Continuous-Energy ENDF/B-VIII.0 Cross Section and SCALE 6.2.4 Performance for Nuclear Criticality Safety Applications: ¹H, C, ^58,60Ni, ^{182,183,184,186}W, ^235,238U, ²³⁹Pu

Abstract

As part of the nuclear data evaluation and validation cycle, the ENDF/B-VIII.0 cross-section library released in 2018 requires testing to determine areas of improvement and deterioration. Previous work by the authors investigated the performance of ¹⁶O, ⁵⁶Fe, and ^63,65Cu cross sections, with this study acting as an extension of the prior work. In addition to the isotopes and nuclear criticality safety benchmarks of interest to the prior work, benchmarks from the International Criticality Safety Benchmark Evaluation Project Handbook were selected for their k_eff sensitivity to ¹H, C, ^58,60Ni, ^{182,183,184,186}W, ^235,238U, or ²³⁹Pu cross sections and were modeled in the SCALE code system maintained by Oak Ridge National Laboratory. In total, 253 benchmark configurations were selected for their sensitivities and modeled using SCALE 6.2.4 Criticality Safety Analysis Sequences (CSAS) continuous-energy Monte Carlo k_eff calculations. This collection includes and expands upon the 99 benchmarks in the prior work. The AMPX-processed ENDF/B-VIII.0 library was decomposed into individual ENDF/B-VIII.0 datum libraries for each isotope of interest. Doing so allowed for the individual substitution of an ENDF/B-VIII.0 cross section in the place of ENDF/B-VII.1, determining isotope-specific effects of ENDF/B-VIII.0 relative to ENDF/B-VII.1. Full library calculations with entirely ENDF/B-VII.1 data or entirely ENDF/B-VIII.0 data were also executed. As a measure of performance, the average relative deviation was determined as the ratio of the deviation between calculated and experimental k_eff to the propagated calculational and experimental uncertainty. With calculated full library and isotope-specific ENDF/B-VIII.0 k_eff’s, an optimized combination of data libraries was estimated and confirmed with SCALE calculations. This showed that reverting ²³⁹Pu, ⁵⁸Ni, ¹⁶O, and ⁶⁵Cu cross sections to ENDF/B-VII.1 resulted in improved performance relative to the full ENDF/B-VIII.0 library. Across all 253 benchmarks, the average relative deviation was 1.29σ for the full ENDF/B-VII.1 library, 1.17σ for the full ENDF/B-VIII.0 library, and 0.97σ for the optimized combination. The reversion of ²³⁹Pu, ⁵⁸Ni, ¹⁶O, and ⁶⁵Cu cross sections to ENDF/B-VII.1 in the 99 benchmarks of the prior work resulted in further improved experimental agreement compared to the previously reported improvement from ¹⁶O and ⁶⁵Cu alone. Therefore, it is suggested that applications with significant sensitivities to ²³⁹Pu, ⁵⁸Ni, ¹⁶O, and ⁶⁵Cu consider their choice of nuclear data library.

Keywords:

• Nuclear criticality safety
• validation
• critical experiment

I. INTRODUCTION

Additions and revisions to nuclear data reported in the 2018 release of the ENDF/B-VIII.0 library have been implemented through AMPX processing for future versions of the SCALE code system developed and maintained by Oak Ridge National Laboratory¹² (ORNL). As part of a continuing effort by the Nuclear Criticality Safety Program (NCSP) to validate sponsored evaluations of continuous-energy cross sections, recent work by the authors studied the performance of ¹⁶O, ⁵⁶Fe, and ^63,65Cu ENDF/B-VIII.0 cross sections using these SCALE libraries.³⁴ These previous findings argued for improvements in ⁵⁶Fe and ⁶³Cu cross sections, with an observed deterioration in experimental agreement for ¹⁶O and ⁶⁵Cu sensitive critical benchmarks. This study expands the scope of the previous work, examining additional isotopes and benchmarks. Similar studies have been performed with NJOY-processed nuclear data utilizing MCNP calculations, though such studies tend to examine all isotopes in aggregate, where this study examines individual isotopic effects.⁵⁶ Isotopes beyond the scope of the authors’ previous work include the following: ¹H, C, ^58,60Ni, ^{182,183,184,186}W, ^235,238U, and ²³⁹Pu. Performance of ¹H and C was analyzed conjunctively with any thermal scattering data of which they are a constituent. As the ENDF/B-VII.1 evaluation of carbon contains only elemental, rather than isotopic, data, both ¹²C and ¹³C ENDF/B-VIII.0 were substituted to provide an elemental comparison between libraries. This assortment, along with isotopes included in the previous study, encompasses all isotopes (¹H, ¹⁶O, ⁵⁶Fe, ^235,238U, and ²³⁹Pu) from the Collaborative International Evaluated Library Organization (CIELO) project as well as other isotopes of interest to the NCSP and nuclear data and criticality safety community.³⁷ While several isotopes have negligible variation between ENDF/B-VII.1 and ENDF/B-VIII.0 releases, this study provides evidence in confirming that ENDF/B-VII.1 and ENDF/B-VIII.0 are in practice identical for said isotopes.⁸⁹

This work functions as an extension of the initial work performed by the authors utilizing many of the same benchmarks, reporting previously produced data along with novel data available as an online supplement to this article. In expanding the benchmark suite, additional experiments were found to have ¹⁶O and ⁵⁶Fe sensitivities, producing new cumulative averages for cross-section performance. As previously cited, positively biased copper benchmarks prompted revisions to copper cross sections, while the CIELO project initiated global cooperation on accepted cross-section data for ¹H, ¹⁶O, ⁵⁶Fe, ^235,238U, and ²³⁹Pu. Also noted in the prior work, the positive copper bias was substantially lessened with ENDF/B-VIII.0 data, while results for ¹⁶O and ⁵⁶Fe agreed with conclusions presented by Hermann et al. and Chadwick et al., conclusions that will see further examination given the expansion of the benchmark suite.

The total hydrogen cross section showed little variation individually, though thermal scattering laws (TSLs) were a significant area of focus in the ENDF/B-VIII.0 release. Unfortunately, as noted in the addendum to Ref. 12 by Shaw et al. and announced in a SCALE user’s notification, polyethylene incoherent elastic scattering was incorrectly normalized by number of atoms per molecule.^10–12 As a result, the following evaluations containing polyethylene were removed from this work: HMF-031, HMT-010, HMT-013, HMT-015, and SMF-011, as all exhibited biases from the corrected cross sections greater than 42.5 pcm, or 3σ stochastic uncertainty, with most approaching a bias of 1% in k_eff (Refs. 13 through 17). Several cases in this study including polyethylene still exhibit ¹H sensitivities, including HMF-020, HMF-072, HMF-084, IMF-022, IMI-001, and LCT-097 (Refs. 18 through 23). The effect of the corrected polyethylene TSL was investigated with the correction having no effect on these cases due to fast systems or a greater sensitivity to water moderation. Thermal scattering data—including that for graphite, heavy water, and all other scattering materials—were not explicitly tested individually in this work. The substitution of hydrogen and carbon included both the free gas data across the full range of neutron energies and the corresponding thermal scattering data for materials of which they are a constituent. Clearly, hydrogen is of extreme importance to the nuclear criticality safety community, present in water and polyethylene moderators. Aqueous chemistry applications are an obvious major criticality concern, with most process criticality accidents involving solutions or slurries.²⁴

ENDF/B-VIII.0 is the first ENDF evaluation to define carbon cross sections isotopically rather than as a single elemental evaluation. The capture cross section of ¹²C is 30% greater at fast energies relative to the ENDF/B-VII.1 elemental definition, while elastic scattering has minor increases with little effect on critical benchmark calculations.¹ While not incorporated in this study, graphite in ENDF/B-VIII.0 introduced varying levels of graphite porosity. This study utilized the crystalline graphite evaluation for data substitution (ENDF-VII.1 has an evaluation only for crystalline graphite).

Nickel evaluations were particularly focused on absorption reactions such as capture and (n,x) reactions. Nickel-60 saw a 50% increase of radiative capture at 1 MeV up to a doubling at 10 MeV, while the (n,α) reaction saw the addition of a threshold at 1 MeV and significant decrease in cross section until 10 MeV. Such a large increase in absorbing reactions is expected to reduce k_eff accordingly.

At the 2018 SCALE Users’ Group Workshop, Holcomb et al. presented further evidence for decreasing k_eff in low-enrichment uranium composite lattice (LCT) benchmarks, but little change was noted in high-enrichment uranium metal system (HMF), high-enrichment uranium solution system (HST), intermediate enrichment metal system (IMF), or low-enrichment uranium solution system (LST) results, all undoubtedly sensitive to both ²³⁵U and ²³⁸U (Ref. 25). Given these results and their sensitivities, it would follow that the compound nature of LCT experiments (read, oxygen in UO₂) had a greater impact than substitution of uranium ENDF/B-VIII.0 cross sections. Uranium-238 neutron multiplicity shows a steady 2% decrease relative to ENDF/B-VII.1 up to 0.1 MeV. Additionally, the VALID suite of benchmarks discovered significant decreases in the bias of plutonium systems, largely driven by reductions in plutonium solution systems (PSTs). This study includes a series of PST experiments, as well as several plutonium metal system (PMF) configurations to compare conclusions.

Tungsten revisions in ENDF/B-VII.1 largely focused on the revisions at fast energies, with the ENDF/B-VIII.0 revision continuing the evaluation into the thermal region.¹⁹ Available International Criticality Safety Benchmark Evaluation Project (ICSBEP) benchmarks sensitive to tungsten are fast systems, so while it is of some value to determine the impact on these experiments, it is expected that thermal variations are unlikely to affect the models in this study.

As noted by Rearden et al., the integral response of k_eff to nuclear data library substitution is dependent on the direction and presence of compensating errors produced only through individual isotope substitution.²⁶ This work and its precursor utilize the individual biases by investigating major isotopes’ individual impacts on the integral response. By doing so, this work aims to provide a finer approach to cross-section validation in critical systems by concentrating on noted isotopes of interest and revision.

Section II summarizes the selection of appropriately sensitive benchmarks, along with methods and codes used for calculating k_eff. Results and accompanying analysis of individual isotopic trends and performance are included in Sec. III. Section IV provides methodology and results for calculating the optimized combination of ENDF/B-VII.1 and ENDF/B-VIII.0 isotopic data to determine the best-performing library for each isotope across all examined systems. Section V examines the effect of removing cases where no impact was observed, to remove Monte Carlo noise in performance metrics—in effect, cases where sensitivities did not line up with changes in nuclear data. Finally, a summary of results and conclusions of the work are in Sec. VI.

II. BENCHMARK SELECTION AND MODELING METHODOLOGIES

Methods for selecting and modeling appropriate criticality safety benchmarks are as established in Ref. 4. Tabulated k_eff sensitivity data in the Database for the International Criticality Safety Benchmark Evaluation Project (DICE) program were parsed for ICSBEP benchmarks with total energy-integrated k_eff sensitivities of 0.01%/%ΔΣ (10 pcm/%ΔΣ) or greater to the isotopes of interest: ¹H, C, ^58,60Ni, ^{182,183,184,186}W, ^235,238U, and ²³⁹Pu, as well as additional benchmarks sensitive to ¹⁶O and ⁵⁶Fe (Refs. 27 and 28). This lower limit on sensitivity strove to identify a unique assortment of applicable experiments while reducing the impact of stochastic uncertainties inherent to Monte Carlo transport. In total, 32 ICSBEP evaluations containing 253 benchmark configurations were selected and modeled. This selection of evaluations and configurations includes and expands upon the 20 evaluations and 99 configurations included in the previous work.⁴

Each selected configuration, or case, was modeled using the SCALE 6.2.4 release with the Criticality Safety Analysis Sequences (CSAS) module utilizing the KENO V.a or KENO VI Monte Carlo transport code. As a result, a direct comparison of k_eff’s with the previous study may produce trivial discrepancies with the previously listed models due to the more recent SCALE release and the stochastic nature of Monte Carlo. Model inputs were derived from Sec. III of the corresponding ICSBEP evaluation, with final stochastic uncertainties in k_eff of 10 pcm. When available, ICSBEP sample KENO inputs were used, with adjustments if needed to account for evaluation revisions or outdated models. Inputs for IMF-020, IMF-022, IMI-001, and LCT-079 inputs were sourced from previously produced ORNL inputs.^29,30 Inputs for HMI-006, HMF-072, HMF-073, IST-002, IST-003, LCT-025, PMF-035, PMF-040, and HMF-085 were independently verified at ORNL for inclusion in the VALID library.^31–39 The CSAS module utilizes KENO Monte Carlo to calculate k_eff, with continuous-energy cross-section libraries chosen to maintain fidelity.

Three groups of the ENDF library were used: the standard SCALE release of the ENDF/B-VII.1 library, the standard SCALE ENDF/B-VIII.0 library available in SCALE beta releases, and a mixed library that linked individual isotope datasets from the ENDF/B-VII.1 and ENDF/B-VIII.0 libraries through a CSAS input shell script. Throughout the paper, “full library” will refer to the use of entirely ENDF/B-VII.1 or entirely ENDF/B-VIII.0 libraries for calculations. To produce mixed libraries, each full library header was decomposed into an individual header file for each isotope of interest, and a base header containing data files was used for all other isotopes. For carbon, with only an elemental evaluation in ENDF/B-VII.1, both ¹²C and ¹³C isotopic data were substituted together as one elemental substitution.

The underlying AMPX-processed data were not altered at any point but were simply rearranged akin to the use of the .00c ACE identifier for MCNP in place of .80c. This mixed library listing was used for the calculation of k_eff for each isotope substitution, along with the optimized variation. While there is no expectation that the use of other cross-section processing tools will produce significantly different results, it should be emphasized that such results were produced with AMPX-generated cross sections for use in CSAS calculations with select benchmarks and may not be observed in all codes or applications. The full list of evaluations and configurations is provided in online Appendix A, along with the calculated k_eff for the varying substitutions, with the benchmark evaluated criticalities and uncertainties in online Appendix B. The appropriate ICSBEP reference for each case is noted by superscript in online Appendixes A and B (Refs. 41–55).

III. RESULTS AND ANALYSIS

Multiple methods of performance analysis are included in absolute and relative terms. Biases of individual cases were determined by the ratio between calculated k_eff (k_C) and documented ICSBEP experimental benchmark k_eff (k_E), or k_C/k_E. The performance of individual isotopes was determined by measuring the deviation of k_C/k_E from unity for full libraries and the mixed library for the isotope of interest, in absolute terms and as factors of the corresponding benchmark suggested uncertainty σ^e. Deviations from unity are presented in units of pcm, or 10⁻⁵ variation in k_eff shown in Eqs. (1)(1) $k_c/k_E=\left(\frac{k_C}{k_E}-1\right)\times 1\mathrm{E}5$(1) and (2(2) ${\sigma }^{\left(c/e\right)}=\frac{k_C}{k_E}\sqrt{{\left(\frac{{\sigma }^c}{k_C}\right)}^2+{\left(\frac{{\sigma }^e}{k_E)}\right)}^2}\times 1\mathrm{E}5.$(2) ), with σ^c constant in all cases at 0.0001:

(1) $k_c/k_E=\left(\frac{k_C}{k_E}-1\right)\times 1\mathrm{E}5$(1)

and

(2) ${\sigma }^{\left(c/e\right)}=\frac{k_C}{k_E}\sqrt{{\left(\frac{{\sigma }^c}{k_C}\right)}^2+{\left(\frac{{\sigma }^e}{k_E)}\right)}^2}\times 1\mathrm{E}5.$(2)

Included as measures of group performance are the average absolute relative deviation (ARD), mean deviation, absolute mean deviation (AMD), and percent bound by 2σ. The average ARD and 2σ bounding are indicators of relative performance; both measures rely on ARD as defined in Eq. (3(3) $\mathrm{A}\mathrm{R}\mathrm{D}=X_i=\frac{{\left|k_C/k_E\right|}_i}{{\sigma }_i^{\left(c/e\right)}}.$(3) ), with k_C/k_E deviation adjusted to account for experimental precision:

(3) $\mathrm{A}\mathrm{R}\mathrm{D}=X_i=\frac{{\left|k_C/k_E\right|}_i}{{\sigma }_i^{\left(c/e\right)}}.$(3)

The average ARD, defined in Eq. (4(4) $Average\mathrm{A}\mathrm{R}\mathrm{D}=\frac{1}{N}{\sum }_i^N{X}_i.$(4) ), is a simple average of adjusted deviations, while the percent bound by 2σ is the percent of cases with an ARD less than 2, where 95% bounding would be expected for a truly normal distribution:

(4) $Average\mathrm{A}\mathrm{R}\mathrm{D}=\frac{1}{N}{\sum }_i^N{X}_i.$(4)

The AMD and mean deviations are calculated in Eqs. (5)(5) $Average\mathrm{A}\mathrm{M}\mathrm{D}=\frac{1}{N}{\sum }_i^N{\left|k_C/k_E\right|}_i,$(5) and (6(6) $MeanDeviation=\frac{1}{N}{\sum }_i^N{\left(k_C/k_E\right)}_i,$(6) ), with uncertainties calculated in Eq. (7)(7) ${\sigma }^{\mathrm{A}\mathrm{M}\mathrm{D},M}=\frac{1}{N}\sqrt{{\sum }_i^N\sigma {{ }_i^{\left(c/e\right)}}^2}.$(7) :

(5) $Average\mathrm{A}\mathrm{M}\mathrm{D}=\frac{1}{N}{\sum }_i^N{\left|k_C/k_E\right|}_i,$(5)

(6) $MeanDeviation=\frac{1}{N}{\sum }_i^N{\left(k_C/k_E\right)}_i,$(6)

and

(7) ${\sigma }^{\mathrm{A}\mathrm{M}\mathrm{D},M}=\frac{1}{N}\sqrt{{\sum }_i^N\sigma {{ }_i^{\left(c/e\right)}}^2}.$(7)

The mean deviation from unity is commonly referred to as the bias in a selection of experiments, effective for displaying trends in k_eff variation. The average AMD calculates the effective distance of calculated values from experimental values, similarly to the average ARD, albeit unadjusted for ICSBEP uncertainty. Equation (8)(8) ${{\chi }_n}^2={\sum }_i^n\frac{{\left(k_{C,i}-k_{E,i}\right)}^2}{{\sigma }^e{{ }^2}_i}.$(8) calculates the chi-squared per degree of freedom:

(8) ${{\chi }_n}^2={\sum }_i^n\frac{{\left(k_{C,i}-k_{E,i}\right)}^2}{{\sigma }^e{{ }^2}_i}.$(8)

Tables I through VII demonstrate the variation in the above evaluated parameters for the isotopes of interest. With an expanded list of ¹⁶O and ⁵⁶Fe sensitive experiments, Table VIII and Table IX demonstrate the variation in results beyond the prior paper, with 92 new ¹⁶O cases and 17 new ⁵⁶Fe cases. Italicized portions of Tables VIII and IX are drawn from Ref. 4 as reference to the new additions of the ¹⁶O and ⁵⁶Fe results.

TABLE I Hydrogen-1 Sensitive Benchmark Performance by Library

Average of 168 Hydrogen-1 Cases	ENDF/B-VII.1	Hydrogen-1 ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	1.03σ	1.04σ	1.27σ
Chi-squared per degree of freedom	2.03	2.10	2.77
Mean deviation (pcm)	−28.9 ± 36.3	−80.1 ± 36.3	−20.4 ± 36.3
Absolute mean deviation (pcm)	390.2 ± 36.3	399.5 ± 36.3	437.2 ± 36.3
2σ bounding	88%	88%	73%

TABLE II Carbon Sensitive Benchmark Performance by Library

Average of 48 Carbon Cases	ENDF/B-VII.1	Carbon ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	1.11σ	1.09σ	0.81σ
Chi-squared per degree of freedom	4.04	3.98	1.52
Mean deviation (pcm)	−18.4 ± 41.2	−2.8 ± 41.2	68.0 ± 41.2
Absolute mean deviation (pcm)	201.3 ± 41.2	190.9 ± 41.2	169.5 ± 41.2
2σ bounding	88%	90%	92%

TABLE III Nickel Sensitive Benchmark Performance by Library

Average of 10 Nickel Cases	ENDF/B-VII.1	Nickel-58 ENDF/B-VIII.0	Nickel-60 ENDF/B-VIII.0	Nickel ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	1.14σ	1.08σ	0.95σ	1.31σ	1.02σ
Chi-squared per degree of freedom	2.10	1.64	1.46	2.32	1.49
Mean deviation (pcm)	229.3 ± 74.9	−18.4 ± 74.9	132.5 ± 74.9	−126.9 ± 74.9	−162.7 ± 74.9
Absolute mean deviation (pcm)	276.1 ± 74.9	240.3 ± 74.9	215.4 ± 74.9	295.3 ± 74.9	241.9 ± 74.9
2σ bounding	70%	90%	100%	80%	90%

TABLE IV Tungsten Sensitive Benchmark Performance by Library

Average of Eight Tungsten Cases	ENDF/B-VII.1	Tungsten-182 ENDF/B-VIII.0	Tungsten-183 ENDF/B-VIII.0	Tungsten-184 ENDF/B-VIII.0	Tungsten-186 ENDF/B-VIII.0	Tungsten ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	0.92σ	0.93σ	0.94σ	0.95σ	0.92σ	0.93σ	0.77σ
Chi-squared per degree of freedom	1.34	1.38	1.37	1.38	1.35	1.35	0.90
Mean deviation (pcm)	311.3 ± 135.7	313.6 ± 135.7	319.1 ± 135.7	313.6 ± 135.7	315.7 ± 135.7	313.3 ± 135.7	192.0 ± 135.7
Absolute mean deviation (pcm)	342.3 ± 135.7	348.8 ± 135.7	346.6 ± 135.7	349.1 ± 135.7	347.5 ± 135.7	347.3 ± 135.7	275.4 ± 135.7
2σ bounding	88%	75%	75%	75%	75%	75%	100%

TABLE V Uranium-235 Sensitive Benchmark Performance by Library

Average of 233 Uranium-235 Cases	ENDF/B-VII.1	Uranium-235 ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	1.34σ	1.47σ	1.19σ
Chi-squared per degree of freedom	4.43	4.42	2.50
Mean deviation (pcm)	42.6 ± 27.1	136.0 ± 27.1	7.7 ± 27.1
Absolute mean deviation (pcm)	387.6 ± 27.1	421.5 ± 27.1	370.9 ± 27.1
2σ bounding	82%	75%	76%

TABLE VI Uranium-238 Sensitive Benchmark Performance by Library

Average of 190 Uranium-238 Cases	ENDF/B-VII.1	Uranium-238 ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	1.10σ	0.96σ	1.01σ
Chi-squared per degree of freedom	3.39	3.02	1.80
Mean deviation (pcm)	20.3 ± 28.3	55.7 ± 28.3	−33.9 ± 28.3
Absolute mean deviation (pcm)	269.5 ± 28.3	256.2 ± 28.3	258.0 ± 28.3
2σ bounding	89%	89%	82%

TABLE VII Plutonium-239 Sensitive Benchmark Performance by Library

Average of 20 Plutonium-239 Cases	ENDF/B-VII.1	Plutonium-239 ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	0.64σ	0.83σ	0.93σ
Chi-squared per degree of freedom	0.61	0.86	1.06
Mean deviation (pcm)	−127.9 ± 96.1	−278.9 ± 96.1	−368.9 ± 96.1
Absolute mean deviation (pcm)	235.9 ± 96.1	329.1 ± 96.1	368.9 ± 96.1
2σ bounding	95%	100%	100%

TABLE VIII Oxygen-16 Sensitive Benchmark Performance by Library

Average of 63 Oxygen-16 Cases	ENDF/B-VII.1	Oxygen-16 ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	1.34σ	1.68σ	1.56σ
Chi-squared per degree of freedom	3.35	4.52	3.82
Mean deviation (pcm)	−37.2 ± 59.0	−174.6 ± 59.0	−53.1.±59.0
Absolute mean deviation (pcm)	578.9 ± 59.0	640.2 ± 59.0	655.3 ± 59.0
2σ bounding	75%	63%	67%
Average of 155 Oxygen-16 Cases	ENDF/B-VII.1	Oxygen-16 ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	1.02σ	1.41σ	1.31σ
Chi-squared per degree of freedom	1.93	3.41	2.84
Mean deviation (pcm)	−30.1 ± 38.8	−163.8 ± 38.8	−27.6 ± 38.8
Absolute mean deviation (pcm)	403.6 ± 38.8	458.9 ± 38.8	457.4 ± 38.8
2σ bounding	88%	68%	71%

TABLE IX Iron-56 Sensitive Benchmark Performance by Library

Average of 22 Iron-56 Cases	ENDF/B-VII.1	Iron-56 ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	2.66σ	2.57σ	1.06σ
Chi-squared per degree of freedom	12.16	11.48	1.91
Mean deviation (pcm)	270.5 ± 80.8	300.1 ± 80.8	77.5 ± 80.8
Absolute mean deviation (pcm)	655.1 ± 80.8	634.0 ± 80.8	405.7 ± 80.8
2σ bounding	45%	50%	82%
Average of 39 Iron-56 Cases	ENDF/B-VII.1	Iron-56 ENDF/B-VIII.0	ENDF/B-VIII.0
Relative deviation	1.86σ	1.80σ	0.93σ
Chi-squared per degree of freedom	7.31	6.91	1.49
Mean deviation (pcm)	13.5 ± 81.1	38.9 ± 81.1	−73.6 ± 81.1
Absolute mean deviation (pcm)	568.6 ± 81.1	552.2 ± 81.1	417.1 ± 81.1
2σ bounding	67%	69%	87%

III.A. Hydrogen Substitution

In general, the substitution of ¹H and its associated thermal scattering data produced a downward trend in k_eff, shown in the Table I’s 51.2 pcm decrease in bias as well as Fig. 1. In effect, ¹H performance measures that of the light water evaluation given that most cases are light water based, and the polyethylene cases still included after excluding for the h-poly SCALE error are, as a result, not overly sensitive to the polyethylene TSL. SCALE defaults hydrogen to using the light water TSL, and while an isotopic evaluation (hfreegas) is available, TSL implementations are directly linked with the isotopic data. Therefore, determining TSL effects independently from the underlying isotopic data is not yet supported. The black bars in Fig. 1 and all such figures represent 3σ Monte Carlo uncertainty. Of the 168 examined cases, 117 had cross-section–induced variations of greater than 42.5 pcm (where $3\sqrt{{10}^2+{10}^2}$, ~42.5 pcm represents 3σ propagated stochastic uncertainty), with 21 cases having a magnitude greater than 100 pcm. Nearly 90% of these 117 were negative. Only nine had statistical increases, of which seven were from LCT-060 (Ref. 40). Of statistical changes, ~40% move toward critical as opposed to 60% that move away. LCT-097 was unaffected, with all 24 showing changes below 50 pcm. No trend in the average energy corresponding to the energy of average lethargy of neutrons causing fission (EALF) was observed, beyond an expected lack of deviation in fast systems. While minor and within statistical variations, every metric indicated a stability or deterioration in performance, which is continued with the substitution of all other ENDF/B-VIII.0 data, indicating that this slight deterioration is not simply an artifact of compensating errors.

Fig. 1. Hydrogen-1 substitution effect on k_C/k_E.

III.B. Carbon Substitution

Table II demonstrates that the substitution of ^12,13C and its associated thermal scattering data produced a mixed effect on k_eff, shown in the 15.6 pcm increase in bias and Fig. 2 displaying increases in k_eff at thermal energies and minor decreases in the intermediate and fast energy ranges. Of the 48 examined cases, 20 had cross-section–induced variations greater than 42.5 pcm: 5 were negative and at intermediate and fast energies while the 15 positive cases were thermal systems in LCT-060. The distribution of improvements with these significant variations is balanced with 12 improving and 8 worsening. Most metrics show statistically irrelevant improvement, with the substitution of all other ENDF/B-VIII.0 data showing significant improvement in the chi-squared value with a countering rise in bias. Figures 2 and 3 show most instances of C substitution trending the same direction as the ENDF/B-VIII.0 full library substitution.

Fig. 2. Carbon substitution effect on k_C/k_E.

Fig. 3. Carbon k_C/k_E by library and configuration.

III.C. Nickel Substitution

Table III demonstrates that the substitution of ⁵⁸Ni, ⁶⁰Ni, and the combination of both isotopes produces a negative effect on k_eff, shown in the 247.7, 96.8, and 356.2 pcm decreases in the average k_C/k_E value, respectively. Of the ten nickel sensitive cases examined, ⁵⁸Ni and its natural abundance showed relevant variations in all cases, with ⁶⁰Ni showing variations in k_eff greater than 42.5 pcm in six cases. Of these, six, three, and eight, respectively, had cross-section–induced variations greater than 100 pcm. All case variations were negative. Respectively, cases with significant variation had five, five, and four improvement, and five, one, and six worsened. Individually, ⁵⁸Ni and ⁶⁰Ni show significantly improved agreement with observed benchmark values. Combined in their natural abundance, however, the magnitude of both changes pushes the performance of the selected models beyond their initial state, as the combined negative biases result in deteriorated performance in the relative deviation, chi-squared, and absolute mean. This is demonstrated in Fig. 4, where ⁵⁸Ni alone reduces the number of cases with k_C/k_E greater than 1 from eight to four, and ⁶⁰Ni reduces the same from eight to six—both, on their own, symmetric about unity. With both substituted, the eight positively biased ENDF/B-VII.1 cases become eight negatively biased Ni ENDF/B-VIII.0 cases.

Fig. 4. Nickel k_C/k_E by library and configuration.

III.D. Tungsten Substitution

As expected, Table IV shows a lack of variation in fast tungsten systems when ENDF/B-VIII.0 tungsten cross sections are substituted. Of all isotopes and the natural abundance, only one case has a variation above 42.5 pcm, a variation of 47.3 pcm for ¹⁸²W, which is a variation that does not emerge in the natural abundance calculation. The only standout metric is the percent bound by 2σ, which is simply a single ENDF/B-VII.1 calculation ~20 pcm below the 2σ cutoff.

III.E. Uranium Substitution

Table V demonstrates the integral performance of revised ²³⁵U cross sections. With an abundance of cases and ICSBEP identifiers, the impacts of such a finely tuned and detailed evaluation such as ²³⁵U may fall out, though the improvement in chi-squared is of note particularly with the full library.

Of the 233 examined cases, 172 have statistically relevant changes, with 119 having variations greater than 100 pcm. Variations are largely increases in bias, reflected in the relevant mean deviation increase of 93.4 pcm, particularly for thermal and intermediate systems. Significant variations trend deteriorating, with 38% showing improvement. Thermal systems with significant variation were largely increases in k_eff, with 101 significantly variable thermal systems doing so as opposed to 34 decreasing, of which 10 were LCT-060 and 20 were LCT-097. In intermediate and fast systems, a pattern appears in Fig. 5 beginning with HMI-006-002’s EALF of 10 keV, where the variation is nearly 750 pcm. This increase in k_eff decreases in magnitude with increasing EALF, flipping negatively upon reaching 100 keV. A similar pattern is seen at thermal energies, as approaching 1 eV deviations level off and begin to trend negative. With the full ENDF/B-VIII.0 library, substantial improvement is seen in the chi-square, with all other isotopes introducing over 3σ suppression in bias relative to ²³⁵U. As noted as a potential explanation to LCT performance compared to other ²³⁵U sensitive categories in Sec. I, LCT systems indeed show greater variations in k_eff from ¹⁶O substitution than ²³⁵U in 34 of the 43 LCT cases in this work.

Fig. 5. Uranium-235 substitution effect on k_C/k_E.

Table VI presents the performance of revised ²³⁸U cross sections. While not nearly as diverse or plentiful as ²³⁵U sensitive experiments, there is still significant selection. There is general improvement in most metrics. Of the 190 examined cases, 113 have statistically relevant changes, with 42 having variations greater than 100 pcm. The 113 cases with significant variation show improvement in 71 of them. Thermal variations in Fig. 6 are shown to be fully positive increases of a lower magnitude than ²³⁵U. Intermediate variations follow a similar but muted ²³⁵U trend, beginning positive and turning negative at fast energies.

Fig. 6. Uranium-238 substitution effect on k_C/k_E.

III.F. Plutonium Substitution

Table VII indicates agreement with prior information on ²³⁹Pu cross-section performance, with 151 pcm decrease in bias and nearly 100 pcm increase in AMD. Also in agreement is the increased magnitude of the decrease in PSTs (benchmarks 6 to 20 in Fig. 7). While all PSTs are from only one evaluation, PST-034, there is a notable difference in the response to ENDF/B-VIII.0 ²³⁹Pu substitution.⁴² Figure 7 shows the clear difference in EALF in the cutoff after case 6. The notable cutoff coincides with a PST-034 plutonium concentration increase from 116 to 363 g/cm³ along with increased gadolinium. Decreases in k_eff are relevant and consistent, though there is insufficient support (i.e., too great an uncertainty in quadrature) in this sample of experiments to confirm prior conclusions. Of the 20 case variations, 19 are greater than 42.5 pcm, with the first 6 PST-034 cases being greater than 100 pcm. Of these, 15 have their absolute deviation increase.

Fig. 7. Plutonium-239 substitution effect on k_C/k_E.

III.G. Oxygen and Iron Suite Expansions

Table VIII presents results from Ref. 4, with an expanded selection of benchmarks. Relative to Ref. 4, newly included ¹⁶O sensitive benchmarks are the IST-002, IST-003, LCT-025, LCT-060, and LCT-097 evaluations. While at face value, these averages appear significantly different, Table X expresses the substitution effect of ¹⁶O between the prior and current studied suites, with propagated uncertainty. Despite a 150% increase in suite size and expanding to include IST systems, the impact is largely constant. Relative measures show more variability than absolute measures, though this is expected given the different weighting by different experimental uncertainties. Of particular significance is the impact of the suite size on uncertainties. Relative to Ref. 4, newly included ⁵⁶Fe sensitive benchmarks are the IST-002, IST-003, and LCT-025 evaluations. Despite an additional 17 cases, no significant change is noticed in the ⁵⁶Fe substitution effect, and prior conclusions remain the same (Table XI).

TABLE X Oxygen-16 Substitution Effect Between Benchmark Suites

Difference in Oxygen-16 Substitution	63 Cases	155 Cases
Relative deviation	0.34σ	0.39σ
Chi-squared per degree of freedom	1.17	1.48
Mean deviation (pcm)	−137.4 ± 83.4	−133.7 ± 54.9
Absolute mean deviation (pcm)	61.3 ± 83.4	55.3 ± 54.9
2σ bounding	−12%	−20%

TABLE XI Iron-56 Substitution Effect Between Benchmark Suites

Difference in Oxygen-16 Substitution	22 Cases	39 Cases
Relative deviation	−0.09σ	−0.06σ
Chi-squared per degree of freedom	−0.68	−0.40
Mean deviation (pcm)	29.6 ± 114.3	25.4 ± 114.7
Absolute mean deviation (pcm)	−21.1 ± 114.3	−16.4 ± 114.7
2σ bounding	5%	2%

IV. OPTIMIZED LIBRARY

A simple script was formulated to utilize actual calculated variations in k_eff by isotope substitution to predict the best-performing combination of ENDF/B-VII.1 and ENDF/B-VIII.0 isotope libraires. While individually, an isotope’s performance may worsen by the metrics used in this paper, conclusively stating such would assume there are no compensating errors or nonlinear dependence between cross sections. An estimated k_eff was calculated with the assumption that observed variations in k_eff due to individual isotope substitutions were sufficiently linear, allowing for the approximation of k_eff for unique combinations of isotopic ENDF data. This approach allowed for the determination of the most agreeable combination of isotopes based on actual changes in k_eff. The script alternated between ENDF/B-VII.1 and ENDF/B-VIII.0 for every isotope that showed variations in k_eff greater than 42.5 pcm, including isotopes of the previous study. This resulted in the inclusion of the following 11 isotopes to alternate: ¹H, C, ¹⁶O, ⁵⁶Fe, ^58,60Ni, ^63,65Cu, ^235,238U, and ²³⁹Pu. Isotopes that showed no variation greater than 42.5 pcm in any case, such as tungsten, remained ENDF/B-VIII.0 data in addition to the base library, nor were individual case changes below 42.5 pcm implemented. With these isotopes, the assumed linearity estimates 2048 variations (two library options with 11 alternating isotopes) in the manner of Eq. (9(9) $Estimated{k_{eff}}^3={k_{eff}}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}-\mathrm{\Delta }{k_{eff}}_{\mathrm{H}1}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}-\mathrm{\Delta }{k_{eff}}_{\mathrm{C}}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}$(9) ), where isotopic Δk_eff refers to the variation in ENDF/B-VII.1 k_eff due to the substitution of said ENDF/B-VIII.0 isotope:

$Estimated{k_{eff}}^1={k_{eff}}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}-\mathrm{\Delta }{k_{eff}}_{\mathrm{H}1}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}$

$Estimated{k_{eff}}^2={k_{eff}}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}-\mathrm{\Delta }{k_{eff}}_{\mathrm{C}}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}$

(9) $Estimated{k_{eff}}^3={k_{eff}}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}-\mathrm{\Delta }{k_{eff}}_{\mathrm{H}1}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}-\mathrm{\Delta }{k_{eff}}_{\mathrm{C}}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}$(9)

…

$Estimated{k_{eff}}^{2,048}={k_{eff}}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}-\mathrm{\Delta }{k_{eff}}_{\mathrm{H}1}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}-\mathrm{\Delta }{k_{eff}}_{\mathrm{C}}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}\dots -\mathrm{\Delta }{k_{eff}}_{\mathrm{P}\mathrm{u}239}^{\mathrm{V}\mathrm{I}\mathrm{I}\mathrm{I}.0}.$

The script estimated the 2048 variations in k_eff for all 253 benchmarks, which allows for the ARD and AMD to be calculated for each estimated data combination. Table XII displays the estimated assortment of isotopes to produce the associated minimum ARD.

TABLE XII Best-Performing ARD Combination of Partial ENDF Libraries

Isotope	Oxygen-16	Iron-56	Copper-63	Copper-65	Hydrogen-1	Uranium-235	Uranium-238	Plutonium-239	Nickel-58	Nickel-60	Carbon	AMD	ARD	Bias
Minimized ARD	ENDF/B-VII.1	ENDF/B-VIII.0	ENDF/B-VIII.0	ENDF/B-VII.1	ENDF/B-VIII.0	ENDF/B-VIII.0	ENDF/B-VIII.0	ENDF/B-VII.1	ENDF/B-VII.1	ENDF/B-VIII.0	ENDF/B-VIII.0	344.5	0.97	70.7

Regarding the previous study, the observed performance holds true for the previously studied isotopes, ¹⁶O, ⁵⁶Fe, and ^63,65Cu. Given the substitutions that produce the most agreeable k_eff, there are notable discrepancies between the use of the optimization of all experiments and the individual performances. However, whereas ²³⁵U sensitive benchmarks show worsened agreement individually in this study, combined with other isotopes, ²³⁵U is key to improved performance in all cases as shown in the full ENDF/B-VIII.0 data for ²³⁵U. Furthermore, whereas individually ⁵⁸Ni improves, as noted before, the natural abundance of nickel worsens from the compounding effect of both isotopes. Given that ⁶⁰Ni independently improves more so than ⁵⁸Ni, it follows that of the two isotopes, ⁵⁸Ni reverts for improved overall agreement.

Using the estimated optimum, the data directories were adjusted accordingly to perform SCALE calculations on the 253 cases with the data configuration in Table XII. Comparison of estimated ARD, bias, and AMD values with calculated values in Table XIII shows excellent agreement. Table XIII displays the performance of all 253 cases with the full ENDF/B-VII.1 and ENDF/B-VIII.0 libraries, as well as the optimized library, i.e., the ENDF/B-VIII.0 library with ENDF/B-VII.1 data for ¹⁶O, ⁶⁵Cu, ²³⁹Pu, and ⁵⁸Ni. All metrics apart from bias show improvement over both full libraries. Supplemental online Appendix C presents cumulative distributions for the three library variants for AMD, chi-squared, and ARD. Figure 8 displays the substitution effect of the full ENDF/B-VIII.0 library, excepting ¹⁶O, ⁶⁵Cu, ²³⁹Pu, and ⁵⁸Ni.

TABLE XIII Full ENDF/B-VIII.0 Library Performance

Average of 253 Cases	ENDF/B-VII.1	Estimated Optimized ARD	Calculated Optimized ARD	ENDF/B-VIII.0
Relative deviation	1.29σ	0.97σ	0.97σ	1.17σ
Chi-squared per degree of freedom	4.13	—	1.72	2.39
Mean deviation (pcm)	29.2 ± 26.1	70.7	75.3 ± 26.1	−22.1 ± 26.1
Absolute mean deviation (pcm)	375.6 ± 26.1	344.5	346.1 ± 26.1	370.7 ± 26.1
2σ bounding	83%	——	89%	78%

Fig. 8. Substitution effect of the optimized ENDF/B-VIII.0 library on k_C/k_E.

Table XIV displays the results from Ref. 4 on the full library performance of the examined benchmarks. With the current suite including all experiments included in the previous suite, optimized performance metrics for the previous suite can be calculated from the newly optimized values presented in this paper. These metrics are expressed in the “Newly Optimized” column of Table XIV for comparison, with the italicized portion of the table taken directly from Ref. 4. It shows that the reversion of ²³⁹Pu and ⁵⁸Ni adds further improvement to the previous suite’s optimization.

TABLE XIV Full ENDF/B-VIII.0 Library Performance*

Average of 99 Cases	ENDF/B-VII.1	Optimized ARD	Newly Optimized	ENDF/B-VIII.0
Relative deviation	2.08σ	1.32σ	1.23σ	1.43σ
Mean deviation	75.4 ± 40.2	10.7 ± 40.2	53.0 ± 40.2	−41.4 ± 40.2
Absolute mean deviation	555.6 ± 40.2——	477.9 ± 40.2	451.5 ± 40.2	501.3 ± 40.2
Root-mean-square deviation	770.2 ± 52.9	738.7 ± 61.3	736.8 ± 62.5	740.9 ± 56.6
2σ bounding	65%	78%	79%	73%

*Reference 4.

Relative to Ref. 4, the full ENDF/B-VII.1 library in Table XIII performs much better with the expanded suite of benchmarks, which is expected given that nearly a third of the previous work centered on copper sensitive experiments that had significant noted issues. The ARD is 0.79σ lower, the bias is on the order of 1σ uncertainty rather than 2σ, the AMD is 180 pcm lower, and the percent bound by 2σ is 18% higher. The full ENDF/B-VIII.0 library sees relative improvement as well. While the previous paper’s optimized library—the result of ¹⁶O and ⁶⁵Cu ENDF/B-VII.1 reversion—improves by only 0.11σ in the ARD, the larger suite presented here improves by 0.20σ, which is higher in absolute and relative terms. Additionally, the previous optimization improved the ARD a further 17% decrease compared to the full library substitution (1.43 to 1.32 relative to 2.09 to 1.43), while the larger suite shows a 167% further decrease (1.17 to 0.97 relative to 1.29 to 1.17), which is due in part to the lower overall change from the full library substitution. Nevertheless, retaining ¹⁶O, ⁶⁵Cu, ²³⁹Pu, and ⁵⁸Ni ENDF/B-VII.1 cross sections results in ENDF/B-VIII.0 performance gains more than double the full library change in the ARD from ENDF/B-VII.1 to ENDF/B-VIII.0, and an additional 38% decrease in chi square.

V. STOCHASTIC OMISSIONS

The inherent stochastic nature of Monte Carlo calculations has the potential to lead to implications that, even statistically irrelevant, can alter conclusions regarding performance. As an average, the bias and other performance metrics may not indicate significant variations, masking cases more sensitive to cross-section variation by using experiments not representative of the cross-section changes. Therefore, performance metrics were reanalyzed, limited to cases where variations from cross-section substitutions were greater than 3σ Monte Carlo uncertainty. The results of this analysis are presented in supplemental online Appendix D. It should also be noted that these changes will specifically enhance changes in k_eff and disregard instances where new nuclear data had no impact. The true impact of the isotope substitution across the full suite is as presented in Sec. III; this method retroactively removes sensitive cases that are not applicable for the specific data change. Additionally, as it is impossible to fully examine all sensitivity profiles and nuclear data changes as a function of energy, a lack of variation between the Sec. III results and Sec. V indicates an adequate selectivity of applicable critical experiments.

VI. SUMMARY AND CONCLUSIONS

As part of the nuclear data cycle, recent nuclear data releases require integral validation, in particular, validation of nuclear data related to nuclear criticality safety criticality experiments. Continuing work by the authors in analyzing the isotopic variation between ENDF/B-VII.1 and ENDF/B-VIII.0 included investigating the effect of a further 11 isotopes: ¹H, C, ^58,60Ni, ^{182,183,184,186}W, ^235,238U, and ²³⁹Pu. Additionally, isotopes previously investigated by the authors were reevaluated with a larger selection of applicable criticality experiments, with ¹⁶O and ⁵⁶Fe sensitive suites increasing by 92 and 17 cases, respectively. These isotopes represent some of the most crucial fissile and moderating materials in nuclear criticality safety operations, fully covering the effects of the CIELO implementation into the ENDF/B-VIII.0 library. Beyond these materials of extreme importance, other materials with more niche applications to nuclear criticality safety were investigated due to substantial cross-section variation.

Cross-section performance was investigated by selecting ICSBEP benchmarks of criticality experiments sensitive to isotopes of interest, substituting the ENDF/B-VIII.0 continuous energy data in place of ENDF/B-VII.1 in SCALE models. In total, 253 experiments were utilized, with a total of 1778 SCALE 6.2.4 CSAS calculations across multiple isotope variations and optimization. Also, 168 ¹H experiments were investigated, with a decrease in bias of 51 pcm (1.00σ experimental uncertainty). Accounting for cases variable beyond Monte Carlo effects, the decrease in bias was 73 pcm (1.03σ). In addition, 48 C experiments were investigated, with minor improvement and thermal increases in bias and fast decreases. In the ten analyzed experiments, ⁵⁸Ni and ⁶⁰Ni both saw major improvements in adjusting absorption reactions. The effects of both evaluation alterations to the natural abundance of nickel resulted in overly corrective changes. Tungsten sensitive experiments were limited to eight cases with mainly fast neutrons, whereas ENDF/B-VIII.0 alterations to ^{182,182,184,186}W were largely made to thermal cross sections. Therefore, no variations of note were found.

Uranium-235 involved investigating 233 sensitive benchmarks, with minor deterioration noticed upon individual isotope substitution. Taken with the remainder of the ENDF/B-VIII.0 evaluation, and with a script to alternate calculated isotope substitution effects, ²³⁵U was necessary for overall improvement. Uranium-235 substitution resulted in a 93 pcm (2.44σ) increase in bias, or 131 pcm (2.68σ) ignoring cases with Monte Carlo variations. Variations were largely positive reflected in the bias increase, though a noticeable trend from intermediate to fast EALF resulted in decreasing magnitude. This decrease in magnitude was also noted increasing from thermal to epithermal. Uranium-238 independently improved with 190 cases, exhibiting a 35 pcm (0.88σ) increase in bias, or 57 pcm (1.00σ) without cases showing no impact. Plutonium-239 follows previous work with decreases in bias across the board in 20 cases, decreasing 151 pcm (1.11σ) with deteriorating performance particularly thermally.

In expanding ¹⁶O and ⁵⁶Fe suites, additional evidence for previous findings was presented, with isotope variations nearly constant despite adding benchmarks with more variability in spectrum and fissile material. Additional experiments for ¹⁶O resulted in significant uncertainty reduction. Both this work and the prior work found a decrease in bias on the order of 135 pcm, which is a variation increasing as a factor of uncertainty from 1.65σ to 2.44σ.

Using all 253 cases, each statistically relevant isotopic variation was scripted to assume linearity and estimate the best combination of all isotopes involved. The full library average relative deviation, being relative to benchmark uncertainty, decreased for ENDF/B-VII.1 of 1.29σ to 1.17σ for ENDF/B-VIII.0. The library arrangement determined to be optimal retained ¹⁶O, ⁶⁵Cu, ²³⁹Pu, and ⁵⁸Ni ENDF/B-VII.1 cross sections, reducing this further to 0.97σ.

In conclusion, it was determined that reverting ENDF/B-VIII.0 cross sections for ²³⁹Pu and ⁵⁸Ni to ENDF/B-VII.1 would result in improved agreement with benchmark k_eff, as would reverting ¹⁶O and ⁶⁵Cu in agreement with the previous study. Other isotopes examined, C, ⁶⁰Ni, ^{182,183,184,186}W, ^235,238U, and ⁵⁶Fe, either had nondifferentiable effects from the new data evaluation or resulted in improvement in k_eff agreement.

Acknowledgments

This work was supported by the NCSP, funded and managed by the National Nuclear Security Administration for the U.S. Department of Energy.

Supplemental Material

Supplemental data for this article can be accessed on the publisher’s website.

Disclosure Statement

No potential conflict of interest was reported by the author(s).