Uncertainty Quantification of ²³⁷Np, ²⁴¹Am, and ²⁴³Am Reaction Rates in Highly Enriched Uranium Fuel Cores at Kyoto University Critical Assembly

Abstract

Experimental analyses of ²³⁷Np, ²⁴¹Am, and ²⁴³Am fission, as well as ²³⁷Np capture reaction rates, are conducted with the Serpent 2 code together with ENDF/B-VIII.0 and JENDL-5 using experimental data for the neutron spectra of thermal and intermediate regions obtained in the solid-moderated and solid-reflected cores with highly enriched uranium fuel at the Kyoto University Critical Assembly. Also, uncertainty quantification of the fission and capture reaction rate ratios of the test samples of ²³⁷Np, ²⁴¹Am, and ²⁴³Am with reference samples of ²³⁵U and ¹⁹⁷Au are evaluated by the MARBLE code system.

In terms of the fission reaction rate ratios of ²³⁷Np/²³⁵U, ²⁴¹Am/²³⁵U, and ²⁴³Am/²³⁵U, a comparison between experiments and Serpent 2 calculations shows an accuracy of about 5%, 15%, and 10%, respectively, together with ENDF/B-VIII.0 and JENDL-5. For the capture reaction rate ratios of ²³⁷Np/¹⁹⁷Au, Serpent 2 calculations reveal a fairly good accuracy at the thermal neutron spectrum. The total uncertainties of the ²³⁷Np/²³⁵U, ²⁴¹Am/²³⁵U, and ²⁴³Am/²³⁵U fission reaction rate ratios by MARBLE with the covariance data of ENDF/B-VIII.0 and JENDL-5 are found to be about 4% at most in all cores, except for about 8% for ²⁴³Am/²³⁵U with ENDF/B-VIII.0 at the intermediate neutron spectrum.

Keywords:

• Minor actinide
• reaction rate ratio
• highly enriched uranium (HEU) fuel
• Kyoto University Critical Assembly (KUCA)
• Serpent 2

I. INTRODUCTION

Nuclear transmutation of minor actinides (MAs) and long-lived fission products into stable short-life and long-life radionuclides is considered a promising approach leading to the volume and hazard reduction of radioactive wastes after partitioning high-level radioactive waste generated in light water reactors (LWRs) into some groups and nuclei. In particular, the nuclear transmutation of the ²³⁷Np, ²⁴¹Am, and ²⁴³Am of MAs is foreseen as implementable in neutron irradiation systems, including thermal, fast, and spallation neutrons in LWRs, fast reactors, and accelerator-driven systems, respectively.

The feasibility of nuclear transmutation from the fission and capture reactions of MAs has been investigated at experimental facilities, and much experimental data have been archived by the IRPhE (International Handbook of Evaluated Reactor Physics Benchmark Experiments Project)^[1] and the ICSBEP (International Criticality Safety Benchmark Evaluation Project)^[2] under the leadership of the Organization for Economic Co-operation and Development, Nuclear Energy Agency.

Experimental analyses of MA nuclear transmutation are generally conducted with the use of irradiated MA foil or sample data in a critical core involving MA fission and capture reaction rates. The accuracy of the analyses is evaluated using the reaction rate ratio of the test (MAs) and reference materials of ²³⁵U, ²³⁹Pu, and ¹⁹⁷Au and comparing the reaction rate ratios with experimental and numerical results. Some previous experimental data of MA irradiation in critical assemblies^[3–8] are summarized in Table I.

TABLE I Summary of C/E Values of Reaction Rate Ratios in Previous MA Irradiation Experiments

Reaction	Ratio	Facility	Spectrum	Code	(C/E)-1 (%)
					JENDL^a	ENDF^b	JEFF^c
Fission	^237Np/^235U	KUCA-B^[Citation4]	Thermal to intermediate	MVP2^[Citation9]	<−7 (J32^[Citation12])	–	–
	^241Am/^235U	KUCA-B^[Citation5]	Thermal to intermediate	MVP2	<−13 (J32)	<−11 (E6^[Citation13])	<−7 (F22^[Citation14])
Capture	^237Np/^197Au	KUCA-B^[Citation3]	Thermal to intermediate	MVP2	<±2 (J32)	<+9 (E6)	–
Fission	^237Np/^239Pu	FCA IX-1 to IX-6^[Citation6]	Intermediate to fast	MVP3^[Citation10]	0 (J40^[Citation15])	<+1 (E71^[Citation16])	<−2 (F32^[Citation17])
	^241Am/^239Pu	FCA IX-1 to IX-6^[Citation6]	Intermediate to fast	MVP3	−3 (J40)	−6 (E71)	−6 (F32)
	^243Am/^239Pu	FCA IX-1 to IX-6^[Citation6]	Intermediate to fast	MVP3	−6 (J40)	−6 (E71)	−5 (F32)
	^237Np/^235U	KUCA-A^d[Citation7]	Intermediate	MCNP6.1^[Citation11]	–	−5 (E71)	–
	^241Am/^235U	KUCA-A^d[Citation7]	Intermediate	MCNP6.1	–	+14 (E71)	–
		KUCA-A^e[Citation7]	Thermal	MCNP6.1	–	+8 (E71)	–
	^243Am/^235U	KUCA-A^f[Citation8]	Intermediate	MCNP6.1	−6 (J40)	−7 (E80^[Citation23])	−6 (F33^[Citation18])
Capture	^237Np/^197Au	KUCA-A^d[Citation7]	Intermediate	MCNP6.1	–	−3 (E71)	–
		KUCA-A^e[Citation7]	Thermal	MCNP6.1	–	−7 (E71)	–

^aJ32 is JENDL-3.2 and J40 is JENDL-4.0.

^bE6 is ENDF/B-VI, E71 is ENFD/B-VII.1, and E80 is ENDF/B-VIII.0.

^cF22 is JEFF-2.2, F32 is JEFF-3.2 and F33 is JEFF-3.3.

^dHEU-Pb zone of HEU-Pb (I) core in Fig. 1a.

^eHEU-PE zone of HEU-Pb (I) core in Fig. 2a.

^fHEU-NU-Al core in Fig. 4a.

In the range of thermal to fission neutrons for the fission and capture reaction rates of ²³⁷Np, ²⁴¹Am, and ²⁴³Am, numerical analyses by Monte Carlo methods^[9–11] have been conducted together with numerous nuclear data libraries.^[12–19] Other experimental analyses have been conducted for the uncertainty of ²³⁷Np inelastic scattering cross sections for criticality at the Los Alamos Criticality Experiments Facility,^[20] the validity of cross sections for MAs in the JEFF-3.1 library^[21] at the fast reactor Phénix,^[22] and the evaluation of MA sample reactivity worth at the Fast Critical Assembly^[23] by JENDL-5.^[24]

Minor actinide irradiation experiments have been carried out at the neutron spectra of the thermal and intermediate regions obtained using highly enriched uranium (HEU) 93 wt% fuel in the solid-moderated and solid-reflected cores (A cores) at the Kyoto University Critical Assembly (KUCA). Experimental analyses of the fission reaction rate ratios of ²³⁷Np, ²⁴¹Am, and ²⁴³Am with ²³⁵U, as well as the capture reaction rate ratios of ²³⁷Np with ¹⁹⁷Au, have been conducted. In previous studies,^[7,8] shown in Table I, comparisons between the experimental and numerical reaction rate ratios showed that the relative difference between the calculations and experiments (C/E) was accurate to around 10% in the KUCA-A cores.

Adding a newly intermediate spectrum core to the KUCA-A cores in the present study, sensitivity analyses of the reaction rates and uncertainty quantification of the reaction rate ratios of MAs induced by nuclear data were carried out in numerical analyses using the Serpent 2 code^[25] and the MARBLE code system,^[26] respectively, together with the nuclear data libraries of ENDF/B-VIII.0 and JENDL-5.

The series of sensitivity and uncertainty analyses of criticality,^[27,28] reactivity,^[29,30] and reaction rates obtained at KUCA has been notably conducive to the validation of the precision of nuclear cross-section data, applying the data assimilation technique together with experimental data, such as the cross-section adjustment method, to the numerical calculations. To improve the completeness of the integral experiments for nuclear data validation, the uncertainty quantification of MA reaction rate ratios is the focus in the present study, as uncertainty analyses of criticality and reactivity have previously been studied in the KUCA-A cores with the use of the SCALE6.2.1^[31] and 6.2.4^[32] code systems.

The objective of this study was to examine quantitatively the uncertainty induced by cross sections in the fission and capture reactions using the measured reaction rate ratios of MAs and considering the effects of neutron spectra ranging between the thermal and intermediate regions on the reaction rate ratios of MAs. The details of the core components and experimental settings in the irradiation experiments in the KUCA-A cores are described in Sec. II. The sensitivity and uncertainty quantification of the reaction rate ratios of MAs using Serpent 2 and MARBLE are presented in Secs. III and IV, respectively. Finally, the conclusions of this study are summarized in Sec. V.

II. EXPERIMENTAL SETTINGS

II.A. Core Configurations

A series of critical irradiation experiments was previously carried out in solid-moderated and solid-reflected cores with HEU fuel involving HEU-lead (Pb) (I) and low-enriched uranium (LEU) model cores. The current experiments were additionally conducted in the HEU-Pb (II) core. Detailed information on the cores, irradiation zones, and unit cells in the experiments is listed in Table II. Details of the structures, compositions, and dimensions of the fuel and core components are described in Ref. [33].

TABLE II Unit Cells of the KUCA-A Cores in the MA Irradiation Experiments

Core	Zone	Unit Cell	Spectrum
HEU-Pb (I)^[Citation7]	HEU-Pb	1/16 in. HEU × 2 + 1/8 in. Pb	Intermediate
	HEU-PE	1/16 in. HEU × 2 + 1/8 in. PE	Thermal
HEU-Pb (II)	HEU-Pb	1/16 in. HEU × 2 + 1/8 in. Pb	Intermediate
LEU model^[Citation8]	HEU-NU-Al	1/16 in. HEU × 2 + 1/16 in. Al × 2 + 1/24 in. NU + 1/16 in. Al × 2 + 1/16 in. HEU × 2	Intermediate

II.A.1. HEU-Pb (I) Core

In the HEU-Pb (I) core with the HEU-Pb zone, shown in Fig. 1a, the normal fuel rod termed “F” is composed of 60 unit cells sandwiched between upper and lower polyethylene (PE) blocks that are 24.35 in. and 20.75 in. long, respectively, in an aluminum (Al) sheath (2.1 × 2.1 × 60 in.), as shown in Fig. 1b. A unit cell is composed of two HEU fuel plates (2 × 2 × 1/16 in. per plate) and one PE plate (2 × 2 × 1/8 in.). Fuel rod “f” is a Pb-zoned special fuel rod with 40 unit cells, two HEU plates, and one Pb plate (2 × 2 × 1/8 in.), as shown in Fig. 1c. The “BTB” is a back-to-back special fission chamber for measuring the reaction rates of the test and reference samples, as shown in Fig. 1d. The dimensions and structures of the BTB are described in Ref. [7]. In the HEU-Pb (I) core with the HEU-PE zone shown in Fig. 2a, numeral “10” corresponds to 10 unit cells of the normal fuel rod shown in Fig. 2b.

Fig. 1. Core configuration and components of the HEU-Pb (I) core with the HEU-Pb zone.^[7]

Fig. 2. Core configuration and components of the HEU-Pb (I) core with the HEU-PE zone.^[7]

II.A.2. HEU-Pb (II) Core

The HEU-Pb (II) core (Fig. 3a) contains the normal F and special f fuel rods shown in Figs. 1b and 1c, respectively. Numeral “54” corresponds to the 54 unit cells of the normal fuel rod shown in Fig. 3b, and the “SFC” is a special single-fission chamber for measuring the reaction rates of the test and reference samples, as shown in Fig. 3c. The dimensions and structures of the SFC are presented in Ref. [8].

Fig. 3. Core configuration and components of the HEU-Pb (II) core with the HEU-Pb zone.

The current MA irradiation experiments of ²³⁷Np and ²⁴³Am were carried out in the HEU-Pb zone of the HEU-Pb (II) core in terms of the reaction rate analyses of ²⁴³Am in the neutron spectrum similar to the HEU-Pb zone of the HEU-Pb (I) core.^[8] The neutron spectrum at the detector position in the HEU-Pb zone of the HEU-Pb (II) core was softer than that of the HEU-Pb (I) core due to the difference in the number of special fuel rods loaded at the test zone.

II.A.3. LEU Model Core

In the LEU model core shown in Fig. 4a, numeral “16” corresponds to the 16 unit cells of the normal fuel rod shown in Fig. 4b. The special fuel rod “LEU” is a LEU model fuel rod with 20 unit cells, four HEU fuel plates, four Al plates (2 × 2 × 1/16 in. per plate), and one natural uranium (NU) plate (2 × 2 × 1/24 in.), as shown in Fig. 4c. The average ²³⁵U enrichment per unit cell in the LEU model fuel is 16.87 wt%. The 20 unit cells of the LEU model fuel rod are sandwiched between 10 unit cells composed of two 1/16-in. HEU plates and one 1/8-in. PE plate of the normal fuel rod in both the upper and lower sides. Also, the SFC was used to measure the MA reaction rates in the HEU-Pb (II) core.

Fig. 4. Core configuration and components of the LEU model core with the HEU-NU-Al zone.^[8]

II.B. Neutron Spectrum

The neutron spectra with a core-wide average of unit cells in the KUCA-A cores were numerically obtained by MCNP6.2^[34] with ENDF/B-VIII.0, demonstrating a thermal neutron spectrum in the HEU-PE zone of the HEU-Pb (I) core of around 0.1 eV and an intermediate spectrum in the HEU-Pb zones of the HEU-Pb (I) and (II) cores and the LEU model core ranging between 1 eV and 10 keV, in addition to that of fast neutrons of around a few megaelectron-volts, as shown in Fig. 5.

Fig. 5. Neutron spectra by MCNP6.2 with ENDF/B-VIII.0 at locations (15, O), (15, K), (15, K), and (15, O) of the BTB and SFC in Figs. 1a, 2a, 3a, and 4a, respectively.

II.C. Measured Results of Reaction Rate Ratios

The measured results of the reaction rate ratios were acquired through KUCA-A core experiments^[7,8] previously carried out in the HEU-Pb (I) and LEU model cores. The experiments were additionally carried out in the HEU-Pb (II) core. The fission reaction rates were evaluated using the ratios of ²³⁷Np/²³⁵U, ²⁴¹Am/²³⁵U, and ²⁴³Am/²³⁵U in the HEU-Pb and HEU-PE zones of the HEU-Pb (I) and HEU-Pb (II) cores and the HEU-NU-Al zone of the LEU model core. Capture reaction rates were also evaluated using the ratio of ²³⁷Np/¹⁹⁷Au in the HEU-Pb and HEU-PE zones of the HEU-Pb (I) core.

The uncertainty of the measured results of the test and reference samples mainly included the statistical errors of the counting rates obtained by the fission and capture events and the effects of the solid angle^[35] induced by varying the sample diameter on the detection efficiencies of the BTB and SFC.

III. NUMERICAL SIMULATIONS

III.A. Reaction Rate Ratios by Serpent 2

Numerical analyses of the MA fission and capture reaction rate ratios were performed by the Monte Carlo calculation code Serpent 2 together with the nuclear data libraries ENDF/B-VIII.0 and JENDL-5. The eigenvalue and reaction rate calculations were conducted simultaneously by Serpent 2 with a variation in the number of histories:

1. For the fission reaction rates, a total of 1.55 × 10⁹ × 5 × 10⁵ histories per cycle, 3.1 × 10³ cycles, and a skipped cycle of 1 × 10².

2. For the capture reaction rates in the HEU-Pb zone of the HEU-Pb (I) core, a total of 1.75 × 10⁹ × 5 × 10⁵ histories per cycle, 3.5 × 10³ cycles, and a skipped cycle of 1 × 10².

3. For the capture reaction rates in the HEU-PE zone of the HEU-PE (I) core, a total of 2.05 × 10⁹ × 5 × 10⁵ histories per cycle, 4.1 × 10³ cycles, and a skipped cycle of 1 × 10².

The numerical errors of the eigenvalue, fission, and capture reaction rates were then obtained with a standard deviation within 2 pcm, 0.5%, and 1.5%, respectively. The numerical results of the reaction rate ratios by Serpent 2 were compared with those of the KUCA-A core experiments, as shown in Table III, involving the fission reaction rate ratios of ²³⁷Np/²³⁵U, ²⁴¹Am/²³⁵U, and ²⁴³Am/²³⁵U, as well as the capture reaction rate ratios of ²³⁷Np/¹⁹⁷Au.

TABLE III Comparison Between Experimental and Numerical Results of the Fission and Capture Reaction Rate Ratios

Reaction	Ratio	Zone	Core	Experiment	Serpent 2		C/E
					ENDF/B-VIII.0	JENDL-5	ENDF/B-VIII.0	JENDL-5
Fission	^237Np/^235U	HEU-Pb	HEU-Pb (I)	0.070 ± 0.005	0.064 ± 0.002	0.065 ± 0.001	0.92 ± 0.08	0.93 ± 0.07
		HEU-Pb	HEU-Pb (II)	0.048 ± 0.003	0.047 ± 0.001	0.047 ± 0.001	0.97 ± 0.06	0.98 ± 0.06
	^241Am/^235U	HEU-Pb	HEU-Pb (I)	0.069 ± 0.004	0.077 ± 0.001	0.082 ± 0.002	1.12 ± 0.06	1.19 ± 0.06
		HEU-PE	HEU-Pb (I)	0.034 ± 0.002	0.035 ± 0.001	0.036 ± 0.002	1.04 ± 0.07	1.07 ± 0.08
	^243Am/^235U	HEU-Pb	HEU-Pb (II)	0.042 ± 0.004	0.037 ± 0.003	0.038 ± 0.001	0.87 ± 0.10	0.91 ± 0.08
		HEU-NU-Al	LEU model	0.042 ± 0.002	0.037 ± 0.003	0.039 ± 0.001	0.88 ± 0.08	0.93 ± 0.04
Capture	^237Np/^197Au	HEU-Pb	HEU-Pb (I)	2.15 ± 0.33	1.92 ± 0.08	1.95 ± 0.07	0.89 ± 0.14	0.91 ± 0.14
		HEU-PE	HEU-Pb (I)	2.02 ± 0.08	2.00 ± 0.09	1.99 ± 0.08	0.99 ± 0.06	0.99 ± 0.05

III.B. Accuracy of Serpent 2

In terms of the fission reaction rate ratios of ²³⁷Np/²³⁵U, a comparison between the experiments and Serpent 2 calculations showed good agreement with a relative difference of around 5% for ENDF/B-VIII.0 and JENDL-5 in the HEU-Pb zones of the HEU-Pb (I) and HEU-Pb (II) cores, as shown in Table III.

The ²⁴¹Am/²³⁵U ratio demonstrated a relative difference of around 5% at the thermal neutron spectrum in the HEU-PE zone of the HEU-Pb (I) core for the two libraries, whereas ²⁴¹Am/²³⁵U in the HEU-Pb zone of the HEU-Pb (I) core demonstrated a discrepancy in the C/E value with a relative difference of around 15%, which is clearly an overestimation by the Serpent 2 calculations. The same ²⁴¹Am/²³⁵U discrepancy was found in an intermediate spectrum, as in the KUCA-B cores shown in Table I, resulting in a meaningful C/E accuracy in Refs. [5,7].

For the ratios of ²⁴³Am/²³⁵U in the HEU-Pb and HEU-NU-Al zones of the HEU-Pb (II) and LEU model cores, respectively, the Serpent 2 calculations with JENDL-5 showed an accuracy with a relative difference of less than 10% as compared to those with ENDF/B-VIII.0, which demonstrated a relative difference of over 10%.

The capture reaction rate ratio of ²³⁷Np/¹⁹⁷Au with ENDF/B-VIII.0 and JENDL-5 provided a fairly good agreement at the thermal neutron spectrum of the HEU-PE zone in the HEU-Pb (I) core, although the intermediate region of the HEU-Pb zone in the HEU-Pb (I) core showed a discrepancy in the C/E value of around 10% for the two libraries. It is noteworthy, however, that the experimental error of the HEU-Pb zone was larger than that of the HEU-PE zone.

The Serpent 2 calculations for these series of MA reaction rate ratios provided pertinent experimental results with certain accuracy, indicating a relative difference in the C/E value of around 5% together with ENDF/B-VIII.0 and JENDL-5, except for that of ²⁴¹Am/²³⁵U, which was over 10% for the two libraries.

IV. UNCERTAINTY QUANTIFICATION OF THE REACTION RATE RATIOS BY MARBLE

The sensitivity coefficients of the reaction rates and the uncertainty of the MA reaction rate ratios were acquired by Serpent 2 and MARBLE based on eigenvalue calculations and sensitivity coefficients, respectively, together with the covariance data of ENDF/B-VIII.0 and JENDL-5. MARBLE is a versatile reactor analysis code system, and in this study, a utility in MARBLE was employed to generate the uncertainty of reaction rate ratios together with covariance data based on the sensitivity coefficients obtained by Serpent 2.

The uncertainty of the MA reaction rate ratios was examined in the main reactions of the test MA samples, ²³⁷Np, ²⁴¹Am, and ²⁴³Am, and the reference samples, ²³⁵U and ¹⁹⁷Au, including the fission, capture, elastic scattering, and inelastic scattering reactions. The statistical errors of the sensitivity of the reaction rates and the uncertainty of the reaction rate ratios estimated by Serpent 2 and MARBLE stood at less than 5% and 10%, respectively, for all the reactions of the test and reference samples. Meanwhile, the uncertainties of the other core components were negligibly small in the reaction rate ratios by MARBLE that involved fuel, moderators, reflectors, and assembly sheath. This was attributed to the very few correlations with the MA reaction rates of the test and reference samples.

IV.A. Fission Reaction Rate Ratios

In the fission reaction rate ratios of ²³⁷Np/²³⁵U, an impact involving ²³⁷Np samples in the HEU-Pb zones of the HEU-Pb (I) and (II) cores was about 3.0% and 1.5% in ENDF/B-VIII.0 and JENDL-5, respectively, as shown in Table IV. The impact of ²⁴¹Am in the fission reaction rate ratios of ²⁴¹Am/²³⁵U ranged between 1.7% and 4.3% for the two libraries, as shown in Table V, indicating a difference between the neutron spectra in the HEU-Pb and HEU-PE zones of the HEU-Pb (I) cores, respectively. The ²⁴³Am in the fission reaction rate ratios of ²⁴³Am/²³⁵U demonstrated a different impact of about 8.0% and 2.3% by ENDF/B-VIII.0 and JENDL-5, respectively, as shown in Table VI.

TABLE IV Breakdown of Uncertainty of ²³⁷Np/²³⁵U for Fission Reaction Rates by Serpent 2 in the HEU-Pb Zone of the HEU-Pb (I) and (II) Cores*

Nuclide	Reaction	HEU-Pb in HEU-Pb (I)		HEU-Pb in HEU-Pb (II)
		ENDF/B-VIII.0	JENDL-5	ENDF/B-VIII.0	JENDL-5
^235U	$(\mathit{n},\mathit{f})$	0.36 ± 0.02	0.33 ± 0.02	0.37 ± 0.01	0.35 ± 0.02
	$(\mathit{n},\mathit{\gamma })$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n}{ }^{\mathrm{\prime }})$	<0.01	<0.01	<0.01	<0.01
^237Np	$(\mathit{n},\mathit{f})$	2.88 ± 0.03	1.54 ± 0.01	2.84 ± 0.03	1.54 ± 0.02
	$(\mathit{n},\mathit{\gamma })$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n}{ }^{\mathrm{\prime }})$	<0.01	<0.01	<0.01	<0.01
	Total	2.91 ± 0.03	1.57 ± 0.02	2.87 ± 0.03	1.58 ± 0.02

*Uncertainty in percent.

TABLE V Breakdown of Uncertainty of ²⁴¹Am/²³⁵U for Fission Reaction Rates by Serpent 2 in the HEU-Pb and HEU-PE Zones of the HEU-Pb (I) Core*

Nuclide	Reaction	HEU-Pb in HEU-Pb (I)		HEU-PE in HEU-Pb (I)
		ENDF/B-VIII.0	JENDL-5	ENDF/B-VIII.0	JENDL-5
^235U	$(\mathit{n},\mathit{f})$	0.36 ± 0.02	0.36 ± 0.02	0.42 ± 0.01	0.42 ± 0.02
	$(\mathit{n},\mathit{\gamma })$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},2\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n}{ }^{\mathrm{\prime }})$	<0.01	<0.01	<0.01	<0.01
^241Am	$(\mathit{n},\mathit{f})$	1.77 ± 0.08	1.72 ± 0.07	3.26 ± 0.10	4.30 ± 0.14
	$(\mathit{n},\mathit{\gamma })$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},2\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n}{ }^{\mathrm{\prime }})$	<0.01	<0.01	<0.01	<0.01
	Total	1.81 ± 0.08	1.76 ± 0.08	3.29 ± 0.10	4.32 ± 0.13

*Uncertainty in percent.

TABLE VI Breakdown of Uncertainty of ²⁴³Am/²³⁵U for Fission Reaction Rates by Serpent 2 in the HEU-Pb and HEU-NU-Al Zones of the HEU-Pb (II) and LEU Cores, Respectively*

Nuclide	Reaction	HEU-Pb in HEU-Pb (II)		HEU-NU-Al in LEU Model
		ENDF/B-VIII.0	JENDL-5	ENDF/B-VIII.0	JENDL-5
^235U	$(\mathit{n},\mathit{f})$	0.37 ± 0.01	0.35 ± 0.02	0.37 ± 0.01	0.36 ± 0.01
	$(\mathit{n},\mathit{\gamma })$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},2\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n}{ }^{\mathrm{\prime }})$	<0.01	<0.01	<0.01	<0.01
^243Am	$(\mathit{n},\mathit{f})$	8.06 ± 0.07	2.27 ± 0.03	8.04 ± 0.05	2.28 ± 0.01
	$(\mathit{n},\mathit{\gamma })$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},2\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n}{ }^{\mathrm{\prime }})$	<0.01	<0.01	<0.01	<0.01
	Total	8.07 ± 0.07	2.30 ± 0.03	8.05 ± 0.06	2.30 ± 0.02

*Uncertainty in percent.

From the results in Tables IV, V, and VI, the impact of the ²³⁵U fission reaction rates was notably smaller, around 0.3%, than that of the MA samples in all the zones and cores. Furthermore, in all the zones and cores, the total uncertainty of the MAs was between 1.5% and 8.0%, and the impact of the other reactions involving the capture, elastic scattering, and inelastic scattering reactions was very small.

IV.B. Capture Reaction Rate Ratios

For the capture reaction rate ratios of ²³⁷Np/¹⁹⁷Au, the impact of ²³⁷Np on the uncertainty by ENDF/B-VIII.0 and JENDL-5 was between 3.3% and 4.3% in the HEU-Pb and HEU-PE zones of the HEU-Pb (I) cores, as shown in Table VII, together with a very small impact from the other reactions. Also, total uncertainties were dominant over the ²³⁷Np capture reaction rates. Here, the impact of the ¹⁹⁷Au capture reactions by JENDL-5 was invisible due to no settings of its covariance data for the ¹⁹⁷Au capture cross sections.

TABLE VII Breakdown of Uncertainty of ²³⁷Np/¹⁹⁷Au for Capture Reaction Rates by Serpent 2 in the HEU-Pb and HEU-PE Zones of the HEU-Pb (I) Core*

Nuclide	Reaction	HEU-Pb in HEU-Pb (I)		HEU-PE in HEU-Pb (I)
		ENDF/B-VIII.0	JENDL-5	ENDF/B-VIII.0	JENDL-5
^197Au	$(\mathit{n},\mathit{\gamma })$	0.77 ± 0.06		1.02 ± 0.08
	$(\mathit{n},\mathit{n})$	<0.01		<0.01
	$(\mathit{n},\mathit{n}{ }^{\mathrm{\prime }})$	<0.01		<0.01
^237Np	$(\mathit{n},\mathit{f})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{\gamma })$	3.96 ± 0.13	3.27 ± 0.10	4.24 ± 0.11	3.48 ± 0.06
	$(\mathit{n},\mathit{n})$	<0.01	<0.01	<0.01	<0.01
	$(\mathit{n},\mathit{n}{ }^{\mathrm{\prime }})$	<0.01	<0.01	<0.01	<0.01
	Total	4.04 ± 0.14	3.27 ± 0.10	4.36 ± 0.13	3.48 ± 0.06

*Uncertainty in percent.

IV.C. Correlation Coefficients

The correlation coefficients between the fission and capture reaction ratios by MARBLE were acquired by combining the sensitivity and efficient matrix and the nuclear data covariance matrix in all cores, as shown in Table VIII. In terms of the fission reaction rate ratios, a strong correlation between identical test samples was observed in similar neutron spectra, while the correlation between the different test samples was small due to the variation between the neutron spectra.

TABLE VIII Correlation Coefficients Between the Fission and Capture Reaction Ratios by Combining the Sensitivity Coefficient Matrix and Nuclear Data Covariance Matrix in the HEU and LEU Model Cores

Bold numbers indicate strong correlation.

The correlation relevant to the fission reaction rate ratios was observed in the sensitivities of ²³⁷Np, ²⁴¹Am, and ²⁴³Am by comparing the ²³⁵U fission reactions shown in Figs. 6, 7, and 8, respectively. For the capture reactions, the correlation was reasonable in the HEU-Pb (I) core together with the sensitivity in the HEU-Pb and HEU-PE zones, shown in Fig. 9, whereas the correlation with the fission reactions was very minimal, as shown in Table VIII.

Fig. 6. Regionwise contribution of energy of the ²³⁷Np and ²³⁵U fission reaction rates by Serpent 2 with ENDF/B-VIII.0 at locations (15, O) and (15, K) in Figs. 1a and 3a, respectively.

Fig. 7. Regionwise contribution of energy of the ²⁴¹Am and ²³⁵U fission reaction rates by Serpent 2 with ENDF/B-VIII.0 at locations (15, O) and (15, K) in Figs. 1a and 2a, respectively.

Fig. 8. Regionwise contribution of energy of the ²⁴³Am and ²³⁵U fission reaction rates by Serpent 2 with ENDF/B-VIII.0 at locations (15, K) and (15, O) in Figs. 2a and 4a, respectively.

Fig. 9. Regionwise contribution of energy of the ²³⁷Np and ¹⁹⁷Au capture reaction rates by Serpent 2 with ENDF/B-VIII.0 at locations (15, O) and (15, K) in Figs. 1a and 2a, respectively.

IV.D. Discussion

The ²⁴¹Am/²³⁵U fission reaction rate ratio revealed a discrepancy of around 15% in the C/E in the KUCA-A core analyses, as shown in Sec. III.B. The experimental uncertainty of the ²⁴¹Am fission reaction rates was investigated with the statistical errors of measured counting rates of the fission events and geometrical effects of the BTB and SFC. Also, the numerical results of the ²⁴¹Am fission reaction rates were acquired based on an adequate standard deviation within 0.5% and a total uncertainty induced by the ²³⁵U and ²⁴¹Am fission cross sections of about 4% at most.

From the experimental and numerical deviations, the discrepancy of the ²⁴¹Am/²³⁵U fission reaction rate ratio for ENDF/B-VIII.0 and JENDL-5 in the KUCA cores remains a notable technical issue to be resolved in the analyses of the MA reaction rates, including unrecognized sources of uncertainties.

In a series of uncertainty analyses of the fission and capture reaction rate ratios, as shown in Tables IV through VII, the difference between ENDF/B-VIII.0 and JENDL-5 was attributable to that of the covariance data of the nuclear cross sections in the two libraries. The total uncertainties of ²³⁷Np/²³⁵U, ²⁴¹Am/²³⁵U, and ²⁴³Am/²³⁵U for fission and ²³⁷Np/¹⁹⁷Au for the capture reactions (Tables IV through VII) in the KUCA-A cores with the use of HEU fuel were negligibly small due to the variation in the neutron spectra and core components compared with the uncertainties of criticality^[25,26] and reactivity^[27,28] discussed in previous studies. Also, since the correlation between the target and other reactions was quite small, no effective values of uncertainties were found in various reactions, as shown in Tables IV through VII.

V. CONCLUDING REMARKS

Uncertainty quantification of the MA fission and capture reaction rate ratios was conducted using Serpent 2 and MARBLE together with ENDF/B-VIII.0 and JENDL-5 and the experimental data obtained from the KUCA-A cores. The fission and capture reaction rate ratios of the test samples of ²³⁷Np, ²⁴¹Am, and ²⁴³Am were evaluated using reference samples of ²³⁵U and ¹⁹⁷Au.

In terms of the fission reaction rate ratios of ²³⁷Np/²³⁵U, ²⁴¹Am/²³⁵U, and ²⁴³Am/²³⁵U, a comparison between the experiments and Serpent 2 calculations showed an accuracy of about 5%, 15%, and 10%, respectively, with ENDF/B-VIII.0 and JENDL-5. For the capture reaction rate ratios of ²³⁷Np/¹⁹⁷Au, Serpent 2 calculations revealed a fairly good accuracy at the thermal neutron spectrum.

The uncertainty of the MA fission and capture reaction rate ratios was found to be around 3%, except for that of ²⁴³Am/²³⁵U, which was about 8%. Also, the total uncertainties of the MA fission reaction rate ratios with ENDF/B-VIII.0 and JENDL-5 were small, about 4% at most in the all cores, except for the fission reaction rate ratio of ²⁴³Am/²³⁵U with ENDF/B-VIII.0 at the intermediate neutron spectrum, which was about 8%. For the MA reaction rate analyses in the KUCA-A cores, the discrepancy in the fission reaction rate ratio of ²⁴¹Am/²³⁵U remains a notable technical issue through a series of experimental analyses of the MA reaction rates.

Acknowledgments

The authors are grateful to all the technical staff at the KUCA for their assistance during the experiments.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (C) [grant number 24K08301] and the Ministry of Education, Culture, Sports, Science and Technology in Japan.