Measurements of thermal-neutron capture cross-section and resonance integral of neptunium-237

ABSTRACT

The thermal-neutron capture cross-section (σ₀) and resonance integral (I₀) were measured for the ²³⁷Np(n,γ) ²³⁸Np reaction by an activation method. A method with a Gadolinium filter, which is similar to the Cadmium difference method, was used to measure the σ₀ with paying attention to the first resonance at 0.489 eV of ²³⁷Np, and a value of 0.133 eV was taken as a cut-off energy. Neptunium-237 samples were irradiated at the pneumatic tube of the Kyoto University Research Reactor in Institute for Integral Radiation and Nuclear Science, Kyoto University. Wires of Co/Al and Au/Al alloys were used as monitors to determine thermal-neutron fluxes and epi-thermal Westcott’s indices at an irradiation position. A γ-ray spectroscopy was used to measure activities of ²³⁷Np, ²³⁸Np and neutron monitors. On the basis of Westcott’s convention, the σ₀ and I₀ values were derived as 186.9 ± 6.2 barn, and 1009 ± 90 barn, respectively.

KEYWORDS:

• Neptunium-237
• Protactinium-233
• thermal-neutron capture cross-section
• resonance integral
• activation method
• gamma-ray spectroscopy
• emission probability

1. Introduction

Associated with the public acceptance of nuclear power reactors, it would be desired to overcome issues of nuclear wastes of minor actinides (MAs) existing in spent nuclear fuels. Neptunium-237, americium-241, and americium-243 among MAs are of importance in the nuclear waste management, because the presence of these nuclides causes long-term radiotoxicity on account of their relatively long half-lives. For example, ²³⁷Np has the extremely long half-life of 2.14 × 10⁶ years [1]. As one candidate to solve the problems, a method of converting radio nuclides to stable ones, that is, ‘nuclear transmutation’ has recently been studied again. The ‘nuclear transmutation’ was extensively studied as known as ‘OMEGA Project’ in the 1980’s. In response to a recent trend, the ‘ImPACT’ project [2] has been promoted for long-lived fission products. When nuclear transmutation of ²³⁷Np is considered by using neutron capture reaction, the accurate neutron capture cross-section of ²³⁷Np is required to evaluate the transmutation rate and/or reaction rate. Furthermore, the build-up of nuclear fissile nuclides through ²³⁷Np is important not only for nuclear waste management, but also for the nuclear fuel cycle. Figure 1 illustrates a part of the nuclear chart displaying relevant reactions and decays [1]. It is well known that the basic concept for Fast Breeder Reactor is attributable to the following reaction chain: ²³⁸U → ²³⁹U → ²³⁹Np → ²³⁹Pu (nuclear fuel). One finds that ²³⁷Np contributes generation of Pu isotopes through neutron capture reactions and decays: ²³⁷Np → ²³⁸Np → ²³⁸Pu and higher order Pu isotopes. Therefore, the neutron capture cross-section of ²³⁷Np is also important in the view point of predicting the production amount of Pu isotopes.

Figure 1. Partial section of the nuclear chart.

In the transmutation and/or burn-out studies of ²³⁷Np by using reactor neutrons, accurate data of neutron capture cross-sections are required to evaluate reaction rates as mentioned above. The accurate data with 5% error on the neutron capture cross-section of ²³⁷Np have been required as registered in the World Request List for Nuclear Data: WRENDA91/92 [3]. Measured and evaluated cross-section data for the ²³⁷Np(n, γ)²³⁸Np reaction are plotted in Figure 2 [4–19]. Conflicting data have been reported by many measurements for the thermal-neutron capture cross-section (σ₀) of ²³⁷Np from the 1960s to the beginning of the 2000s as seen from Figure 2. One finds that the data greatly vary more than their measurement errors, and past reported data are distributed around 170 barn and 180 barn.

Figure 2. Past reported values for the thermal-neutron capture cross-section of ²³⁷Np [4-19]. Data marked in italics indicate evaluated ones

As reasons of such discrepancies, two points could be considered as follows: (1) It seems that these discrepancies in the thermal-neutron capture cross-sections might be caused by taking 0.5 eV as the cut-off energy in measurements. Figure 3 plots the neutron capture cross-section curve of ²³⁷Np. Since ²³⁷Np has the huge first resonance at the neutron energy of 0.489 eV, the conventional cut-off energy of 0.5 eV cannot be applied for ²³⁷Np. When a 1mm-thick Cd filter was used to take 0.5 eV as the so-called ‘Cd cut-off energy,’ contributions to the reaction by the first resonance, which is not sufficiently shielded, would result in overestimation for the thermal-neutron capture cross-section of ²³⁷Np. In view of behavior of the cross-section curve in Figure 3, the cut-off energy of around 0.1 eV could get rid of the influence of the first resonance at 0.489 eV. (2) Data of γ-ray emission probabilities used for analysis are also considered to be one of factors that cause discrepancies. When quantitating the amount of ²³⁷Np target and ²³⁸Np reaction product by a γ-ray spectroscopy, emission probabilities of 312-keV γ ray emitted from ²³³Pa in radiative equilibrium with ²³⁷Np, and of 984-keV γ rays from ²³⁸Np directly affect the result of the neutron capture cross-section of the ²³⁷Np(n, γ)²³⁸Np reaction. As well as examining the evaluated data of γ-ray emission probabilities used for analysis, it is also necessary to re-measure and verify γ-ray probabilities if necessary.

Figure 3. Cross section curves of ²³⁷Np from evaluated libraries of JENDL-4.0 [16] and ENDF/B-VII [17].

Thus, present work is aimed to confirm that there would be problems in how to set the cut-off energy, and then to measure the thermal-neutron cross-section σ₀ and resonance integral I₀ of the ²³⁷Np(n, γ)²³⁸Np reaction.

2. Experiments

2.1. Target preparation and irradiations

The partial decay scheme of ²³⁷Np is drawn in Figure 4. In this study, the amount of the ²³⁷Np samples was quantified by the γ-ray spectroscopy for 312-keV γ ray emitted from ²³³Pa. The 984-keV γ rays emitted from ²³⁸Np generated after neutron irradiation and 312-keV γ rays are simultaneously measured in consideration of loss in sample preparations and neutron irradiations. The reaction rate can be derived by taking a ratio of yields of these γ rays [13]. As the ratio is taken, there are the following advantages: the dead time of the γ-ray measurements is cancelled out, relative detection efficiencies are sufficient for analysis, and the error of a calibration source used for detection efficiencies is also cancelled.

Figure 4. Partial decay scheme of ²³⁷Np.

Certainly, even in the case of α-ray measurements, an amount of ²³⁷Np can be quantified with 4.8-MeV α ray. Then, let ²³⁸Np generated sufficiently decay into ²³⁸Pu. By measuring 5.5-MeV α ray from ²³⁸Pu, the product amount of ²³⁸Np is evaluated, and then the reaction rate of ²³⁷Np(n, γ)²³⁸Np can be derived. However, it is necessary to carry out α-ray measurements by exposing the samples. At that time, loss in handling samples is concerned. Furthermore, since the α-ray energies are close to 4.8 MeV and 5.5 MeV, it is also concerned that 5.5-MeV α-ray peak tails in a low energy side because of a sample thickness and affects the 4.8-MeV α-ray peak. In any case, ²³⁸ Np (2.117 days [1]) must be sufficiently decayed out after the neutron irradiation, and therefore we decided to carry out the experiments only with the γ-ray spectroscopy from the viewpoint of rapid experiments. 

Figure 5 schematically gives an outline of target compositions. A ²³⁷Np standardized solution (0.5 mol/L(M) HCl), which was supplied by Nycomed Amersham plc., was used for ²³⁷Np samples. Its product code was NGZ44, and its specific activity was 231 kBq per gram of solution. Six ²³⁷Np standardized solutions equivalent to about 200 Bq (0.5 μl), were dropped onto pieces of glass micro filters by a glass capillary. The filters were dried by an infrared ramp. After drying, each filter impregnated with the ²³⁷Np solution was sealed with a polyethylene vinyl film. These were used as the ²³⁷Np samples.

Figure 5. Outline of target compositions.

Wires of Au/Al alloy (Au: 0.112 ± 0.01 wt%, 0.510 mm in diameter) and Co foils (Co: 99.9 ± 0.1% in purity, 5μm in thickness) were used to monitor neutron fluxes at an irradiation position. Since ⁵⁹Co and ¹⁹⁷Au have different sensitivities to thermal and epi-thermal neutrons, those nuclides are appropriate to determine the thermal and epi-thermal fractions in the neutron flux. The amount of ⁵⁹Co and ¹⁹⁷Au contained in each wire and foil was determined by weight measurements with a microbalance (METLER TRED UMT2). Nuclear data for monitor wires are summarized in Table 1 [1,20,21]. A set of Co and Au monitors was rapped with a polyethylene vinyl film, and attached to the ²³⁷Np sample. The ²³⁷Np sample with the monitor set was used as an irradiation target (called ‘a bare target’). The target was housed in the polyethylene capsule for the Pneumatic tube of the KUR. In this way, three capsules were prepared for irradiations with no filter.

Table 1. Nuclear data used for the monitor wires [1,20,21]

Material and Specification	Amounts ^a (mg)	Irradiation Time (sec)	Half-life ^a	σ0 ^a (barn)	I0 ^a (barn)	g-factor	Parameter s0 ^a	Gth	Gepi	Detected γ-rays
										γ-ray Energy Eγ (keV)	Emission Probability Iγ ^a (%)
Co/Al alloy	#1 1.303 2	600	5.2714 5 (years)	37.18 6	75.9 20	1.0004		1.00	1.00
	#2 1.314 2	300^b
	#3 1.266 2	600					1.74 6 ^c			1173.237 4	99.9736 7
Co:99.9%	#4 1.274 2	300^b								1332.501 5	99.9856 4
0.005mm^t	#5 1.312 2	600					1.32 6 ^d
	#6 1.296 2	300^b
Au/Al alloy	#1 0.544 1	600	2.69517 21 (days)	98.65 9	1550 28	1.0054		1.00	0.99	411.80205 17	95.58 12
	#2 1.631 2	300^b
	#3 0.540 1	600					17.2 3 ^c
Au:0.112  wt%	#4 1.772 2	300^b
0.510 mmϕ	#5 0.587 1	600					16.7 3 ^d
	#6 1.795 2	300^b

^a In our notation, 0.5436 1 is 0.5436 ± 0.0001, 5.2714 5 is 5.2714 ± 0.0005, 75.9 20 is 75.9 ± 2.0, etc.

^b The irradiation time was limited to 300 s when a Cd (or Gd) shield was used.

^c Parameter s₀ in the case of the cut-off energy of 0.5 eV.

^d Parameter s₀ in the case of the cut-off energy of 0.133 eV.

For the remained three ²³⁷Np samples, the same monitor set was attached to each of them to obtain the resonance integral, and then the ²³⁷Np sample was sandwiching both sides with a Gadolinium (Gd) foil of 20 mm × 20 mm × 25mm μm^t size (called ‘a Gd filtered target’). Each Gd filtered target was housed in the polyethylene capsule. Three capsules were also prepared for irradiations with the Gd filter. Here, the reason for choosing the 25-μm-thickness Gd filter is as follows: In this work, careful attention was paid to huge resonances of ²³⁷Np at the neutron energy of 0.489 eV as shown in Figure 3. The cut-off energy of 0.1eV could avoid this resonance. However, it is not always good to give the cut-off energy of 0.1 eV using a Cadmium (Cd) filter with an adequate thickness as usual. Figure 6 draws cross-section curves of ^natCd and ^natGd. When using the Cd filter with the thickness giving the cut-off energy of 0.1 eV, as shown in Figure 6, neutron shielding starts around 0.2 eV where the cross section becomes equal to that at 0.1 eV. Furthermore, since the cross sections of Cd gradually decrease from 0.2 eV, neutrons with energy less than 0.1 eV will pass through the Cd filter. That is, the usual Cd-ratio method [22] cannot be applied. Although the Cd filter is convenient for setting usual cut-off energy (0.5 eV), it is not suitable for setting lower energy to avoid a resonance like present case. On the other hand, cross sections of Gd have a linear increase behavior down to 0.1 eV and gently increases with energy lower than 0.1 eV. Since Gd has the large neutron capture cross-section as about 10,000 barn at 0.1 eV, it would be effective to filter thermal neutrons. Therefore, Gd was used in the present experiments as the filter instead of Cd in the usual Cd-ratio method.

Figure 6. Neutron capture cross-section curves of Cd and Gd.

The thickness of the Gd filter was optimized in the neutron transmission. Results of neutron transmission in changing the thickness of Gd foils are plotted in Figure 7. When using a 25-μm-thickness Gd foil, the effective thickness [23] is estimated as 50 μm. The effective thickness is a mean pass length that isotropic neutrons take when they pass through a sample with a certain thickness. The energy at which transmission is halved can be estimated as 0.133 eV as seen from Figure 7. Thus, the 25-μm-thickness Gd foil was chosen, and the cut-off energy was set as 0.133 eV in the present experiments.

Figure 7. Transmission for Gd filters with several thickness.

Neutron irradiations were carried out using the pneumatic tube Pn-2 of the Kyoto University Research Reactor (KUR) of the Kyoto University Research Reactor Institute (current name, Institute for Integrated Radiation and Nuclear Science, Kyoto University). The KUR was operated under 1 MW power. Irradiations of bare and Gd filtered targets were performed for 10 and 5 min, and done three times, respectively.

2.2. Activity measurements

The γ rays from irradiated monitor wires were measured by a high-purity Ge-detector whose performance was characterized by a relative efficiency of 25% to a 7.6 cm × 7.6 cmϕ NaI (Tl) detector and an energy resolution of 1.9 keV full width at half-maximum (FWHM) at the 1.33 MeV peak of ⁶⁰Co. The peak detection efficiencies were determined with a set of calibrated mixed sources: ¹¹³Sn, ¹³⁷Cs, ⁸⁸Y, and ⁶⁰Co. The error of the detection efficiency due to the uncertainties of the calibration γ source intensities was estimated as 2%. The radioactivities of ²³⁷Np samples and flux monitors were measured at a distance of 100 mm from the surface of the detector head to the samples. Figure 8 shows the γ-ray spectrum obtained by the ²³⁷Np sample irradiated without the Gd filter. The irradiation time was 600 s and the live time of the measurement was 13,704 s. The 312-keV γ ray due to ²³³Pa and γ rays with energies from 883 keV to 1029 keV ascribed to ²³⁸Np were measured with good signal to noise ratio.

Figure 8. An example of γ-ray spectrum obtained from the measurement of the irradiated ²³⁷Np sample without the Gd filter (the bare target).

3. Analysis

3.1. Westcott’s convention

Since the details of the convention and/or theory that we used to determine the thermal-neutron capture cross-section and resonance integral were described elsewhere, here we present only a simple outline of Westcott’s Convention [24,25]. The effective cross-section $\hat{\sigma }$ is defined by equating the reaction rate R to product of $\hat{\sigma }$and nυ₀:

(1) $R=n{\upsilon }_0\hat{\sigma },$(1)

where nυ₀ is the ‘neutron flux’ in the convention with the neutron density n, and with the velocity of neutron υ₀ = 2,200 m/s.

When the cross-section behavior departs from the 1/υ law, a simple relation for $\hat{\sigma }$ can be obtained as follows:

(2) $\hat{\sigma }={\sigma }_0\left(g{G}_{th}+r{(T/T_0)}^{1/2}{s}_0{G}_{epi}\right),$(2)

where σ₀ is the thermal-neutron capture cross-section; g is a factor as a function of the temperature related to departure of the cross-section behavior from the 1/υ law; r is an epithermal index in Westcott’s convention.; T is neutron temperature and T₀ is 293.6 K; the quantity r(T/T₀)^1/2 gives the fraction of epithermal neutron in the neutron spectrum; the G_th and G_epi denote self-shielding coefficients for thermal and epi-thermal neutrons, and they are taken as unity in this analysis under the present sample conditions. The value of 0.988 [19] was taken as Westcott’s g-factor [24] for ²³⁷Np. The parameter s₀ is defined by:

(3) $s_0=\frac{2{I_0}^{\prime }}{\sqrt{\pi }{\sigma }_0},$(3)

where I₀ʹ is the reduced resonance integral, i.e. the quantity obtained by subtracting a 1/υ-component from the resonance integral I₀. The resonance integral I₀ is expressed by:

(4) $I_0=I(1/\upsilon )+{I_0}^{\prime },$(4)

where the term I(1/υ) in Equation (4)(4) $I_0=I(1/\upsilon )+{I_0}^{\prime },$(4) is the 1/υ contribution to the resonance integral above the cut-off energy E_c and derived as:

(5) $I\left(1/\upsilon \right)={\int }_{E_C}^{\mathrm{\infty }}g{\sigma }_0\sqrt{\frac{E_0}{E}}\frac{dE}{E}=2g{\sigma }_0\sqrt{\frac{E_0}{E_C}},$(5)

where E₀ is the thermal neutron energy 25.3 meV.

3.2. Neutron flux and cross-section determination

Substituting Equation (2)(2) $\hat{\sigma }={\sigma }_0\left(g{G}_{th}+r{(T/T_0)}^{1/2}{s}_0{G}_{epi}\right),$(2) into Equation (1)(1) $R=n{\upsilon }_0\hat{\sigma },$(1) , reaction rates can be written in the simplified forms as:

(6) $R/{\sigma }_0=g{G}_{th}{\varphi }_1+G_{epi}{\varphi }_2{s}_0,$(6)

for irradiation without a Gd filter, and

(7) $R^{\prime }/{\sigma }_0=g{G}_{th}{{\varphi }_1}^{\prime }+G_{epi}{{\varphi }_2}^{\prime }{s}_0,$(7)

for irradiation with a Gd filter. Here the ϕ₁ and ϕ₁ʹ are neutron flux components in the thermal energy region; the ϕ₂ and ϕ₂ʹ are those in the epi-thermal energy region. The prime (ʹ) refers to irradiation with a Gd filter. The reaction rates were calculated from peak counts of γ rays from ⁶⁰Co and ¹⁹⁸Au. Figure 9 shows the experimental relation between R/σ₀ (or Rʹ/σ₀) and s₀ obtained by the flux monitors.

Figure 9. Relation between R/σ₀ (or Rʹ/σ₀) and the parameter s_0.

The values of s₀, I₀ for monitors are summarized in Table 1. The neutron flux components ϕ₁ and ϕ₁ʹ are derived with the relation in Figure 9; the slope of each solid line gives the epi-thermal flux components, i.e. ϕ₂ or ϕ₂ʹ. For example, the thermal-neutron flux component in the irradiation #1 was (4.44 ± 0.11) × 10¹² n/cm²/s. Table 2 lists the results of reaction rates R and Rʹfor the flux monitors and neutron flux components ϕ₁, ϕ₂ , ϕ₁ʹ, and ϕ₂ʹ, which were obtained for three sets of irradiation. Here the systematic errors for the reaction rates of the monitors were examined quantitatively as summarized in Table 3.

Table 2. Reaction rates for neutron monitors and neutron flux components at Pneumatic tube of KUR

Monitors	R/σ0 (×10^12/cm^2s) Bare	Rʹ/σ0 (×10^12/cm^2s) with Gd	Thermal-neutron flux ϕ1 or ϕ1^ʹ (×10^12 n/cm^2s)	Epi-thermal neutron flux ϕ2 or ϕ2^ʹ (×10^12 n/cm^2s)
Co #1, #2*	4.74 ± 0.10	0.637 ± 0.012	ϕ1 = 4.44 ± 0.14	ϕ2 = 0.173 ± 0.014
Au#1, #2*	7.42 ± 0.18	3.24 ± 0.08	ϕ1 '= 0.414 ± 0.019	ϕ2 '= 0.169 ± 0.006
Co #3, #4*	4.73 ± 0.09	0.660 ± 0.012	ϕ1 = 4.43 ± 0.11	ϕ2 = 0.169 ± 0.014
Au#3, #4*	7.34 ± 0.18	3.33 ± 0.08	ϕ1 '= 0.432 ± 0.020	ϕ2 '= 0.173 ± 0.007
Co #5, #6*	4.74 ± 0.09	0.651 ± 0.012	ϕ1 = 4.43 ± 0.11	ϕ2 = 0.173 ± 0.014
Au#5, #6*	7.42 ± 0.18	3.38 ± 0.08	ϕ1 '= 0.418 ± 0.020	ϕ2 '= 0.177 ± 0.007

* Asterisks denote irradiations with the Gd shield.

Table 3. Systematic errors for flux monitor measurements

Nuclides	Items and used data	Errors (%)	Nuclides	Items and used data	Errors (%)
^197Au	Cross section: σ0 98.65 ± 0.09(b)	0.09	^59Co	σ0 37.18 ± 0.06(b)	0.16
	Half-life: T1/2 2.69517 ± 0.00021(d)	0.01		T1/2 5.2714 ± 0.0005(yr)	0.01
	Emission probability: Iγ 95.58 ± 0.12(%)	0.13		Iγ 99.9736 ± 0.0007(%)	0.001
	Weight: m ex. 0.544 ± 0.001(mg)	0.18		m ex. 1.303 ± 0.002(mg)	0.15
	Abundance: 0.112 ± 0.001 (%)	0.89		Abundance 99.9 ± 0.1(%)	0.10
	Efficiency: εγ fitting error only fitting + source errors(1.6%)	1.25 2.03*		εγ fitting error only fitting + source errors(1.6%)	0.75 1.77 *
	Total systematic error:	2.22 (%)		Total systematic error:	1.78 (%)

* These systematic errors due to the calibration source error are canceled at the time of division of reaction rates.

Solving Equations (6)(6) $R/{\sigma }_0=g{G}_{th}{\varphi }_1+G_{epi}{\varphi }_2{s}_0,$(6) and (7(7) $R^{\prime }/{\sigma }_0=g{G}_{th}{{\varphi }_1}^{\prime }+G_{epi}{{\varphi }_2}^{\prime }{s}_0,$(7) ) for the parameter s_0, the s₀ is written as:

(8) $s_0=-\frac{g{G}_{th}{\varphi }_1-g{G}_{th}{{\varphi }_1}^{\prime }(R/R^{\prime })}{{\varphi }_2{G}_{epi}-{{\varphi }_2}^{\prime }{G}_{epi}(R/R^{\prime })}.$(8)

The parameter s₀ is obtained from the ratio of R to Rʹ for irradiated target samples and the neutron flux components ϕ₁, ϕ₂, ϕ₁ʹ, and ϕ₂ʹ obtained by flux monitors in Table 2. The σ₀ is obtained by substituting the parameter s₀ into Equation (6)(6) $R/{\sigma }_0=g{G}_{th}{\varphi }_1+G_{epi}{\varphi }_2{s}_0,$(6) , and then the I₀ʹ is derived from Equation (3)(3) $s_0=\frac{2{I_0}^{\prime }}{\sqrt{\pi }{\sigma }_0},$(3) . For E_c = 0.133 eV, the 1/υ contribution to the resonance integral is estimated to be I(1/υ) = 0.862 σ₀ from Equation (5)(5) $I\left(1/\upsilon \right)={\int }_{E_C}^{\mathrm{\infty }}g{\sigma }_0\sqrt{\frac{E_0}{E}}\frac{dE}{E}=2g{\sigma }_0\sqrt{\frac{E_0}{E_C}},$(5) . Finally, the resonance integral I₀ is given as:

(9) $I_0={I_0}^{\prime }+0.862{\sigma }_0.$(9)

4. Results and discussions

The amounts of ²³⁷Np and produced ²³⁸Np in the samples were obtained from γ-ray yields, and the reaction rates of the ²³⁷Np(n,γ)²³⁸Np reaction for three sets of irradiation were derived as listed in Table 4. The systematic errors were examined quantitatively as summarized in Table 5.

Table 4. Experimental results of the reaction rates of the ²³⁷Np(n,γ)²³⁸Np reaction

Sample No. (Bare)	Reaction rate R (×10^−10/s)	Sample No. (with the Gd)	Reaction rate R’ (×10^−10/s)
#1	9.82 ± 0.21	#2	2.44 ± 0.06
#3	9.77 ± 0.21	#4	2.45 ± 0.06
#5	9.89 ± 0.22	#6	2.42 ± 0.05

Table 5. Systematic errors estimated for the ²³⁷Np reaction rate in this experiment

Nuclides	Items and used data	Errors (%)
^233Pa	Half-life: T1/2 26.967 ± 0.002(d)	0.01
^237Np	Half-life: T1/2 2.114 ± 0.007 × 10^6(yr)	0.33
^238Np	Half-life: T1/2 2.117 ± 0.002(d)	0.09
^233Pa	Emission probability: Iγ(312keV) 38.5 ± 0.4(%)	1.04
^238Np	Emission probability: Iγ(984keV) 25.2 ± 0.13(%)	0.52
^233Pa	Efficiency: εγ (312keV) fitting error only	1.53
^238Np	Efficiency: εγ (984keV) fitting error only	0.73
	Total systematic error:	2.08 (%)

The detection efficiencies derived from the same efficiency curve were used for analyzing spectral data of monitors and ²³⁷Np samples. When the error of the calibration source is taken into consideration for the reaction rates of the monitors and ²³⁷Np samples, the total systematic error would be overestimated.

It should be noted that the systematic error due to the calibration source is canceled when dividing the reaction rates of ²³⁷Np samples by those of the monitors in the derivation of cross sections. That is, the cross section of ²³⁷Np is obtained by comparing the cross sections of ¹⁹⁷Au and ⁵⁹Co monitors. This is why the errors obtained by fitting the efficiency curve were considered in the systematic error in the reaction rates of the monitors and ²³⁷Np samples.

Here we also examined the gamma-ray emission probabilities among the data required for deriving the reaction rates of the ²³⁷Np samples. Results of examining gamma-ray emission probabilities are summarized in Tables 6 and 7 [26–38]. The gamma-ray emission probability Iγ for 312-keV γ ray emitted from ²³³Pa was used as 38.5 ± 0.4% by Terada et al. [26], because it was the latest data at the present time. Firstly, they quantified a ²³⁷Np sample by γ-ray spectroscopy and determined its radioactivity. Next, 312-keV γ rays emitted from ²³³Pa in radiative equilibrium with ²³⁷Np were measured by γ-ray spectroscopy. The gamma-ray emission probability was derived from the radioactivity of ²³⁷Np and the yields of 312-keV γ ray.

Table 6. Gamma-ray emission probabilities Iγ for 312-keV gamma ray from ²³³Pa

Authors	Year	Iγ (%)	Method	Ref.
Terada et al.	2016	38.5 ± 0.4	α- and γ-spectroscopy	[26]
Leconte et al.	2012	37.79 ± 0.64	γ-spectroscopy	[27]
DeVries et al.	2008	38.08 ± 0.51	α- and γ-spectroscopy	[28]
Harada et al.	2006	41.6 ± 0.9	α- and γ-spectroscopy	[14]
Shchukin et al.	2004	37.5 ± 2.4	α- and γ-spectroscopy 4πβγ Coincidence mesur.	[29]
Luca et al.	2000	37.80 ± 0.23	α- and γ-spectroscopy 4παγ Coincidence mesur.	[30]
Woods et al.	2000	38.7 ± 0.4	α- and γ-spectroscopy	[31]
Gehrke et al.	1979	38.6 ± 0.5	4πβγ Coincidence mesur.	[32]

Table 7. Gamma-ray emission probabilities Iγ for 984-keV gamma ray from ²³⁸Np

Authors	Year	Iγ (%)	Method	Ref.
Leconte et al	2012	24.99 ± 0.34	γ-spectroscopy	[27]
Letourneau et al.	2010	25.64 ± 0.4	α- and γ-spectroscopy	[33]
Rengan et al.	2006	25.17 ± 0.13	β- and γ-spectroscopy	[34]
Harada et al.	2006	25.20 ± 0.13	α- and γ-spectroscopy	[14]
Chukreev et al.	2002	25.19 ± 0.21	Evaluation	[35]
Chang et al.	1990	25.19 ± 0.21	4πβγ Coincidence mesur.	[36]
Lederer et al.	1981	27.8	γ-spectroscopy	[37]
Winter et al.	1972	25.4	γ-spectroscopy	[38]

The gamma-ray emission probability for 984-keV γ ray emitted from ²³⁸Np was reported to be 25.19 ± 0.21% [36] by 4πβγ coincidence measurement, which was smaller than the previous value of 27.8% [37]. Subsequently, Harada et al.[14]. derived the value of 25.20 ± 0.13% by α- and γ-ray spectroscopic methods. The value of Ref. [36] was used for the present analysis because the same result was obtained with higher accuracy by using different measurement method from that of the preceding study.

The thermal-neutron capture cross-section σ₀ and resonance integral I₀ were derived by analysis based on Westcott’s convention with the obtained reaction rates and information on the neutron flux components. The results of σ₀, s₀, I₀ʹ, and I₀ obtained by the three irradiation sets are summarized in Table 8 together with the weighted averages. Firstly, the thermal-neutron capture cross-section σ₀ and the parameter s₀ were derived for three irradiation sets only with the statistical error, and then weighted averages were obtained both for the σ₀ and s₀. The variations in values due to irradiations were estimated to be ±3 barn for the σ₀ and ±0.3 for the s₀, respectively. Next, for the results of the weighted averages of the σ₀and s₀, the systematic errors and the error of the variation due to measurement were taken into consideration. Finally, I₀^ʹ and I₀ were derived from Equations (3)(3) $s_0=\frac{2{I_0}^{\prime }}{\sqrt{\pi }{\sigma }_0},$(3) and (9(9) $I_0={I_0}^{\prime }+0.862{\sigma }_0.$(9) ) using the σ₀ and s₀ in consideration of systematic errors as described above. In the present work, the thermal-neutron capture cross-section σ₀ was obtained as 186.9 ± 6.2 barn. The present results for the thermal-neutron capture cross-section σ₀ and the resonance integral I₀ are summarized in Table 9 together with the past reported values and evaluations. The evaluation value based on reported experimental data is 178.1 barn in JENDL-4.0 [16], and the present result is found to be about 5% larger than that. That is, ²³⁷Np tends to absorb thermal-neutrons by about 5% from the evaluated data. Neptunium-237, which has along half-life of 2.14 × 10⁶ years [1], is transmuted to ²³⁸Np through the neutron capture reaction. Since ²³⁸Np decays in only 2.117 days [1], it is expected to artificially accelerate the decay of long lived ²³⁷Np nuclide.

Table 8. Results^a of σ₀, s₀, I₀^ʹ, and I₀ for the ²³⁷Np(n,γ)²³⁸Np reaction

Sample No.	σ0 (barn)	s0	I0^ʹ (barn)	I0 (barn)
No.1 and 2	184.8 ± 6.7	5.39 ± 0.54	883 ± 94	1043 ± 96
No.3 and 4	186.2 ± 6.6	5.14 ± 0.53	848 ± 92	1008 ± 94
No.5 and 6	189.2 ± 6.7	4.89 ± 0.50	821 ± 89	984 ± 91
Weighted average:	186.9 ± 6.2	5.12 ± 0.51	848 ± 88	1009 ± 90

^aErrors include the systematic errors and errors due to measurement variations as well as the statistical errors.

Table 9. Present and reported values for ²³⁷Np capture cross-section and resonance integral

Authors Year		σ0 (barn)	I0 (barn)	Cut-off Energy (eV)	Ref.
Present work		186.9 ± 6.2	1009 ± 90	0.133	―
ENDEF/B-VII.1	2011	175.4	664.8	0.5	[17]
JENDL-4.0	2011	178.1	701.1	0.5	[16]
Letourneau et al.	2010	182.2 ± 4.5	-	Thermal Flux	[15]
Harada et al.	2006	169 ± 6	-	0.385	[14]
Katoh et al.	2003	141.7 ± 5.4	862 ± 51	0.385	[13]
Kobayashi et al.	1994	158 ± 3	652 ± 24	0.5	[10]
Jurova et al.	1984	158 ± 4	730 ± 30 860 ± 40	0.5 mm^t Cd 0.35 mm^t Cd	[9]
Eberle et al.	1971	184 ± 6	805 ± 10	No information	[8]

5. Conclusion

The thermal-neutron capture cross-section and the resonance integral of the ²³⁷Np(n,γ) ²³⁸Np reaction were measured by the activation method. With careful attention to the first resonance of ²³⁷Np, the cut-off energy was taken as 0.133 eV with the Gd filter having appropriate thickness. The thermal-neutron capture cross-section σ₀ was obtained as 186.9 ± 6.2 barn on the basis of the Westcott’s convention. The resonance integral I₀ was obtained as 1009 ± 90 barn under the condition that the cut-off energy was 0.133 eV. The thermal-neutron capture cross-section of ²³⁷Np was obtained with the error of 3.3% which satisfied the requirement of 5% in the World Request List.

Acknowledgments

The authors would like to appreciate staffs of Kyoto University Research Reactor Institute for their support. This work has been carried out in part under the Visiting Researcher’s Program of the Research Reactor Institute, Kyoto University. One of the authors (S.N.) would also like to express our gratitude to Makoto ISHIKAWA, Dr. Hideo HARADA and Dr. Osamu IWAMOTO of JAEA for their constructive comments and encouragement.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 2011-2013 (23561019, Shoji Nakamura).