© Copyright, 2009 CEA

Rapport CEA-R-6227 -CEA Cadarache*Direction de L’Énergie Nucléaire
Département d’Études des Réacteurs
Service de Physique des Réacteurs et du Cycle
Laboratoire d’Études de Physique

UNRESOLVED RESONANCE RANGE CROSS SECTIONPROBALITY AND SELF SHIELDING FACTORSby

Jean-Christophe Sublet *Roger N. Blomquist(Argonne National Laboratory, USA)
Sedat Goluoglu(Oak Ridge National Laboratory, USA)
Robert E. MacFarlane(Los Alamos National Laboratory, USA)

- Juillet 2009 -RAPPORT CEA-R-6227 – Jean-Christophe Sublet, Roger N. Blomquist, Sedat Goluoglu,
Robert E. MacFarlane«Sections Efficaces dans le Domaine non-résolu, Tables de Probabilités et Facteurs d’Auto
Protection»
Résumé - Les méthodes et performances de quatre codes de traitements sont comparées dans ledomaine non-résolu d’une sélection d’évaluations. Les évaluations ont été choisies de manière à
faire un bilan de ce que contiennent les bibliothèques majeures telles que, ENDF/B-VII ou JEFF3.1.1. Les résultats comparatifs sont accompagnés d’études détaillées concernant les formats etformalismes utilisés ainsi que leur interprétation au travers des codes de traitements.
Après quelques itérations, les résultats montrent un assez bon accord en ce qui concerne lessections efficaces à dilution infinie. De bien plus large différences apparaissent quand lessections effectives auto-protégées sont comparées. Les sections à dilution infinie sont souvent
bien graphiquement connues, cependant ce sont les sections effective auto protégées dérivées destables de probabilités qui sont réellement utilisées et interprétées par les codes de transport et decriticité dans ce domaine en énergie. Cette étude suggère que les formats et formalismes utilisés
dans le domaine énergétique non-résolu des évaluations existantes soient révisés et toutes
ambiguïtés levées. Il serait aussi souhaitable que le calcul des sections effectives auto-protégées
par les différents codes converge avec une précision accrue.
2009 – Commissariat à l’Énergie Atomique – France
RAPPORT CEA-R-6227 – Jean-Christophe Sublet, Roger N. Blomquist, Sedat Goluoglu,
Robert E. MacFarlane«Unresolved Resonance Range Cross Section, Probability Tables and Self Shielding
Factors»
Abstract - The performance and methodology of four processing codes have been compared in
the unresolved resonance range of a selected set of isotopes. Those isotopes have been chosen toencompass most cases encountered in the unresolved energy range contained in major libraries
like ENDF/B-VII or JEFF-3.1.1. The code results comparison is accompanied by data format
and formalism examinations and processing code fine-interpretation study.
After some improvements, the results showed generally good agreement, although not perfectwith infinitely dilute cross sections. However, much larger differences occur when shelf-shielded
effective cross sections are compared. The infinitely dilute cross section are often plot checked
but it is the probability table derived and self-shielded cross sections that are used andinterpreted in criticality and transport calculations. This suggests that the current evaluation data
format and formalism, in the unresolved resonance range should be tightened up, ambiguities
removed. In addition production of the self shielded cross sections should be converged to amuch greater accuracy.
2009 – Commissariat à l’Énergie Atomique – France

ISSN 0429 - 3460

Rapport CEA-R-6227-

Unresolved Resonance Range Cross Section, Probability
Tables and Self Shielding Factors

byJean-Christophe Sublet (CEA, DEN, Cadarache, France)
Roger N. Blomquist (Argonne National Laboratory, USA)
Sedat Goluoglu (Oak Ridge National Laboratory, USA)
Robert E. MacFarlane (Los Alamos National Laboratory, USA)

June 11, 2009

© Copyright, 2009 CEAi

Abstract
The performance and methodology of four processing codes have been compared in theunresolved resonance range of a selected set of isotopes. Those isotopes have beenchosen to encompass most cases encountered in the unresolved energy range containedin major libraries like ENDF/B-VII or JEFF-3.1.1. The code results comparison isaccompanied by data format and formalism examinations and processing code fineinterpretation study.
After some improvements, the results showed generally good agreement, although not
perfect with infinitely dilute cross sections. However, much larger differences occur
when shelf-shielded effective cross sections are compared. The infinitely dilute crosssection are often plot checked but it is the probability table derived and self-shieldedcross sections that are used and interpreted in criticality and transport calculations. Thissuggests that the current evaluation data format and formalism, in the unresolved
resonance range should be tightened up, ambiguities removed. In addition productionof the self shielded cross sections should be converged to a much greater accuracy.

Sections Efficaces dans le Domaine Non-Résolu, Tables deProbabilités et Facteurs d’Auto Protection
Résumé
Les méthodes et performances de quatre codes de traitements sont comparées dans ledomaine non-résolu d’une sélection d’évaluations. Les évaluations ont été choisies demanière à faire un bilan de ce que contiennent les bibliothèques majeures telles que,
ENDF/B-VII ou JEFF-3.1.1. Les résultats comparatifs sont accompagnés d’études
détaillées concernant les formats et formalismes utilisés ainsi que leur interprétation au
travers des codes de traitements.
Après quelques itérations, les résultats montrent un assez bon accord en ce qui concerne
les sections efficaces à dilution infinie. De bien plus large différences apparaissent quand
les sections effectives auto-protégées sont comparées. Les sections à dilution infinie sontsouvent bien graphiquement connues, cependant ce sont les sections effective auto
protégées dérivées des tables de probabilités qui sont réellement utilisées et interprétées
par les codes de transport et de criticité dans ce domaine en énergie. Cette étude suggère
que les formats et formalismes utilisés dans le domaine énergétique non-résolu desévaluations existantes soient révisés et toutes ambiguïtés levées. Il serait aussi souhaitable
que le calcul des sections effectives auto-protégées par les différents codes converge avec
une précision accrue.

iiDisclaimer
Neither the authors nor CEA, ANL, ORNL or LANL accepts responsibility for consequences
arising from any errors either in the present documentation or in the cross section libraries
and tables therein described.

Acknowledgements
The authors would like to acknowledge the instrumental and constructive contributions of D.
E. Cullen (Lawrence Livermore National Laboratory) and C. R. Lubitz (Knolls Atomic
Power Laboratory). One author (JCS) wishes to acknowledge the contributions of P. Ribon(CALENDF’s real father)

Corresponding author: jean-christophe.sublet@cea.friii

Tables of contents
Abstract ..............................................................................................................................ii
Résumé...............................................................................................................................ii
Disclaimer ........................................................................................................................ iii
Acknowledgements.......................................................................................................... iii
1
Introduction........................................................................................................................1
2
Unresolved resonance range computation .........................................................................1
3 Unresolved range parameters interpretations and formalism sensitivity...........................44
Methods used by CALENDF.............................................................................................6
5
Effective cross sections comparisons.................................................................................9
5.1
Summary of the methods used in NJOY....................................................................9
5.2
Summary of the methods used in AUROX................................................................9
5.3
Summary of the methods used in PURM ................................................................10
5.4
Pu238 UR cross sections..........................................................................................11
5.5
Pu239 UR cross sections..........................................................................................14
5.6
Pu240 UR cross sections..........................................................................................18
5.7
U-233 UR cross sections..........................................................................................21
5.8
U-238 UR cross sections..........................................................................................24
5.9
W-184 UR cross sections.........................................................................................28
6
Conclusions......................................................................................................................30
References........................................................................................................................32
Appendix A......................................................................................................................33
Appendix B ......................................................................................................................36

Table 1 UR file 2 parameters interpretation ..............................................................................3

Figure 1 UR cross sections comparisons – 4 codes ...................................................................2
Figure 2 U-238 CALENDF inelastic effective cross section.....................................................3
Figure 3 U-238 CALENDF capture effective cross section ......................................................3
Figure 4 Pu239 CALENDF effective cross section...................................................................4
Figure 5 Pu240 NJOY effective cross section ...........................................................................4
Figure 6 Water sphere neutron spectrum, S.D. 0.06% in the UR ..............................................6
Figure 7 Solid sphere neutron spectrum, S.D. < 0.3% in the UR ..............................................6
Figure 8 CALENDF - NJOY pointwise data in the UR ............................................................7
Figure 9 NJOY - CALENDF “statistical” resonance in the UR................................................7
Figure 10 CALENDF ladders parametric study on elastic ........................................................8
Figure 11 CALENDF ladders parametric study on capture.......................................................8
Figure 12 Pu238 UR cross section comparison – 4 codes .......................................................11
Figure 13 Pu239 UR cross section comparison – 4 codes .......................................................14
Figure 14 Pu240 UR cross sections comparison – 4 codes .....................................................18
Figure 15 U-233 UR cross sections comparison - 4 codes ......................................................21
Figure 16 U-238 UR cross section comparison – 4 codes .......................................................24
Figure 17 W-184 UR cross section comparison – 4 codes ......................................................28iv

1 Introduction
There have been significant improvements in our capabilities to predict nuclear criticality andshielding experiments in recent years. This has been due to many factors, one of them being
improved nuclear data evaluations properly handled by our processing codes. This allows tobegun paying more attention to what always has been thought to be an important energy
range, but not too well comprehended: the unresolved energy range [1]. It is clear that thisintermediate energy range play a prominent role in many applications, not only the so called
fast ones. The tendency of neutrons to slow down from a mean fission energy indicates that itis only a passing, transitory range for the thermal driven plant but quickly becomes animportant integral response range for plants sensitive to the unresolved variety of its main
constituent isotopes. It is clear as well that cladding, shielding, coating or many structural
materials also have an unresolved resonance range that need to be accounted for.
This report is intended to be a contribution to the form of representation of unresolved
resonance regions in the ENDF-102 data format [2], and the interpretation of the format byprocessing codes. Evaluator and engineer tend to plot the cross sections versus energy mostly
infinitely dilute and rarely the self shielded form of the data. All comparisons are usually
made at that infinite dilute level although criticality or transport codes rarely use this level ofrepresentation having to account for dilution effects. Validation, qualifications andbenchmarking exercises also rely on shielded processed data to compute their results,
although their feedback and interpretation are usually weighted and applied on the infinitely
dilute level.
It is for all these reasons that we reassessed our interpretation capabilities in the unresolved
energy range, highlighting their effects on the cross sections that shape the neutron transportand criticality code computational results.

2 Unresolved resonance range computation
In the unresolved region the cross sections are computed from file 2 (resonance parameters)
and file 3 (cross sections) following the rules set in the ENDF-102 Data formats andprocedures for ENDF data file report [2]. It stipulates that in this energy range only Single
Level Breit-Wigner SLBW formalism is allowed. However several options are available for
specifying the energy dependence of the parameters. Let us only consider the energydependent UR format (LRF=2). It provides average resonance parameters on a grid ofenergies and an interpolation code INT. The current ENDF procedures say that one should
compute the unresolved cross sections at these energy grid points. Intermediate values are tobe obtained by interpolating on the cross sections using the scheme defined by INT. Thisapproach has the advantage of being economical in the UR calculation and of giving a uniqueresult for the cross sections. However, the cross sections that it produces have discretesegments that show up as straight unphysical lines when plotted according to INT.
The PREPRO processing code [3] computes new parameters at intermediate energies using
the interpolation law INT, and then it uses these new parameters to compute the crosssections at the intermediate points. It continues subdividing intervals until it ends up withlinearly interpolated cross sections on a finer grid that are within a specified tolerance of the
shape that comes from the UR formulas. This deviation from the rules stems from the factthat another recommendation made in the ENDF-102 manual is largely ignored by the1evaluators. They also should supply parameters on a dense enough grid to insure no
significant difference (percent levels) between parameter or cross section interpolation. In
interpolating the parameters to a finer grid the processing code compensates for crude andnon ENDF-102 compliant unresolved resonance range parameters sets. Those findings have
led to a modifications proposal [4] made in 2009 to the ENDF-102 governing board.

Figure 1 UR cross sections comparisons – 4 codes

The NJOY [5] results quoted in this study embed this new recommendation, in contrast to
earlier pre NJOY-259 versions (giving results similar to AUROX), having been computedwith the -296 version of the code, while it can be seen from Fig. 1 that neither AUROX [6]nor PURM [7] did it yet, nothing in principal would stop them to do so in the near future.
It should be clear also that the CALENDF [8] method and philosophy are more in line with
the PREPRO ones, although this particular code takes rather different approaches.
To weigh the effects of the UR parameters interpretations, it is useful to examine the existing
ENDF/B-VII [9] evaluations to see how they are affected by those issues and to see how
serious interpretation problem might be in practice. The factors that influence this include
how many energy grid points were used, what the step size is between two energies, whatvalue was used for INT, and how smoothly the parameters vary with energy.
Evaluations with smoothly varying parameters were developed based on theory andsystematics with a minimum of adjustment to experiment. They make up the large majorityof the ENDF/B-VII evaluations. In the selected set of evaluations of Tables I, these will belabeled with a shape of constant or lin-lin. In a few cases, parameters were adjusted to fit
high resolution experimental data. Those parameters normally fluctuate strongly and don’t
show a smooth variation with energy. They are labeled as “rough” in the tables. Anothercomplication comes from competitive reactions like inelastic scattering. Then the competitive
Γx width can vary strongly even though the other parameters are smooth. The ENDF-102
LSSF flag indicates, when equal to 1, that the file 2 parameters are to be used uniquely for
shelf-shielding the cross section that are normalized to the values contained in file 3.
Computation of the effective cross section in the unresolved range may be done in different
ways. The first is direct calculation with Bondarenko [5] self-shielding factors or effective
cross sections derived from the probability tables with their own self-shielding factors. The
2

second route, cross section production, employed in this study, is actually our most applicablecalculation. One needs to keep in mind that the effective cross section may strongly varywith dilution but also differentially from one channel to another.
Table 1 UR file 2 parameters interpretation

Evaluation
W-184
U-233
U-238
Pu-238
Pu-239Pu-240UR range (eV)2.65E+03- 1.00E+05
6.00E+02- 4.00E+04
2.00E+04- 1.49E+05
2.00E+02- 1.00E+04
2.50E+03- 3.00E+04
5.70E+03- 4.00E+04

Points/decade3 / 2.5
17
18
constant
48
constant

INT
5
2
5

LSSF

2

1
1

Shape
lin-linrough
lin-lin, Gxrough

The following Figs. 2 to 5 show the computation from CALENDF and NJOY of probability
tables derived effective cross sections at different dilutions, highlighting those differencesand exemplifying the effects.

Figure 2 U-238 CALENDF inelastic effective cross section

Figure 3 U-238 CALENDF capture effective cross section

3

Figure 4 Pu239 CALENDF effective cross section

Figure 5 Pu240 NJOY effective cross section

In the U-238 the energy dependant self-shielding factors varies from 11, 13 and 5 % forrespectively the elastic, capture and inelastic cross section in-between 20 to 150 KeV. For the
Pu239 the same channels experience variation of 12, 32 and 0 % in-between the energies of
2.5 and 30 KeV.

3 Unresolved range parameters interpretations and formalism
sensitivity
The unresolved resonance range treatment in ENDF has never been improved since it was
defined in the 80’s, and contains some ambiguities. The fact that only a single formalism isallowed, Single Level Breit-Wigner already caused some concern [10]. This is particularly
true if differences are the results of altered resonance shapes or forbidden additional
reactions, and not due merely to changes in the allowed underlying dilute-average crosssections.
4In order to gain insight into the importance of the resonances shapes and depressions, anddifferent formalisms, the following calculational benchmark has been devised. The
CALENDF code has been modified to allow for a user choice of the formalism used in theunresolved resonance range. The choices include: Single Level Breit-Wigner, Multi Level
Breit-Wigner, Breit-Wigner, and Reich Moore with a flag to set on and off accounting forexternal resonances. It should be understood that the original evaluation parameters are notmodified in any way, just the way they are going to be interpreted is adapted. Modified
ENDF/B-VII evaluations have been created with non-zero fission spectra only, in theunresolved resonance range of each isotope. This is done in order to isolate the effects ofinterest from differences in slowing down. It in fact maximizes the effect of resonances
shapes.
When using the Monte Carlo code TRIPOLI [11] one can choose, or not, to sample
CALENDF probability tables in and only the unresolved range of an evaluation. Without
probability table sampling, the code access the smooth NJOY unresr data contained in the
pointwise processed file. So for each “new” evaluation, one has a choice of fourinterpretations in and only the unresolved range that will be refer as:
MNBW
SLBW
RM
infd

= Multi Niveau Breit-Wigner CALENDF interpreted PT’s
= Single Level Breit-Wigner CALENDF interpreted PT’s
= Reich Moore CALENDF interpreted PT’s
= no PT’s, smooth NJOY unresr infinitely dilute cross section

A single geometry is used, a 30 cm sphere filled independently with two types of materials:
H2O (ENDF/B-VII) plus one isotope or the isotope alone. With 100 millions (1.0x108)
histories and the Red-616 group structure, the neutron source is also been sample in a flat
spectra within the unresolved range.
The results on U-238 with different formalism interpretation in the unresolved resonancerange are show for a water sphere in Fig. 6 and a solid sphere in Fig. 7. It clearly
demonstrates that, with respect to the fact that the parameters are identical, only theirformalisms interpretations are different- Whatever the formalism, the shape impact is negligible, when a moderator is present.
- In a solid fuel, large difference exists between results with and without probability
treatments, and this whatever the formalism.
Other base fuels, U-235 and Pu239 and moderator Na and Carbon have also been studied
leading to the same conclusions.
This demonstrates that in the unresolved resonance range, the formalism is not so important,but it needs to be accompanied by a probability table treatment in order to allow the transport
code to better represent reality. This is said with the knowledge that only one probability code
has been used in this study, and that other processing codes may interpret differently, as it
will be shown later, the same data parameter file. The end results derived from them may
differ slightly.
The impact of opening other, forbidden channels has not been assessed in this calculational
benchmark.

5

Figure 6 Water sphere neutron spectrum, S.D. 0.06% in the UR

Figure 7 Solid sphere neutron spectrum, S.D. < 0.3% in the UR

4 Methods used by CALENDF
The code works with a set of energy groups defined across an energy range, in the unresolved
resonance range (URR). Based on the average resonance parameters and the required
accuracy, CALENDF defines energy zones adapted to the group structure. A 616 groupstructure, 50 bins per energy decades, equally spaced in the log of energy between, 10-5 and20 MeV, coded Red-616 (Appendix A), is used in this study. If the group structure is coarse,
several discontinuous zones are selected. If the structure is fine, a zone may cover several
groups. Average parameters are computed for each zone using file 2 of the evaluation.
Random ladders of resonances are generated with energies extracted from a table of 1185
values that are the eigenvalues of a random matrix (Dyson and Mehta) and with resonancewidths chosen from the distribution laws with stratified and antithetic sampling. A few
resonances are added below and above the range of the energy zone to handle edge effects.
6

The cross sections for each ladder are computed on a fine energy grid using the MNBW
formalism (Multi Niveau Breit-Wigner, MNBW, is a slightly modified Multi Level BreitWigner treatment) and psi-chi Doppler broadening. There are no normalizations done except
for the cases with LSSF=1. The moments of these cross-sections are computed, and theprobability tables deduced from them. The table orders will mainly depend on the required
accuracy, with a maximum of 11. The probability tables for all zones and ladders are merged
to get the final table for each energy group. The Gauss-quadrature mathematical principle
gives those probability tables their sturdiness, allowing many utilitarian operations such astable condensation, isotope mixing, or interpolation.
Figs. 8 and 9 illustrate some features of the performance of the CALENDF methods whengenerating resonant pointwise cross section in the unresolved range of an evaluation andcomparing it with the NJOY unresr module results; smoothed averaged structure against
statistically generated resonances. Below, in the resolved resonance range or above in thecontinuum, both codes lead to the same cross section levels.

Figure 8 CALENDF - NJOY pointwise data in the UR

Figure 9 NJOY - CALENDF “statistical” resonance in the UR

7

In Figs. 10 and 11, showing W-194 elastic and capture cross sections, the large oscillations in
the CALENDF probability table derived effective cross sections are caused by using definitegroup bounds for each sampling step, in this case 616 groups. The oscillations amplitudes aredifferent from one channel; elastic with up to 40%, to another; capture with only 20%. They
gradually go away when more ladders are averaged in (from 4 to 128 ladders) or whenapproaching the continuum, and integral results becomes reasonable, even with the statisticaloscillations in the detailed cross sections. An optimum number of 16 ladders, for a crosssection reconstruction accuracy of 0.02% has been assessed and used in this study.

Figure 10 CALENDF ladders parametric study on elastic

Figure 11 CALENDF ladders parametric study on capture

However, it ought to be said that even if one can see a better, more physically eye-pleasing
agreement with 16 ladders and of course with the results of the other codes as well, this may
still conceal problems. A code adopting a Gaussian orthogonal ensemble (GOE) tocharacterize the distribution of resonance energies (in contrast to a Wigner distribution) andusing a single, well stratified, random sampling may be more realistic.

8

5 Effective cross sections comparisonsHere are comparisons of the results from four different processing codes; NJOY-PURR,CALENDF, AUROX and PURM on the six evaluations described in Table I. Those isotopes
have been chosen to encompass most cases encountered in the unresolved energy range of
any ENDF/B-VII or JEFF-3.1.1 evaluations. In a major library, like ENDF/B-VII containing
393 isotopes, it is interesting to account for the fact that 252 of them have a declaredunresolved energy range (140 for JEFF-3.1.1). The minimum energy encountered for anunresolved range is 1 eV and the maximum is 1 MeV.
What was asked of the participants were all unresolved range cross-sections in the unresolved
range of those six ENDF/B-VII evaluations, at 293.6 Kelvin, both infinitely dilute, and 1
barns, in simple 2E11.4 column format. However simple this may seem, it took quite a few
iterations to finalize the series of graphs in this section.
To understand the differences it is useful to summarize the methods used for the unresolved
resonances range in the various codes, but for CALENDF used as a reference, not a standard,
which methods have already been described.

5.1 Summary of the methods used in NJOY
The probability tables are generated using the PURR module of NJOY [5]. For each energy
given in the evaluation, the parameters for a long series (or “ladder”) of resonances areconstructed using Wigner spacing for resonance centers and the chi-squared distributions
from the evaluation for resonance widths. The code then randomly selects an energy in therange of the series and computes the cross sections at that point using Single-Level BreitWigner (SLBW) resonance shapes and psi-chi Doppler broadening. In the beginning, it does
this for a number of random energies to get a rough idea of the distribution of the total crosssection; it then analyzes this rough idea to construct a set of total cross section bins for the
rest of the process (typically, 20 bins are used). It then returns to the first ladder and samples
it with random energies. The resulting total cross sections are added to the appropriate bin in
the probability table, and the conditional averages for scattering, fission, and capture are
accumulated in the bin corresponding to the total cross section. The code then constructs a
new ladder and repeats the sampling process. This is continued for the requested number ofladders (in this case study 128). For materials with the ENDF LSSF parameter set to zero,
the table cross sections are renormalized to match the computed infinitely dilute values. For
LSSF=1, the values in the table are converted to self shielding factors, and then transport
code multiplies these factors times the cross sections from the standard ENDF file to get theappropriate value. Note that there are no energy bounds (such as group bounds) in thisprocess. Therefore, it computes cross sections that have basically the same smoothness as theunresolved resonance range evaluation.

5.2 Summary of the methods used in AUROXThe unresolved resonance processing code, AUROX [6], uses the ladder method, but with
unoptimized standard bins, some of which are always empty during the ladder sampling
process. Cross sections are computed from the SLBW parameters and Doppler broadened
9with the psi-chi method. Ladder sampling continues until the statistical convergence of theresonance components of the average total, elastic, fission, and capture cross sections (2%),
or when 500 ladders have been sampled. Each table is then collapsed to 20 bins whoseboundaries are optimized on equal probabilities. In the transport code, elastic, capture, andfission cross sections are treated using conditional means, i.e., a total cross section sampledfrom a table is associated with a set of mean partial cross sections. The LSSF parameter
determines whether the cross sections sampled from the table are added to the file 3 data orused as self-shielding factors.

5.3 Summary of the methods used in PURM
PURM (Probability tables for the Unresolved Region using Monte Carlo) [7] is a module thatuses a Monte Carlo approach to calculate probability tables on an evaluator-defined energy
grid in the unresolved-resonance region (URR). For each probability table, PURM samples
pairs of resonances surrounding the reference energy. The resonance distribution is sampled
for each spin sequence (i.e., L-J pair), and PURM uses the Dyson and Mehta Δ3 statistics test
to determine the number of resonances to sample for each spin sequence. For each resonance,
PURM samples the resonance widths from a Chi-square distribution for a specified numberof degrees of freedom. Once the resonance parameters are sampled, PURM calculates thetotal, capture, fission and scatter cross sections at the reference energy using the Single-level
Breit-Wigner formalism with appropriate treatment for temperature effects. The energy crosssection calculation constitutes a single iteration or history. For the cross-section calculationand corresponding probability-table calculation, PURM processes a user-specified number ofbatches with a corresponding number of histories per batch. For each history, PURM
calculates the total, capture, fission, competitive reaction and scatter cross section at thereference energy, and the corresponding contribution to the capture, fission, scattering andcompetitive reaction probability table is determined for each history. Total is re-calculated assum of partial reactions including inelastic given as competitive. After completing thespecified number of histories for a batch, a batch estimate for the probability for each crosssection band within a table is obtained by dividing the number of tallies for the band by the
total number of histories processed. Additional batches are processed until the user-specified
number of batches is complete. Due to the nature of the calculational procedures, PURM
provides a mechanism for monitoring the convergence of the cross-section calculation. For
each reaction, a plot of the calculated cross section is provided by batches run.
The resulting cross sections in the probability table are renormalized such that the averagevalue of a cross section (total, fission, capture, elastic and competition) is equal to the infinite
dilute value for that cross section.

10

5.4 Pu238 UR cross sections
The next figures show the comparison of effective cross sections, total, elastic, capture andfission infinitely dilute, then at 1 barn for the 4 codes. It shows the unacceptably large
differences that can occur when the processing codes interpolate the cross section (PURM,
AUROX) in-between the evaluator given energy grid or the parameters (NJOY, CALENDF).
In this particular case, the self- shielded cross sections show some significant differences not
all well understood. Earlier anomalous results for capture have been traced to an obscurecode bug in AUROX, now corrected. We believe this kind of inter-comparison is very useful
because it highlights both processing code bugs and the effects of modeling differences.

Figure 12 Pu238 UR cross section comparison – 4 codes

11

12

13

5.5 Pu239 UR cross sections
The next figures show the comparison of effective cross sections, total, elastic, capture andfission infinitely dilute, then at 1 barn for the 4 codes. A much better agreement thanpreviously can be seen in the infinitely dilute cross section. AUROX was missing the 3.55
KeV data point but was corrected during this study and this was leading to a peaked 17.7%
differences. CALENDF methods tend to smooth averages across a band that includes therough 100 eV width parameters given in the file 2. Those large step fluctuations, qualified as
gross structures by the evaluator raise some questions on their validity and concern over theirinterpretation. The above 8 KeV differences can be trace back to the presence of an MF-3,
MT-51, inelastic level that is only accounted for in the CALENDF probability tables, but thennot shelf-shielded. MF-3 cross section can be read independently from file two, although careshould then be taken in calculating the total. Here again the PURM 1 barn self-shielded crosssection departs from results of the others codes.
Figure 13 Pu239 UR cross section comparison – 4 codes

14

15

16

Even for CALENDF, the inelastic channel read from file 3 cannot be shelf-shielded because
there are no Γx in the file 2. However, nothing would prohibit using the self-shielding factorsof the total to account for it.

17

5.6 Pu240 UR cross sections
An even much nicer agreement is seen on the infinitely dilute unresolved resonance range
cross section for this isotope, in line with what ought to be expected. Earlier 1 barn PURM
results departed by values ranging from 20 to 30% from results of the other codes, however
the code has been corrected in the course of this study, making the comparison morereasonable.
Figure 14 Pu240 UR cross sections comparison – 4 codes

18

19

20

5.7 U-233 UR cross sections
This is the first of the two LSSF=1 evaluations considered here, in which the cross sections
are given in file 3 and should not be computed. As expected, only negligible differences
occur with CALENDF results plotted on a group structure different from the energy grid atwhich the cross sections are given. Self shielded 1 barn cross section comparison also agree
remarkably well but for the PURM results that can derive by up to 20%.
Figure 15 U-233 UR cross sections comparison - 4 codes

21

22

23

5.8 U-238 UR cross sections
This is the second of the two LSSF=1 evaluations, and, of course, a rather important one. The
circa 1% differences between the CALENDF results and all the others are also due to thegroup structure differences that appear in the resolved range at the lowest energy and thecontinuum at the highest. It is interesting to note that this occurs only for the total and elastic
channels. As a point of reference, and if PURM results are set aside, NJOY-PURR, AUROX
and CALENDF agree within a 1% in computing the total, elastic and capture 1 barn effective
cross sections of U-238. One may notice that here again, only CALENDF includes theinelastic channel from its probability tables and self-shield it as well with the competitive
widths found in the file 2. This is unique behavior amongst these codes and perfectlylegitimate (but often overlooked) by the ENDF-102 data format.
Figure 16 U-238 UR cross section comparison – 4 codes

24

25

26

27

5.9 W-184 UR cross sections
This is the only non-fissionable isotope compared in this work, and it is included tounderstand better our interpretation of a broad and shaped unresolved range. Here,CALENDF departs notably from the other codes in its cross section interpretation. It samples
the parameters at deeper levels, and the results show more pronounced structure. Still, thefour different codes’ broad group averages show rather good agreement across this twodecade energy range. As before the humps demonstrate the impact of a cross section against
parameters interpolations. It is notable in this case that the differences seen in the 1 barn selfshielded comparison do not show any clear pattern or trend, with differences rather uniform
at around 20% levels.
Figure 17 W-184 UR cross section comparison – 4 codes

28

29

6 Conclusions
The primary conclusion is that these four processing codes usually agree within a target
accuracy of 1% for both infinitely dilute and 1-barn self-shielded effective cross sections(with the exception of PURM) when the parameters files data and ENDF-102 rules have been
properly and consistently interpreted by both the evaluators and those who processed thedata. In our comparison, this only occurred on one fourth (1/4) of the evaluations, and whenthe LSSF=1 flag has been properly used. In all other cases, and due to a lack of clarity andconstraints in the ENDF-102 data format, both infinitely dilute and self-shielded cross section
results from those four codes can diverge significantly; well above the few percent frequently
tolerated in this range for cross section averages and pointwise data. These variations ininterpretation lead to some large differences between transport codes’ results due to the crosssections. There seems to exist no one transport code that can make use of the output from
more than one of theses processing codes (see Appendix B) and so singularly test theirdifferences.
A secondary conclusion derives from the fact that processing codes have to palliate the data
format deficiencies, either because the format rules have not been well defined, have beeninterpreted differently, or are inconsistent or unphysical. Typically, in the cases here,
parameter interpolation gives better physical results than cross section interpolation based onfile 2 interpolation specifications. Inconsistently applied unresolved resonance range
parameters file will inevitably lead to different results.
Another secondary conclusion is that when the rule or data set are not properly pinned down,
the processing codes will inevitably be developed to compensate. This is the case here when
CALENDF, having read in the competition widths from U-238 file 2, is making use of themin self-shielding the inelastic competition. It is the only one of these processing codes doingso.
This study focuses on the data derived from probability table treatment in the unresolved
resonance range, mostly but not uniquely used by Monte Carlo codes. Other self-shielding30

methodologies that can be used in this range and below by other method may lead to evengreater differences.
This study shows a clearer way forward on the issues of data formats, formalisms, andinterpretation in the unresolved resonance range The ENDF-102 rules should be modified
along the following lines:
•
•

•
•
•

Privileges, enforces LSSF=1 formalism (self-shielding from file 2, cross section in file 3).
Allow all competition channels to be open in this range, e.g., inelastic levels, directcomponents, charge particle emissions. This would make the sum-up and energy
interpolation rules clear, but would not require that everybody could or should use themall.
Account for the effect of multiple fission channels.
Allow for other formalisms in the UR : MLBW, RML.
Make the formats and specifications unambiguous.

One would like to remark at that deep level of interpretation that what is clearly written in afile is always better interpreted, although it may still be complemented and devise. What is
not there, but is needed, will have to be generated and subject to interpretation.

31

References[1] "A Code Comparison Study for the Bigten Critical Assembly", R. E. MacFarlane et al.,Los Alamos National laboratory report, LA-UR-08-4668, July 2008. Available at
http://t2.lanl.gov/publications/publications.html[2] "ENDF-102 ENDF-6 Data Formats and Procedures for the Evaluated Nuclear Data
File ENDF-VII", M. Herman, ed., Brookhaven National Laboratory report BNL-NCS44945-05-Rev., June 2005. Available at
http://www.nndc.bnl.gov/publications/publications.html#manuals[3] "PREPRO 2007: 2007 ENDF/B pre-processing Codes", Dermott E. Cullen, IAEA-NDS39, Rev. 13, March 17, 2007, Nuclear Data Section, International Atomic Energy Agency,
Vienna, Austria. Available at http://www-nds.iaea.or.at/ndspub/endf/prepro/[4] "ENDF-102 unresolved range recommendations proposal", D. E. Cullen and R.E
MacFarlane, February 2009. Available http://www.nndc.bnl.gov/csewg/formatprop.jsp[5] "The NJOY Nuclear Data Processing System, Version 91," Los Alamos National
Laboratory report LA-12740-M, by R. E. MacFarlane and D. W. Muir, (October 1994). For
latest information, see http://t2.lanl.gov/codes/njoy99.
[6] "U3R, a Code to Calculate Unresolved Resonance Cross Section Probability Tables", AIAEC-13024, by J. M. Otter, R. C. Lewis, and L. B. Levitt, July, 1972.
[7] "Calculating probability Tales for the Unresolved-Resonance Region Using Monte Carlo
Methods", M.E. Dunn and L.C. Leal, Nuclear Science and Engineering: 148, 30-42 (2004).
[8] "CALENDF-2005: User manual", J-Ch. Sublet, P. Ribon and M. Coste-Delclaux,
CEA-R-6131, ISSN 0429-3460, 2006. Available http://www.nea.fr/abs/html/nea-1278.html[9] "ENDF/B-VII.0: Next Generation Evaluated Nuclear Data Library for Nuclear Scienceand Technology", M.B. Chadwick, P. Oblozinsky, M. Herman, N.M. Greene, R.D.
McKnight, D.L.Smith, P.G. Young, R.E. MacFarlane, G.M. Hale, S.C. Frankle, A.C. Kahler,
T. Kawano, R.C. Little, D.G. Madland, P. Moller, R.D. Mosteller, P.R. Page, P. Talou, H.
Trellue, M.C. White, W.B. Wilson, R. Arcilla, C.L. Dunford, S.F. Mughabghab, B.
Pritychenko, D. Rochman, A.A. Sonzogni, C.R. Lubitz, T.H. Trumbull, J.P. Weinman, D.A.
Brown, D.E. Cullen, D.P. Heinrichs, D.P. McNabb, H. Derrien, M.E. Dunn, N.M. Larson,
L.C. Leal, A.D. Carlson, R.C. Block, J.B. Briggs, E.T. Cheng, H.C. Huria, M.L. Zerkle, K.S.
Kozier, A. Courcelle, V.Pronyaev and S.C. van der Marck, Nuclear Data Sheets, vol. 107,
pp. 2931-3060, 2006.
[10] "Methods for Calculating Cross-sections and Shielding Factors in the Unresolved
Resonance region", JEF/DOC-79, 1985. Available:
http://www.nea.fr/html/dbdata/projects/jeffdoc.html[11] "TRIPOLI 4 User guide", O. Petit, F-X. Hugot, Y-K. Lee, C. Jouanne, A. Mazzolo,
CEA-R-6169, ISSN 0429-3460, 2008. Available at http://www.nea.fr/abs/html/nea1716.html.

32

Appendix A
Here are the boundaries of the Red-616 group structure used by CALENDF.
2.00000E+07
1.73780E+07
1.44544E+07
1.20226E+07
1.00000E+07
8.31764E+06
6.91831E+06
5.75440E+06
4.78630E+06
3.98107E+06
3.31131E+06
2.75423E+06
2.29087E+06
1.90546E+06
1.58489E+06
1.31826E+06
1.09648E+06
9.12011E+05
7.58578E+05
6.30957E+05
5.24807E+05
4.36516E+05
3.63078E+05
3.01995E+05
2.51189E+05
2.08930E+05
1.73780E+05
1.44544E+05
1.20226E+05
1.00000E+05
8.31764E+04
6.91831E+04
5.75440E+04
4.78630E+04
3.98107E+04
3.31131E+04
2.75423E+04
2.29087E+04
1.90546E+04
1.58489E+04
1.31826E+04
1.09648E+04
9.12011E+03
7.58578E+03
6.30957E+03
5.24807E+03
4.36516E+03
3.63078E+03
3.01995E+03
2.51189E+03
2.08930E+03
1.73780E+03
1.44544E+03
1.20226E+03
1.00000E+03
8.31764E+02
6.91831E+02
5.75440E+02
4.78630E+02
3.98107E+02
3.31131E+02
2.75423E+02
2.29087E+02

1.99526E+07
1.65959E+07
1.38038E+07
1.14815E+07
9.54993E+06
7.94328E+06
6.60693E+06
5.49541E+06
4.57088E+06
3.80189E+06
3.16228E+06
2.63027E+06
2.18776E+06
1.81970E+06
1.51356E+06
1.25893E+06
1.04713E+06
8.70964E+05
7.24436E+05
6.02560E+05
5.01187E+05
4.16869E+05
3.46737E+05
2.88403E+05
2.39883E+05
1.99526E+05
1.65959E+05
1.38038E+05
1.14815E+05
9.54993E+04
7.94328E+04
6.60693E+04
5.49541E+04
4.57088E+04
3.80189E+04
3.16228E+04
2.63027E+04
2.18776E+04
1.81970E+04
1.51356E+04
1.25893E+04
1.04713E+04
8.70964E+03
7.24436E+03
6.02560E+03
5.01187E+03
4.16869E+03
3.46737E+03
2.88403E+03
2.39883E+03
1.99526E+03
1.65959E+03
1.38038E+03
1.14815E+03
9.54993E+02
7.94328E+02
6.60693E+02
5.49541E+02
4.57088E+02
3.80189E+02
3.16228E+02
2.63027E+02
2.18776E+02

1.90546E+07
1.58489E+07
1.31826E+07
1.09648E+07
9.12011E+06
7.58578E+06
6.30957E+06
5.24807E+06
4.36516E+06
3.63078E+06
3.01995E+06
2.51189E+06
2.08930E+06
1.73780E+06
1.44544E+06
1.20226E+06
1.00000E+06
8.31764E+05
6.91831E+05
5.75440E+05
4.78630E+05
3.98107E+05
3.31131E+05
2.75423E+05
2.29087E+05
1.90546E+05
1.58489E+05
1.31826E+05
1.09648E+05
9.12011E+04
7.58578E+04
6.30957E+04
5.24807E+04
4.36516E+04
3.63078E+04
3.01995E+04
2.51189E+04
2.08930E+04
1.73780E+04
1.44544E+04
1.20226E+04
1.00000E+04
8.31764E+03
6.91831E+03
5.75440E+03
4.78630E+03
3.98107E+03
3.31131E+03
2.75423E+03
2.29087E+03
1.90546E+03
1.58489E+03
1.31826E+03
1.09648E+03
9.12011E+02
7.58578E+02
6.30957E+02
5.24807E+02
4.36516E+02
3.63078E+02
3.01995E+02
2.51189E+02
2.08930E+02

33

1.81970E+07
1.51356E+07
1.25893E+07
1.04713E+07
8.70964E+06
7.24436E+06
6.02560E+06
5.01187E+06
4.16869E+06
3.46737E+06
2.88403E+06
2.39883E+06
1.99526E+06
1.65959E+06
1.38038E+06
1.14815E+06
9.54993E+05
7.94328E+05
6.60693E+05
5.49541E+05
4.57088E+05
3.80189E+05
3.16228E+05
2.63027E+05
2.18776E+05
1.81970E+05
1.51356E+05
1.25893E+05
1.04713E+05
8.70964E+04
7.24436E+04
6.02560E+04
5.01187E+04
4.16869E+04
3.46737E+04
2.88403E+04
2.39883E+04
1.99526E+04
1.65959E+04
1.38038E+04
1.14815E+04
9.54993E+03
7.94328E+03
6.60693E+03
5.49541E+03
4.57088E+03
3.80189E+03
3.16228E+03
2.63027E+03
2.18776E+03
1.81970E+03
1.51356E+03
1.25893E+03
1.04713E+03
8.70964E+02
7.24436E+02
6.02560E+02
5.01187E+02
4.16869E+02
3.46737E+02
2.88403E+02
2.39883E+02
1.99526E+02

1.90546E+02
1.58489E+02
1.31826E+02
1.09648E+02
9.12011E+01
7.58578E+01
6.30957E+01
5.24807E+01
4.36516E+01
3.63078E+01
3.01995E+01
2.51189E+01
2.08930E+01
1.73780E+01
1.44544E+01
1.20226E+01
1.00000E+01
8.31764E+00
6.91831E+00
5.75440E+00
4.78630E+00
3.98107E+00
3.31131E+00
2.75423E+00
2.29087E+00
1.90546E+00
1.58489E+00
1.31826E+00
1.09648E+00
9.12011E-01
7.58578E-01
6.30957E-01
5.24807E-01
4.36516E-01
3.63078E-01
3.01995E-01
2.51189E-01
2.08930E-01
1.73780E-01
1.44544E-01
1.20226E-01
1.00000E-01
8.31764E-02
6.91831E-02
5.75440E-02
4.78630E-02
3.98107E-02
3.31131E-02
2.75423E-02
2.29087E-02
1.90546E-02
1.58489E-02
1.31826E-02
1.09648E-02
9.12011E-03
7.58578E-03
6.30957E-03
5.24807E-03
4.36516E-03
3.63078E-03
3.01995E-03
2.51189E-03
2.08930E-03
1.73780E-03
1.44544E-03
1.20226E-03
1.00000E-03
8.31764E-04
6.91831E-04
5.75440E-04
4.78630E-04
3.98107E-04

1.81970E+02
1.51356E+02
1.25893E+02
1.04713E+02
8.70964E+01
7.24436E+01
6.02560E+01
5.01187E+01
4.16869E+01
3.46737E+01
2.88403E+01
2.39883E+01
1.99526E+01
1.65959E+01
1.38038E+01
1.14815E+01
9.54993E+00
7.94328E+00
6.60693E+00
5.49541E+00
4.57088E+00
3.80189E+00
3.16228E+00
2.63027E+00
2.18776E+00
1.81970E+00
1.51356E+00
1.25893E+00
1.04713E+00
8.70964E-01
7.24436E-01
6.02560E-01
5.01187E-01
4.16869E-01
3.46737E-01
2.88403E-01
2.39883E-01
1.99526E-01
1.65959E-01
1.38038E-01
1.14815E-01
9.54993E-02
7.94328E-02
6.60693E-02
5.49541E-02
4.57088E-02
3.80189E-02
3.16228E-02
2.63027E-02
2.18776E-02
1.81970E-02
1.51356E-02
1.25893E-02
1.04713E-02
8.70964E-03
7.24436E-03
6.02560E-03
5.01187E-03
4.16869E-03
3.46737E-03
2.88403E-03
2.39883E-03
1.99526E-03
1.65959E-03
1.38038E-03
1.14815E-03
9.54993E-04
7.94328E-04
6.60693E-04
5.49541E-04
4.57088E-04
3.80189E-04

1.73780E+02
1.44544E+02
1.20226E+02
1.00000E+02
8.31764E+01
6.91831E+01
5.75440E+01
4.78630E+01
3.98107E+01
3.31131E+01
2.75423E+01
2.29087E+01
1.90546E+01
1.58489E+01
1.31826E+01
1.09648E+01
9.12011E+00
7.58578E+00
6.30957E+00
5.24807E+00
4.36516E+00
3.63078E+00
3.01995E+00
2.51189E+00
2.08930E+00
1.73780E+00
1.44544E+00
1.20226E+00
1.00000E+00
8.31764E-01
6.91831E-01
5.75440E-01
4.78630E-01
3.98107E-01
3.31131E-01
2.75423E-01
2.29087E-01
1.90546E-01
1.58489E-01
1.31826E-01
1.09648E-01
9.12011E-02
7.58578E-02
6.30957E-02
5.24807E-02
4.36516E-02
3.63078E-02
3.01995E-02
2.51189E-02
2.08930E-02
1.73780E-02
1.44544E-02
1.20226E-02
1.00000E-02
8.31764E-03
6.91831E-03
5.75440E-03
4.78630E-03
3.98107E-03
3.31131E-03
2.75423E-03
2.29087E-03
1.90546E-03
1.58489E-03
1.31826E-03
1.09648E-03
9.12011E-04
7.58578E-04
6.30957E-04
5.24807E-04
4.36516E-04
3.63078E-04

34

1.65959E+02
1.38038E+02
1.14815E+02
9.54993E+01
7.94328E+01
6.60693E+01
5.49541E+01
4.57088E+01
3.80189E+01
3.16228E+01
2.63027E+01
2.18776E+01
1.81970E+01
1.51356E+01
1.25893E+01
1.04713E+01
8.70964E+00
7.24436E+00
6.02560E+00
5.01187E+00
4.16869E+00
3.46737E+00
2.88403E+00
2.39883E+00
1.99526E+00
1.65959E+00
1.38038E+00
1.14815E+00
9.54993E-01
7.94328E-01
6.60693E-01
5.49541E-01
4.57088E-01
3.80189E-01
3.16228E-01
2.63027E-01
2.18776E-01
1.81970E-01
1.51356E-01
1.25893E-01
1.04713E-01
8.70964E-02
7.24436E-02
6.02560E-02
5.01187E-02
4.16869E-02
3.46737E-02
2.88403E-02
2.39883E-02
1.99526E-02
1.65959E-02
1.38038E-02
1.14815E-02
9.54993E-03
7.94328E-03
6.60693E-03
5.49541E-03
4.57088E-03
3.80189E-03
3.16228E-03
2.63027E-03
2.18776E-03
1.81970E-03
1.51356E-03
1.25893E-03
1.04713E-03
8.70964E-04
7.24436E-04
6.02560E-04
5.01187E-04
4.16869E-04
3.46737E-04

3.31131E-04
2.75423E-04
2.29087E-04
1.90546E-04
1.58489E-04
1.31826E-04
1.09648E-04
9.12011E-05
7.58578E-05
6.30957E-05
5.24807E-05
4.36516E-05
3.63078E-05
3.01995E-05
2.51189E-05
2.08930E-05
1.73780E-05
1.44544E-05
1.20226E-05
1.00000E-05

3.16228E-04
2.63027E-04
2.18776E-04
1.81970E-04
1.51356E-04
1.25893E-04
1.04713E-04
8.70964E-05
7.24436E-05
6.02560E-05
5.01187E-05
4.16869E-05
3.46737E-05
2.88403E-05
2.39883E-05
1.99526E-05
1.65959E-05
1.38038E-05
1.14815E-05

3.01995E-04
2.51189E-04
2.08930E-04
1.73780E-04
1.44544E-04
1.20226E-04
1.00000E-04
8.31764E-05
6.91831E-05
5.75440E-05
4.78630E-05
3.98107E-05
3.31131E-05
2.75423E-05
2.29087E-05
1.90546E-05
1.58489E-05
1.31826E-05
1.09648E-05

35

2.88403E-04
2.39883E-04
1.99526E-04
1.65959E-04
1.38038E-04
1.14815E-04
9.54993E-05
7.94328E-05
6.60693E-05
5.49541E-05
4.57088E-05
3.80189E-05
3.16228E-05
2.63027E-05
2.18776E-05
1.81970E-05
1.51356E-05
1.25893E-05
1.04713E-05

Appendix B
CALENDF - Pu239 2950 eV probability table
NOR = 8, table order
NPAR = 3, partials; elastic, absorption, fission
I = -7, first negative moments
tables de probabilite pour 94-Pu-239 LANLDIST-DEC06
ZA= 94239. MAT=9437 TEFF= 293.6
54 groupes de 2.5119E+3 a 3.0200E+4 IPRECI=4
IG 193 ENG=2.884030E+3 3.019950E+3 NOR= 8 I= -7 NPAR=3 KP=
2 101 18001.445989-2 9.275984+0 7.938243+0 3.784994-1 9.592410-1
2.530904-1 1.204427+1 1.050705+1 4.120089-1 1.125216+0
3.786562-1 1.597588+1 1.196700+1 1.341964+0 2.666910+0
2.264860-1 2.397558+1 1.420897+1 3.557534+0 6.209075+0
9.747106-2 3.855881+1 2.245308+1 7.251606+0 8.854119+02.563850-2 6.079895+1 3.779216+1 1.117563+1 1.183115+1
3.701015-3 9.447885+1 6.799134+1 1.523110+1 1.125642+1
4.970289-4 1.325152+2 1.094414+2 1.423427+1 8.839522+0
Probability
Total
Elastic
Absorption
FissionCALENDF - SIGTTEUM - Pu239 2950 eV average value
2.370043+1
Total

1.663062+1
Elastic

3.709518+0
Capture3.360296+0
Fission36

PURM - Pu239 2950 eV probability table
FINAL TABLE
Table
6, Energy Point for Table:
SigAve: 2.35776E+01
1.64716E+01

2.95000E+03 eV
3.39770E+00
3.70829E+00

0.00000E+00(tcfso)------------------------------------------------------------------------------------------------------------------Band
Band limits
Cummulative
Probability
Total
CaptureFission
ScatterOther------------------------------------------------------------------------------------------------------------------1
1.0758E+01
1.2943E-01
1.2943E-01
1.1458E+01
2.5003E-01
3.9960E-01
1.0808E+01
0.0000E+00
21.1966E+01
2.8050E-01
1.5107E-01
1.2593E+01
6.2297E-01
8.8073E-01
1.1089E+01
0.0000E+00
31.3311E+01
3.8999E-01
1.0949E-01
1.4011E+01
1.2240E+00
1.4405E+00
1.1347E+01
0.0000E+00
41.4806E+01
4.7698E-01
8.6989E-02
1.5592E+01
1.8691E+00
1.9774E+00
1.1746E+01
0.0000E+00
51.6468E+01
5.5164E-01
7.4667E-02
1.7357E+01
2.5440E+00
2.5174E+00
1.2296E+01
0.0000E+00
61.8318E+01
6.1630E-01
6.4656E-02
1.9300E+01
3.2150E+00
3.1232E+00
1.2962E+01
0.0000E+00
72.0376E+01
6.7261E-01
5.6311E-02
2.1492E+01
3.9796E+00
3.6814E+00
1.3831E+01
0.0000E+00
82.2664E+01
7.2279E-01
5.0178E-02
2.3895E+01
4.5942E+00
4.4480E+00
1.4853E+01
0.0000E+00
92.5210E+01
7.6789E-01
4.5100E-02
2.6558E+01
5.3440E+00
5.0476E+00
1.6166E+01
0.0000E+00
102.8041E+01
8.0623E-01
3.8344E-02
2.9550E+01
6.1162E+00
5.7205E+00
1.7713E+01
0.0000E+00
113.1191E+01
8.4000E-01
3.3767E-02
3.2880E+01
6.9616E+00
6.2504E+00
1.9668E+01
0.0000E+00
12
3.4694E+01
8.6961E-01
2.9611E-02
3.6562E+01
7.6667E+00
6.9653E+00
2.1930E+01
0.0000E+00
133.8590E+01
8.9520E-01
2.5589E-02
4.0709E+01
8.5789E+00
7.5763E+00
2.4554E+01
0.0000E+00
144.2925E+01
9.1764E-01
2.2444E-02
4.5167E+01
9.2099E+00
8.5327E+00
2.7424E+01
0.0000E+00
15
4.7746E+01
9.3542E-01
1.7778E-02
5.0309E+01
9.8300E+00
9.4260E+00
3.1053E+01
0.0000E+00
165.3109E+01
9.5150E-01
1.6078E-02
5.5847E+01
1.1088E+01
9.5642E+00
3.5194E+01
0.0000E+00
175.9074E+01
9.6306E-01
1.1556E-02
6.2244E+01
1.1644E+01
1.0592E+01
4.0008E+01
0.0000E+00
18
6.5708E+01
9.7198E-01
8.9222E-03
6.9306E+01
1.2477E+01
1.0466E+01
4.6363E+01
0.0000E+00
197.3089E+01
9.8071E-01
8.7333E-03
7.7202E+01
1.4113E+01
8.5620E+00
5.4527E+01
0.0000E+00
208.1298E+01
1.0000E+00
1.9289E-02
1.0189E+02
1.7977E+01
1.0432E+01
7.3486E+01
0.0000E+00
9.0429E+01

37

AUROX - Pu239 2950 eV probability table
INDEX
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Average

CUM. PROB.
1.45525E-02
3.16110E-02
6.52933E-02
1.20041E-01
1.94416E-01
2.86526E-01
3.88354E-01
4.88874E-01
5.84038E-01
6.72148E-01
7.48130E-01
8.10114E-01
8.60227E-01
8.97912E-01
9.24842E-01
9.45576E-01
9.60244E-01
9.72256E-01
9.91565E-01
1.00000E+00

TOTAL XSEC
1.04826E+01
1.10850E+01
1.14058E+01
1.17532E+01
1.21018E+01
1.24702E+01
1.28405E+01
1.32258E+01
1.36305E+01
1.40430E+01
1.44630E+01
1.48995E+01
1.53499E+01
1.58165E+01
1.62938E+01
1.67868E+01
1.73025E+01
1.78255E+01
1.88066E+01
2.11962E+01
1.37738E+01

ELASTIC9.11199E+00
9.77098E+00
1.00173E+01
1.03083E+01
1.05319E+01
1.07881E+01
1.10111E+01
1.12556E+01
1.15180E+01
1.17578E+01
1.20270E+01
1.23176E+01
1.26796E+01
1.30367E+01
1.34119E+01
1.37613E+01
1.41483E+01
1.45391E+01
1.54151E+01
1.75584E+01
1.16412E+01

FISSION
1.03418E+00
9.92191E-01
1.06561E+00
1.09848E+00
1.20375E+00
1.27943E+00
1.39126E+00
1.49212E+00
1.59540E+00
1.72737E+00
1.83605E+00
1.94907E+00
2.00309E+00
2.07655E+00
2.14404E+00
2.26831E+00
2.37176E+00
2.47680E+00
2.53128E+00
2.73069E+00
1.61124E+00

38

NJOY-PURR - Pu239 2950 eV probability tableprobability tabletmin 2.936E+02 5.027E+00
tmax 2.936E+02 6.131E+00 8.366E+00 9.660E+00 1.063E+01 1.139E+01 1.263E+01 1.373E+01 1.496E+01 1.630E+01 1.780E+01
1.993E+01 2.258E+01 2.684E+01 3.409E+01 4.857E+01 6.522E+01 8.073E+01 8.827E+01 1.036E+02 1.513E+02
prob 2.936E+02 7.344E-05 2.705E-03 1.092E-02 2.261E-02 3.487E-02 8.695E-02 8.645E-02 8.649E-02 7.910E-02 7.232E-02
8.273E-02 7.824E-02 9.087E-02 9.785E-02 9.521E-02 4.175E-02 1.713E-02 8.628E-03 3.866E-03 1.238E-03
tot 2.936E+02 5.791E+00 7.783E+00 9.170E+00 1.022E+01 1.104E+01 1.204E+01 1.318E+01 1.433E+01 1.561E+01 1.702E+01
1.882E+01 2.118E+01 2.457E+01 3.016E+01 4.018E+01 5.534E+01 7.293E+01 8.398E+01 9.361E+01 1.148E+02
els 2.936E+02 4.289E+00 6.468E+00 7.875E+00 8.927E+00 9.701E+00 1.048E+01 1.117E+01 1.170E+01 1.217E+01 1.267E+01
1.331E+01 1.427E+01 1.580E+01 1.880E+01 2.510E+01 3.620E+01 5.183E+01 6.189E+01 6.578E+01 7.881E+01
fis 2.936E+02 9.861E-01 8.062E-01 7.641E-01 7.706E-01 8.074E-01 9.272E-01 1.134E+00 1.422E+00 1.790E+00 2.197E+00
2.704E+00 3.331E+00 4.175E+00 5.293E+00 6.938E+00 8.719E+00 8.901E+00 7.593E+00 1.143E+01 1.665E+01
cap 2.936E+02 5.166E-01 5.086E-01 5.308E-01 5.179E-01 5.291E-01 6.350E-01 8.694E-01 1.209E+00 1.646E+00 2.152E+00
2.804E+00 3.579E+00 4.595E+00 6.071E+00 8.137E+00 1.043E+01 1.220E+01 1.450E+01 1.640E+01 1.933E+01

39

ÉDITÉ PAR
LA DIRECTION DES SYSTEMESD’INFORMATION
CEA / SACLAY 91191 GIF-SUR-YVETTE CEDEX FRANCE