NEA/WPEC–18

International Evaluation Co-operation

VOLUME 18
EPITHERMAL CAPTURE CROSS-SECTION OF 235 U

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

CO-ORDINATORMONITOR

C.R. Lubitz

R.W. Roussin

Lockheed Martin Corp.
USA

Oak Ridge National Laboratory
USA

NUCLEAR ENERGY AGENCY
ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENTORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT
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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 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 a view to assessing and improving the quality and completeness ofevaluated data.
The parties to the project are: ENDF (United States), JEF/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, are organised through the Nuclear Data Section of theInternational Atomic Energy Agency (IAEA).
The following report was issued by a Subgroup investigating a problem
with the early releases of the ENDF/B-VI evaluated neutron cross-sections for235
U (6.0, 6.1 and 6.2). Despite the high quality of the fits to a variety of accurate
differential data, thermal benchmarks and other soft-spectrum critical facilities
were not well calculated. It appeared that both thermal-averaged η (nu-fission/
absorption) and the capture resonance integral were low, so that low-leakage
thermal assemblies calculated low, but with increasing leakage, the consequent
hardening of the spectrum created a trend of strong over-calculation. It was
shown in Release 6.3 that a reasonable adjustment to the Release 6.2 resonanceparameters could remedy both difficulties, and the objective of the Subgroup
was to produce a new high-quality fit to the differential data incorporating thesefindings.
The opinions expressed in this report are those of the authors only and do notnecessarily represent the position of any Member country or internationalorganisation. This report is published on the responsibility of the Secretary-Generalof the OECD.

3

Members of Subgroup 18

P. Blaise, S. Cathalau
Commissariat à l’Énergie Atomique (CEA Cadarache)
C. MounierCommissariat à l’Énergie Atomique (CEA Saclay)
H. Matsunobu
Sumitomo AE Industries
T. Nakagawa, H. Takano
Japan Atomic Energy Research Institute (JAERI)
Y. Popov
DUBNA
C.J. Dean, D. Hanlon, R.J. Perry
AEA Technology Winfrith
M.C. Moxon
Atomic Energy Research Establishment (AERE) Harwell
H. Derrien, J.A. Harvey, N.M. Larson,
L.C. Leal, L.W. Weston, R.Q. Wright
Oak Ridge National Laboratory (ORNL)
C. Durston
S. Levy, Inc.
A.C. Kahler, Jr.
Bettis Atomic Power Laboratory
C.R. Lubitz, J.P. Weinmann
Lockheed Martin Corp. (LMC)
R.E. MacFarlane, M.S. Moore
Los Alamos National Laboratory (LANL)

4

CONTENTS

SUMMARY ...................................................................................................

7

1.

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

9

2.

Review of235

U neutron cross-section evaluation work........................

11

2.1

ENDF/B-VI Release 6.0 ................................................................

11

2.2

ENDF/B-VI Release 6.1 ................................................................

13

2.3

ENDF/B-VI Release 6.2 ................................................................

14

2.4

ENDF/B-VI Release 6.3 ................................................................

14

2.5

ENDF/B-VI Release 6.4 ................................................................

15

2.6

Leal-Derrien-Wright – January 1996 ...........................................

15

2.7

Leal-Derrien-Wright-Moxon – March 1997 .................................

15

2.8

Leal-Derrien-Wright – May 1997 .................................................

16

2.9

Moxon – May 1997 .......................................................................

17

2.10 Leal-Derrien-Wright-Larson – August 1997
(ENDF/B-VI Release 6.5)..............................................................

17

2.11 Moxon – September 1997..............................................................

19

2.12 The role of integral testing............................................................

19

235

3.

Current status ofU evaluation ..........................................................

20

4.

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

21

5.

Conclusions ............................................................................................

23

REFERENCES..............................................................................................

25

TABLES AND FIGURES.............................................................................

31

5

SUMMARY

Subgroup 18 was formed to investigate a problem with the early releases of235
the ENDF/B-VI neutron cross-sections for U (6.0, 6.1 and 6.2). Despite highquality fits to accurate differential data, thermal benchmarks were not wellcalculated. It appeared that both thermal-averaged η (nu-fission/absorption) andthe capture resonance integral were low, so that the multiplication constants(“eigenvalues”) of low-leakage assemblies calculated low, but with increasing
leakage, the consequent hardening of the spectrum created a trend of strong
over-calculation. It was shown in Release 6.3 that a reasonable adjustment to theRelease 6.2 resonance parameters could remedy both difficulties, and theSubgroup’s objective was to produce a new high-quality fit to the differentialadata incorporating these findings .
This report reviews the evaluation work at Oak Ridge National Laboratory(ORNL), Atomic Energy Research Establishment (AERE) Harwell, and Lockheed
Martin Corp. (LMC) which led to ENDF/B-VI Release 6.5. The important role
which benchmark testing in France, the UK and the US (and elsewhere in theworld) played in shaping the final product is mentioned but not in great detail.
A large number of published reports give more information, and we apologise to
those authors whose work is not explicitly cited.
The current status is as follows: The Leal-Derrien-Wright-Larson evaluation(August 1997) using the Bayesean-fit code SAMMY, was extensively tested andwas adopted for ENDF/B-VI Release 6.5 and JEFF3. It gives good agreementwith differential and integral data, and for thermal benchmarks. The calculationof intermediate-energy critical assemblies is improved relative to most earlier
versions, but more could be done in this important area. The fit to fastbenchmarks is unchanged from previous releases.
A fit to the 0-150 eV region produced by M.C. Moxon at Harwell with theleast-squares code REFIT used only differential data and arrived at somewhat
different shapes for the thermal-region cross-sections and to some extent theaInitially it was thought that only the capture resonance integral adjustment would be
DGGUHVVHGEXWWKHJURXSH[SDQGHGLWV³FKDUWHU´WRLQFOXGH WKHUPDO  DOVR +RZHYHU
the name of the subgroup was never changed.
7

resonances also. Coupling this analysis to a set of higher energy cross-sections,and to a suitable nubar (average number of neutrons per fission) file will permit
testing it in practical calculations, a task for the future.
Other topics remaining to be addressed include an improved unresolved
resonance region and a better representation of the energy-dependence of nubar.
235
A related issue, which clouds the interpretation of low-enriched U benchmarks,
238
is the question of whether the U thermal and resonance capture cross-sections
are correct.

8

EPITHERMAL CAPTURE CROSS-SECTION OF 235U

1.

Introduction

As noted in the summary, Subgroup 18 was formed to investigate a problem
with Releases 6.0, 6.1 and 6.2 of the ENDF/B-VI neutron cross-sections for 235U.
The fits to differential data documented in References [1] and [2] appeared to
produce low values for both thermal-averaged η and the capture resonanceintegral, so that the multiplication constants (“eigenvalues”) of low-leakage
assemblies calculated low, but with increasing leakage, trended to strong
over-calculation. Typical of such calculations are the results in Figure 1, showingba collection of solution-tank eigenvalues calculated with a continuous-energyMonte Carlo code [3]. The introduction of an energy-dependent (“drooping”) ηin the sub-thermal region in Releases 6.1 and 6.2 improved the calculation oftemperature coefficients but did not help the eigenvalues. In Release 6.3 [4] it
was shown that a reasonable adjustment to the Release 6.2 resonance parameters
could remedy both problems, and the Subgroup’s objective was to produce a
new fit to the differential data incorporating these findings.
Basically, Release 6.3 showed that the average radiation width needed to be
increased from an average of 35 meV to about 38, and that this could beachieved by giving more weight to the microscopic capture measurements in
Ref. [5]. In addition, it lent strength to the opinion that thermal-averaged η wasbeing pulled down too much by the Cross-Section Evaluation Working Group(CSEWG) standards value of nubar [6].
This report reviews the evaluation work at ORNL, AERE Harwell and
LMC which has influenced ENDF/B-VI through Release 6.5. The discussion
concerns the thermal and resolved resonance regions, and the important role
which benchmark testing has played, although the most recent work at Oak Ridge
and Harwell concerns the unresolved resonances. A large number of publishedb

The Rocky Flats assemblies are numbered according to the International Handbook of
Evaluated Criticality Safety Benchmark Experiments [35] and not the CSEWG
benchmark numbering system.
9reports give more detail, and we apologise to those authors whose work is not
explicitly cited.
235

The current status of the U evaluation work is as follows: The evaluationof Leal-Derrien-Wright-Larson (August 1997) was extensively tested in France,
the UK and the US. It achieves the principal objectives of the subgroup,
specifically, to agree with both differential and integral data and to adequately
predict the criticality of thermal and intermediate-hardness benchmarks. On thisbasis, it was adopted for ENDF/B-VI Release 6.5 and for JEFF3. A single
Reich-Moore resolved-resonance region, arrived at by Bayesean fitting with the-5computer code SAMMY [7], covers the energy range from 10 eV to 2.25 keV.
Agreement is good with differential and integral data, and for thermalbenchmarks. The calculation of intermediate-energy assemblies is improved
with respect to Release 6.3. The fit to fast benchmarks is unchanged fromprevious Releases. Figure 2 [8] illustrates the improvement in eigenvaluecleakage trend when Release 6.5 is used .
An alternative fit by M.C. Moxon at AERE Harwell used the least-squares
code REFIT over the range from 0-150 eV. It relied solely on differential data
and arrived at somewhat different shapes for the thermal-region cross-sections
and to some extent in the resonances also. Figures 3 and 4 compare the fission
and capture cross-sections from this evaluation with the ENDF/B-VI Release 6.5
values used by Leal-Derrien-Wright-Larson (see Section 2.10) in the region
below 1 eV. Differences in the fission are visible, and are quite pronounced in
the capture. Numerical values for the thermal cross-sections and g-factors forthis and other evaluations are given in the table at the end of this report.
In order to test Moxon’s work in practical calculations it will be necessary
to couple it to a set of higher energy cross-sections, and to a suitable nubar file, atask for the future.
Some important topics remain to be addressed, primarily an improved
treatment of the unresolved-resonance region and an improved representation of
the energy-dependence of nubar. A related issue, which clouds the interpretationof low-enriched 235U benchmarks, is the question of whether the 238U thermal
and resonance capture cross-sections are correct.

c

Further improvement results from the use of Release 6.5 hydrogen capture, down from332.6 mb in Releases 6.0-6.4, to 332.0, but not included in the Figure 2 values.
10

2.

Review of 235U neutron cross-section evaluation work
2.1

ENDF/B-VI Release 6.0
d235

The original release of ENDF/B-VI Release 6.0 U in 1990 was acollaboration among the Oak Ridge, Los Alamos and Argonne National
Laboratories, the last two providing the high-energy cross-sections, and ORNL
the resonance analysis. The latter culminated in an extensive Reich-Moore
multilevel fit to the resolved-resonance region 0-2250 eV [1,2]. The work was
carried out with the powerful resonance-fitting code SAMMY, which uses
Bayes’ method for the fitting procedure and makes it possible to deal
sequentially, yet consistently, with the many large data sets requiring analysis.
The evaluation techniques were a major advance over the earlier single-level
treatments in ENDF/B-I through V, the latter of which ended the resolved region
at 82 eV and treated the thermal region (0-1 eV) as tabulated data in File 3.
The ENDF/B-VI evaluators recognised that the experimentally observed structurein the cross-sections above 100 or 150 eV was largely due to clumps ofresonances. However, it was their opinion that fitting it as if it were the result ofindividual resolved “pseudo-resonances” would preserve the structure and leadto more accurate self-shielded multi-group cross-sections than could be obtained
from a traditional treatment in terms of average unresolved resonance parameters.
This important question has never been settled, and remains one of the tasks for
future investigation.
In the CSEWG review procedure, which involved special meetings at
Oak Ridge, the Thermal Benchmark Testing Subcommittee, under thechairmanship of J.R. Hardy and (later) M.L. Williams, observed that there weretwo “differential-integral” discrepancies which affected the evaluation [9]:1. The 2 200 m/s values for capture and fission, and their associatedWestcott g-factors, produced a Maxwellian-averaged η which was
lower than the value inferred from eigenvalue calculations of thermal
reactors. Quantitatively, the effect was measured by the parameter
K1 = νσfission-σabsorption (in which the cross-sections are the Westcott
Maxwellian-averages, g-factor times 2 200 m/s value). The integral
value derived by Hardy from an analysis of the Gwin-Magnuson
aqueous assemblies was 722.7±3.9, whereas the ENDF file gave aboutd235

Successive versions of ENDF/B-VI materials are designated as Mods. U has
undergone modification in every release of ENDF/B-VI, so the Mod number, whichstarted as 1 in Release 6.0, is one greater than the release number. We use the latter, as
more familiar to most users. (The number of releases, and the fact that different ones
may contain quite different cross-sections, makes it important for users and authors oftechnical articles to insure adequate identification of which ENDF/B-VI materials theyused. The term ENDF/B-VI by itself is not unique.)11719e. The 2 200 m/s values were the then-recommended thermal
constants that resulted from an extensive round of least-squares fitting
to pointwise and reactor-averaged thermal data, following a tradition
started many years earlier by G.H. Westcott. The CSEWG discussionsof the least-squares results were spirited. Within the CSEWG Task
Force on Thermal Constants, led by B.R. Leonard and J.R. Stehn, somebelieved that least-squares was the best one could do. On the other
hand, some believed that the results were too sensitive to the choice of
input uncertainties, and that the output uncertainties were unrealisticallylow. It was noted that the main input data at the low-K1 end were the
Chalk River reactor-average-alpha measurements, which were high andcarried low uncertainties, and some low nubar data. A complete
discussion of the relevant data can be found in [10], where an exhaustive
least-squares fit to the thermal constants resulted in K1 = 712.6.
235
That low value epitomised the integral-differential conflict for U.
That disagreement in philosophy is still with us, and as recent experiencehas shown, a straightforward fit to the thermal “differential” data still yields a
K1 which is below the integral value [6]. The result of the low K1 was thateigenvalues (multiplication constants) for well-thermalised assemblies calculatedaround 0.5% low using Release 6.0.
2. The resonance integral for radiative-capture was some 10 barns below
the integral value of about 142 barns. Correspondingly, its ratio to thefission integral (epithermal alpha) was 6-7% below the integral value of0.51. A consequence of this fact, and of the low K1, was that
Release 6.0 calculated low multiplication constants for very-thermal,
large, low-leakage assemblies; but the calculated values rose sharply
with increasing leakage, as shown in Figure 1. As the leakage increased,
and the spectrum hardened, the low alpha caused the calculated
eigenvalues to increase. Nevertheless, the evaluation was accepted for
ENDF/B-VI Release 6.0. One reason was a matter of principle among
many of the CSEWG members that ENDF should represent a pure viewof the microscopic measurements, and not allow itself to be influenced
by integral considerations which (then, and still today) can manifest
themselves in ad hoc adjustments to cross-sections, without a clear
physical basis. M.L. Williams has also pointed out that benchmark(Phase II) testing was hampered by a lack of suitable processing codes
and adequate funding [11].

e

The calculations leading to the value 722.7 were not published in the open literature.
The methods used are described in internal CSEWG correspondence and in
unpublished laboratory memoranda. Current experience with thermal benchmarks
supports the value.
12Another consideration, as valid today as it was then, is whether the integral
data are accurate. Perhaps the thermal benchmarks are afflicted with some
unknown error, and that in fact the low K1 resulting from a least-squares fit to
the microscopic measurements is correct. It would be undesirable to change theevaluation in order to fit incorrect benchmarks.
It is impossible to answer this criticism. However, one cannot simply ignore
the integral measurements, so in the recent evaluation activities at ORNL and
LMC a more pragmatic attitude has been adopted. Essentially, the argument isthat all the experiments are “wrong”, if by “right” one means they give the true
value. The microscopic measurements can only define an envelope ofcredibility, and it is possible to stay within that envelope and still match the
integral data. In particular, “pure” least-squares fits to the microscopic data areto be preferred only in the absence of other indications. The weakest links inthe microscopic measurements appear to be the normalisation of capture
measurements and the specification of the true resolution in measurements of theratio alpha. In the fitting process, one is severely limited in the extent to which a“true” radiation width can be extracted from the Doppler and resolution-broadened
data. In the most recent contributions from Leal, et al. and Moxon (Sections 2.10
and 2.11), the radiation width is constrained to be either very close to, or exactly
equal to, an average value of about 38 meV. Insofar as that value is itself
determined by the differential data, these procedures are in the direction of
reducing reliance on integral quantities.
Finally, present evaluation methods assume a constant value of nubar in thethermal region, and that value is not simultaneously fit. It seems plausible that
adding a fit to an energy-dependent nubar would allow improved fits to thermalbenchmark eigenvalues without as large an effect on the cross-sections.
In the most recent evaluation from ORNL (August 1997), which has been
adopted for ENDF/B-VI Release 6.5, integral data have been incorporated into
the basic fitting process by adding to SAMMY the ability to fit integral values,in particular, resonance integrals and K1. This provides a mathematical bridge
between the two worlds, but puts an added burden on the evaluator to ensure theresults are physically reasonable. The procedure provides better representationof the integral data while maintaining the excellent fit to the differential data
(see Section 2.10)
2.2

ENDF/B-VI Release 6.1

Release 6.1 (1991) introduced an energy-dependence in sub-thermal η,
so-called “drooping η”. The possibility of such an energy-dependence had been
hypothesised by Santamarina, et al. [12], and later confirmed by measurements
13

at Geel, Harwell and ORNL [13]. This episode was an early example of thecloser international co-operation on evaluation activities fostered by theOrganisation for Economic Co-operation and Development’s Nuclear Energy
Agency (OECD/NEA) which has proven so fruitful.
This modification removed most, but not all, of the discrepancy between
measured and calculated temperature coefficients which had stimulated theoriginal investigation. However, since no other modifications were introduced,
Release 6.1 continued to test poorly on thermal benchmark eigenvalues. As with
Release 6.0 before it, the resolved-resonance region was split into elevensub-regions, covering the energy range 0.00001-2250 eV.
2.3

ENDF/B-VI Release 6.2

Release 6.2 (1993) did not change the cross-sections.
2.4

ENDF/B-VI Release 6.3

Release 6.3 [4] was an adjustment to Release 6.2, carried out at LMC by
C. R. Lubitz, in close collaboration with J.A. Harvey, A.C. Kahler, N.M. Larson,
L.C. Leal, M.C. Moxon, J.P. Weinman, L.W. Weston and R.Q. Wright.
This adjustment increased the epithermal capture to agree, on average, with themeasured differential capture cross-sections of Perez and de Saussure [5] and it
increased K1 to improve the calculation of the very thermal assemblies. Detailsof the adjustment process are provided in the report. Because it was an adjustment
to average cross-sections measured over energy bins, the improvements came at
the expense of decreasing the agreement with the detailed differential
measurements.
As expected, Release 6.3 did quite well on the thermal benchmarks, raising
eigenvalues for the very thermal cores, and greatly reducing the trend withleakage. Since the cross-sections above 900 eV are identical to Release 6.2, its
calculated fast benchmark eigenvalues are also identical. A. Jonsson reported
improvements in reactivity enrichment dependence [14] at the 1995 CSEWG
meeting, with other groups reporting similar positive findings. Release 6.3 did
not do well on intermediate-spectrum cores, however, calculating 1-2% high on
the HISS (HUG) and the two UH3 benchmarks which RQ Wright had added to235
the set being used to test U. It is possible that the “low-alpha syndrome” which
affected Release 6.2 below 900 eV extends up higher in energy, but the results
are also sensitive to possible errors in nubar.

14

The adjustment process, which was done using bin-averaged cross-sections,maintained the discontinuities in the unbroadened cross-sections at the resonancesub-region boundaries. Although smoothed out by subsequent Doppler broadening
in the processor code NJOY [15,16], they remained an unattractive feature.
Release 6.3 also had a formatting error in that the increased value of thermal
nubar was put into the total-nubar file, but not into the prompt-nubar file.
That meant that processing codes like MCNP [17] which reconstituted the total
from prompt + delayed got slightly lower thermal eigenvalues than they shouldhave (nubar = 2.4320 instead of 2.4338, or 74 pcm).
2.5

ENDF/B-VI Release 6.4

ENDF/B-VI Release 6.4 (1996) is the same as Release 6.3, but corrected
the prompt nubar file.
2.6

Leal-Derrien-Wright – January 1996

In 1994, H. Derrien was sponsored by CEA Cadarache, Électricité de240
France and NEA to work at ORNL with O. Bouland on Pu. At the same time235
he consulted with Leal on U, and later became a full participant in the work.
In January of 1996, Leal, Derrien and Wright completed a preliminary
re-evaluation from 0 to 2.25 keV, which put all the resonances into one region,
thus eliminating the need for tailoring “external” resonances in each of theprevious eleven regions. The evaluation covered eleven differential data sets
(two fission and capture, one fission and absorption, six fission alone and two
transmission). The new work matched the higher epithermal alpha and K1 of
Release 6.3, and in addition provided excellent detailed fits to the differential
data. It did well on the thermal benchmarks and produced better (lower)
eigenvalues for the three intermediate-spectrum HISS (HUG) and UH3 cores.
However, M.C. Moxon [18] observed that the radiation widths fluctuatedmore than was expected theoretically. Moxon also questioned whether the target
backings had been adequately accounted for in the experimental and evaluation
phases of the work, and whether the free-gas model was adequate for Doppler
broadening the low-energy resonances.
2.7

Leal-Derrien-Wright-Moxon – March 1997

To help resolve these questions, NEA, the UK and LMC jointly sponsored
Moxon in a two-month visit to ORNL in late 1996. He and N.M. Larson worked
to reconcile numerical and procedural differences between Moxon’s code

15

REFIT [19,20] and SAMMY. All numerical constants were made consistent.
Detailed comparisons among SAMMY, REFIT, NJOY and other codes led to amore accurate treatment of the low-energy free-gas model for Doppler
broadening in REFIT [21]. Despite the validity of Moxon’s observation thatcrystalline-binding models provide a better description of low-energy Doppler
238
broadening than a free-gas, the effect is probably more important for U than235
for U, for which larger effects are still not adequately understood. Since
crystalline-broadening is not yet available in ENDF-processing codes, practicalconsiderations made it desirable to continue the work with the free-gas model.
The width fluctuations were reduced in subsequent SAMMY fits by constraining
the search region. During Moxon’s stay at Oak Ridge, Leal, Derrien and Moxon,
together with J.A. Harvey and R. Spencer of ORNL and M.S. Moore of LANL,
were able to answer most questions regarding the ORNL experimental
data-reduction procedures, e.g. ORNL confirmed that the target backings had
been properly treated.
Other differences between SAMMY and REFIT, besides the use or non-useof Bayesean methods, remain. Examples are the way in which the neutron-burst
moderation is calculated, the way the resolution function is synthesised from its
components and the multiple-scattering correction to capture and fission yields(included in both codes but implemented differently). The practical impact ofsuch differences has not been assessed, and there is currently no support for
further harmonisation of the two codes. It should be emphasised, however, thatthe existence of two such sophisticated analysis tools and the expertise which
235
their authors and users have brought to bear on the U cross-sections, haveresulted in higher-quality fits than was possible as recently as five years ago.
The resulting data set was benchmark-tested by Dean, et al. [22] and in the
US by R.Q. Wright, A.C. Kahler and J.P. Weinman. The consensus was that thedifferential and integral characteristics were reasonable, but the evaluators feltthat more could (and should) be done.
2.8

Leal-Derrien-Wright – May 1997

Subsequently, Leal, Derrien and Wright produced an interim set for
discussion at the May 1997 Cadarache meeting of the Working Party on
International Evaluation Co-operation (WPEC). The generation of this set
utilised a new capability in SAMMY, allowing the inclusion of integral data
(resonance integrals and K1) within the fitting procedure, thus putting this phaseof the work on a more objective basis.

16

2.9

Moxon – May 1997

Independently, Moxon produced a fit to the 0-100 eV region that differed
235
from previous U evaluations in having a rather low capture g-factor, about
0.95 instead of the traditional 0.99. This may have been the result of removing
the original normalisation and background from the 1966 de Saussure capture
and fission data [23] and re-fitting it with REFIT. Like the May 1997 ORNL fit,
this was an interim version, for discussion at the Cadarache meeting. The only
action taken there was to recommend that an attempt to reach a consensus
be made before the October 1997 CSEWG meeting. That turned out not to bepossible, and the two evaluation efforts are still separate.
In Moxon’s data set a relatively low Maxwellian-averaged fission
outweighed the low capture g-factor, and implied a low K1 unless it could becoupled with a nubar much higher than the ENDF/B-VI standards value. Such ahigher nubar (2.4374) exists in the measurements of Gwin, et al. [24], whichhave already been adopted by both the Joint European File (JEF) and theJapanese Evaluated Nuclear Data Library (JENDL). A “hybrid” data set, createdby inserting Moxon’s cross-sections from 0-10 eV into the January 1996 ORNL
evaluation and replacing the nubar file with the JEF values, was benchmark
tested and performed satisfactorily on the thermal benchmarks. However, it did
poorly on the harder-spectrum cases. Whether this is a low-α or a high nubar
problem is not known. Another question is whether the different capture shapewhich produces the low g-factor in Moxon’s work will affect temperature
coefficients.
2.10 Leal-Derrien-Wright-Larson – August 1997
(ENDF/B-VI Release 6.5)
After the WPEC meeting at Cadarache, ORNL and Moxon continued torefine their fits, and in August 1997 a new Leal-Derrien-Wright-Larson (LDWL)
data set was made available for testing. It incorporated the integral-quantity
fitting capabilities of SAMMY to deal with the earlier problems of low K1 andepithermal alpha. Most noticeably, thermal nubar was increased from theRelease 6.3 value (2.4338) to 2.4367 over the range from 0 to 1 eV. This value
was arrived at by treating thermal nubar as a search parameter in the SAMMY
runs, while using the benchmark value of K1 as a quantity to be fitted. The value
2.4367 is close to a smooth average through the fluctuating Gwin data points inthis interval, and is also (fortuitously) exactly the ENDF/B-V value. By cutting
off the increase at 2 eV, the fit avoids the deleterious effect of a higher nubar on
the harder-spectrum cores. A task for the future is to provide a less ad hoc
solution to this problem. The radiation widths in the new LDWL data set have an
average value over 0-100 eV of about 40 meV, with a standard deviation of
17

10%. It seems reasonable to expect that on average the capture will be the samefrom such a narrow distribution as from a constant radiation width, making thisan acceptable degree of fluctuation.
At the October 1997 CSEWG meeting, A.C. Kahler and J.P. Weinman
presented continuous-energy Monte Carlo benchmark results with this new data
set for about 25 benchmarks including ORNL spheres and cylinders, ORNL
L-series, Rocky Flats, HISS (HUG) and two UH3 intermediate-spectrum
cases [25]. The best results were obtained using a reduced hydrogen capture
cross-section, 332.0 mb instead of 332.6, as recommended by Kahler, and a
version of oxygen that was slightly-modified from the Los Alamos evaluation in
ENDF/B-VI Release 6.0 [26]. The effect of reducing the hydrogen capture wasto raise the low-leakage end of the thermal benchmark “trend line” about
100 pcm. The modified oxygen has more forward scattering and the resulting
additional leakage lowered the high-leakage end about the same amount.
Together they produced a flat trend line with an average eigenvalue very close tounity. The intermediate-spectrum cases are close together at about 1% high.
The thermal cases are therefore about the same as Release 6.3, while the threeharder cores are better, although not quite as close to unity as with theJanuary 1996 evaluation of Leal-Derrien-Wright. In view of its good differential
fits and benchmark performance, it was accepted for inclusion in ENDF/B-VI
Release 6.5 (as was the new hydrogen capture). A decision on the oxygen isawaiting completion of a new evaluation at Los Alamos National Laboratory by
G. Hale and P.G. Young.
In December of 1997, two papers were presented at a meeting of the
JEF Working Group on Data Evaluation and Benchmark Testing [27,28]. Bothshowed significant improvements using LDWL over the JEF2.2 data set, which
is similar to ENDF/B-VI Release 6.2. The studies covered a wide range ofquantities, among them buckling measurements, k-infinities, spent-fuel analyses,
and temperature dependent Westcott g-factors. In each area the LDWL set
improved the agreement between calculation and experiment. Of particularinterest were the spent-fuel results, since they test the cross-sections in a waythat is relatively independent of any remaining problems with nubar. As a resultof these favourable findings, the new data were adopted for JEFF3.
Complete details of the LDWL evaluation were given in an ORNL
report [29] and a slightly abbreviated version in the open literature [30]. Detailsof the inclusion of integral quantities into the analysis were also published as an
ORNL report [31] and in the open literature [32].

18

2.11 Moxon – September 1997
Moxon has released a version of his latest work to the Nuclear Energy
Agency Data Bank in Paris [33]. It extends his earlier work to higher energies,
and achieves satisfactory fits to the differential data using a single value of theradiation width, close to the 38.2 mV he recommended in earlier works [34].
As of this date, it has not been reviewed or benchmark tested, since that will
require it to be coupled with a nubar file and higher energy cross-sections.
Moxon’s work represents a “pure” fit to the microscopic data, so that if it is to be
useful in integral calculations, it will probably require a new treatment of nubar.
That is also a topic for further investigation, as is the significance of the unusual
Westcott g-factor for capture, noted above in connection with his May 1997
work. The work utilises a J-dependent scattering radius, and the ENDF formats
and processing codes should be expanded to treat this as-yet not “allowed”
feature.
2.12 The role of integral testing
The extent to which successive releases of ENDF/B-VI agreed or disagreed
with integral benchmarks has from the start been an essential element in shaping
its development. With the evolution of Release 6.3 and subsequent refinements,
and the enhanced degree of international co-operation resulting from theformation of Subgroup 18, that aspect of the evaluation process became more
integrated into the data-fitting process. At Oak Ridge, R.Q. Wright routinely
checked successive iterations of the differential-data fitting and/or adjustment
process, and provided feedback on their integral adequacy. At Bettis Atomic
Power Laboratory and at LMC, A.C. Kahler and J.P. Weinman continuously
monitored progress with highly accurate point-energy Monte Carlo calculations.
The major releases were checked by the CSEWG Thermal and Fast Reactor
Testing Subcommittees under M.L. Williams (Lousiana State University) and
R.D. McKnight (Argonne National Laboratory). R.D. Mosteller at Los Alamos
National Laboratory used both CSEWG benchmarks and the newer collection
embodied in the International Criticality Safety Benchmark Evaluation
Project [35] under J. Blair Briggs (Idaho National Energy Laboratory) to assess
both ENDF and other data sets. Large-scale calculation of both published andproprietary benchmarks were carried out by the UK, France, Japan andelsewhere [22,27,28,37-39]. The reader is referred to the minutes of the annual
CSEWG meetings at Brookhaven, to the transactions of the annual and topicalmeetings of the American Nuclear Society, and to the proceedings of theInternational Conferences on Nuclear Data for Science and Technology, for
Basic and Applied Science, for Reactor Safety, and related meetings.

19

Since there are many different methods used to measure the benchmarks
and to calculate them, and because many of them are proprietary, it is difficult toincorporate the results directly into the evaluation process. Instead they provide
broad-brush indications of where problems exist, and can focus the evaluators’
attention on the appropriate differential data.
3.

Current status of235

U evaluation

The current ENDF/B-VI evaluation (Release 6.5) [29,30] reaches some
important goals:
1. The problems with the capture cross-section in the earliest releases areunderstood, at least for the thermal benchmarks:
a. An average capture width of 38.03±1.70 meV in the range from 0 to
50 eV was obtained from the SAMMY analysis of a large set ofexperimental differential data, based on well-resolved time-of-flight
experiments [39]. This agrees with the value (38.20±1.24) originallyobtained by M.C. Moxon from an analysis of selected resonances in
0-20 eV [34], and with the value (38.2) obtained independently in
Release 6.3 (0-100 eV) by adjusting the Release 6.2 capture
cross-section upwards to match the bin-averaged capture of [5].
b. The average capture width increased to 39.4±2.0 (+3.6%) when
integral data were added to the experimental database [39]. Thisvalue agrees with the above to within the uncertainties.
c. The capture resonance integral is 140.9 b, giving an alpha value of0.509, consistent with integral measurements.
d. The capture widths, which were constrained in the fitting process,still show fluctuations of the order of 10%. This is considered to be
acceptable in order to provide the best possible fit to the differential
data. Moxon arrived at an alternative fit using a fixed value of the2radiation width, achieving comparable χ (goodness-of-fit) values,
but at present there is no evidence indicating a technologicaldifference between the two approaches. The point to be taken fromthese works is that one cannot expect a straightforward fit to thedifferential data to produce correct radiation widths. A value
obtained some other way has to be imposed on the least-squares
procedure.
2. Combining the resonance parameters into one region eliminated the20discontinuities between the eleven sub-regions in previous ENDF/B-VI
releases, and simplified the representation of the distant level
contribution.
3. The ORNL evaluation [40] reproduces below 0.1 eV the shape of η
proposed by Santamarina, et al. [12]. The Gwin 1997 η data are well
reproduced in the energy range below 1 eV, as discussed in [30].
The only problem is with the Wartena, et al. data [41] in the high energy
wing of the 0.3 eV resonance where the data are questionable.
4. Good agreement is obtained in benchmark results for highly enrichedthermal assemblies and improved results for intermediate spectrum
cases. Studies continue to show poorer agreement in low-enrichment
cores, but that effect cannot be reliably disentangled from the 238U
cross-section questions.
5. The necessity to treat nubar without a theoretical shape continues to be
an undesirable aspect of the evaluation process. JEF and JENDL haveadopted “raw” discontinuous experimental data, and LDLW used it
to “fit” the parameter K1. An improvement is needed in this area(see below).
4.

Topics for future investigation
1. Resonances above 100 to 150 eV are only partially resolved, but
are parameterised in ENDF/B-VI as if they were actual resonances.
The effect of these pseudo-resonances on the accuracy of the calculated
self-shielding effects should be examined, and compared with aconventional treatment in terms of average parameters.
2. The unresolved resonance region should be re-evaluated, using theReich-Moore formalism instead of Single-Level Breit-Wigner (SLBW)
and incorporating the very accurate total cross-section obtained from
Harvey’s transmission data [42]; this could modify the fission and/or
the capture cross-sections by a few per cent. A preliminary multilevel fit
has been carried out by Moxon and shows a significant increase in α
relative to an SLBW treatment [43]. Similar work is in progress at
ORNL.
3. The ENDF/B-VI fission standard should be reconsidered [44]. If thisstandard is retained with its claimed accuracy, then the inconsistency
between it and the ENDF/B-VI Release 6.5 evaluation will remain
to be resolved, and will show up in the unresolved resonance region.
21

The current standard is based on the alpha measurements of Corvi,
et al. [45] and of Muradyan, et al. [46]; the important data of Beer andKäppeler [47] obtained at Karlsruhe with a very high resolution were
not considered. These data, in excellent agreement with the de Saussure,et al. data [48], are 6-7% higher than the Corvi data. Taking for alphaan average value of Corvi, Beer and de Saussure will give fission
cross-sections 2-3% smaller than the standard values if the total
cross-section is kept at the Harvey value.
4. Possible variation of nubar in the resonances was not considered in the
ORNL (Release 6.5) evaluation. Both theory and experiment show thatnubar varies from resonance to resonance, yet that variation is universally
ignored in the cross-section evaluation process [24, 49-53]. The current
good fits to the capture, fission and total cross-sections suggest thatthese are now “well-known” and are incompatible with integral
reactivity measurements unless coupled to a much higher nubar than has
been used in earlier releases of ENDF/B-VI. Introducing a soundtheory-based description of the energy-dependence of nubar could havea beneficial effect on many calculations, since it would open up an
important new degree of freedom. Any correlation between nubar andalpha could affect both the thermal and intermediate-spectrum
calculations. Other areas would be discrepancies between α and η
measurements, and calculated temperature coefficients.
5. Crystalline Doppler broadening is currently under intense scrutiny for
238
U, but it has not been shown to be of comparable importance for 235U.
M.C. Moxon has used an Einstein model in REFIT to achieve better fits
235
to the wings of the low-energy resonances in U, but a test of thatrefinement in reactor calculations has not been carried out.
6. There does not appear to be any calculation that would test the degreeof fluctuation in the radiation widths. As discussed above, using a
constant width, or a narrow distribution, appear to be technologicallyindistinguishable.
7. More intermediate-energy benchmarks are needed to test the evaluation,and in general more effort needs to go into understanding discrepant
results from different organisations. First priority should go to the
publication of new highly enriched, homogeneous benchmarks.
238
8. The question of over-absorption in U continues to cloud benchmark
235
results for low-enriched U. Modern computational techniques, mostimportantly continuous-energy Monte Carlo calculations, could settle
the issue of whether the basic data are responsible, or whether the22

problem is in the reduction to multi-group cross-sections and related
calculational approximations. To reach this goal, it would be desirable
to first ensure an adequate degree of consistency among the various
codes, so that calculational differences could be reliably ascribed to thebasic data.
5.

Conclusions

235
An extensive effort has gone into the evaluation and testing of the U
resonance region since the start of ENDF/B-VI in 1990. In Release 6.5 wearrived at a credible data set that fits a variety of both differential and integral
data. Some questions remain, such as the extension of better methods to theunresolved region; incorporating a theory and experiment-based variation of
nubar; objectively deciding whether in fact the pseudo-resonances are superior
to an accurate, conventional fit using average parameters based on channel238
fission theory; and clarifying the role of U cross-sections in low-enrichedbenchmarks.

23

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27

[35] J. Blair Briggs, ed., “International Handbook of Evaluated Criticality
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[49] F.J. Hambsch, H.H. Knitter and C. Budtz-Jorgensen, “Fission Mode
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29

TABLES
AND FIGURES

31

33

Figure 1. Eigenvalues of homogeneous critical assemblies vs. leakage (Oak Ridge and Rocky Flats).
Calculated by continuous-energy Monte Carlo, using ENDF/B-VI Release 0 cross-sections.

EIGENVALUES34

ABOVE THERMAL LEAKAGE

Figure 2. Eigenvalues of homogeneous critical assemblies vs. leakage (Oak Ridge and Rocky Flats).
Calculated by continuous-energy Monte Carlo, using ENDF/B-VI Release 5 cross-sections.

EIGENVALUES35

ABOVE THERMAL LEAKAGE

Figure 3. A comparison of the fission cross-section
below 1 eV from ENDF/B-VI.5 and Moxon

36

Figure 4. A comparison of the capture cross-section
below 1 eV from ENDF/B-VI.5 and Moxon

37