factor to the absolute cross section which was obtained using the ²³⁵U reference in the energy region between 100 eV and 1 keV. In this energy region, the distortion due to the resonance peaks is negligible. The normalization factor is given as follows.

where the summation is taken over the energy bins between 100 eV and 1 keV. The solid angle for the fission fragments was calculated using GEANT 3.21 program [18] by taking into account the diameters of the sample and the collimator, and the distance between them. The solid angles for the fission fragment were estimated to be 0.272 for ²³⁷Np and its reference sample, 0.350 for Am, 0.347 for ²³⁵U(A), for ²⁴⁵Cm, and for ²³⁵U(B). The smaller collimators were used in the ²⁴⁵Cm measurement because of a high counting rate of ²⁴⁵Cm. It should be noted that the effect of the angular distribution of the fission fragments on the detection efficiency is not considered because of the semi-isotropic neutron flux in KULS.

In the present study, the reference cross sections and were taken from JENDL-4.0 [14] which is broadened according to the neutron-energy resolution function of KULS [13], typically 40%. The neutron-energy resolution function was obtained by fitting the data shown in Figure 5 and Table 3 of [13]. The resolution function, i.e. the neutron-energy distributions at individual slowing times, is also given in Figure 3 of [13] in the energy region above a few eV. The resolution functions seem to have a well symmetric-Gaussian shape in a space in this energy region. At low energies, however, the resolution function will deviate from the symmetric shape, since the thermal motions of lead nuclei become non-negligible at the collision with low-energy neutrons. The shape of the resolution function was calculated with the Monte-Carlo simulation of PHITS code [19]. In the energy region below 1 eV, the resolution function becomes to have an asymmetric-Gaussian shape which tails toward low energy side. The ratio of the width in the lower energy side to that in the higher energy side is 1.5 at 1 eV and becomes 2.0 at 0.1 eV. The energy dependence of the asymmetricity of the resolution function was taken into account in the broadening of the JENDL-4.0 evaluation.

Figure 5. The open circles show the cross section for ²³⁷Np before subtracting the background from ²³⁹Pu. The result of the background subtraction performed using the JENDL-4.0 evaluation is shown by the closed circles.

3.3. Background subtraction

As described before, the impurity of ²³⁹Pu is included in the ²³⁷Np sample. Although the ratio of the number of atoms ²³⁹PuNp was small (), the background due to ²³⁹Pu should be corrected. The open circles in Figure 5 show the fission yield of ²³⁷Np before subtracting the background. The solid curve is the JENLD-4.0 evaluation which is broadened by the neutron energy resolution function of KULS. The bump structure around 0.25 eV is caused from the impurity of ²³⁹Pu. The dashed curve is the evaluation by taking into account the ²³⁹Pu impurity. Since the dashed curve well reproduces the experimental data, the ²³⁹Pu background was subtracted using the JENDL-4.0 evaluation. The closed circles show the result after subtracting the background.

4. Results and discussion

4.1. Cross sections

The cross sections obtained in this work are shown in Figures 6–8. In these figures, the results in the energy range from 0.1 eV to 2 keV are shown by the closed circles, whereas the results below 0.1 eV are shown by the × symbols. As described in [9,20], the energy-time relation of the neutrons in the lead slowing-down neutron spectrometers deviates from at lower energies below 0.1 eV, because the neutron energies are asymptotically down to the thermal neutron energy. Therefore, the results obtained in the energy region below 0.1 eV are invalid. Above 2-keV neutron energies, the measurement was disturbed by the electrical noises due to the electron-beam injection.

Figure 6. The cross section for ²³⁷Np obtained in this work (closed circles) is compared with the other experimental data, Yamanaka et al. [1], Carlson et al. [3], Gerasimov et al. [2] and Tovesson and Hill [4].

Figure 7. The resulting cross section for Am shown by the closed circles is compared with other experimental data, Gerasimov et al. [2], Kai et al. [8] and Alekseev et al. [9].

Figure 8. The resulting cross section for ²⁴⁵Cm shown by the closed circles is compared with Block et al. [12], Gerasimov et al. [2], and Alekseev et al. [9].

The cross section for ²³⁷Np is shown in Figure 6 and summarized in Table 2. The error bars show the quadratic sum of the statistical uncertainty of the yields for the ²³⁷Np and the ¹⁰B events and the other experimental uncertainties described later. The large errors below 1 eV is due to the background subtraction of ²³⁹Pu. In the figure, other experimental data are also shown for comparison. The data of Carlson et al. [3] and Tovesson and Hill [4] were obtained by the TOF method, while the other data were obtained using lead slowing-down neutron spectrometers. The data of Tovesson and Hill [4] which are given in terms of the cross-section ratio of ²³⁷Np to ²³⁵U were transformed using the cross section of ²³⁵U from JENDL-4.0. The dashed curve is the data of Tovesson and Hill (only data above 10 eV are shown). The solid curve is the JENDL-4.0 evaluation. These curves are broadened by the neutron energy resolution function of KULS. It should be noted that the data of Carlson et al. are not broadened, because their energy resolution seems to be comparable to ours. The data of Gerasimov et al. [2] and the JENDL-4.0 evaluation show the general agreement with the result of the present work in the energy region below 15 eV, whereas the cross sections obtained by Yamanaka et al. [1] and Carlson et al. [3] show larger values in this energy region. Around 1 keV, the data of Carlson et al. [3] and Gerasimov et al. [2] are in good agreement with the present result, while the data of Yamanaka et al. [1] and Tovesson and Hill [4] show larger values. All the experimental data show the bump structure at 1 keV which does not exist in the JENDL-4.0 evaluation.

Table 2. The cross-section values for ²³⁷Np.

En (eV)	(b)	En (eV)	(b)	En (eV)	(b)
0.100–0.112		2.81–3.16		79.4–89.1
0.112–0.126		3.16–3.54		89.1–100
0.126–0.141		3.54–3.98		100–112
0.141–0.158		3.98–4.46		112–126
0.158–0.178		4.46–5.01		126–141
0.178–0.200		5.01–5.62		141–158
0.200–0.251		5.62–6.31		158–178
		6.31–7.07		178–200
0.251–0.282		7.07–7.94		200–224
0.282–0.316		7.94–8.91		224–251
0.355–0.447		8.91–10.0		251–282
		10.0–11.2		282–316
0.316–0.355		11.2–12.6		316–355
0.447–0.501		12.6–14.1		355–398
0.501–0.562		14.1–15.8		398–447
0.562–0.631		15.8–17.8		447–501
0.631–0.708		17.8–20.0		501–562
0.708–0.794		20.0–22.4		562–631
0.794–0.891		22.4–25.1		631–708
0.891–1.00		25.1–28.2		708–794
1.00–1.12		28.2–31.6		794–891
1.12–1.25		31.6–35.5		891–1000
1.25–1.41		35.5–39.8		1000–1122
1.41–1.58		39.8–44.7		1122–1259
1.58–1.77		44.7–50.1		1259–1413
1.77–1.99		50.1–56.2		1413–1585
1.99–2.23		56.2–63.1		1585–1778
2.23–2.51		63.1–70.8		1778–1995
2.51–2.81		70.8–79.4		1995–2239
Note: The first and second errors are the statistical and the other experimental uncertainties, respectively.

The closed circles in Figure 7 show the result of this work for Am. The shown error bars are the total uncertainties. The cross-section values are summarized in Table 3. The previous data obtained using lead slowing-down neutron spectrometers are also shown for comparison. Our results agree with the previous data in the energy region below 0.3 eV and above 30 eV. However, in the energy region between 0.3 and 30 eV, the data of Gerasimov et al. [2] and Kai et al. [8] are slightly smaller than the present results. In this energy region, the JENDL-4.0 evaluation shown by the solid curve is close to the results of Alekseev et al. [9] which show smaller values than the present and the other experimental data.

Table 3. The cross-section values for Am.

En (eV)	(b)	En (eV)	(b)	En (eV)	(b)
0.100–0.112		2.82–3.16		79.4–89.1
0.112–0.126		3.16–3.55		89.1–100
0.126–0.141		3.55–3.98		100–112
0.141–0.158		3.98–4.47		112–126
0.158–0.178		4.47–5.01		126–141
0.178–0.200		5.01–5.62		141–158
0.200–0.224		5.62–6.31		158–178
0.224–0.251		6.31–7.08		178–200
0.251–0.282		7.08–7.94		200–224
0.282–0.316		7.94–8.91		224–251
0.316–0.355		8.91–10.0		251–282
0.355–0.398		10.0–11.2		282–316
0.398–0.447		11.2–12.6		316–355
0.447–0.501		12.6–14.1		355–398
0.501–0.562		14.1–15.8		398–447
0.562–0.631		15.8–17.8		447–501
0.631–0.708		17.8–20.0		501–562
0.708–0.794		20.0–22.4		562–631
0.794–0.891		22.4–25.1		631–708
0.891–1.00		25.1–28.2		708–794
1.00–1.12		28.2–31.6		794–891
1.12–1.26		31.6–35.5		891–1000
1.26–1.41		35.5–39.8		1000–1122
1.41–1.58		39.8–44.7		1122–1259
1.58–1.78		44.7–50.1		1259–1413
1.78–2.00		50.1–56.2		1413–1585
2.00–2.24		56.2–63.1		1585–1778
2.24–2.51		63.1–70.8		1778–1995
2.51–2.82		70.8–79.4		1995–2239
Note: The first and second errors are the statistical and the other experimental uncertainties, respectively.

The cross section for ²⁴⁵Cm obtained in the present study is shown by the closed circles in Figure 8 and summarized in Table 4. The shown error bars are the total uncertainties. The other experimental data obtained using lead slowing-down neutron spectrometers are also shown for comparison. The data of Block et al. [12] agree well with the present result in the entire energy region. The data of Gerasimov et al. [2] show a general agreement with our result. The discrepancies in the resonance energy ranging from 1 to 30 eV might be due to the differences of the energy resolution of the spectrometers. Below 2 eV, the data of Alekseev et al. [9] and the JENDL-4.0 evaluation show lower values than the present result. In the energy region above 50 eV, all the experimental data agree with each other, whereas the JENDL-4.0 evaluation shows smaller values.

Table 4. The cross-section values for ²⁴⁵Cm.

En (eV)	(b)	En (eV)	(b)	En (eV)	(b)
0.100–0.112		2.82–3.16		79.4–89.1
0.112–0.126		3.16–3.55		89.1–100
0.126–0.141		3.55–3.98		100–112
0.141–0.158		3.98–4.47		112–126
0.158–0.178		4.47–5.01		126–141
0.178–0.200		5.01–5.62		141–158
0.200–0.224		5.62–6.31		158–178
0.224–0.251		6.31–7.08		178–200
0.251–0.282		7.08–7.94		200–224
0.282–0.316		7.94–8.91		224–251
0.316–0.355		8.91–10.0		251–282
0.355–0.398		10.0–11.2		282–316
0.398–0.447		11.2–12.6		316–355
0.447–0.501		12.6–14.1		355–398
0.501–0.562		14.1–15.8		398–447
0.562–0.631		15.8–17.8		447–501
0.631–0.708		17.8–20.0		501–562
0.708–0.794		20.0–22.4		562–631
0.794–0.891		22.4–25.1		631–708
0.891–1.00		25.1–28.2		708–794
1.00–1.12		28.2–31.6		794–891
1.12–1.26		31.6–35.5		891–1000
1.26–1.41		35.5–39.8		1000–1122
1.41–1.58		39.8–44.7		1122–1259
1.58–1.78		44.7–50.1		1259–1413
1.78–2.00		50.1–56.2		1413–1585
2.00–2.24		56.2–63.1		1585–1778
2.24–2.51		63.1–70.8		1778–1995
2.51–2.82		70.8–79.4		1995–2239
Note: The first and second errors are the statistical and the other experimental uncertainties, respectively.

4.2. Experimental uncertainties

The experimental uncertainties for the present measurement are summarized in Table 5. The numbers of atoms in each sample were determined by spectrometry. The uncertainties of the half-life, the intensities of emission, the solid angle for -particle detection, and the -counting statistics were taken into account. The large uncertainty of for the number of the ²³⁷Np atoms is mainly due to that of emission intensities in the decay of ²³⁷Np.

Table 5. The experimental uncertainties considered in the present analysis are listed (in percent).

Source of the uncertainty	^237Np	Am	^245Cm
Number of atoms of MA	12	7.2	2.4
Number of atoms of ^235U	4.9	5.2	4.9
Selection of fission of MA	0.3	0.1	0.1
Selection of fission of ^235U	0.1	10	0.2
Solid angle for MA	1.9	2.1	5.6
Solid angle for ^235U	1.9	2.1	3.9
Total	13	14	8.7

The discrimination level for the fission events was set around the valley between the fission fragments and particles in the pulse-height spectrum. The number of the fission events below the discrimination level was estimated by fitting the valley with two exponential functions. The uncertainty in the selection of fission fragment was of the order of 0.1% except for ²³⁵U(A). For the reference sample of ²³⁵U(A), the selection efficiency for the fission events was estimated to be 58.1% from the two separated measurements of ²⁴⁵Cm as described before. The uncertainty of the selection efficiency for ²³⁵U(A) was calculated from the uncertainties of the parameters appearing in the ²⁴⁵Cm measurements.

The uncertainty of the solid angle for the fission fragments was estimated from the diameters of the sample and the collimator, and the distance between the sample and the collimator. The reason for the larger uncertainties of the solid angles in the ²⁴⁵Cm measurement than those of the others is that the smaller collimators were used due to high counting rate.

Except for the statistical uncertainty, the experimental uncertainties were totally 13% for ²³⁷Np, 14% for Am, and 8.7% for ²⁴⁵Cm measurements.

5. Conclusion

The cross sections for the neutron-induced fission of ²³⁷Np, Am, and ²⁴⁵Cm have been obtained using KULS in the neutron energy region from 0.1 eV to 2 keV. In order to avoid the interference between the resonance structures of the MAs and ²³⁵U, the relative cross sections were deduced by the reference source method with ¹⁰B. Then the relative cross sections were normalized to the absolute values obtained using the reference cross section for ²³⁵U in the energy region from 100 eV to 1 keV.

For the ²³⁷Np, the cross section below 15 eV is in good agreement with the results of Gerasimov et al. [2] and Tovesson and Hill [4], whereas the results of Yamanaka et al. [1] and Carlson et al. [3] show larger values in this energy region. The resulting cross section for Am is in good agreement with the data of Gerasimov et al. [2], Kai et al. [8], and Alekseev et al. [9] in the energy region below 0.3 eV and above 30 eV. In the energy region between 0.3 and 30 eV, on the other hand, the result of this work is slightly larger than the results of the previous experiments. The result for ²⁴⁵Cm is in quite good agreement with that of Block et al. [12] in the entire energy region. In the energy region below 2 eV, it is found that the energy dependence of the cross section is very similar to that of Gerasimov [2], whereas the data of Alekseev et al. [9] and the JENDL-4.0 evaluation are slightly lower than the present result.

Acknowledgements

The authors wish to acknowledge the efforts of the operation crews at KURRI-LINAC. The present study is the result of “Study on nuclear data by using a high intensity pulsed neutron source for advanced nuclear system” entrusted to Hokkaido University by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT).

Additional information

Notes on contributors

Kentaro Hirose

Present address: Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan