ENDF/B-VIII.0 CROSS SECTION TESTING FOR COPPER NUCLEAR CRITICALITY SAFETY APPLICATIONS

In the update from ENDF/B-VII.1 to ENDF/B-VIII.0, copper cross sections were significantly altered in the intermediate and fast spectrum of the ENDF-VIII.0 library. Performance of this ENDF data requires validation to determine whether recent evaluation has proven beneficial. To examine the performance of the new library, particularly new copper data, critical benchmarks from the ICSBEP handbook were chosen for their sensitivity to copper cross section changes and modeled using SCALE continuous energy Monte Carlo simulations. Selected benchmarks were modeled in ENDF-VII.1 and ENDF-VIII.0 to compute kkeeffff within a statistical uncertainty of 10 pcm and compared in reference to the benchmark experimental criticality. Due to spectrum choices in selection based on the changes to cross section data, the set of benchmarks consist of intermediately enriched uranium, highly enriched uranium, or plutonium systems. 11 separate benchmark evaluations containing 32 individual configurations highly sensitive to copper were selected, modelled, and compared to benchmark experimental criticality. This work demonstrates a significant decrease in the deviation between calculated and experimental criticality as a result of the ENDF-VIII.0 library; a decrease in absolute mean deviation from 522.5±39.3 to 249.6±39.3, and a decrease in root mean square deviation from 630.8±46.1 to 338.1±74.9. Additionally, the role of recently evaluated copper data in this improved agreement is presented, confirming the benefit of reaffirming cross section data.


INTRODUCTION
Having long been recognized in criticality safety applications as a source of discrepancies between calculated and experimental , copper ( 63 Cu and 65 Cu) was identified as an isotope of interest by the US Department of Energy's Nuclear Criticality Safety Program (NCSP) and re-evaluated, being recently incorporated into the ENDF-VIII.0 cross section library. As was expected, there were significant alterations to the ENDF-VII.1 library, particularly in the elastic scattering and neutron capture cross sections.
For a comprehensive understanding of the changes in the cross sections, Brookhaven National Laboratory's (BNL) National Nuclear Data Center (NNDC) was used to plot and determine ENDF-VIII.0 relative to ENDF-VII.1, as opposed to the select energy ranges mentioned in the release [1]. Doing so illustrated the energies which had undergone the greatest changes: the intermediate, resonant, and fast energy regimes.
In order to validate ENDF-VIII.0 and demonstrate the effects of the new copper cross sections, the International Criticality Safety Benchmark Evaluation Project (ICSBEP) and International Reactor Physics Experiment Evaluation (IRPhE) Handbooks were inspected for benchmarked experiments containing significant amounts of copper. The IRPhE Database and Analysis Tool (IDAT) and Database for the International Handbook of Evaluated Criticality Safety Benchmark Experiments (DICE) databases were utilized to search the handbooks, as well as provide a rudimentary quantitative method for determination of copper significance. These programs contained cross section sensitivity data for most benchmarks. The sensitivity of a benchmark to an isotope or reaction indicates the dependence of the problem's criticality on said isotope's or reaction's change; such as occurs from a change in the cross section library or density. Using an arbitrary yet significant cutoff of .01 %Δk/%Σ for filtering experiments, experiments highly sensitive to copper cross sections ( 63 Cu and 65 Cu scattering and capture cross sections) could be found. Using the list of selected benchmarks, as well as additional expert opinion on benchmark quality and spectrum suitability, a final list of 11 benchmark evaluations containing 32 configurations was compiled. This paper presents the selected benchmarks and their corresponding criticalities in ENDF-VII.1 and ENDF-VIII.0 and studies the impacts copper cross section changes have made in the agreement between calculated and experimental data, as well as overall changes from the ENDF-VIII.0 library.

BENCHMARK SELECTION AND MODELING
At the root of the selection process was the use of sensitivity data to determine benchmarks which would appropriately contain copper. As stated, this selection was done through use of the DICE database included with the ICSBEP handbook. Sensitivity data is a quantitative measure of the importance of macroscopic cross sections on criticality. Therefore, copper sensitive benchmarks will contain more copper, with copper having a larger impact on than benchmarks with less copper or with more important materials (i.e. a core surrounded by copper will be more copper sensitive than the same core surrounded by water with a similar volume of copper surrounding that). Benchmarks that contain significant volumes of copper with no significant sensitivity provide no use for testing the impacts of copper cross section changes; with the wrong spectrum or low sensitivity, changes cannot be attributable to copper, and cannot be measured. Values tabulated and presented by DICE are reaction independent energy integrated cross section sensitivities, which for summed total reactions is equivalent to density perturbations [2]. As shown by Rearden et al. (2010), the sensitivity coefficient for a reaction can be expressed thusly for a perturbation α in the reaction's macroscopic cross section.
Using DICE, the sensitivity energy profile can be plotted as well to see overlap between the sensitivity profile and energies of interest from cross section changes. For benchmarks that have significant copper sensitivity in the intermediate and fast spectrum, Equation 1 demonstrates how such a change in cross sections can impact these sensitive benchmarks. Using this selection process, and the cutoff of .01 %Δk/%Σ, a final list of 11 benchmark evaluations was compiled. Included evaluations are as follow: PMF-013 [3]; PMF-014 [4]; PMF-040 [5]; HMF-072 [6]; HMF-073 [7]; HMF-084 [8]; HMF-085 [9]; HMI-006 [10]; IMF-020 [11]; IMF-022 [12]; IMI-001 [13]. In evaluation HMF-084 only the 6 th and 18 th configurations were used, and in HMF-085 only the 1 st 2 nd and 4 th . After selection of benchmarks, the SCALE code system and control module CSAS were used to model the configurations in continuous energy Monte Carlo simulations, following dimensional material and temperature specifications found in Section 3 of the ICSBEP evaluation. Simulations were performed to produce a statistical uncertainty in criticality of 10 pcm for all calculated data presented. In the occasions where simplified benchmark specifications were provided, they were ignored in favor of detailed models for accuracy.

ENDF/B-VII.1 AND ENDF/B-VIII.0 AND EXPERIMENTAL DEVIATION
Using models of the benchmark, the CSAS module was used to run criticality calculations on the inputs. For ENDF-VII.1 data, the "ce_v7.1_endf" identifier was used in the SCALE 6.2.3 release. As ENDF-VIII.0 data is not yet publicly available with SCALE releases, ENDF-VIII.0 simulations were done on the Romulus Linux cluster at Oak Ridge National Laboratory, using SCALE 6.2.3. ENDF-VIII.0 data was linked from SCALE 6.3 beta cross section data using a bash shell and called by the arbitrary identifier "ce_v8.0_endf". Criticality values calculated in ENDF-VII.1 and VIII.0 are tabulated in Table I, as well as the associated benchmark experimental criticality (experimentally determined criticality value, adjusted by simplification bias detailed in ICSBEP Section 2) and uncertainty. Experimental benchmark criticalities are subtracted from calculated criticalities in ENDF-VII.1 and VIII, producing the C-E (pcm) data tabulated in Table 1. Since the Monte Carlo uncertainty is small, C-E values have uncertainty effectively the same as the experimental criticalities as error propagation results in a change in uncertainty of <1 pcm, and therefore are not displayed. Figure 1 incorporates Table 1 data into a plot, displaying the range of effects ENDF-VIII.0 has on C-E. Uncertainty in experimental criticality is shown to 2σ, with 95% containment easier to visualize than 68%. Regardless of choice of σ, it is notable the improvement ENDF-VIII.0 data results in, with 41% of benchmarks in ENDF-VII.1 bounded by 2σ, as opposed to 94% of ENDF-VIII. Expressing deviation in terms of σ results in an average deviation of 3.49σ for ENDF-VII.1 and 1.24σ for ENDF-VIII. A summary of the deviations comparing ENDF-VII.1 and VIII.0 is included in Table II.  Beyond expression of deviation in relative terms of σ, absolute deviations were calculated as the absolute mean and root mean square (RMS) of C-E values. The standard derivations of both were used, and error propagated accordingly. For absolute mean, error propagation is elementary, but RMS error propagation is slightly more detailed and is expressed in Equation 2 with and representing individual configuration C-E values and associated uncertainties.
(2) These determinations of average deviation and associated uncertainty result in absolute and RMS means of 523±39 and 631±46 for ENDF-VII.1, and 250±39 and 338±75 for ENDF-VIII. A summary of deviations comparing ENDF-VII.1 and VIII.0 are included in Table II.

EFFECT OF ENDF/B-VIII.0 COPPER ON AND EXPERIMENTAL DEVIATION
With the system criticalities changing from the full adaptation of ENDF-VIII.0 data as shown, further study was conducted to determine the role of copper cross section changes on criticality. Rather than model benchmarks entirely in ENDF-VII.1 and ENDF-VIII, the base library of the benchmark was taken to mean all other isotopes present, apart from copper. The base library was constructed by disassembling the ENDF-VII.1 and ENDF-VIII.0 xml files that direct SCALE cross section library determinations and using a shell bash command to link the ENDF-VIII.0 designations for Cu-63 and Cu-65 into the ENDF-VII.1 base library. All isotopes apart from Cu-63 and Cu-65 are now ENDF-VII.1, while Cu-63 and Cu-65 use ENDF-VIII.0 data; the only new ENDF-VIII.0 data in the model is that of copper. This allows the effect of the copper data update to be determined, as the effect of only ENDF-VIII.0 copper data can be compared to the already produced ENDF-VII.1 systems. The results of this isotope swapping can be seen in Table III.
Of interest is the rightmost column, the deviations from experimental criticality where the copper cross sections are replaced with ENDF-VIII. As expected for the sensitivity profile and known cross section changes, in every case the C-E value decreases. Of course, whether this results in improved agreement with experimental results is not a given. In the same manner as in the comparison between VII.1 and VIII, the relative deviation, absolute mean, and root mean square were calculated to determine the change in overall deviation between calculated and experimental criticalities. In the same method as above, the absolute mean decreased from an average of 522.5±39.3 pcm to an average of 295.5±39.3 pcm, with the RMS decreasing from 630.8±46.1 pcm to 363.8±39.7 pcm, and relative deviation decreasing from 3.49σ to 2.10σ. When presented alongside data for full library comparison in Table IV and Figure 2, the effect of the copper data changes is shown to be a significant factor in the entire change from the library update. Whereas 24 of the 32 benchmarks improve with a full library update, 21 of them improve from the copper cross section data alone. With ENDF-VIII.0 copper cross sections, the percentage of uncertainty-bounded experiments rises from 42% to 72%, accounting for more than half of the full library change to 94%.

CONCLUSIONS
In this selection of copper sensitive benchmarks, substantial improvement in the agreement between calculated and experimental criticality was observed as a result of updating ENDF-VII.1 to ENDF-VIII. The average deviation between the two decreased a full 2σ relative to experimental uncertainty. In absolute terms, the RMS and absolute mean deviations decreased nearly 300 and over 250 pcm respectively. As expected, there was a substantial decrease in criticality due to the introduction of ENDF-VIII.0 copper cross section data alone. This decrease countered the significant supercriticality observed in many ENDF-VII.1 simulations of the selected benchmarks. As a result, copper cross sections accounted for a significant portion of the noted overall improvement between the C-E values of ENDF-VII.1 and ENDF-VIII. Considering the improvement in absolute deviation (absolute mean and RMS) and statistical agreement (calculations falling within experimental uncertainty) over multiple independent experimental assemblies, there is a substantial basis for arguing that these improvements are a result of genuine improvements in copper cross section data.