NEA/WPEC–3

International Evaluation Co-operation

VOLUME 3
ACTINIDE DATA
IN THE THERMAL ENERGY RANGE

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

CO-ORDINATORSMONITORH. Tellier

H. Weigmann

M. Sowerby

CEA, C.E. Saclay
FranceIRMM Geel
Belgium

AEA Harwell
U.K.

NUCLEAR ENERGY AGENCY
ORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENTORGANISATION FOR ECONOMIC CO-OPERATION AND DEVELOPMENT
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to contribute to sound economic expansion in Member as well as non-member countries in
the process of economic development; andto contribute to the expansion of world trade on a multilateral, non-discriminatory basis inaccordance with international obligations.

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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)
to promote the exchange of information on nuclear data evaluations, validation,and related 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 arecompiled. The Working Party determines common criteria for evaluated nuclear
data files with a view to assessing and improving the quality and completenessof evaluated 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 are organised through the Nuclear Data Sectionof the International Atomic Energy Agency (IAEA).
The following report was issued by a Subgroup investigating actinide datain the thermal energy range. Thermal nuclear constants for the primary actinides
have been extensively studies, but the most recent evaluations are not in fullagreement with thermal reactor calculations. The objective of the Subgroup was
to identify the origin of these differences and to reassess the recent evaluations.
A considerable effort was devoted to the η of U-235, where analysis of lattice
temperature coefficient measurements has suggested an energy dependent shape
below thermal energy.
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

Members of Subgroup 3

FRANCEUNITED KINGDOMTELLIER, Henri
Commissariat à l’Energie Atomique
C.E. Saclay

HALSALL, M.J.
AEA Technology
Winfrith Technology Centre

GERMANY

UNITED STATES OF AMERICA

MATTES, Margarete
Institut für Kernenergetik und
Energiesysteme
Universität Stuttgart

WESTON, L.
Oak Ridge National Laboratory

INTERNATIONAL ORGANISATIONSDERUYTTER, A.J.
Division Head,
Nucl. Physics and Measurements
Inst. for Reference Materials andMeasurements
Joint Research Centre
Geel, Belgium

JAPAN
MATSUNOBU, Hiroyuki
Sumitomo Atomic Energy Industries Ltd.
Tokyo
TSUCHIHASHI, Keichiro
Deputy Director
Dept. of Reactor Engineering
JAERI
Tokai Mura

WEIGMANN, H.
Institute for Reference Materials andMeasurements
Joint Research Center
Geel, Belgium

4CONTENTS
Thermal neutron actinide data ...................................................................... 7
1. Introduction ................................................................................................ 7
2. Uranium-238............................................................................................... 9
3. Thorium-232 ............................................................................................... 9
4. Plutonium-240 ............................................................................................ 10
5. Uranium-235............................................................................................... 11
6. Uranium-233............................................................................................... 17
7. Plutonium-239 ............................................................................................ 17
8. Conclusion .................................................................................................. 19
References......................................................................................................... 21
Analysis of η measurementsfor U-235 in the thermal neutron energy region .......................................... 23
1. Introduction ................................................................................................ 23
2. Experimental techniques and difficulties.................................................... 24
3. Results......................................................................................................... 26
4. Problems at higher energies........................................................................ 29
5. Conclusion .................................................................................................. 30
References......................................................................................................... 31

5

THERMAL NEUTRON ACTINIDE DATA *1. Introduction
During the 70’s, the physicists involved in the cross-section measurements
for the low-energy neutrons were almost exclusively interested in the resonanceenergy range. The thermal range was considered as sufficiently known.
In the beginning of the 80’s, reactor physicists had again to deal withthe delicate problem of the power reactor temperature coefficient, essentially forthe light water reactors. The measured value of the reactivity temperature
coefficient does not agree with the computed one. The later is too negative.
For obvious safety reasons, it is an important problem which must be solved.
Several causes were suggested to explain this discrepancy. Among all thesecauses, the spectral shift in the thermal energy range seems to be very important.
Sensibility calculations show that this spectral shift is very sensitive to the shapeof the neutron cross-sections of the actinides for energies below 1 eV.
Consequently, reactor physicists require new and accurate measurements inthe thermal and sub-thermal energy ranges [1,2]. A part of these newmeasurement results was recently released and reviewed [3]. The purpose of thisstudy is to complete the preceding review with the new information which is
now available. In reactor physics the major actinides are the fertile nuclei, i.e.,uranium-238, thorium-232 and plutonium-240 and the fissile nuclei, i.e.,uranium-233, uranium-235 and plutonium-239. For the fertile nuclei the main
datum is the capture cross-section, and for the fissile nuclei the data of interestare ν , the fission and capture cross-sections or a combination of these data suchas η or α. In the following Sections, we will review the neutron data of the
major actinides for the energy below 1 eV.

*

Author: H. Tellier, C.E. Saclay, CEA, France.

7

Figure A-1
Uranium-238 capture cross-section measurement comparison
between Geel metal sample and JEF-2 evaluated values

Figure A-2
Recent measurements of thorium-232 capture cross-section and comparison with
ENDF/B-VI evaluated values
82. Uranium-238
At low energy, the cross-section shapes of uranium-238 are givenby the 4.4 eV “p”-wave and the 6.67 eV “s”-wave resonances. These two
resonances induce for capture cross-section a l/v behaviour in the thermal range.
It is the shape which is universally adopted by all evaluated files. But partof the temperature
coefficient
discrepancy
could be explain bya non-l/v-dependence on the uranium-238 capture cross-section for the lowenergy neutron. The cross-section must decrease with the energy faster thanthe l/v shape. This effect can be obtained with the assumption of a weak boundlevel near the zero energy. L. Erradi proposed a small resonance at –0.005 eV[4]. This hypothesis was supported by the measurement of the fission crosssection at 0.025 eV which was performed in Grenoble [5]. The experimental
value cannot be exclusively explained by the contribution of the nearby
resonances. An extra resonance is needed. If this resonance is close to the zeroenergy as in the Erradi’s assumption, it must have an impact on the cross-section
shape in the thermal range. The non-l/v-shape which is obtained with the –0.005 eV resonance is not incompatible with the Harwell measurement of theuranium 238 capture cross-section [6] but only because the experimental
uncertainties of this measurement are rather large. New and more accurate
measurements of the uranium-238 capture cross-section were required.
These measurements were performed at the Geel laboratory [7]. As it can beseen in Figure A-1 which represents the experimental variation of σ γ E
as a function of the neutron energy, and a comparison with the JEF evaluation,these results confirm without ambiguity a l/v behaviour for the capture crosssection. The assumption of the resonance in the immediate vicinity of the zeroenergy and the explanation of part of the temperature coefficient discrepancy bysuch a resonance must be dropped. Reasonably, we must consider
that the uranium-238 capture cross-section problem is solved as far as
the thermal energy range is concerned.

3. Thorium-232
Nowadays, the use of thorium fuel cycle in thermal neutron reactors is
no longer a high priority and the physicists’ interest for thorium nuclear datais less important in the case of low energy neutron than in the fast range.
Consequently the situation is fundamentally different from that of uranium-238.
That is why no request recently appeared for the thermal neutron energy range.
In this energy domain there exists only two recent differential measurements
which give access to the shape of the thorium-232 capture cross-section.
These are respectively the measurement performed in Brookhaven for energies
9between 35 and 1000 meV [8] and the experiment of RPI which covered neutronenergies above 10 meV [9]. These two sets of experimental data are compared in
Figure A-2 which displays the variation of σ γ E versus the neutron energy. If
we take into account the experimental uncertainties, the agreement between bothmeasurements is good enough above 50 meV. They are also in good agreementwith the recommended value of the ENDF/B-VI evaluation. In the very lowenergy domain, between 10 and 25 meV, only one measurement significantly
deviates from the evaluated recommendation. The experimental cross-section
decreases less than a l/v shape. We know that the temperature coefficient of amultiplying lattice is very sensitive to the shape of the fertile nucleus capture
cross-section below 25 meV. In the case of a thorium cycle revival, the observed
discrepancy between the measurement and the evaluation must be clarified as it
was recently done for uranium-238. New and accurate measurement of thethorium-232 capture cross-section would be needed in the thermal and subthermal energy range.

4. Plutonium-240
For this isotope, the cross-section behaviour in the thermal energy range ismainly governed by the 1.056 eV resonance. Consequently it is necessary
to have a very accurate knowledge of these resonance parameters. Only two
measurements of the 1.056 eV resonance parameters were recently carried out:
the Brookhaven experiment [10] and the Oak Ridge one [11]. In the Brookhavenexperiment, total and capture cross-sections with room temperature and cooled
samples were used. In the Oak Ridge measurement, transmission measurementswith seven thicknesses of sample were performed. Thus it was expected that theresults could be very satisfactory. Unfortunately, as it can be seen from Table 1,
both sets of results are significantly discrepant.
Table A-1 : Parameters of the 240Pu 1.056 eV resonanceΓn (meV)Γγ

2.32 ± 0.06

32.4 ± 0.6

Brookhaven(81) [10]2.45 ± 0.02

30.3 ± 0.3

Oak Ridge(87) [11]

(meV)

10

LABORATORYA detailed analysis of both experiments leads to be more confident in
the second set of results. But the interpretation of spent fuel isotopic composition
suggests tendencies closer to the high value of radiative capture width.
The difference between the two series of resonance parameters induces a changeof 1.2% in the contribution of the 1.056 eV resonance to the capture crosssection at 0.025 eV and a change of 4.5% in the resonance integral value. These
modifications become very important each time that plutonium-240
is significantly involved. It is mainly the case for irradiated fuel analysis or forplutonium recycling is light water reactor. The discrepancy between bothdifferential measurements and the tendency deduced from the integral
experiments must be clarified then.

5. Uranium-235
In the case of a fissile nucleus, the problem is even more complex than fora fertile nucleus. In addition to the capture cross-section, other fundamental
nuclear data are involved, the number ν of neutrons which are emitted
in a fission and the fission probability. These three quantities, or a combinationof them such as η or α must be investigated. As the temperature coefficient isvery sensitive to the shape of the various nuclear parameters versus the neutronenergy (see above), several differential measurements were performed during thelast years. They are relative to the fission cross-section, ν and η in the very lowenergy range.

a) νOne measurement of ν was recently performed in the energy range which weare interested in. The Oak Ridge experiment gives the ratio of the uranium-235
prompt ν over the Californium νsp of spontaneous fission for the neutronenergies between 5 meV and 1 eV [12]. According to these results, which aredisplayed in Figure A-3, nothing appears in the vicinity of the 0.29-eV
resonance and we can reasonably keep the assumption of a constant value of ν
below 1 eV. This flat shape, which is adopted in all evaluated files, has
important consequences for the capture cross-section behaviour at low energy.

11Figure A-3
Ratio of uranium-235 ν to that of californium-252 in the thermal energy range andcomparison with evaluated values

Figure A-4
Recent measurements of uranium-235 fission cross-section and comparison with
ENDF/B-V and JEF-2
12b) Fission cross-section
Since 1984, very accurate measurements were performed in the low-energy
neutron range [13, 14, 15]. As it can be seen from Figure A-4, above 20 meV
and in particular in the 0.290 eV resonance all these results are in agreementwith each other and also with the most recent evaluated files ENDF/B-V and
JEF-2. In the sub-thermal energy range, below 5 meV, only the Geel experimentgives information.
According to this measurement the uranium-235 fission cross-section reaches
an l/v shape for energies higher than it was assumed in ENDF/B-V.
On the contrary, JEF-2 which was released after the Geel experiment takes into
account its results below 10 meV and adopts a fission cross-section shape closer
to a l/v behaviour.
c) η measurements
To explain the temperature coefficient discrepancy of the uranium fuelreactor, it is η = νσfσαwhich is the most sensitive parameter. In all previous

evaluated files, including ENDF/B-V and JEF-1 η was assumed to havea constant value below 0.1 eV. As the reactor physicists proposed to increase η
between 5 and 100 meV, measurements of this neutron parameter were needed
to validate the shape modification. Four measurements of η were recently
performed in the range of interest.
The first one is the Geel experiment [16]. This experiment was performed
with a linac and a liquid methane moderator to enhance the importance ofthe low-energy neutrons. It covered the neutron energy between 2 and 450 meV.
As shown in Figure A-5 the results suggest an increase of η between 2 and80 meV, which would represent an improvement in reactor physics calculations.
A second measurement was carried out with the Harwell linac [17].
Unfortunately the number of low-energy neutron was not very high.
Consequently the accuracy was not good enough. Nevertheless this experiment
did not show a significant shape of η versus the neutron energy as displayedin Figure A-6. It is contradictory with the Geel results.

13

Figure A-5
Experimental results of uranium-235 η measurements of Geel and Grenoble
in the low-energy neutron range

A third experiment was performed in Grenoble [18]. Instead of a linear
accelerator, as in Geel, the neutron source was constituted by a cold neutron
beam of the high flux reactor and more neutron of low energy were obtained.
The accuracy was then expected to be better because the background would belower. In the energy range between 2 and 150 meV, this experiment perfectly
confirms the Geel results and the shape of η versus energy as shownin Figure A-5.
Finally a fourth experiment was carried out with the Oak Ridge linac [19].
The preliminary results of the last experiment are compared with the Harwell
results in Figure A-6. These two series of results seem more or less in agreementand do not show a significant shape of η.
These four experimental results can be split into two sets: the first set
indicates a shape of η (Geel and Grenoble data) and the second set does not(Harwell and Oak Ridge data). As the low neutron flux was higher
in the Grenoble experiments, it is possible to given a more important weightto these results and to propose a slope for the η shape below 100 meV.
This attitude was adopted for the preliminary version of JEF-2. But fromthe physical point of view, the disagreement between both sets of results is not
acceptable. On behalf on the NEA Nuclear Science Committee, a working groupcarefully studied the various corrections (count loss, background subtraction,
absorption...) which were applied to the raw data of the four measurements. The
final recommendations of the working group have not been established yet but
14the preliminary results are encouraging. It seems that it may be quite possible todefine a curve of η with an energy-dependent shape. η would increase by afactor of about 1.3 between 3 and 80 meV and this energy dependence would becompatible with the four experimental data [20]. This shape would be close to
the reactor physicists’ suggestion.

Figure A-6
Experimental results of uranium-235 η measurements of Harwell and Oak Ridge
below 500 meVd) α measurement
A complementary and important information upon the uranium-235 crosssection in the thermal energy range is given by the recent Geel measurementof α [21]. This result is very interesting because it constitutes an independent
way of obtaining information about η =ν. As it can be seen in Figure A-7,
1+ α

the experimental values of α are not reproduced by the ENDF/B-V evaluation.
As all previous files, ENDF/B-V recommends a flat shape of α below 100 meV.
As ν is energy-independent, this shape corresponds to a constant value of η.
On the contrary, a slope for η was adopted in JEF-2 and this file, which was
released before the experimental values of η, is in good agreement withthe measurement results. It is an important fact, because we now have a coherent
set of experimental data for ν, σf, η and α, which confirm the slope of η, as it
was suggested by the integral experiment.

15

Figure A-7
Uranium-235 α-parameter measurement and comparison with
ENDF/B-V and JEF-2 recommended values

Figure A-8
Ratio of uranium-233 ν to that of californium-252 and comparison with evaluatedvalues below 1 eV

16

6. Uranium-233
For the same reasons as for thorium, the uranium-233 nuclear data in the lowenergy range have not been systematically studied over these last years.
Nevertheless there exist some scarce results, mainly for ν and the fission crosssection. These measurements were generally performed in the same campaign asuranium-235 when physicists had uranium-233 samples at their disposal. For ηand α, nothing new is available.

a) νThe only result about ν below 1 eV is the one of Oak Ridge [12] which gives
the ratio of uranium-238 prompt ν to the spontaneous fission ν of californium252. No significant structure was observed in this energy range, as shown in
Figure A-8 and we can reasonably admit the flat shape which is adopted in
ENDF/B-VI. Note that the ENDF/B-VI absolute value of ν is not in agreementwith the tendency which is deduced from the buckling measurements [22].

b) Fission cross-section
At the opportunity of the campaign of measurements on fissile nuclei,
an accurate determination of the shape of the uranium-233 cross-section shape
was carried out with the Geel linac [23]. In order to enhance the low-energy
neutron flux and obtain a good accuracy in the thermal and sub-thermal energy
range, a liquid nitrogen-cooled moderator was used. In these experimental
conditions we can be very confident in the results which are displayedin Figure A-9. They are also in fair agreement with the ENDF/B-VI
recommendation. Reasonably we can admit that the shape of the uranium-233
fission cross-section is well known below 1 eV.

7. Plutonium-239
All old evaluations of the plutonium-239 neutron data, including ENDF/B-V, areconsidered to be not satisfactory by reactor physicists. As a matter of fact, in allthese files it was adopted a flat behaviour of ν in the low-energy range, the spinof the resonances was not considered and it was used a Breit and17

Figure A-9
Experimental fission cross-section of uranium-233 and comparison with ENDF/B-VI

Figure A-10
Ratio of plutonium-239 ν to that of californium-252 and comparison with
Fort’s theoretical calculation
18

Wigner formalism to compute the cross-sections. With high burnup fuels andrecycling, plutonium has become more and more important in the thermal
neutron reactors. An updating of the plutonium-239 neutron data was strongly
required. This updating was performed by Derrien et al. [24] who took into
account of new experimental results, concerning ν [12], the fission cross-section[13] and the total cross-section [11], and used a Reich and Moore formalism
which is more convenient for the fissile nuclei.

a) νAs opposed to uranium-233 and uranium-235 cases, the recent measurementof plutonium-239 ν [12] shows an important decrease in the vicinity of the lowenergy resonance at 0.3 eV. This strong structure is well reproduced by
the Fort’s theoretical calculation which takes into account the spin effect andthe (n,γf) effect of the J = 1 resonances of plutonium-239 [25]. Figure A-10
represents a comparison between the experimental values of ν , normalised tothe spontaneous fission ν of californium-252, and the evaluation of Fort et al.
As the agreement is very good, this shape of ν was included in JEF-2.

b) Fission cross-section
All new evaluated files use the resonance parameter set which was deduced
from Derrien’s analysis. The behaviour of plutonium-239 cross-sections in
the thermal range is well reproduced by the contributions of low-energy
resonances and bound level. Once the initial version of the recent evaluated files
was released, a new measurement of the plutonium-239 fission cross-section
became available [23]. Figure A-11 shows the comparison of these newexperimental values with the recommended values of JEF-2 below 1 eV.
The agreement is quite satisfactory and the new fission cross-section
measurement constitutes a confirmation of the recommended values. Today,
no request upon the plutonium-239 fission cross-section seems necessary as far
as the low energy is concerned.

8. Conclusion
The status of the thermal neutron data for the major actinides has been greatly
improved for the last few years. The recent measurements of the microscopic
data led to a better knowledge of the cross-section shapes in the low-energy

19domain. Several problems of great importance in reactor physics were solved.
Let us mention for instance the l/v-dependence of the uranium-238 capture
cross-section and the behaviour of the uranium-235 fission cross-section below
20 meV. The structure of the plutonium-239 ν , which was not taken into
account in the past, was well established and theoretically explained. We canreasonably expect that the uranium-235 η discrepancy will be solved in the near
future. Nevertheless there remain some problems which have to be further
investigated. The most important one today is the discrepancy between both setsof parameters of the 1.056 eV plutonium-240 resonance. This disagreement has
an important impact on high burnup fuels or plutonium recycle studies.
The difference between the evaluated values and the measured valuesof the thorium-232 capture cross-section below 20 meV and the problemof the absolute value of the uranium-233 ν have a lower priority. But in the caseof new interest for the thorium cycle, requests upon these two actinides willcertainly be needed.

Figure A-11
Comparison between Geel last fission cross-section and JEF-2 recommended values
for plutonium-239 below 500 meV20

References[1]

J.L. Rowlands, “Neutron physics and Nuclear Data”, Harwell, 7 (1978).

[2]

J. Bouchard, C. Golinelli et H. Tellier, “Neutron Data for Science andTechnology – Anvers”, 21 (1982).

[3]

H. Tellier, “Neutron Data for Science and Technology - Jülich” (1991).

[4]

L. Erradi, Thèse Doctorat es sciences, Paris Orsay (1982).

[5]

P. D’Hont et al., “Annals of Nuclear Energy”, 11, 485 (1984).

[6]

M.C. Moxon and J.E. Jolly, “Uranium and Plutonium ResonanceParameters - Vienna”, 124, INDC-129 (1981).

[7]

F. Corvi and G. Froni, “Nuclear Data for Science and Technology –Mito”, 127 (1988).

[8]

R. E. Chrien et al., Nuclear Science and Engineering, 72, 202 (1979).

[9]

R.C. Little et al., Nuclear Science and Engineering, 79, 175 (1981).

[10] H.J. Liou and R.E. Chrien, “Uranium and Plutonium ResonanceParameters - Vienna”, 438, INDC-129 (1981).
[11] R.R. Spencer et al., Nuclear Science and Engineering, 96, 318 (1987).
[12] R. Gwin et al., Nuclear Science and Engineering, 87, 381 (1984).
[13] R. Gwin et al., Nuclear Science and Engineering, 88, 37 (1984).
[14] C. Wagemans and A.J. Deruytter, “Nuclear Data for Basic and Applied
Science - Santa Fe”, I, 499 (1985).

21

[15] R.A. Schrack, “Nuclear Data for Science and Technology - Mito”, 101(1988).
[16] J.A. Wartena et al., Report IAEA Tecdoc 491, 123 (1987).
[17] M.C. Moxon et al., “Nuclear Data for Science and Technology – Mito”,
75 (1988).
[18] J.A. Wartena et al., Report NEANDC (E) 312, III (1989).
[19] M.C. Moxon et al., Private communication to the NEA Data Bank (1990).
[20] H. Weigmann, Private Communication (1991).
[21] H. Weigmann et al. “Nuclear Data for Science and Technology – Jülich”(1991).
[22] H. Tellier and J. Vanuxeem : (This meeting).
[23] C. Wagemans et al., “Nuclear Data for Science and Technology – Mito”,
91 (1988).
[24] H. Derrien et al., Nuclear Science and Engineering, 106, 434 (1990).
[25] E. Fort et al., Nuclear Science and Engineering, 99, 375 (1988).

22

ANALYSIS OF η MEASUREMENTS FOR URANIUM-235
IN THE THERMAL NEUTRON ENERGY REGION **Abstract
Existing experimental data on η of 235U in the thermal and sub-thermalenergy regions are reviewed. Special attention is given to the various systematic
uncertainties. When combined with recent fission cross-section data,an R-matrix fit yields a good representation of the data in the energy region
below ∼0.2 eV. At higher energies problems remain and they need further
investigation.

1. Introduction
The detailed energy-dependence of neutron cross-sections and relatedparameters of fissile nuclei for sub-thermal neutron energies has recently foundconsiderable attention because of its effect on the temperature reactivity
coefficient of thermal reactors [1]. One of the quantities thus considered is η ***of 235U.
Several measurements of the energy dependence of this quantity have been
performed in recent years. The two earlier ones were carried out at Harwell [2]and Geel [3], and the later measurements at the ILL, Grenoble [4], andat ORELA by a Harwell-ORNL collaboration [5]. Finally a measurementof the related quantity α was done at Geel [6].
Preliminary analysis of some of these data seemed to show discrepant results,
although the differences were at the limit of the combined systematic
uncertainties. Therefore, a Subgroup of the NEA Working Party on International
Evaluation Co-operation was set up to further investigate this problem. In thisnote the conclusions of the Subgroup are addressed.
*****

Authors: M.C. Moxon, J.A. Wartenay, H. Weigman, JRC, Institute for Reference Materials
and Measurements.
Number of fission neutrons emitted per neutron absorbed.

23

In Section 2 we will briefly discuss the experimental techniques applied andtheir difficulties. In Section 3 we will present our findings for the thermaland sub-thermal energy regions, and in Section 4 we will point out still existing
problems at somewhat higher energies (above ∼0.3 eV).

2. Experimental techniques and difficulties
As a general statement it may be said that systematic corrections which had
to be applied to the measured data are important, and so are systematic
uncertainties, as they are compared with the size of the effect underinvestigation. However, some of the experiments differ strongly in the applied
techniques, and as a consequence the relative importance of the various
systematic uncertainties is rather different.
The principle method to measure the energy dependence of η is simple:
A beam of low-energy neutrons first passes through a flux monitor before it hits
a “black” metallic U sample. The transmission of this sample is almost zerofor neutron energies below 0.1 eV. Fission neutrons emerging from this sample
are detected by a NE-213 liquid scintillation detector. Pulse shape discrimination
is used to distinguish neutrons from γ-rays. The shape of the neutron flux ismeasured by replacing the black U sample by a neutron capture sample which isalso “black” for neutrons in the energy range of interest. Samples of 10B and Cd
have been used. Thus the shape of the neutron flux is directly obtained from theyield of γ-rays from the capture sample. The flux monitor is used only to record
possible changes of the neutron flux shape between the fission measurementswith the black U sample and the flux measurement with the capture sample.
The earlier Harwell and Geel as well as the more recent Harwell-ORNL
measurements used a linac pulsed white neutron source and conventional
time-of-flight technique. The most difficult problem in these measurements is todetermine backgrounds, especially in the sub-thermal region: Every fission eventin the U sample produces neutrons which may be back-scattered fromthe surroundings and produce a delayed fission event in the sample at a latertime. A decaying background with a few ms delay is indeed seen
in measurements with a Cd filter. The true background cannot be readilymeasured because any background filter, e.g., Cd, will take away most of
the source of the background as well.
In the latest analysis of the Harwell-ORNL data much effort has been
devoted to reconstruct the background by folding the delayed component

24

observed in the measurement with the Cd filter into the foreground fission rate.
This and an extrapolation to zero filter thickness were best possible to be carriedout on the Harwell-ORNL data. Measurements on samples of Pb and C provided
an additional guideline for the determination of the background and the effect of
the filters used to determine the background.
In the measurement at the ILL reactor the flux at the thermal neutron guide
was sufficient to allow the use of a double chopper setup: Two choppers,
separated by about 3 m, essentially produced a pulsed monoenergetic beam.
The sample for the η measurement (or the capture sample for the flux
measurement) was placed another 0.9 m downstream from the second chopper.
Thus the time signal from the detector could be used to separate background
events due to out-of-time neutrons from true events. With this method
the uncertainty in background determination could be reduced. On the other
hand, instantaneous count rates during the neutron pulse were high, andtherefore also the count-loss corrections, which reach a maximum of ∼6%
at about a 60-meV neutron energy. In the original analysis no correction wasapplied for a count-rate dependent cross talk between γ-rays and neutron output
channels of the PSD circuit. Recent inclusion of this effect resulted in a slight
reduction of the energy dependence of η (by 0.2% between thermal and 2 meV).
In all the η measurements corrections have to be applied for incomplete
absorption and for multiple scattering of the incident neutrons in the U sample.
These finite sample size corrections are very small at low neutron energies,
but increase sharply as the absorption cross-section drops at energies above
0.3 eV. We will come back to this point in Section 4.
In addition, a correction must be applied for absorption and multiplicationof the emitted fission neutrons in the U sample: It depends on the place inthe sample where the primary fission event took place and therebyon the incident neutron energy. The maximum amount of this correction reaches∼3.5% for the Geel and Grenoble measurements, whereas it is smaller for
the Harwell-ORNL measurements due to the use of a detector which subtended alarger solid angle to the sample.
In contrast to the η measurements, in the α measurement performed at Geel,the count-loss and finite sample size corrections are both negligible. The method
is based on the measurement of the intensity ratio of specific low-energy capture
γ-rays and prompt fission γ-rays with a Ge-detector. However, it is based on theassumption that the relative yields of the measured γ-rays per capture and fission
event, respectively, do not vary as a function of neutron energy. This will only
be fulfilled as long as the relative contributions of different resonances to the25cross-sections do not strongly vary, i.e. only for an energy interval which issmaller than the typical resonance width. The method is thus limited to the
sub-thermal and near-thermal energy region. The main experimental uncertainty
is due to a limited statistical precision.

3. Results
With the improved determination of the various corrections as describedabove, the different data are in fairly good agreement for neutron energies below∼0.3 eV. At higher energies some problems remain; they will be further
discussed in Section 4.
In the “low-energy region” we attempted to produce a “best curve”
representing the general behaviour of the experimental data. This was carried out
by a simultaneous R-matrix fit of the fission and capture cross-sections of 235U
obtained from the following experiments:• Fission cross-sections data of Wagemans et al. [7],• η data from the experiments at Geel, Grenoble, and the Harwell-ORNL
data,• α data from Geel.
The Reich-Moore R-matrix routine MULTI [8] was used to carry out the fit
to the data over the energy range 1.5 to 300 meV. We started from the resonanceparameters as given by Leal et al. [9], omitting however the states at -3.49 and-1.50 eV as they were found to have very little effect on the cross-sections. We
then iterated on the parameters of the resonances between -1.0 and 1.5 eV. The
best overall fit to the data was obtained for the parameter set given in Table B-1.

26

Table B-1 Resonance parameters obtained from the R-matrix fit
E [eV]

[meV]

[meV]

[meV]

–0.406535.6

0.1339–1.281–191.43–0.01730.07

5.35 E-06

–3.31

0.68

4

0.284842.85

4.749E-03

107.4–4.8753

1.141862.92

17.03 E-03

104.

4

0.107

[meV]

J

η-values calculated from the R-matrix fit are compared with someof the experimental data in Figure B-1a. The left part of Figure B-1a shows
the calculated η (full curve) together with the experimental data fromthe Grenoble measurement (circles) and with η as calculated from the measured
α values of the Geel α experiment (crosses). The broken curve represents η
as calculated by NJOY from the resonance parameters of Leal et al. The rightpart of Figure B-1a shows the same curves together with the experimental datafrom the Harwell-ORNL measurement. The error bars indicated in Figure B-1a
only represent statistical errors.
It is seen that the R-matrix fit of Figure B-1a is a good representation of bothsets of data, especially at sub-thermal energies. It is also valid for the data fromthe earlier Geel η experiment (not shown), except for the lowest energies(E < 3meV) where background problems were severe. There is a slightsystematic difference between this fit and the data in the 70-to-100-meV region,
from the Grenoble and the Harwell-ORNL experiments. However,this difference is within the systematic uncertainties. The decrease of η fromthermal energy to 2 meV as represented by the fit curve is 1.6%.
Figure B-1b shows the difference between the R-matrix fit and the experimental data of Figure B-1a. On the same scale, Figures B-1c and B-1d show
the most important systematic uncertainties of the experimental data originatingfrom the various sources discussed above. The numbers indicated in the figures
have the following meaning:
1) Uncertainty due to background errors in the measurement of fission
neutrons from the U sample,
2) Uncertainty due to background errors in flux measurement,27

Figure B-1
a Experimental η data and R-matrix fit
b Difference between fit curve and datac & d various systematic uncertainties
left column refers to data from Grenoble (and Geel-α) experimentright column to Harwell-ORNL experiment283) Uncertainty due to possible changes in the shape of the incident neutron
spectrum,4) Uncertainty in the determination of count loss corrections,5) Uncertainty in the correction for absorption and multiplication of fission
neutrons,
6) Change in the finite sample size correction due to the addition of 1 b to
the 235U total cross-section,7) Change in the finite sample size correction due to the addition of 1 b to
the 235U scattering cross-section.
It is seen from Figure B-1 that differences between the present fit curve andthe experimental data are generally smaller than the combined systematic
uncertainties, with the possible exception of the lowest data point fromthe Grenoble experiment. Furthermore, it is seen that the most importantsystematic uncertainties in the left (Grenoble) and right (Harwell-ORNL)
columns of the figure originate from different sources: count loss corrections for
the Grenoble case, backgrounds for the Harwell-ORNL one. The fact that thereis nevertheless fair agreement now between these two data sets adds additional
confidence in the final result.

4. Problems at higher energies.
At energies above 0.3 eV essentially, only the Harwell-ORNL measurementson the thickest sample yield potentially useful data. For the early Geelmeasurements final sample size corrections become too large and dependent on
the input cross-section values, whereas the Geel α measurements become
unreliable because of the reason previously mentioned in Section 2.
At Grenoble, no neutron was available above about 0.15 eV.
From a preliminary analysis of the Harwell-ORNL data it seems that η would
be significantly smaller than those resulting from the evaluation of Leal et al. in
the region between 0.3 and 1 eV. However, finite sample size corrections
become very large above 0.3 eV also for the Harwell-ORNL data. They dependon the cross-sections used in the calculation, and especially on the assumed
value of the scattering cross-section. Various changes to the evaluated crosssections in the region of about 0.3 to 1 eV were used in the calculation of the29corrections in order to get agreement between the values of η determined frommeasurements on the three sample thicknesses. One of the least controversial
modifications was to increase the elastic scattering cross-section by between 1
and 2 barns, keeping α and the total cross-section fixed. With such a
modification resultant η-values would increase, but not by an amount sufficientenough to reach agreement with the evaluation of Leal et al.
On the other hand, inspecting the evaluation of Leal et al. in the low-eV
region, two observations can be made:1) In the minima between resonances the fission cross-section calculated
from the resonance parameters stays slightly higher than the data points;
2) The average radiative width given by Leal et al., i.e.

Γγ = 36meV ,is significantly smaller than in earlier evaluations. Both these observations
indicate that η-values deduced from this evaluation may be slightly on thehigh side.
In view of these circumstances, it seems to us that a re-evaluation of all crosssections and resonance parameters in the lower-eV region, taking into accountthe data obtained in the Harwell-ORNL η measurements, might be worth-while.
Modified cross-sections, especially for elastic scattering, resulting from such a
re-evaluation might lead to improved calculations of correction factors for the η
measurements in the region above 0.3 eV. At present no definite η-value can begiven for this energy region.

5. Conclusion
According to what has been said previously, we believe that below ∼0.2 eVthere is good agreement now between the different experiments measuring
the neutron energy dependence of η for 235U, and that the R-matrix fit shown in
Figure B-1 is a good representation of these data. Possible modifications of
the parameters of higher energy resonances will only have a minor effect on
the fit below 0.2 eV. However, at higher energies some further investigations arenecessary, possibly a re-evaluation of the lower resonance region. This lies
beyond the scope of the present Subgroup.
The present shape of η in the thermal and sub-thermal energy regions havebeen recently used at Saclay [10] in a sophisticated re-analysis of the KRITZ and
JAERI temperature coefficient experiments. The computed value30

of the temperature coefficient which is mainly sensitive to the low-energy shapeof η is now in good agreement with the measurements: The difference between
the computed temperature coefficient and the measured one is reduced to-0.2×10-5/°C in the case of the KRITZ experiment and to -0.6×10-5/°C for the
JAERI experiment, as compared with 3 and 4×10-5/°C for a flat shape of η [10].

References[1]

A. Santamarina and H. Tellier, Proc. Intern. Conf. on Nuclear Data for
Science and Technology, Mito 1988, p.47 – JAERI Tokyo 1988.

[2]

M.C. Moxon, J.B. Brisland and D.S. Bond, Proc. Intern. Conf. on Nuclear
Data for Science and Technology, Mito 1988, p.75 – JAERI Tokyo 1988;
M.C. Moxon, private communication.

[3]

J.A. Wartena, H. Weigmann and C. Burkholz, Report IAEA Tecdoc-491(1987) p.123.

[4]

H. Weigmann, P. Geltenbort, B. Keck, K. Schreckenbach and
J.A. Wartena, Proc. Intern. Conf. on the Physics of Reactors, Marseilles
1990, Vol. 3, PI, p.33.

[5]

M.C. Moxon, J.A. Harvey and N.W. Hill, “The Measurement of η for 235U
in the Neutron Energy Region below 300 meV (TBP)”.

[6]

H. Weigmann, J.A. Wartena and C. Burkholz, Proc. Intern. Conf. on
Nuclear Data for Science and Technology, Jülich 1991, p.38,– Springer Verlag, Berlin Heidelberg 1992.

[7]

C. Wagemans, P Schillebeecks, A.J. Deruytter and R. Barthelemy,
Proc. Intern. Conf. on the Physics of Reactors, Marseilles 1990, Vol. 1,
III, p.9.

[8]G.F. Auchampaugh,
LA-5473-MS, 1974.

[9]

L.C. Leal, G. de Saussure, and R.B. Perez, Nucl. Sci. Eng. 109 ( 1991 ) 1.

Los

Alamos[10] H. Tellier, private communication 1994.

31

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