Nuclear Science

NEA/WPEC-22
ISBN 92-64-02317-8International Evaluation Co-operation

VOLUME 22
NUCLEAR DATA FOR IMPROVED
LEU-LWR REACTIVITY PREDICTIONS

A report by the Working Partyon International Evaluation Co-operationof the NEA Nuclear Science Committee

CO-ORDINATOR
A. Courcelle
CEA Cadarache
FRANCEMONITOR
R.D. McKnight
Argonne National Laboratory
USA© OECD 2006
NEA No. 6199
NUCLEAR ENERGY AGENCY
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FOREWORD

A Working Party on International Evaluation Co-operation was establishedunder the sponsorship of the OECD/NEA Nuclear Science Committee (NSC) topromote the exchange of information on nuclear data evaluations, validation andrelated topics. Its aim is also to provide a framework for co-operative activities
between the members of the major nuclear data evaluation projects. This
includes the possible exchange of scientists in order to encourage co-operation.
Requirements for experimental data resulting from this activity are compiled.
The working party determines common criteria for evaluated nuclear data files
with the goal of assessing and improving the quality and completeness ofevaluated data.
The parties to the project are ENDF (United States), JEFF/EFF (NEA Data
Bank member countries) and JENDL (Japan). Co-operation with evaluation
projects of non-OECD countries, specifically the Russian BROND and Chinese
CENDL projects, is organised through the Nuclear Data Section of theInternational Atomic Energy Agency (IAEA).
The working party formed a subgroup to investigate a systematic reactivity
under-prediction of thermal light water reactors fuelled with low-enricheduranium. The keff discrepancy (~ -500 pcm) was demonstrated with accurate
Monte Carlo transport codes and the most recent nuclear data libraries(ENDF/B-VI.8, JENDL-3.3 and JEFF-3.0) available at that time. This reportpresents the trends given by the analysis of relevant integral experiments as wellas the evaluation work, which focused mainly on 238U nuclear data. During thecourse of this work, new evaluations of 238U thermal capture cross-section,
resonance parameters and inelastic scattering data were performed and provide
a satisfactory solution of the problem. Finally, other nuclear data impacting thekeff of thermal benchmarks, such as 16O(n,D) cross-section and 1H-H2O thermal
scattering data, were also examined.
The opinions expressed in this report are those of the authors only and do not
represent the position of any member country or international organisation. This
report is published on the responsibility of the Secretary-General of the OECD.

3

Acknowledgements
The authors gratefully acknowledge subgroup members: H. Derrien,
L.C. Leal, N.M. Larson, C.R. Lubitz, J.P. Weinman, R.E. MacFarlane,
A.C. Kahler, H.C. Huria, Y.A. Chao, A. Santamarina, J-C. Sublet, M.J. Jimenez,
P. Romain, B. Morillon, A. Trkov, A. Hogenbirk, S. van der Marck, C. Dean
and M.C. Moxon.
The authors are also indebted to the subscribers of the ueval@nea.fr
mailing, as well as many other contributors to this work for helpful discussions
and advice: V. Maslov, A. Dos Santos, Haicheng Wu, J.M. Palau, O. Bouland,
C. Mounier, P. Ribon, D. Bernard, G. Noguère, J.M. Vidal, R. Jacqmin, E. Fort,
C. Chabert, E. Dupont, E. Bauge, B. Roque, O. Litaize, C. Jouanne, O. Serot,
R. Dagan, K. Okumura, H. Takano, A. Koning, J. Rowlands, P. Oblozinsky,
Y. Danon, R. Block, G. Arbanas, T. Kawano, P. Young, D. Madland, A. Carlson,
D. Naberejnev, M. Mattes, D. Hanlon, U. Bitelli, P. Page, M. Chadwick,
H. Henrikson, Y. Rugama, A. Nouri and C. Nordborg.

4

TABLE OF CONTENTS

Foreword ...........................................................................................................

3

Members of Subgroup 22..................................................................................

6

Summary ...........................................................................................................

7

1.

Introduction ...............................................................................................

9

2.

Statement of the problem........................................................................... 10

3.

Analysis of 238U integral trends ................................................................. 11

4.

238

U evaluation work.................................................................................. 14

4.1 Thermal capture cross-section ........................................................... 14
4.2 Adjusted cross-sections for sensitivity studies .................................. 15
4.3 Resolved resonance parameters ......................................................... 17
4.4 Unresolved resonance range .............................................................. 21
4.5 Inelastic scattering data...................................................................... 22
5.

Integral tests of the new 238U evaluations.................................................. 24
5.1 Effect of new resonance parameters .................................................. 24
5.2 Substitution analysis .......................................................................... 25
5.3 Summary of keff benchmarking studies.............................................. 26

6.

Other nuclear data...................................................................................... 28
6.1 Oxygen (n,D) cross-section................................................................ 28
6.2 235U prompt-neutron fission spectrum ............................................... 29
6.3 H-H2O cross-section and S(D,E,T) .................................................... 29

7.

Conclusion................................................................................................. 31

8.

Topics for future investigation .................................................................. 31

5

Members of Subgroup 22

H. Derrien, L.C. Leal, N.M. Larson
Oak Ridge National Laboratory (ORNL)
United States (ENDF)
C.R. Lubitz, J.P. Weinman
Knolls Atomic Power Laboratory (KAPL)
United States (ENDF)
R.E. MacFarlane, A.C. Kahler*
Los Alamos National Laboratory (LANL)
United States (ENDF)
H.C. Huria, Y.A. Chao
Westinghouse USA
United States (ENDF)
A. Courcelle, A. Santamarina, J-C. Sublet
Commissariat à l’énergie atomique (CEA Cadarache)France (JEFF)
M.J. Jimenez, P. Romain, B. Morillon
Commissariat à l’énergie atomique (CEA Bruyères-le-Chatel)
France (JEFF)
A. TrkovInternational Atomic Energy Agency (IAEA)
A. Hogenbirk, S. van der Marck
Netherlands Energy Research Foundation (NRG Petten)
Netherlands (JEFF)
C. Dean, M.C. Moxon
United Kingdom (JEFF)* Formerly at Bettis Atomic Power Laboratory (BAPL).

6

SUMMARY

Subgroup 22 was conceived to investigate a systematic reactivity
under-prediction of thermal LEU-LWR (low-enriched uranium, light water
reactor). This keff discrepancy (~ -500 pcm) was demonstrated with accurate
Monte Carlo transport codes and the latest nuclear data libraries (ENDF/B-VI.8,
JENDL-3.3 and JEFF-3.0) available in 2002. This report presents the trends
given by the analysis of relevant integral experiments as well as the evaluation
work, mainly focused on 238U nuclear data. New evaluations of the 238U thermal
capture cross-section, resolved and unresolved resonance parameters and inelastic
scattering data were performed and provide a credible solution to the problem.
Reduced capture in the resolved resonances and a softer secondary inelastic
scattering spectrum contributed about equally to the increased reactivity of
the new data set. The newer inelastic data are mainly the result of improved
theoretical models and more accurate differential measurements, but the choiceof resonance parameters, although the state of the art in fitting procedures
required some reliance on the integral benchmark data for its final form.
Other nuclear data impacting the keff of thermal benchmarks were also
examined, such as the 16O(n,D) reaction, which had been the subject of discussion
for several years. Based on a review of recent differential measurements, thatcross-section was reduced by an amount that is consistent with the integral
indications. A summary of the latest work on 1H-H20 thermal scattering data isalso given. The end result of these changes is an average eigenvalue over abroad class of assemblies which is close to unity.

7

NUCLEAR DATA FOR IMPROVED
LEU-LWR REACTIVITY PREDICTIONS

1.

Introduction

In the framework of the Working Party on International Nuclear Data
Evaluation and Co-operation (WPEC), Subgroup 22 was initiated in 2002 withthe objective to solve a discrepancy between the experimental and calculated keffof thermal LEU-LWR (low-enriched uranium, light-water reactor). A significant
keff under-prediction (~ -500 pcm) was reported with the most recent nuclear
data libraries available in 2002: ENDF/B-VI.8, JENDL-3.3 and JEFF-3.0.
The two characteristics of those data sets which led to the under-prediction
were an over-absorption in the resonance region and a too-hard inelastic secondary
spectrum. Although those characteristics had been present for many years, they
were partially compensated by a too-low resonance capture cross-section in theearly releases of 235U evaluations. When Subgroup 18 [1] issued a revised 235U
data set that produced good agreement for the high-enriched uranium (HEU)
benchmarks, it exacerbated the under-prediction for LEU.
Initially, there were some questions as to whether the Subgroup 18 work on
U was correct, but the satisfactory conclusion to Subgroup 22’s work on 238U
suggests that the combination of the two data files is reasonable. Both data sets
were developed with strong reliance on integral benchmarks, which we recognise
does not produce unique results. The quantity and quality of the criticality
benchmark database resulting from the work of the International Criticality
Safety Benchmark Experiment Project (ICSBEP), however, makes this relianceless risky than at any previous time.

235

This report reviews the analysis of relevant integral measurements as wellas the nuclear data evaluation work performed at several laboratories, mainly at
the following:x

Oak Ridge National Laboratory (ORNL);x

Los Alamos National Laboratory (LANL);xCommissariat a l’énergie atomique (CEA);
9xInternational Atomic Energy Agency (IAEA);

x

Knolls Atomic Power Laboratory (KAPL);x

Bettis Atomic Power Laboratory (BAPL);

x

Nuclear Research and Consultancy Group NRG-Petten;

xJapan Atomic Energy Research Institute (JAERI);x

Westinghouse USA.

Communication within the group was efficiently carried out through a
NEA mailing list “ueval” (uranium evaluation) which allowed the group tofunction without face-to-face meetings. Archives of the discussions can befound at http://www.nea.fr/lists/ueval.html. It is hoped that this report willreflect the strong interactions that have been established between nuclear data
evaluators and reactor physicists to solve the problem.
2.

Statement of the problem

Before Subgroup 22 was set up, several benchmarking studies using
continuous-energy Monte Carlo (CEMC) had raised the issue of LEU reactivity
underestimation [2,3]. The problem was reported after extensive integral testingof the 235U evaluation of the resolved resonances by the ORNL group [4],adopted in ENDF/B-VI.8, JEFF-3.0 and JENDL-3.3.
A description of the work on 235U resonance parameters by ORNL andalternative fits by M. Moxon can be found in the final report of the WPEC
Subgroup 18 [1]. It was shown that the latest ORNL 235U evaluation, featuring asignificant increase of the 235U capture resonance integral, improves the predictionof keff of HEU systems and corrects the longstanding underestimation of 236U
build-up measured in pressurised water reactors (PWRs) (see for instance,
papers by Chabert, et al. [5]).
Further studies by Kahler [6] and Weinman, et al. [7], involving benchmarks
from the ICSBEP handbook and the Cross-section Evaluation Working Group(CSEWG) benchmarks book confirmed the problem with the newest nuclear
data libraries available in 2002. ENDF/B-VI.8 produced the lowest values ataround -700 pcm.
The under-prediction was reported for a large set of independent integral
experiments performed at various laboratories and using different experimental
methods to measure criticality (variation of moderator height, control rod

10adjustment, critical boron technique, etc.). It was therefore assumed that the keff
discrepancy was not due to common experimental error. Since independentMonte Carlo codes and processing methodologies were used, it was also assumed
that the problem was not the consequence of approximations or errors intransport computer codes.
The subgroup activities therefore focused on the analysis and re-evaluationof nuclear data impacting the keff of thermal lattices. The isotopes underinvestigation were 235U, 238U, 16O and H2O. However, given the extensive work
devoted to 235U in the resonance range and the good performance of the latest
files for HEU benchmarks and post-irradiation experiments (PIE), the work
concentrated on 238U and, to a lesser extent, on 16O and H2O.
3.

Analysis of 238U integral trends

The resonance parameters of 238U below 10 keV are the same in ENDF/
B-VI.8, JEFF-3.0 and JENDL-3.3 and result from the work of a previous 238U
task force. The evaluation work performed at that time is summarised in the
final report by M. Moxon and M. Sowerby [8].
The first task undertaken by Subgroup 22 was to analyse integral
experiments sensitive to 238U capture in order to test the accuracy of the Moxon
resonance parameters and suggest trends to nuclear data evaluators. Several
types of integral measurements were studied.
1. The keff bias was analysed as a function of 238U capture fraction1 [6,7].
The computations presented at the 2003 CSEWG meeting show a clear
trend of decreasing keff with increasing 238U capture fraction as illustrated
in Figure 1. This striking correlation was interpreted as an overestimationof the 238U capture shielded resonance integral (SRI). However, similar
trends with other integral parameters such as the above thermal fission
fraction (ATFF) [6] or the 235U capture and fission fraction [9] werereported. Hence, it was argued that the observed trends might be
attributable not only to 238U but also to 235U cross-section deficiencies.
2. Experimental 238U spectral indices Vc238U/Vf235U and the modified
conversion ratio CU238/Ftot provide relevant information on the accuracyof 238U capture. The CEA-Cadarache team performed a detailed analysisof spectral indices measured at the EOLE facility [10] with JEF-2.2(using the Moxon resonance parameters for 238U). As illustrated in
1

Ratio of 238U capture rate over total absorption rate.

11

Table 1, the calculations, performed with the TRIPOLI4 Monte Carlocode (with a small statistical uncertainty), showed that the calculated
238
U capture rate was systematically overestimated by about 1.5 r 1.0%.
Recent measurements of 28U (ratio of epithermal to thermal neutron
capture in 238U) were performed at the Brazilian IPEN/MB01 andreported at the Santa Fe nuclear data conference in 2004 [11].
Computations using ENDF/B-VI.5 data slightly under-predict 28U.
MCNP calculations with JEFF-3.0 (Moxon’s evaluation for 238U) [12]of the DIMPLE benchmark gave (C-E)/E = 3.1 r 1.9% for CU238/FU235,
but the uncertainty of the Monte Carlo calculations was too high forconclusions to be drawn. Other studies involving older benchmarks
such as TRX, compiled in the CSEWG benchmark book, also did notprovide decisive evidence for 238U capture overestimation.
Figure 1. Calculated eigenvalues of 17 configurations of the
Leu-Comp-Therm-006 benchmark, plotted as a functionof 238U capture fraction, using 238U cross-sections from
ENDF/B-VI.5 and a new evaluation presented in Section 4
Calculations by J.P. Weinman, et al. [7] with the RACER Monte Carlo Code12

Table 1. Comparison between calculated and measured valuesof spectral indices for several thermal lattice experiments
performed at CEA-Cadarache, as published in PHYSOR-2000 [10]Experiment name,fuel type
Mistral-1 UO2Mistral-2 UO2-PuO2
Erasme-S UO2-PuO2
Erasme-R UO2-PuO2

Spectralindex
CU238/Ftot
CU238/Ftot
Vc238U/Vf235U
Vc238U/Vf235U(C-E)/E
+2.2%
+2.3%
+1.6%
-0.2%

Experimental
uncertainty
r2.0%
r1.5%
r2.3%
r2.1%

3. A series of experiments performed in the late 1950s and early 1960s
used an activation technique to measure the 238U capture rate of isolated
fuel rods of various compositions (UO2 and U metal) and geometries.
These experiments were carefully reviewed by Eric Hellstrand in1966 [13], and recommended values of the 238U effective resonanceintegral were tabulated as a function of surface-to-mass ratio of the rod
S M using the following empirical formula: I eff a  b S M . The
results, known as the “Hellstrand correlations” were revisited in different
ways. The first methodology (A. Courcelle and A. Santamarina at
CEA-Cadarache [14], H. Huriah at Westinghouse [15], consisted ofdefining an idealised pin-cell benchmark, in which the computed SRI
can be directly compared with the Hellstrand correlations values. In thesecond study by D. Hanlon and C. Dean [16], a specific experiment
performed by Hellstrand and his collaborators [17] in the R1 reactor at
Stockholm was modelled in detail with the Monte Carlo code MONK.
Initially, it was believed that these experimental data would help decide
the issue, but because of the large experimental uncertainties, it was
concluded that the Hellstrand correlations were not sufficiently accurate
to draw firm conclusions (see Figure 2). According to Hellstrand
himself, “limits of error below 3.5% (on 238U capture SRI) could
scarcely be obtained”.
4. Measurements of 239Pu production versus burn-up in post-irradiation
experiments (PIE) are also a valuable check of the 238U capture SRI.
In the French experiments with UO2 fuel, CEA computations with
JEF-2.2 indicated that the 239Pu/238U isotopic ratio was systematicallyoverestimated by 1 to 3% depending on the experimental configuration
and burn-up [5,10,18]. Again, this discrepancy is in the uncertainty rangeof the experiments but supports a 238U SRI decrease of about 0.5-1.5%.
Adjustment studies based on PIE results [18,19] confirmed this estimate.
13

Figure 2. Comparison of calculated and experimental
values of the 238U effective resonance integral
The left figure summarises the results of Hanlon, et al. [16] who investigated
one measurement performed in the R1 reactor at Stockholm [17]. The figure on theright shows the comparison between Monte Carlo calculations by Courcelle [14] andHuriah, et al. [15] and the compilation of four measurements by Hellstrand [13].
In all cases, the resonance parameters of Moxon [8] were used.

In the above four categories, only a limited number of experiments were
investigated and a broader set would be needed to provide more accurate
conclusions on 238U capture. In themselves, these findings do not demonstrate asignificant problem with the 238U evaluation of Moxon, since they lie within theuncertainty margins (3V) of the integral measurements. Nevertheless, theysuggest a small decrease of the 238U effective capture resonance integral by
about 1%. This estimate is considered to be within the experimental uncertainty
of both present-day integral and differential measurements. Given the highsensitivity of the reactivity of uranium-fuelled systems to 238U capture, theproposed modification would eliminate the decreasing trend of keff bias withincreasing 238U capture fraction and improve the keff prediction.
4.

238

U evaluation work

4.1 Thermal capture cross-section
In a typical thermal light water UO2 lattice, approximately 20% of the 238U
captures occur below 4 eV. Therefore, it was appropriate to review the accuracy

14

of the 238U thermal capture cross-section, especially considering that discrepant
recommendations were provided in the open literature:xV0 = 2.708 b (from the CSEWG Standards Committee);xV0 = 2.718 b (from the resonance parameters of Moxon2 [8];xV0 = 2.680 r 0.019 b (from the latest Mughabghab work [20]).

To investigate these differences, the 238U(n,J) thermal cross-section was
reviewed in detail by A. Trkov and co-workers. A detailed description of thework was published in Nuclear Science and Engineering [21]. From an extensive
review of the original publications, the published values were corrected for more
recent standard cross-sections and other data used in the experimental analyses.
In addition, a new activation measurement, performed by G. Molnar, et al. [22]at Budapest, was also investigated. Due to its importance in the experimental
determination of the thermal 238U(n,J) through activation measurements, thegamma-ray emission probabilities from the E decay of 239Np were also evaluated.
The least-squares fit was performed with the ZOTT99 code in the log-domain
to avoid Peele’s Pertinent Puzzle, widely discussed in the field of standard
cross-section evaluation. The final 238U(n,J) thermal value is as follows:
V0 = 2.683 r 0.012 b
This value is 1.5% lower than in the JEFF, ENDF and JENDL evaluations
based on Moxon’s resonance parameters and consequently decreases slightly
the calculated capture rate in thermal benchmarks. It was also concluded thatmost of the measurements were relatively old and that new measurementswith accuracy better than 1% would be beneficial to confirm the present
recommended value.
4.2 Adjusted cross-sections for sensitivity studies
Considering that the integral trends suggested a small reduction of the
U resonance capture cross-section, C.R. Lubitz (KAPL) made two different
adjustments of the Moxon resonance parameters to assess the relative impact ofchanging radiation and neutron widths. The first consisted of a uniform
reduction by 1.35% of the radiation widths of the s-wave positive-energy
resonances, whereas the second lowered the neutron widths by 0.74%, leaving
the radiation widths unaltered. The first of these numbers made the average
238

2

A CSEWG recommendation to reduce this value to the Standards value was apparently
never implemented in the ENDF file.

15

radiation width in the resolved resonance region agree with the slightly lower
value determined by Fröhner [23] for the unresolved region. The second number
was chosen so that both data sets had the same dilute capture resonance integral,276.6 b. The effective radius was not modified and was 9.42 fm in both cases.
Using the negative-energy resonances, the thermal capture cross-section was
adjusted to 2.708 b in both adjustments. A similar approach was used toinvestigate the resonance range of 235U [24].
The effect of these modified parameters on capture SRI and keff were, ofcourse, not equivalent, the *J adjustments giving a higher effect (-0.7%) than*n (-0.2%) on the SRI at dilution Vd = 50 b. As expected, both sets improved
the keff prediction of low-enriched thermal lattices.
Sensitivity coefficients of capture SRI to resonance parameters versus
dilution, calculated by Mounier [18], are shown Figure 3, and corroborate theeffect of the KAPL adjustment.
Figure 3. Sensitivity coefficients of the shielded capture resonanceintegral to a uniform change of the resonance parameters (*J and *n)
below 150 eV, as a function of dilution (from Mounier, et al. [18])This figure shows the high sensitivity of the capture SRI
to *J in the dilution range typical of LWR (20-100 b)

16

4.3 Resolved resonance parameters
A new evaluation of 238U resonance parameters was performed at ORNL incollaboration with CEA-Cadarache. This work was motivated not only by thereactivity prediction problem, but also by the possibility of improving theresonance parameters with previously unanalysed differential measurements.
A full account of the work is available in Ref. [25], in an ORNL report [26], andwill be submitted for publication in Nuclear Science and Engineering.
The experimental database used in the evaluation is presented in Table 2.
The data were analysed with the Bayesian Reich-Moore code SAMMY [27].
Compared with previous work, the ORNL/CEA evaluation benefited from thehigh-resolution transmission measurements [28], from 1 to 100 keV, performed
by Harvey, et al. at the Oak Ridge Electron Linear Accelerator (ORELA, see
Figure 6). The capture data of Macklin [29], partially analysed by Moxon in theprevious 238U task force [8], were fully included in the fit. The capture data
performed at Harwell by Moxon, et al. [30], valuable for the evaluation ofresonance parameters below 100 eV, were unfortunately not available.
Table 2. Main differential experiments used in the
SAMMY analysis of 238U resonance parameters
Other measurements were analysed (subthreshold fission and thick transmission
measurements for p-wave resonances) but are not quoted in this table

Energy rangeof analysis
Thermal range
6-38 eV
6-10 keV
0.5-4 keV
300 eV-10 keV
1 keV-20 keV
250 eV-20 keV

Reference
Corvi, et al. [31]Meister, et al. [32]de Saussure, et al. [33]Olsen, et al. [34]Olsen, et al. [35]Harvey, et al. [28]Macklin, et al. [29]Measurement
type
CaptureTransmission
CaptureTransmission
Transmission
Transmission
CaptureMost of the conclusions drawn in the previous 238U task force wereconfirmed by the new ORNL/CEA work. In particular, sequential fits of capture
data along with transmission data detected significant errors in normalisation in
the capture data: ~ -10% in the de Saussure, et al. data above 100 eV and ~ +15%
in the Macklin, et al. data. In addition to normalisation errors, the SAMMY
fit suggested that a constant background cross-section of about 50 mb forde Saussure and 110 mb for Macklin should be subtracted. The existence of adirect capture component was at first suspected since the simple Lane-Lynnmodel [36] gives an estimate of 80 mb. However, more realistic calculations by
17

G. Arbanas [37] indicated that the direct and semi-direct capture cross-section
should not exceed a few millibarns. The final resonance file is self-contained inFile 2, no File 3 background being required.
The effective radius, which depends on the choice of external resonances,is 9.48 fm, close to the previous Moxon value of 9.43 fm. The thermal scatteringcross-section was evaluated by compiling the measurements of coherent
scattering length, and the value of Vs = 9.28 b, which is lower than in Moxon’s
evaluation (Vs = 9.38 b) was chosen. The ORNL/CEA evaluation adopted therecommendation described in the previous section for the 238U(n,J) thermal
cross-section: V0 = 2.683 b (2.718 b in Moxon’s evaluation).
Measurements of the large resonances at 6.67, 20.86 and 36.6 eV were
carefully analysed with the Crystal Lattice Model (CLM) instead of the
traditional, simpler Free Gas Model (FGM) with effective temperature for
Doppler broadening. The CLM, first derived by W. Lamb [38] and newly
implemented in the SAMMY code, accounts for the chemical binding between
atoms in the U-oxide or U-metal samples. The CLM was experimentally
validated with low-temperature transmission experiments performed by Meister,
et al. [32] at GELINA (see Figure 4), and used for the final fit.
Figure 4. SAMMY fits of the UO2 transmission data from Meister,
et al. [32] measured at GELINA at low temperature (T = 23.7 K)
The middle figure displays the residual with the Free Gas Model with afitted temperature; the bottom figure shows the improvement of the residualwith the Crystal Lattice Model without any temperature adjustment [39]18At room temperature or higher, Doppler-broadened cross-sections
reconstructed from the resonance parameters using either the CLM or the usual
free-gas-at-ambient-temperature method, will be indistinguishable. However,
the reduced capture resulting from the low-temperature CLM fitting is still
significant.
As shown in Table 3, the ORNL/CEA final resonance parameters below
102 eV are fairly close to Moxon’s. The average radiation width below 102 eV
is 23.1 meV, consistent with the previous determination. The main difference isslightly lower neutron widths.
Table 3. 238U resonance parameters below 102.5 eV from
Moxon and the final version of the ORNL/CEA evaluation
Energy
eV
6.674
20.87
36.68
66.03
80.75
102.5
Effective radius

Moxon
Moxon
*J meV*n meV
23.00
1.493
22.91
10.26
22.89
34.13
23.36
24.60
23.00
1.865
23.42
71.70
Rc = 9.43 fm

ORNL/CEA ORNL/CEA*J meV*n meV
23.00
1.476
22.86
10.09
23.00
33.55
23.31
24.18
23.39
1.874
24.08
70.77
Rc = 9.48 fm

Figure 5. SAMMY fits of the three 238U capture data sets available
Two samples from Macklin, et al. [29] and one sample from de Saussure, et al. [33]).
Experimental data were significantly renormalised as explained in the text.

19

Figure 6. SAMMY fits of sample transmission data from
Harvey, et al. [28] through 238U sample thicknesses of 3.62, 0.250
and 0.083 cm, respectively, from the upper curve to the lower curve
Figure taken from [26]The Harvey transmission and Macklin capture data allowed the extensionof the resolved range from 10 keV to 20 keV. However, above 10 keV, theexperimental resolution made the resonance analysis difficult such that evenresonance energies could not be reliably determined. A “pseudo-resonance”
approach was used; a set of resonances was statistically generated and modified
to fit the structure of transmission and capture data but which does not represent
actual resonances. Between 10 and 20 keV, the average capture cross-section
derived from the new resolved resonance parameters is about 5% lower thanthe value deduced from Fröhner’s [23] ENDF/B-VI.8 unresolved resonanceparameters. More work is needed to understand this discrepancy.
Extensive statistical tests of the ORNL/CEA s-wave resonance parameters
were performed by comparing the resonance data with the Gaussian-Orthogonal
Ensemble predictions [40]. Reasonable agreement was found up to 3 keV forthe s-wave resonances. The impact of the new resonance parameters on integral
benchmarks is described in Section 5.1.

20

4.4 Unresolved resonance range
The capture cross-section in the unresolved resonance range above 20 keV
is important for fast and intermediate-spectrum reactors (less so for thermalbenchmarks) and has not received extensive testing by Subgroup 22. The capture
cross-section was previously studied in the framework of Subgroup 4 [41],and new evaluations were subsequently released by Kawano, et al. [42] andMaslov [43]. Recent work includes the following:
1. Above 20 keV, new coupled-channel calculations were performed by
CEA/BRC [44] using the ECIS95 code and optical-model parameters
based on the study of [45]. The capture cross-section was calculatedwith a modified version of the GNASH statistical code. This evaluation
was adopted in File 3 of JEFF-3.1, along with average parameters from
Fröhner [23] in File 2.
2. Following the work on the 238U resolved-resonance parameters, a new
analysis of the unresolved resonance range was also performed [40].
The work was based on the statistical model as implemented in
SAMMY, adapted from Fröhner’s FITACS code. Average parameterssuch as the neutron strength function, scattering radii and averageradiative widths were not determined by nuclear models but were fitted
to a comprehensive experimental transmission and capture databaseusing starting values and uncertainties from a statistical analysis ofs- and p-wave resolved resonances below 20 keV. This work benefited
from the Harvey (ORELA) transmission data described in the previous
section.
3. The CSEWG Standards Committee under A.D. Carlson produced a
new evaluation of 238U capture [46]. It is not an official standard but
is rather a by-product of the standards evaluation process. Capture
cross-section values are not based on nuclear models but are the resultof simultaneous adjustment by the GMA code of a large experimental
database containing absolute measurements, cross-section ratios, etc.
After some smoothing and slight modifications, this evaluation was thebasis of the preliminary ENDF/B-VII.E2 library (File 3) [47,48].
The last two analyses relied heavily on experimental data. As in Fröhner’swork, the evaluated capture cross-section is based mainly on the measurements
by Kazakov, et al. [49] and Moxon, et al. [30], whose normalisations are
consistent. As shown in Figure 7, the newest evaluations of capture cross-section
are close to Fröhner’s and the small differences between them have little impact
on the thermal benchmarks.

21

Figure 7. Comparison of recently evaluated 238U capture cross-sectionsin the unresolved resonance range [40,46], ENDF/B-VII.E2 [47]and JEFF-3.1 [44] with the reference measurements of Kazakov,
et al. [49], Moxon, et al. [30] and Fröhner’s evaluation [23].
The lower figure shows the percentage difference with Fröhner’s.

4.5 Inelastic scattering data
Over the past 20 years, extensive work has been devoted to the theoreticalmodelling of 238U inelastic cross-sections. In 1989, WPEC Subgroup 4 [41]simulated a series of measurements on 238U(n,nc) with the aim to resolve observed

22

discrepancies and to reduce the uncertainties in previous data. Experimental
neutron spectrum and partial inelastic cross-section measurements listed inRef. [41] provided valuable insight.
In the meantime, coupled channel calculations were improved, as were
statistical and pre-equilibrium models, leading to better predictions of theinelastic cross-section and secondary-neutron spectra. As a result of Subgroup 4efforts, improved evaluations of 238U inelastic data were produced by Maslov,
et al. [43] and Kawano, et al. [42].
Recently, two independent evaluations by the LANL and BRC groups were
undertaken and successive releases were distributed to Subgroup 22 for testing.
This work was summarised at the Santa Fe conference by Young, et al. [47,48]
and by Lopez-Jimenez, et al. [44]. Compared with the ENDF/B-VI.8 and JEF-2.2
evaluations, which predate Subgroup 4, the new models agree better withexperimental data. Of particular interest are the spectra of secondary neutrons
produced by inelastic scattering and fission, as measured by Baba, et al. [50] at
different incident energies. As shown in Figure 8, the recent evaluations ofdouble-differential cross-section are of better quality than in ENDF/BVI.8
or JEF-2.2.
Figure 8. Comparison of angle-integrated neutron emission spectra (mainly
fission and inelastic) from various evaluations with the measurementof Baba, et al. [50] at incident neutron energy En = 2.03 MeV
Figure from [48]23

As displayed in Figure 9, the new evaluation features a softer inelastic
secondary neutron spectrum compared with the previous one of ENDF/B-VI.8
or JEF-2.2. The influence of these new data on the smaller thermal benchmarks
was found to be significant, increasing keff by reducing the neutron leakage, as
explained in Section 5.
Figure 9. Comparison of multi-group transfer matrix at incident neutronenergy of 2.231 MeV for preliminary evaluations performed at LANL
(labelled as u238l) and the previous version in ENDF/B-VI.8 (u238e)5.

Integral tests of the new 238U evaluations

5.1 Effect of new resonance parameters
The new 238U resonance parameters provide a lower capture cross-section
both in the thermal and resonance ranges. The impact of these changes is easily
assessed by computing the effective resonance integral for different dilution
values under the infinite-medium assumption. As shown in Figure 10, the capture
SRI is lowered by about 0.6% at 50 barns dilution with the new set of resonances.
In actual reactor calculations, the observed effect is a decrease of thecalculated 238U reaction rate and a corresponding increase of keff between
100 and 300 pcm depending on the moderation ratios. More importantly, theobserved slope of keff bias versus 238U capture is well corrected [7], as shown in
Figure 1.

24

Figure 10. Comparison between the 238U effective resonanceintegral (integration from 1.0 eV to 10 keV) of the ORNL/CEA
and Moxon evaluations for various dilution values
ORNL4 is a preliminary version of the resonance parameters that were adopted in JEFF-3.1,
while ORNL5 is the final version (adopted in the preliminary ENDF/B-VII.E2 library)

5.2 Substitution analysis
A powerful way to determine the importance of cross-section changes inbenchmark calculations is reaction-substitution analysis. The idea is to substitutereaction by reaction the cross-section values from one evaluation into anotherand to perform benchmark calculations after each substitution. An illustration ofthis technique was presented by J. Weinman using the Leu-Comp-Therm-006
benchmark. The aim was to understand the large keff increase (about 600 pcm)
between calculations with the new 238U file and the previous ENDF/B-VI.5
evaluation. This study shows the importance of the new resonance parameters
and the new inelastic transfer cross-section in the keff change (see Table 4). The
transfer matrix is “normalised” so its effect is independent of changes in the25Table 4. Result of substitution analysis performed by J. Weinman tocompare ENDF/B-VI.5 evaluation and the new 238U file combining
preliminary LANL and ORNL/CEA work. It shows the change
in eigenvalue for each reaction and highlights the impact of
the resonance parameters and inelastic transfer matrix.
Changein keff
relativeto base
case

Unc.
2V

Change inkeff forreaction
type

Unc.
2V

0.00274-0.00052-0.00085
0.00047
0.003250.000620.000450.000430.000450.000440.000430.00045

Case description

keff

Unc.
2V

Base case: ENDF/B-VI.5
Prev. case + inel. transfer
Prev. case + inel. xs
Prev. case + elastic xs
Prev.s case + el. moments
Prev. case + capture xs
Prev. case + fission xs
Base case +LANL/ORNL 238U

0.99191
0.99465
0.99413
0.99329
0.99376
0.99701
0.997620.00032
0.000310.000300.00033
0.000290.00032
0.000310.002740.000220.001380.00185
0.005100.00057

0.000450.000440.000460.000430.000450.000450.99809

0.00030

0.006180.00044

inelastic cross-section itself. The 47 pcm difference between the last two rows isdue to the inconsistency inherent in changing resonance cross-sections forelastic scattering and capture separately.
5.3 Summary of keff benchmarking studies
The successive versions of the ORNL/CEA resolved range evaluation andthe fast range data from LANL and BRC were merged into two complete 238U
test files. Within the working group, several CEMC codes were used:x

MCNP [51] (versions 4 and 5), developed at LANL;x

RCP [6], developed at BAPL;x

RACER [52], developed at KAPL;x

TRIPOLI4 [53], developed at CEA-Saclay;x

MONK8 [54], developed at SERCO Assurance.

Subgroup 22 did not perform a rigorous comparison of these codes, but inmost cases reasonably good consistency was found. Eigenvalue differences
between TRIPOLI4 and MCNP up to 150 pcm for some Leu-Comp-Therm
configurations were initially noticed, but were resolved by a closer comparison26

of the two codes. Code differences hinder analysis of cross-section effects at the
100 pcm level but did not preclude agreement that the combination of the
ORNL/CEA resonances and the LANL/BRC inelastic data provided a satisfactory
solution to the keff problem.
Integral testing, mainly by Weinman, Kahler, MacFarlane, van der Marck,
Trkov and Sublet, demonstrated the improvement of the reactivity prediction
for a large number of low-enriched thermal lattices. The paper presented by
MacFarlane [55] at the 2004 Santa Fe nuclear data conference provides a good
example of the performance of these files with MCNP5. More recent references
are available in the form of JEFDOCs [56,57] or as contributions to the CSEWG
meeting [58-60].
The most recent keff calculations (April 2006) were performed with JEFF-3.1
and ENDF/B-VII (E2 version), which includes the new 238U files. An example
of such calculations is presented in Figure 11. Benchmarking results arecontinuously posted on the CSEWG website3 for the ENDF project, and on the
JEFF website4.
Figure 11. Calculated eigenvalues for Leu-Comp-Therm benchmarks
with ENDF/B.VI.8 and ENDF/B-VII.E2 cross-section data sets
Calculations were performed at LANL by Kahler and MacFarlane with MCNP5

34

http://www.nndc.bnl.gov/csewg/
http://www.nea.fr/html/dbdata/projects/nds_jef.htm

27

6.

Other nuclear data

6.1 Oxygen (n,D) cross-section
ENDF/B-VI.8 and JEFF-3.0 share the same evaluation based on the workof G. Hale [61] at LANL using the R-matrix EDA code. Recent R-matrix analysisof 16O(n,D) was also performed at ORNL with the SAMMY code by R. Sayer,
et al. [62]. The 16O(n,D) cross-section in JENDL-3.3 is significantly lower thanthe other evaluations, as shown in Figure 12. This difference has a small but
non-negligible impact of about 50 pcm on thermal reactor benchmarks (withUO2 fuel and H2O moderator).
Figure 12. Comparison of 16O(n,D) cross-section from
ENDF/B-VI.8, JENDL-3.3 and the recent evaluation by Page,et al. [63] adopted in the preliminary ENDF/B-VII.E2 libraryExperimentally, 16O(n,D) cross-sections are usually derived by reciprocity
from the inverse reaction 13C(D,n). Despite the large number of experiments,
most of them were performed with a rather poor energy (neutron or D)
resolution. Values for 16O(n,D) from ORNL and LANL evaluations rely mainlyon the measurements of Bair, et al. [64] and Drotleff, et al. [65]. The Bair, et al.
publication suggests, in an added note in proof, to renormalise upward theoriginal data. Regardless of how the Bair data are renormalised, they are still
significantly higher than the Drotleff data (by about 10-20%) and higher thanolder data such as Sekharan, et al. [66] or Walton, et al. [67] (by 50%).
28

Subgroup 22 sent a request to the WPEC High Priority Request List to
simulate a new measurement and solve this problem [68]. Fortunately, after
further investigation, two recent measurements by Heil, et al. [69] andHarissopulos, et al. [70] were found. A detailed analysis of the two experiments
is still needed to draw a solid conclusion on the 16O(n,D) cross-section, though apreliminary analysis supported a significant decrease of the 16O(n,D), placing
the level of the cross-section close to that of JENDL.
Page, et al. at LANL [63] proposed a preliminary evaluation, displayed in
Figure 12, and integral testing demonstrated the slight increase of keff of thermallattices (about 30-40 pcm).
6.2 235U prompt-neutron fission spectrum
At the 2003 WPEC meeting in San Diego, D. Madland concluded the workof Subgroup 9 on the evaluation of fission neutron spectra. The final report [71]pointed out large discrepancies in the peak and tail regions between the twomost recent measurements of the 235U spectrum for thermal neutrons. The latest
evaluation proposed by Madland was still preliminary, but was found to
deteriorate the prediction of the Heu-Sol-Therm as well as Leu-Comp-Thermbenchmarks and was not adopted in the latest versions of ENDF or JEFF.
Despite the work done at Los Alamos to understand the discrepancy andimprove the theoretical modelling, a highly accurate measurement of the 235U
thermal fission spectrum is strongly needed.
6.3 H-H2O cross-section and S(D,E,T)5
The subgroup initially targeted the hydrogen-in-water cross-section forinvestigation for three reasons:
1. The precise value of the 1H capture cross-section was the subject ofsome disagreement in the nuclear data community.
2. The low-energy scattering cross-section, as represented by the S(D,E,T)
formalism in ENDF-formatted data libraries, was recently re-evaluatedby M. Mattes and J. Keinert [72] at IKE.
3. Thermal reactor eigenvalues are very sensitive to 1H-H20 thermal
scattering data.
5

In addition to its dependence on the temperature through D(T) and E(T), the scatteringfunction has other temperature dependencies which complicate interpolation procedures.

29

A full description of the Mattes-Keinert evaluation is available in the
INDC report [72]. Compared with previous ENDF and JEF evaluations, thisnew work proposes an improved modelling of water dynamics with a modified
parameterisation of hindered rotation and translations as well as bending andstretching vibrations of the H2O molecule. The new IKE model leads to a better
prediction of the double-differential neutron scattering cross-section of water asshown in Figure 13.
Figure 13. Double-differential neutron scattering cross-section of water atroom temperature computed with the ENDF/B-VI scattering data and the
new IKE model, compared with experimental data of Bischoff, et al. [73]Incident neutron energy = 154 meV, scattering angle T = 60q).
The figure is taken from the INDC report [72].

More recent developments in this area are embodied in the new ENDF/
B-VII.0 nuclear data library. The thermal capture cross-section of 1H remains at
332.0 mb, although it is recognised that a fit to only the differential data gives
332.6 mb. Benchmark testing showed that the new Mattes-Keinert S(D,E,T)
evaluation lowered thermal eigenvalues by the order of 100 pcm relative to
ENDF/B-VI.8, due to small changes in the total cross-section. Modifications by
MacFarlane [74] of the D and E grids reduced the impact of these changes toabout 50 pcm, within the spread due to current code differences. The energies of
the rotational modes were also slightly increased to bring the cross-section in
the 50 meV region closer to the measured data. These changes increased thepredicted keff by almost 200 cm in some cases.
Contributing to the remaining uncertainty, the total cross-section of boundhydrogen as a function of temperature is not specified in File 7 but must bereconstituted by a difficult integration in D,E space.
30

7.

Conclusion

Good co-operation between reactor physicists and nuclear data evaluators
was crucial in improving the prediction of thermal reactors and finding a credible
solution to the keff underestimation problem. The status of new evaluations is asfollows:x

The 238U evaluation of resolved resonance parameters is completed.
A preliminary version of this work was included in the JEFF-3.1 libraryreleased in 2005, and the final version was adopted in the E2 version of
the future ENDF/B-VII library.

x

The CEA/BRC evaluation of 238U data above the resonance range wasadopted in JEFF-3.1 and the new LANL work was included in ENDF/
B-VII.E2.

xWith the help of recent 13C(D,n) measurements, a new 16O(n,D)
evaluation performed at LANL, featuring a lower (n,D) cross-section,
was proposed and adopted in ENDF/B-VII.E2.

x

The new evaluation of 1H-H20 thermal scattering data by Mattes, et al.
was included in the JEFF-3.1 library. ENDF/B-VII.E2 includes a
modified version of this evaluation proposed by MacFarlane.

The successive versions of new evaluations were continuously tested
against keff measurements. The combination of the new inelastic data (LANL or
BRC) with the new resonance-parameter set gives a satisfactory correction of
the reactivity underestimation. Modifications to the 16O and 1H-H20 data have aslight influence on reactivity but contribute to the improvements. Most recent
validation work of the new ENDF/BVII.E2 and JEFF-3.1 libraries confirmed
the good prediction of uranium-fuelled thermal systems with the new data sets.
This work illustrated the importance of using large collections of benchmarks
to assess the quality of the evaluated data.
8.

Topics for future investigation
1. There should be a co-ordinated effort to compare the continuous-energyMonte Carlo codes. Despite the overall consistency observed between
various codes using the same nuclear data, some differences in thecalculated eigenvalues need to be understood. The existing comparison,often based on keff, should be extended to reaction rates in the thermaland epithermal energy range.

31

2. Recent studies suggest [75] that thermal lattices using mixed-oxide fuelare not well predicted with the newest nuclear-data libraries. This
discrepancy requires further investigation and might be related toplutonium nuclear data. Accurate prediction of Doppler coefficient isstill a challenging issue.
3. All the benchmarking presented in this report used fresh-fuelconfigurations. Modern nuclear data libraries tend to give consistent
results in the prediction of keff at zero burn-up, but large differences are
expected in depletion calculation at high burn-up. These differences areworth being understood. Clean integral experiments, easy to calculate
and capable of measuring the keff versus burn-up, are still lacking.
4. Further integral tests are needed at high temperature to fully validate
the new resonance parameters and thermal scattering data. It should beverified that the temperature reactivity coefficient is accurately predictedwith the new files.
5. Several issues regarding the evaluation of the 238U resonance range
merit more extensive examination:x

The evaluation of the 238U p-wave resonance parameters and s-waves
above several keV still needs some improvement. Statistical analysisof the ORNL/CEA resonance parameter shows that the traditional
statistics deviate strongly from the GOE theory, indicating thepresence of a significant proportion of missed and spurious
resonances and of errors in spin determination.

x

Despite the low resolution of the available measurements, the energy
range 10-20 keV was described by a set of resolved resonanceparameters. As previously stated, the average cross-section deduced
from resolved resonance parameters is lower by about 5% than thatin the previous evaluations in ENDF/B-VI.8 and JEF-2.2, whichused average resonance parameters. Further work should clarify
this discrepancy.

x

The capture measurement performed by Moxon at Harwell [30]
was not included in the ORNL/CEA fit because it was notavailable. The data were recently found and sent by Moxon to the
NEA. Their analysis would be a valuable check of the parametersof the resonances below 100 eV.

xDespite work at ORNL and CEA to identify the various sources of
uncertainties, a full covariance matrix for 238U cross-section is still
not available and has been strongly requested by nuclear-data users.

32

6. As shown by Subgroup 9, the status of the 235U prompt-neutron fission
spectrum is still not satisfactory. Recent measurements are discrepant,and the most recent evaluation at LANL deteriorates the keff predictionof intermediate-spectra systems such as the highly enriched solutions
described in the ICSBEP handbook.
7. New measurements of 16O(n,D) are in progress at IRMM [76] andshould be compared with the new evaluation proposed by Page, et al.
when the data are available.
8. In the discussion of solid-state effects, the modelling of the spectrum ofelastically scattered neutrons in the 238U resonances has been raised.
The static model implemented in the current neutron-transport codesis crude. The need for a more rigorous crystal lattice formalism forresonant scattering, as in [77] and [78], in reactor calculations is still
an open topic. The expected effect is an increase of the calculated
238
U capture rate due to upscattering of neutrons in resonances.
A non-negligible impact on thermal-benchmark calculations might be
expected as well.
9. Nubar (average number of prompt neutrons emitted in fission) is a very
sensitive quantity for thermal benchmarks. At thermal energy, theprompt nubar of 235U is accurately known but in the resonance range,
differential experimental data [79,80] suggest significant fluctuations(of the order of 0.5%) which are currently not represented in the mostrecent nuclear data libraries. Both reliable measurements and modellingof the shape of nubar in the resonances are still lacking.

33

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