ENDF/B-VIII.0: The 8th Major Release of the Nuclear...

ENDF/B-VIII.0: The 8th Major Release of the Nuclear Reaction Data Librarywith CIELO-project Cross Sections, New Standards and Thermal Scattering Data

D.A.Brown,1 M.B.Chadwick,2, ∗ R.Capote,3 A.C.Kahler,2 A.Trkov,3 M.W.Herman,1 A.A. Sonzogni,1 Y.Danon,4

A.D.Carlson,5 M.Dunn,6 D.L. Smith,7 G.M.Hale,2 G.Arbanas,8 R.Arcilla,1 C.R. Bates,2 B.Beck,9 B.Becker,10

F.Brown,2 R. J.Casperson,9 J.Conlin,2 D.E. Cullen,9 M.-A.Descalle,9 R.Firestone,11 T.Gaines,12 K.H.Guber,8

A. I. Hawari,13 J.Holmes,14 T.D. Johnson,1 T.Kawano,2 B.C.Kiedrowski,15 A. J.Koning,3 S.Kopecky,16 L. Leal,17

J. P. Lestone,2 C.Lubitz,18 J. I.Márquez Damián,19 C.M.Mattoon,9 E.A.McCutchan,1 S.Mughabghab,1

P.Navratil,20 D.Neudecker,2 G.P.A.Nobre,1 G.Noguere,21 M.Paris,2 M.T.Pigni,8 A. J. Plompen,16 B.Pritychenko,1

V.G.Pronyaev,22 D.Roubtsov,23 D.Rochman,24 P.Romano,7 P. Schillebeeckx,16 S. Simakov,25 M.Sin,26

I. Sirakov,27 B. Sleaford,9 V. Sobes,8 E. S. Soukhovitskii,28 I. Stetcu,2 P. Talou,2 I. Thompson,9 S. van der Marck,29 L.Welser-Sherrill,2 D.Wiarda,8 M.White,2 J. L.Wormald,13 R.Q.Wright,8 M.Zerkle,14 G. Žerovnik,16 and Y. Zhu13

1Brookhaven National Laboratory, Upton, NY 11973-5000, USA2Los Alamos National Laboratory, Los Alamos, NM 87545, USA

3International Atomic Energy Agency, PO Box 100, A-1400 Vienna, Austria4Rensselaer Polytechnic Institute, Troy, NY 12180, USA

5National Institute of Standards and Technology, Gaithersburg, MD 20899-8463, USA6Spectra Tech, Inc., Oak Ridge, TN 37830, USA

7Argonne National Laboratory, Argonne, IL 60439-4842, USA8Oak Ridge National Laboratory, Oak Ridge, TN 37831-6171, USA

9Lawrence Livermore National Laboratory, Livermore, CA 94551-0808, USA10Gesellschaft für Anlagen und Reaktorsicherheit, Schwertnergasse 1, D-50667 Köln, Germany

11Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA12AWE plc, Reading RG7 4PR, United Kingdom

13North Carolina State University, Raleigh, NC 27695, USA14Naval Nuclear Laboratory, West Mifflin, PA 15122, USA

15University of Michigan, Ann Arbor, MI 48109, USA16EC-JRC, B-2440 Geel, Belgium

17Institut de Radioprotection et de Sûreté Nucléaire, 92262 Fontenay aux Roses, Cedex, France18Naval Nuclear Laboratory, Niskayuna, NY 12309, USA

19Centro Atómico Bariloche, S. C. de Bariloche, Argentina20TRIUMF, Vancouver, BC V6T 2A3, Canada

21CEA, DEN, DER, SPRC, Cadarache, 13108 Saint-Paul-lèz-Durance, France22PI Atomstandart at SC Rosatom, Moscow, Russian Federation23Canadian Nuclear Laboratories, Chalk River, Ontario, Canada

24Paul Scherrer Institut, 5232 Villigen, Switzerland25Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz, 1 76344 Eggenstein-Leopoldshafen, Germany

26University of Bucharest, Bucharest-Magurele, RO-077125, Romania27Institute for Nuclear Research and Nuclear Energy, BAS, BG-1784 Sofia, Bulgaria

28Joint Institute for Energy and Nuclear Research, Minsk, Belarus29NRG, Westerduinweg 3, 1755 LE Petten, The Netherlands

(Received 18 September 2017; revised received 21 November 2017; accepted 14 December 2017)

We describe the new ENDF/B-VIII.0 evaluated nuclear reaction data library. ENDF/B-VIII.0 fullyincorporates the new IAEA standards, includes improved thermal neutron scattering data and usesnew evaluated data from the CIELO project for neutron reactions on 1H, 16O, 56Fe, 235U, 238U and239Pu described in companion papers in the present issue of Nuclear Data Sheets. The evaluationsbenefit from recent experimental data obtained in the U.S. and Europe, and improvements in theoryand simulation. Notable advances include updated evaluated data for light nuclei, structural materials,actinides, fission energy release, prompt fission neutron and γ-ray spectra, thermal neutron scatteringdata, and charged-particle reactions. Integral validation testing is shown for a wide range of criticality,reaction rate, and neutron transmission benchmarks. In general, integral validation performance ofthe library is improved relative to the previous ENDF/B-VII.1 library.

Available online at www.sciencedirect.com

Nuclear Data Sheets 148 (2018) 1–142

0090-3752/© 2018 Published by Elsevier Inc.

www.elsevier.com/locate/nds

https://doi.org/10.1016/j.nds.2018.02.001

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

http://www.elsevier.com/locate/ndshttps://doi.org/10.1016/j.nds.2018.02.001https://doi.org/10.1016/j.nds.2018.02.001http://www.sciencedirect.comhttp://creativecommons.org/licenses/by-nc-nd/4.0/http://crossmark.crossref.org/dialog/?doi=10.1016/j.nds.2018.02.001&domain=pdf

ENDF/B-VIII.0 Library . . . NUCLEAR DATA SHEETS D.A. Brown et al.

CONTENTS

I. INTRODUCTION 3

II. OVERVIEW OF ENDF/B-VIII.0LIBRARY 4

III. NEUTRON CROSS SECTIONSUBLIBRARY 5A. Z=0-20 5

1. n, the Neutron 52. 1H 53. 2H 64. 3He 85. 6Li 86. 9Be 97. 10B 118. 12C 119. 13C 1210. 16O 1411. 18O 1512. 40Ar 1513. 40Ca 16

B. Z=21-60 181. 56Fe 182. 54Fe, 57Fe and 58Fe 203. 59Co, 58−62,64Ni 204. 63,65Cu 205. 73,74,75As 246. 78Kr, 132Te, and 124Xe 247. 105Rh 24

C. Z=61-88 251. 169Tm 252. Dy, Yb, Os 253. 174,176,177,178,179,180,181,182Hf 254. 197Au 255. 182,183,184,186W 256. 190−198Pt 27

D. Z=89-95 281. 233U 282. 235U 283. 238U 344. 239Pu 375. 240Pu 426. 241Am 42

E. TENDL+EMPIRE Isotopes 43F. Primary Gammas 44G. Prompt Fission Neutrons, ν̄p, for 53 Minor

Actinides 45

IV. PROMPT FISSION GAMMAOBSERVABLES 45A. 235U(n,f) Prompt Fission γ-Ray

Properties 46

∗ Corresponding author: [email protected]

B. 238U(n,f) Prompt Fission γ-RayProperties 50

C. 239Pu(n,f) Prompt Fission γ-RayProperties 52

V. PROMPT FISSION NEUTRONMULTIPLICITY DISTRIBUTION P(ν) 54A. Experimental data 55B. Empirical Formula 55C. Theoretical Calculations 55D. Evaluation 55E. Delayed Neutrons from ENDF/B-VI.8 57F. Components of Energy Release Due to

Fission (MT=458) 57

VI. NEUTRON REACTION COVARIANCES 59A. Overview of ENDF/B-VIII.0

Covariances 59B. Covariance Quality Assurance 60C. Relation to Integral Data Uncertainties 60D. Outlook 62

VII. THERMAL NEUTRON SCATTERINGSUBLIBRARY 62A. Yttrium Hydride (YH2) 63B. Water Ice (Ih) 63C. Light Water (H2O) 63D. Heavy Water (D2O) 64E. Beryllium (Be-metal) 65F. Graphite (Crystalline) 67G. Nuclear/Reactor Graphite 67H. Beryllium Oxide (BeO) 68I. Silicon Dioxide (SiO2, α and β Phases) 68J. Silicon Carbide (SiC) 69K. Polyethylene (CH2) 70L. Polymethyl Methacrylate (C5O2H8) 70M. Uranium Dioxide (UO2) 71N. Uranium Mononitride (UN) 73

VIII. NEUTRON CROSS SECTION STANDARDSSUBLIBRARY 74

IX. CHARGED-PARTICLE REACTIONSUBLIBRARIES 76A. p + 7Li 76B. d + 7Li 77C. t + 7Li 78D. 3He + 3He 78E. Charged-particle Elastic Scattering on

4He 78

X. DECAY DATA SUBLIBRARY 79

XI. ATOMIC SUBLIBRARIES 79

XII. INTEGRAL DATA TESTING SUMMARY 81A. Criticality Testing 81B. Delayed Neutron Testing 84C. Calculated Critical Masses 85

2

mailto:[email protected]


D. Reaction Rates in Critical Assemblies 88E. Atomic Mass Spectrometry (AMS) at 25

keV and 426 keV 90F. Maxwellian-Averaged Cross Sections

(MACS) 92G. Thermal Integral Quantities in

ENDF/B-VIII.0 97H. Quasi-differential Benchmarks for n+ Be 99I. 14 MeV Neutron Transmission 99

XIII. ENDF-6 and GNDS FORMAT OPTIONS 100A. ENDF-6 Format Changes 101B. GNDS Format 102

XIV. DATA PROCESSING with NJOY, AMPX,FUDGE and PREPRO 103A. NJOY 103B. AMPX 104C. FUDGE 104D. PREPRO 105

1. Overview 1052. Features of 2017 Version 1053. Specific Code Improvements 105

XV. FUTURE WORK 106

Acknowledgments 106

References 107

A. Summary of Changes Between ENDF/B-VII.1and ENDF/B-VIII.0 121

B. Summary of Criticality keff C/E ChangesBetween ENDF/B-VII.1 andENDF/B-VIII.0 135

I. INTRODUCTION

The ENDF library project is coordinated by theCross Section Evaluation Working Group (CSEWG) andCSEWG is releasing the new ENDF/B-VIII.0 library, in-corporating work from across the US and the interna-tional nuclear science community over the last six years.The library is being issued in the traditional ENDF-6 for-mat, as well as in an alternative new Generalized NuclearDatabase Structure (GNDS) format.

As was the case for previous ENDF releases [1, 2], theENDF/B-VIII.0 library has not been developed in iso-lation, but rather, it continues to evolve through closeinteractions with parallel organizations around the world,most notably with Europe (JEFF) [3], Japan (JENDL)[4, 5], and with South Korea. Collaborations with theInternational Atomic Energy Agency (IAEA) have hadnumerous impacts, most notably on Collaborative Inter-national Evaluation Library Organization (CIELO) nu-clides [6–8], the standards [9, 10], prompt fission neutronspectra (PFNS) evaluations [11], and dosimetry cross sec-tions [12, 13]. A number of collaborations via the NuclearEnergy Agency (NEA) Working Party on Evaluation Co-operation (WPEC) provided valuable contributions, espe-cially CIELO (Subgroup 40) [6, 7], a plutonium resonanceanalysis (Subgroup 34) [14], a new GNDS format option(Subgroup 38) [15], data adjustment studies (Subgroup39) [15], and thermal scattering data (Subgroup 42) [16].

The new ENDF/B-VIII.0 library, in contrast toENDF/B-VII.1, has major changes for neutron reactionson the major actinides and other nuclides that impactsimulations of nuclear criticality. The important isotopes1H, 16O, 56Fe, 235,238U, and 239Pu have been the focus ofthe international CIELO collaboration, and the resultingadvances have been incorporated into ENDF/B-VIII.0.Additional information on the CIELO collaboration find-ings is given in companion articles in the present edition ofNuclear Data Sheets: a CIELO overview [8], uranium [17],plutonium capture [18], iron [19], and prompt fission neu-tron spectra (PFNS) [20]. Additionally a major updateto the standards has been made by a group of researchersunder the auspices of the IAEA, and these new standardshave been mostly incorporated into ENDF/B-VIII.0 (andare also documented in a companion article [10]). Othernotable advances in ENDF/B-VIII.0, described further inthis article, include updates to neutron reactions on mi-nor actinides, structural materials, light nuclei, dosimetrycross sections, fission energy release, decay data, charged-particle reactions, and thermal neutron scattering data formodeling neutron reactions on molecules at low energies.The previous ENDF/B-VII.1 library was built upon

the earlier ENDF/B-VII.0 library in various ways: exten-sive nuclear reaction data on uncertainties (covariancedata evaluations) were provided; minor actinide crosssection evaluations were improved; structural materialevaluations were advanced through use of recent resolvedand unresolved resonance analyses of new measured data;new light nucleus R-matrix evaluations were developed

3


TABLE I. Overview of the ENDF/B library releases and the 15sublibraries in ENDF/B-VIII.0. Shown in the columns are thenumber of materials present in each sublibrary in each release.Here Spontaneous Fission Yields is abbreviated as SFY andNeutron-induced Fission Yields as NFY.

Sublibrary VIII.0 VII.1 VII.0 VI.8Neutron 557 423 393 328Thermal n-scattering 33 21 20 15Proton 49 48 48 35Deuteron 5 5 5 2Triton 5 3 3 1Helium3 3 2 2 1Alpha 1 n/a n/a n/aPhotonuclear 163 163 163 n/aAtomic relaxation 100 100 100 100Electron 100 100 100 100Photoatomic 100 100 100 100Decay data 3821 3817 3838 979SFY 9 9 9 9NFY 31 31 31 31Standards 10 8 8 8

for the nuclides 3He, 9Be, and 6Li; fission product datafor fast and 14 MeV neutrons incident on plutonium werere-evaluated, including details of the neutron energy de-pendence over the fast neutron range from 0.5–2.0 MeV;new data for fission energy release were provided; and anew decay data library was developed. But for all theseupgrades, the previous ENDF/B-VII.1 preserved much ofthe ENDF/B-VII.0 library capabilities, and most notablythe major actinides were not changed, and there was theintent that VII.1 should generally preserve, and improveupon, the good integral criticality performance testingseen in ENDF/B-VII.0 [1, 21]. Indeed ENDF/B-VII.1 didgenerally perform well in such integral validation tests,as described by Kahler et al. [22]. But it has taken thispresent ENDF/B-VIII.0 effort - including related CIELOproject work - to accomplish the many upgrades made toimportant nuclides such as the actinides, and those in thenew standards.

II. OVERVIEW OF ENDF/B-VIII.0 LIBRARY

ENDF/B-VIII.0 represents the biggest change to theENDF library in many years, including CIELO evalua-tions (1H, 16O, 56Fe, 235U, 238U, 239Pu), revised neutronstandards and a vastly expanded thermal scattering lawsublibrary along with numerous other significant changes.Indeed, the CIELO and thermal scattering law sublibraryimprovements are primarily responsible for the improvedperformance in integral benchmarks documented in Sec-tion XII. The library is also much larger: the neutronsublibrary has expanded 32% to contain 557 evaluations(see Table I).

Highlighted changes in the neutron sublibrary include

• CIELO evaluations: New 1H, 16O, 56Fe, 235U,

238U, 239Pu, including prompt fission neutron spec-tra (PFNS) and prompt fission gamma spectra(PFGS)

• Light elements: New n, 2H, 3He, 6Li, 9Be, 10B, C(12,13C, tuned to match natC standards), and 35,37Cl;adopted 18O from ROSFOND [23, 24]

• Structural materials: New 40Ca, constituentsof steel (54,56,57,58Fe, 58−62,64Ni), 59Co, 63,65Cu,174−182Hf, 182−186W and revised 105Rh, 132Te

• Rare earths: Adopted Dy and Yb from JENDL-4.0• Noble gases: Revised 40Ar, 78Kr, 124Xe; 20−22Nefrom TENDL-2015

• Minor actinides: New 236mNp, 240Pu, new nubarsand revised 241,243Am

• Misc. materials: New 73−75As and 197Au;190−198Pt adopted from TENDL-2015

• Unstable isotopes: Added all isotopes withT1/2 ≥ 1 year and all the intermediate nuclei neededto produce these isotopes through neutron-inducedreactions using a combination of TENDL-2015 eval-uations and EMPIRE calculations

• Primary gammas: Added to 6,7Li, 11B, 19F, 23Na,27Al, 28Si and 35,37Cl to support nondestructive as-say applications

These changes, especially to CIELO isotopes, carbonand gold, are rooted in the revised neutron standards. Inthis sublibrary we have:

• Added the integral of the 235U(n,f) cross sectionfrom 7.8–11 eV as a standard

• Added the Au(n, γ) 30 keV Maxwellian-averagedcross section as a standard

• Added high energy fission reference cross sections235U(n,f), 238U(n,f) from 200 MeV up to 1 GeV;209Bi(n,f) and natPb(n,f) from about 20 MeV up toto 1 GeV

• Revised thermal neutron constantsThe changes to the thermal scattering law (TSL) sub-

library are significant since every evaluation except ben-zene was either revised dramatically or (re)evaluated. Inaddition, all evaluations except benzene have the modelinputs provided (in the form of NJOY/LEAPR files) sothat more detailed checking and peer review is possible.Together we have:

• Fuels: New UO2 and UN• Moderators: New heavy and light water, graphite(reactor grade and crystalline), polyethylene, lucite,and yttrium hydride

4


• Reflectors: Revised Be and BeO• Natural materials: New ice and SiO2• Cladding: New SiC

There were also many updates to other libraries:

• Light Charged Particles: New alpha sublibrary,p,d,t on 7Li and 3He on 3He

• Decay sublibrary: Improved beta intensities forsome fission products; modified K X-ray energiesfor selected actinides

• Atomic sublibraries: Minor fixes and reformat-ting resulting in a update of all three atomic subli-braries

All these changes were performed in an environmentof dramatically improved quality assurance enabled bycomputational advances. Much of the ENDF/B workflowhas been automated now. This process started with theintroduction of the GForge collaboration environment in-stalled at the National Nuclear Data Center which in-cludes both revision control, library release managementand bug tracking. GForge has now been connected tothe ADVANCE continuous integration system [25]. AD-VANCE runs a battery of physics and format checks onevery changed evaluation of every commit. This checkingwith ADVANCE completely automates the traditionalENDF/B Phase I testing. ADVANCE also benefits fromthe code modernization push that led to both the devel-opment of the FUDGE and NJOY2016 processing codes.These processing improvements in turn led to new testsand identification of issues in various evaluations. Theprocessing code modernization efforts in the US, Europeand Asia are in large part a result of the roll out of thenew GNDS formatting option discussed in Section XIII.

III. NEUTRON CROSS SECTION SUBLIBRARY

A. Z=0-20

1. n, the Neutron

A new evaluation of the n− n scattering cross sectionis available at energies up to 50 MeV in ENDF/B VIII.0.It uses essentially the same R-matrix parameters as theN − N analysis1 described in the next section. That is,the isospin-1 parameters used to describe p− p scatteringare also used to predict values of the n − n scatteringcross section. This charge-symmetric model is modified byallowing a single energy shift of all the p−p (T = 1) energy

1 In subsections IIIA 1 and IIIA 2, ‘N ’ refers to ‘nucleon’ and notto ‘nitrogen’ as is used elsewhere in this paper.

0.1

1

10

10-6 10-5 0.0001 0.001 0.01 0.1 1 10

n-N Elastic Cross Sections

n-nn-p

Elas

tic C

ross

Sec

tion

(b)

Incident Neutron Energy (MeV)

FIG. 1. (Color online) The elastic cross sections for n − n(blue curve) and n − p (red curve) scattering calculated atenergies below 20 MeV from the charge-independent N−N R-matrix analysis. They are similar below about 600 keV, withthe differences above that energy coming from the T = 0contributions to n− p scattering.

levels to account for the Coulomb difference between thedi-neutron and di-proton systems. The value of this energyshift is determined by fitting the experimental value of thesinglet n−n scattering length, a0 =-18.5 fm [26]. The n−nscattering cross section resulting from this calculation isshown in Fig. 1, compared to the n − p scattering crosssection from the same analysis. They are similar belowabout 600 keV, but above that energy the contributionsfrom the T = 0 states make the n− p cross section crossover and become larger than the n−n cross section. Notethat the n − n scattering cross section shown in Fig. 1is half the integrated differential elastic scattering crosssection, as is appropriate for identical particles, whereasthe n − p scattering cross section is equal to the angle-integrated differential elastic scattering cross section.

2. 1H

The n − p scattering cross sections used in this newversion (VIII.0) of the ENDF/B file came from a charge-independent (CI) analysis of the N−N system at energiesup to 50 MeV, part of the IAEA standards. The channels,reactions, and data included in the analysis are summa-rized in Table II. The CI R matrix has the form

R(E) =∑λ,T

γ(T )λ γ̃

(T )λ

E(T )λ − E

, (1)

where T = 1 for �+s even, and T = 0 for �+s odd. The rel-ativistic energy is given in terms of the total 4-momentumsquared, Mandelstam’s s-variable, and the total p+p chan-nel mass M , by E = (s −M2)/2M . The same isospin-1reduced widths γ

(1)λ are used to describe p− p and n− n

scattering, as well as the T = 1 part of n − p scatter-ing (making it a CI model), but the corresponding p− p

5


TABLE II. Channel configuration (top) and data summary(bottom) for the charge-independent N − N analysis up to50 MeV. Since the number of free parameters is 43 resonanceparameters + 83 normalizations, the chi-squared per degreeof freedom for the analysis is 0.90.

Channel ac (fm) lmaxp+ p 3.26 3n+ p 3.26 3γ + d 84.6 1n+ n 3.26 3

Reaction # Pts. χ2 Observable Types

p(p, p)p 675 951 σ(θ), Ay(p), Cx,x′ , Cy,y′ ,Kx′x ,K

y′y ,K

x′z

p(n, n)p 4815 3764 σT, σ(θ), Ay(n), Cy,y′ ,Ky′y

p(n, γ)d 86 179 σint, σ(θ), Ay(n)d(γ, n)p 88 77 σint, σ(θ),Σ(γ), Py(n)n(n, n)n 1 0 a0Norms. 80 86Total: 5745 5057 20

eigenenergies E(1)λ are shifted by a Coulomb energy dif-

ference, ΔZ , that depends only on the total charge of thesystem (Z = 0 for n− n, and Z = 1 for n− p).This simple, Coulomb-corrected, CI model appears to

work well for describing all the N − N data up to 50MeV, obtaining a chi-square per degree of freedom of 0.90.Figure 2 shows the fit to selected n− p total cross sectionmeasurements. The fits to some of the n− p differentialcross sections and polarizations are shown in Figs. 3 and 4,respectively. It should be remembered that many othermeasurements not shown, for example, for p−p scattering,and for n−p capture, are also fit quite well by this analysis,and they further constrain the results for n− p scattering.The new analysis preserves the values of the low-

energy n− p scattering lengths, a0 = −23.719(5) fm anda1 = 5.414(1) fm obtained in an earlier analysis that wentup to 30 MeV, which formed the basis for the ENDF/BVII.1 hydrogen evaluation. The changes from that ear-lier analysis remain small at higher energies, as shownin Fig. 5 [10], which plots the ratios of ENDF/B-VIII.0to ENDF/B-VII.1 for the total cross section and for thezero-degree proton laboratory differential cross section. Asmall change in the thermal capture cross section, from332.00 mb to 332.58 mb, now agrees better with one ofthe most precise experimental values [27].Although the analysis goes to 50 MeV, we provided

cross sections for ENDF/B-VIII.0 only up to 20 MeV.This is because the analysis will eventually be extended to200 MeV (a preliminary version already exists for energiesup to 100 MeV).

3. 2H

During post-release testing of the final version ofENDF/B-VI (ENDF/B-VI.8), it was discovered [55] thatcalculated eigenvalues (keff) for a set of D2O solutionbenchmarks from the ICSBEP project [56] had decreased

0.1

1

10

0.0001 0.001 0.01 0.1 1 10

n-p Total Cross Section

ENDF/B-VIII.0Dilg `75Fujita `76Allen `55Daub `13Davis `71Abfalterer `01Lisowski `80

Tota

l Cro

ss S

ectio

n (b

)


FIG. 2. (Color online) The n− p total cross section between100 eV and 50 MeV. The red curve is ENDF/B-VIII.0, andthe colored symbols are from various measurements [28–35].

substantially (by about 1000 pcm) relative to an earlierversion, ENDF/B-VI.4. The cause was traced to modifica-tions made to the deuterium cross sections in ENDF/B-VI.5 and retained through ENDF/B-VII.0 and VII.1.In the ENDF/B-VI.5 evaluation, σs(E) and Ps(E, μ)below E � 4 MeV were compared to results of acoupled-channels R-matrix analysis [57]. The σs(E) fromENDF/B-VI.4 was found to be consistent with this R-matrix analysis and was retained. However, the Ps(E, μ)data below E = 3.2 MeV were replaced with new tabu-lated distributions from the R-matrix analysis [57], anda sparse energy grid Ei was chosen for the tabular dataPs(Ei, μj) at 0.01 - 0.1MeV < E < 1 - 10 MeV.It was also noticed [58] that the existing experimental

data on the angular distributions of out-scattered neu-trons in the 2H(n, n) reaction were old, sparse, and eveninconsistent, and it was recommended [58] that new mea-surements and theoretical study [59, 60] to be undertaken.Although the ENDF/B-VII.1 evaluation of 2H performsreasonably well in comparison with the new neutron scat-tering measurements at E < 2 MeV [61] and in modellingheavy water reactor benchmarks [62, 63], the recent exper-imental results [64] on backward-to-forward ratio in theneutron angular distributions at 0.2MeV < E < 2 MeVfavour the evaluations of Ps(E, μ) based on the three-body theory (Faddeev [65] or Alt-Grassberger-Sandhas(AGS) [66] equations) and the modern nucleon-nucleon(NN) potentials [67] rather than the evaluations based onR-matrix analysis.In the nuclear data releases world-wide, some evalua-

tions of MF=4, MT=2 data for 2H(n, n) are based onthe three-body theory, such as, in CENDL-3.1, JENDL-3.3and -4.0, and in JEFF-3.2. The JEFF-3.2 evaluation ofboth σs(E) and Ps(E, μ) of the

2H(n, n) reaction is basedon the solution of the three-body Faddeev equations withthe INOY03 NN potentials [68]. The trial evaluations ofneutron scattering data based on different choices for the

6


0.071

0.072

0.073

0.074

0.075

0.076

0.077

0.078

0 30 60 90 120 150 180

n-p Scattering at 10.04 MeV

ENDF/B-VIIII 10.04Boukharouba `01

Diff

eren

tial C

ross

Sec

tion

(b/s

r)

Center-of-Mass Angle (degrees)

0.048

0.05

0.052

0.054

0.056

0.058

0.06

0.062

0 30 60 90 120 150 180


ENDF/B-VIII 14.1Allred `53Buerkle `97Seagrave `55Nakamura `60Greiner `65Suhami `67Shirato `74

Diff

eren

tial C

ross

Sec

tion

(b/s

r)Center-of-Mass Angle (degrees)

0.032

0.033

0.034

0.035

0.036

0.037

0.038

0 30 60 90 120 150 180

n-p Scattering at 22.5 MeVENDF/B-VIII 22.5Drosg `78Flynn `62Scanlon `63

Diff

eren

tial C

ross

Sec

tion

(b/s

r)


0.016

0.018

0.02

0.022

0.024

0.026

0.028

30 60 90 120 150 180


ENDF/B-VIII 36Fink `90Romero `70

Diff

eren

tial C

ross

Sec

tion

(b/s

r)


0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.022

0 30 60 90 120 150 180


ENDF/B-VIII 47.5Scanlon `63

Diff

eren

tial C

ross

Sec

tion

(b/s

r)


0.01

0.012

0.014

0.016

0.018

0.02

0.022

0 30 60 90 120 150 180

n-p Scattering at 50 MeV

ENDF/B-VIII 50Fink `90Montgomery `77

Diff

eren

tial C

ross

Sec

tion

(b/s

r)


FIG. 3. (Color online) The differential cross section for n− p scattering at energies between 10 and 50 MeV. The red curve isENDF/B-VIII.0, and the points are from various measurements [36–48].

NN potentials [69] show good performance in the esti-mates of criticality (keff) of the heavy water benchmarks(critical assemblies and nuclear reactors) [56], includingthe notorious HEU-SOL-THERM-004 (HST-4) [55, 70].Therefore, to improve the performance of deuterium

nuclear data, the evaluation of deuterium (2H) is mod-ified in the final release of ENDF/B-VIII.0 in compar-ison with the ENDF/B-VII.1 version (retained up toENDF/B-VIII.0β4). The evaluation of the angular dis-tributions of neutrons in the elastic scattering reaction(MF= 4, MT= 2) is modified by using data from theJEFF-3.2 evaluation of 2H, for the incident neutron ener-gies 10−5 eV ≤ E ≤ 28.0 MeV. At higher neutron energies,the ENDF/B-VII.1 data is retained. As a result, the com-bined data block of MF=4, MT=2 makes use of the dualrepresentation, namely, LTT=3, or Legendre moment ex-pansion, at E ≤ 28.0 MeV taken from JEFF-3.2 datafile and using JEFF grid for Ei and the tabular form at28.0MeV < E < 150.0 MeV from the original ENDF/B-VII.1 file. In Fig. 6, we show differential cross sectionsσs(E, μ) = (σs(E)/2π)Ps(E, μ) of

2H(n, n) in the center-of-mass reference frame at 1.0MeV < E < 2.4 MeV. Onecan notice that, in ENDF/B-VIII.0, the backward scat-tering weight (contributions of μ near μ = cos 180◦ = −1

into∫Ps(E, μ) dμ) is increased at E � 1 MeV in compar-

ison with ENDF/B-VII.1 (Fig. 6) in the center-of-massframe. On the other hand, the agreement of the evalu-ated data with the experimental results of Vedrenne [71]for the angular distributions of out-scattered neutronsneeds an improvement at low incident neutron energiesE � 1 - 5 MeV, from both the experimental and theoreti-cal standpoints.Cross sections (MF= 3 data) for n+2H are the

same in ENDF/B-VIII.0 and B-VII.1. For example, inENDF/B-VIII.0, the thermal cross sections of deuteriumare

σs,th = 3.395± 0.051 (±1.5%) b,σth(n, γ) = 0.506± 0.015 (±3%) mb.

The value of σth(n, γ) lies higher, but within ±2σ of theevaluated cross-section uncertainty (MF=33), than theresult of recent measurements by Firestone and Revay [72](measured value of 0.489± 0.006 mb).

For E = 14 MeV, MF= 3, 33 of 2H, ENDF/B-VIII.0

7


-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0 30 60 90 120 150 180

n-p Polarization at 10.03 MeV

ENDF/B-VIII 10.03Holsin `88

P y (

n)


-0.005

0

0.005

0.01

0.015

0.02

0.025

0 30 60 90 120 150 180


ENDF/B-VIII 14.1Brock `81Weisel `92

P y (

n)Center-of-Mass Angle (degrees)

-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0 30 60 90 120 150 180


ENDF/B-VIII 16.9Tornow `88

P y (

n)


-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0 30 60 90 120 150 180


ENDF/B-VIII 33.0Wilczynski `84

P y (

n)


FIG. 4. (Color online) The neutron polarization for n− p scat-tering at energies between 10 and 33 MeV. The red curveis ENDF/B-VIII.0, and the points are from various measure-ments [49–53].

Neutron energy, MeV

0 5 10 15 20

Ratio

0.985

0.990

0.995

1.000

1.005

ENDF/B-VIII to ENDF/B-VII, 0 degrees

ENDF/B-VIII to ENDF/B-VII, total

n-p Total


Ratio

EN

DF/B

-VIII

to E

NDF

/B-V

II

FIG. 5. (Color online) The cross-section ratios of VIII.0/VII.1for the n − p total cross section (black curve) and the differ-ential cross section for detecting protons at zero degrees inthe laboratory system (red curve) at energies below 20 MeV.Figure taken from Fig. 1 of Ref. [54].

give the following estimates:

σs,14MeV = 0.644± 0.032 (±5%) b,σ14MeV(n, 2n) = 0.166± 0.036 (±21.5%) b,

σ14MeV(n, γ) = 9.5± 7.6 (±80%) μb.

4. 3He

No new work was done on the n+3He cross sectionsfor ENDF/B VIII.0. A newer R-matrix analysis of thereactions in the 4He system exists that could form thebasis of an updated evaluation, and we are consideringusing it in a future update to ENDF/B-VIII.0.

10-1

100

0 20 40 60 80 100 120 140 160

Angle (degree)

Einc = 1.20 MeV

G.Vedrenne, 1966

ENDF/B-VII.1

ENDF/B-VIII.0

10-1

100

dσ

/dΩ

(b

/sra

d)

Einc = 1.71 MeV

G.Vedrenne, 1966

ENDF/B-VII.1

ENDF/B-VIII.0

10-1

100 2

H(n,n) Angular Distributions

Einc = 2.22 MeV

G.Vedrenne, 1966

ENDF/B-VII.1

ENDF/B-VIII.0

FIG. 6. Differential elastic scattering cross sections of deu-terium σs(E, μ) at 1.0MeV < E < 2.4 MeV; comparison ofthe ENDF/B-VII.0 (=VII.1) evaluation, the ENDF/B-VIII.0evaluation and available experimental data from Vedrenne [71](EXFOR 21148014).

5. 6Li

The R-matrix analysis informing the n+6Li evaluationused the EDA code and included data for all reactionsopen in the 7Li system at energies up to En = 4 MeV(Ex=10.7 MeV). The data set initially included more than3900 experimental points for the reactions listed in Ta-ble III. The fit to these data was quite good overall, witha χ2 per degree of freedom of 1.36. The differential crosssections and analyzing powers for t+4He elastic scatter-ing were especially well represented. The parameters ofthis fit were then used to provide the n+6Li cross sectionsand covariances input to the least-squares fitting code GMAfor the 2017 standard cross section analysis, described inSec. VIII. The GMA analysis included calculations from an-other R-matrix fit, as well as experimental data for ratiomeasurements involving the 6Li(n, t)4He cross section.For the general-purpose ENDF/B-VIII.0 file, however,

it was decided to re-fit the 7Li system data set with theexperimental cross sections for the 6Li(n, t)4He reactionreplaced with the (unsmoothed) standard cross sectionsand uncertainties from the GMA analysis. This procedure

8


TABLE III. Channel configuration (top) and data summary(bottom) for the 7Li system analysis. Chi-squared per degreeof freedom for the analysis is 1.36.

Channel ac (fm) lmaxt+4He 4.02 5n+6Li 5.0 3n+6Li∗ 5.5 1d+5He 6.0 0

Reaction Energy Range # Data Observables(MeV) Points

4He(t, t)4He Et=0–14 1661 σ(θ), Ay(θ)4He(t, n)6Li Et=8.75–14.4 37 σint, σ(θ)4He(t, n)6Li∗ Et=12.9 4 σ(θ)6Li(n, t)4He En=0–4 1406 σint, σ(θ)6Li(n, n)6Li En=0–4 800 σT, σint, σ(θ), Py(θ)

6Li(n, n′)6Li∗ En=3.35–4 8 σint6Li(n, d)5He En=3.35–4 2 σint

Total: 3918 13

0.1

1

0.001 0.01 0.1 1 10

6Li(n,t)4He Cross Section

ENDF/B-VIII.0SowerbyNISTPoenitzMacklinGiorginisDrosgBartleWNR `08

Reac

tion

Cros

s Se

ctio

n (b

)


FIG. 7. (Color online) The cross section for the 6Li(n, t)4Hereaction. The red curve is ENDF/B-VIII.0, and the points arefrom various measurements [73–81] (listed in the order citedin the figure). The evaluated thermal cross section is 938 b.

1

10

0.001 0.01 0.1 1

6Li(n,n)6Li Cross Section

ENDF/B VIII.0ENDF/B VII.1Knitter `78Smith `77

Elas

tic C

ross

Sec

tion

(b)

Incident Neutron Energy (MeV)FIG. 8. (Color online) The cross section for n+ 6Li elasticscattering. The red solid curve is ENDF/B-VIII.0, the greendashed curve is ENDF/B-VII.1. The data are from Knitter[82] and Smith [83].

1

10

0.0001 0.001 0.01 0.1 1

n+6Li Total Cross Section

ENDF/B VIII.0ENDF/B VII.1Smith `77

Tota

l Cro

ss S

ectio

n (b

)


FIG. 9. (Color online) The total cross section for neutrons on6Li. The red solid curve is ENDF/B-VIII.0, the green dashedcurve is ENDF/B-VII.1. Data points are from Ref. [83].

allowed the standards cross section to influence the fit,while imposing the smoothing and unitary constraintson all the n+6Li cross sections that result from a multi-channel R-matrix analysis. The resulting 6Li(n, t) crosssection changed very little from the GMA analysis, andmostly within its uncertainties. It also still gives a verygood representation of the direct measurements of the re-action cross section, as shown in Fig. 7. The elastic andtotal cross sections are shown in Figs. 8 and 9, respec-tively. The differences with ENDF/B VII.1 are generallysmall, and good agreement with the experimental datawas maintained. The version VIII.0 cross sections werematched to those of version VII.1 at around 3.8 MeV, andthey are identical to VII.1 above that energy.

6. 9Be

ENDF/B-VIII.0 adopts the previous ENDF/B-VII.1cross section evaluation, but replaces the elastic angulardistribution and the (n, 2n) angular and energy distribu-tions from the JENDL-4.0 evaluation, see Fig. 10. Thiswas motivated by the fact that the JENDL-4.0 evaluationby Shibata was more recent. Additionally, using theseJENDL-4.0 angular distributions tended to reduce calcu-lated criticality in fast plutonium and HEU assemblies, asdescribed in the integral data testing section of this paper(Section XII), leading to generally-improved comparisonswith measured criticality (although a large spread in C/Evalues remains).

The (n, 2n) cross section is unchanged relative to VII.1and shown in Fig. 11. The total cross section is shownin Fig. 12; again, this is unchanged compared to VII.1,and includes the changes made after ENDF/B-VII.0 toreproduce the measurement of Danon et al.The small 9Be(n,γ) cross section is shown in Fig. 13.

9


0.2

0.5

1

0 45 90 135 180

0.30 MeV

dσ

/dΩ

(b/s

r)

θcm (degrees)

Lane, 1961ENDF/B-VII.1ENDF/B-VIII.0

0.2

0.5

1

0 45 90 135 180

0.55 MeV

θcm (degrees)

0.2

0.5

1

0 45 90 135 180

0.63 MeV

θcm (degrees)

0.01

0.1

1

5

0 45 90 135 180

0.93 MeV

dσ

/dΩ

(b/s

r)

θcm (degrees)

0.01

0.1

1

5

0 45 90 135 180

2.25 MeV

θcm (degrees)

0.01

0.1

1

5

0 45 90 135 180

13.94 MeV

θcm (degrees)

Hogue, 1978

FIG. 10. (Color online) 9Be angular distributions dσ/dΩ as a function of center-of-mass angle. Each panel gives, in the upper-rightcorner the incident neutron energy (MeV). The red curves are the new ENDF/B-VIII.0 evaluation; the line-connected datapoints in green are the ENDF/B-VII.1 evaluation; data are shown in black as taken from Lane [84] and Hogue [85].

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10 12 14 16 18 20

(n,2

n)

Cro

ss s

ectio

n (

b)

Incident neutron energy (MeV)

Fischer, 1957Catron, 1961Drake, 1977

Takahashi, 1987

Murata, 2007JENDL-4.0

ENDF/B-VIII.0

Be(n,2n)9

FIG. 11. (Color online) 9Be(n, 2n) cross section as a functionof incident neutron energy (MeV). The red curve is the newENDF/B-VIII.0 evaluation (unchanged from ENDF/B-VII.1).Data are from Refs. [86–90].

1

10

100

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

101

To

tal cro

ss s

ectio

n (

b)


Hibdon, 1949Schwartz, 1971

Auchampaugh, 1979Harvey, 1982

Schwartz, 1983Finlay, 1993

Danon, 2009Rapp, 2012

JENDL-4ENDF/B-VII.1ENDF/B-VIII.0

Be(n,tot)9

FIG. 12. (Color online) Total cross section for neutrons on 9Be.The red curve is the new ENDF/B-VIII.0 evaluation (=VII.1)compared to JENDL-4.0. Data are from Refs. [91–97].

10


10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

10-12 10-10 10-8 10-6 10-4 10-2 100 102

Cap

ture

cro

ss s

ectio

n (b

)


JENDL-4ENDF/B-VII.0

ENDF/B-VIII.0

FIG. 13. (Color online) Capture cross section for neutrons on9Be. The red curve is the ENDF/B-VIII.0, which is identical tothe ENDF/B-VII.1 evaluation. It is compared to JENDL-4.0and ENDF/B-VII.0.

7. 10B

The ENDF/B-VIII.0 evaluation is based at low energieson an R-matrix analysis of reactions in the 11B system.The data set initially included more than 6600 experi-mental points for the reactions listed in Table IV. The

TABLE IV. Channel configuration (top) and data summary(bottom) for the 11B system analysis. Chi-squared per degreeof freedom for the analysis is 1.14.

Channel ac (fm) lmaxn+10B 4.05 1α+7Li 4.00 3α+7Li∗ 6.17 3t+8Be 6.00 2


10B(n, n)10B En = 0− 1.04 385 σT, σint, σ(θ)10B(n, α0)

7Li En = 0− 0.98 2815 σint, σ(θ)10B(n, α1)

7Li∗ En = 0− 1.01 2875 σint, σ(θ)10B(n, t)8Be En=0-0.42 3 σint7Li(α, n)10B Eα=4.45-5.49 588 σint, σ(θ)

Total: 6666 10

new evaluation gives much better agreement with mea-surements than before, as can be seen in Figs. 14–18. The(n, α1) cross section (Fig. 16) was changed in the 1.5–6MeV region to agree better with the Schrack data. Thetotal (n, α) cross section (Fig. 17) was changed in that re-gion to agree better with the Giorginis data. The changesin the (n, α0) cross section (Fig. 15) resulted from sub-tracting the (n, α1) cross section from the total (n, α)cross section. The total neutron cross section shown inFig. 18 was changed at energies above 8 MeV to agreebetter with the data of Abfalterer and the 200 m data ofWasson, and the difference was put into the elastic crosssection. An increase in the elastic cross section was not in-consistent with some of the measurements in that energyregion.

0.1

1

10

0.01 0.1 1

10B(n,α) Cross Sections

VIII.0 (n,α1)

VIII.0 (n,α0)

Schrack `78Schrack `93Schrack `94Martin `81Sealock `81

Reac

tion

Cros

s Se

ctio

n (b

)


(n,α1)

(n,α0)

σth

(n,α1) = 3602 b

σth

(n,α0) = 242 b

FIG. 14. (Color online) A comparison of the evaluated10B(n, α) cross sections in ENDF/B-VIII.0 (red curve) withvarious measurements [74, 98–100] in the standards energyregion below 1 MeV.

0.01

0.1

0.01 0.1 1 10

10B(n,α0)7Li Cross Section

ENDF/B-VII.1ENDF/B-VIII.0

Reac

tion

Cros

s Se

ctio

n (b

)


FIG. 15. (Color online) A comparison of the evaluated cross sec-tions in ENDF/B-VIII.0 (red curve) and -VII.1 (green curve)for the 10B(n, α0)

7Li reaction. The differences are large in theregion from about 2.5 MeV to 6.5 MeV, in order to agree bet-ter with new data for the (n, α1) and (n, α) reactions in thatregion.

8. 12C

The ENDF/B-VIII.0 release is the first ENDF/B re-lease to include 12C (98.9%) and 13C (1.1%) isotopicevaluations in lieu of a natural carbon evaluation. Thecross sections for n+12C were taken at energies below 6.5MeV from an R-matrix analysis of the 13C system thatincluded reactions among the channels n+12C, n+12C*,and γ+13C. A summary of the channel configuration anddata for the reactions included is given in Table V. Al-though particular attention was paid to the data in thestandards region (En < 2 MeV) for the carbon isotopes,the analyses extend to energies well above that for boththe 13,14C systems. The types of data used are mostly

11


0.1

1

0.1 1 10

10B(n,α1)7Li* Cross Section

ENDF/B-VIII.0ENDF/B-VII.1Schrack `93

Reac

tion

Cros

s Se

ctio

n (b

)


FIG. 16. (Color online) The evaluated cross sections inENDF/B-VIII.0 (red curve) and -VII.1 (green curve) for the10B(n, α1)

7Li∗ reaction. The differences are large in the regionfrom about 1.5 MeV to 6 MeV, in order to agree better withthe data of Schrack et al. [98].

0.1

1

0.1 1 10

10B(n,α0+α

1) Cross Section

ENDF/B-VIII.0ENDF/B-VII.1Giorginis `06

Reac

tion

Cros

s Se

ctio

n (b

)


FIG. 17. (Color online) The evaluated cross sections inENDF/B-VIII.0 (red curve) and -VII.1 (green curve) for thesummed 10B(n, α0 + α1) reactions. The differences are largein the region from about 2.3 MeV to 6 MeV, in order to agreebetter with the data of Giorginis et al. [101].

differential and integrated (total) cross sections, but someanalyzing-power measurements are also included.The fits to the data are generally quite good, as can

be seen in Figs. 19 and 20. Some of the cross sectionswere allowed to renormalize, as given in Table VI. Mostof the normalization factors for the total cross section arenear unity, although the ones at 2 % may be significant,in view of the discussion below. Much larger renormaliza-tions (+11 to -13 %) are required to make the Geel andWender data consistent with the calculations and witheach other. Some changes were also made in the n+12Ccapture cross section, as can be seen in Fig. 21. The flatregion between 0.2 and 7 MeV in ENDF/B-VII.1 has beenreplaced with a more physically reasonable behavior when

1.4

1.5

1.6

1.7

1.8

1.9

2

4 6 8 10 12 14 16 18 20

n+10B Total Cross Section

AbfaltererWasson ENDF/B-VII.1ENDF/B-VIII.0

Tota

l Cro

ss S

ectio

n (b

)


FIG. 18. (Color online) The evaluated total cross section forn+10B in ENDF/B-VIII.0 (red curve) and -VII.1 (green curve)compared with the data of Abfalterer [102] (blue triangles) andof Wasson [103] (red points). The evaluated cross section waschanged in the region above about 8 MeV in order to agreebetter with these data.

TABLE V. Channel configuration (top) and data summary(bottom) for the 13C system analysis. Chi-squared per degreeof freedom for the analysis is 1.54.

Channel ac (fm) lmaxn+12C(0+) 4.6 4n+12C*(2+) 5.0 1

γ+13C 50.0 1


12C(n, n)12C En = 0− 6.45 6940 σT, σ(θ), An(θ)12C(n, n′)12C* En = 5.3− 6.45 443 σint, σ(θ)12C(n, γ)13C En = 0− 0.2 7 σint

Total: 7390 5

joined to the higher-energy data above 10 MeV.The elastic cross section in the new evaluation gradually

becomes larger than ENDF/B-VII.1, until the differenceapproaches 2 % at energies in the minimum below thefirst resonance. This is at the upper end of the standardscross section range (1.8 MeV), and is of concern becausethe difference lies outside the uncertainty of both evalua-tions. There appear to be no consequential effects of thedifference on critical benchmarks, however. At energiesabove about 6.5 MeV, the cross sections were matchedsmoothly onto the existing (VII.1) natural carbon evalua-tion, so that the two evaluations are the same above thatenergy.

9. 13C

The n+13C (14C system) analysis fits solely the to-tal cross section data of Cohn (1961), Auchampaugh(1979), and Abfalterer (2001) as shown in Fig. 22. De-spite the relatively poor description of the data at ener-

12


0

1

2

3

4

5

6

7

0 1 2 3 4 5 6

n+12C Total Cross Section

ENDF/B-VIII.0sigLowEDimentDanon `07Daub `13Auchampagh `77CierjacksPerey

Tota

l Cro

ss S

ectio

n (b

)


5/2+

5/2-

3/2+

3/2+

1/2-

9/2+

3/2-

5/2+

7/2-

5/2-

FIG. 19. (Color online) Total cross section for n+12C com-pared to experimental data [93, 104–108]. The Jπ values ofthe resonances are indicated above the peaks. Figure adaptedfrom Fig. 4 of Ref. [109].

0

0.1

0.2

0.3

0.4

0.5

4.8 5.2 5.6 6 6.4

12C(n,n')12C* Cross Section

ENDF/B-VIII.0Geel x 0.87RogersWender x 1.11Galati

Inel

astic

Cro

ss S

ectio

n (b

)


9/2+

3/2-

5/2+

7/2-

5/2-

FIG. 20. (Color online) Cross section for n+12C inelastic scat-tering to the first level compared to experimental data [110–113]. The Jπ values of the resonances are indicated above thepeaks. Figure adapted from Fig. 5 of Ref. [109].

gies En � 0.7 MeV with an overall χ2/datum of 2.24 overregion 0 ≤ En ≤ 20 MeV, the present analysis is notableas it is an R-matrix description of the data through theentire region and it is the largest such analysis to date, in-corporating six two-particle partitions (n+13C0, n+

13C∗1,n+13C∗2, α+

10Be, n+13C∗3, and n+12C) encompassing 90

channels in the channel-spin basis with �max = 3.

10-6

10-4

10-2

100

102

10-4

10-2

100

102

104

106

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Cro

ss S

ection (

b)

Ratio V

III.0 / V

II.1

Incident Neutron Energy (eV)

12C(n,γ)

ENDF/B-VII.1 - Nat

C

ENDF/B-VIII.0 - 12

CRatio

FIG. 21. (Color online) Cross sections for n+12C capture. Thedotted black curve is ENDF/B-VII.1 and the new cross sectionis the red curve. The green curve gives the ratio to ENDF/B-VII.1.

TABLE VI. Normalizations and energy shifts (ΔE) for the13C-system cross-section data analyzed.

Authors (n, n) : Energy Range Norm. ΔEDiment 74 – 1341900 eV 1.006 0Danon 24 – 948 keV 1.004 0Daub 0.8 – 935 keV 1.013 0

Auchampaugh 1.20 – 6.45 MeV 1.020 0Cierjacks 1.90 – 6.45 MeV 1.020 0Perey 1.91 – 6.44 MeV 1.008 0

Authors (n, n′) :Geel et al. 4.82 – 6.44 MeV 0.868 -58 keV

Wender et al. 4.82 – 6.45 MeV 1.112 0Rogers et al. 4.93 – 6.58 MeV 1.0 (fixed) 0Galati et al. 6.24 – 6.33 MeV 1.0 (fixed) 0

1

10

0.1 1 10

Tota

l cro

ss s

ection (

b)


Cohn, 1961Auchampaugh, 1979

Abfalterer, 2001ENDF/B-VIII.0

C(n,tot)13

FIG. 22. (Color online) 13C total cross section (in barn) as afunction of the incident neutron energy (MeV) compared withdata [93, 102, 114].

13


TABLE VII. Channel configuration (top) and data summary(bottom) for the 17O analysis. Chi-squared per degree of free-dom for the analysis is 1.75.

Channel ac (fm) lmaxn+16O 4.4 4α+13C 5.4 5γ+17O 10. 1


16O(n, n)16O En = 0− 7 2540 σT, σ(θ), Pn(θ)16O(n, α)13C En = 2.35− 5 672 σint, σ(θ), Pn(θ)16O(n, γ)17O En = 0.02− 0.56 12 σint13C(α, n)16O Eα = 0− 5.4 870 σint13C(α, α)13C Eα = 2− 5.7 1168 σ(θ)17O(γ, n0)

16O Eγ = 4.4− 6.7 186 σ(90◦)Total: 5448 10

10. 16O

The new evaluation of n+16O cross sections for neutronenergies up to 7 MeV is based on an R-matrix analysis ofall possible reactions between the channels n+16O,α+13C,and γ+17O in the 17O system.This is summarized in Table VII. Particular attention

was paid to the data in the low-energy region for n+16Oelastic scattering, shown in Fig. 23. The thermal crosssection is lower than before, but still at the upper end ofthe range of recommended values, in excellent agreementwith a high-precision measurement by Schneider [115].

TABLE VIII. Normalizations and energy shifts (ΔE) for the17O-system cross-section data analyzed.

Authors (n, n) : Energy Range Norm. ΔESchneider 0.0253 eV 1.0 (fixed) 0

Dilg, Koester, Block 0.13 – 23.5 keV 1.0 (fixed) 0Ohkubo (corr. for H) 0.8 – 935 keV 0.9989 0Johnson & Fowler(including LOX) 49 – 3139 keV 0.9799 0Cierjacks et al. 3.143 – 7.0 MeV 1.0378 0Authors (α, n) :Drotleff et al. 346 – 1389 keV 1.0 (fixed) 0Heil et al. 416 – 899 keV 1.0 (fixed) 0Kellog 445 – 1045 keV 1.506 0

Bair & Haas 0.997 – 5.402 MeV 0.941 -4 keV

At higher energies, as shown in Fig. 24, the 17O anal-ysis follows in great detail the total cross section mea-surements of Ohkubo [116], Johnson [117], Fowler [118],and Cierjacks [119] with reasonable normalization fac-tors (see Table VIII). It also agrees quite well with the13C(α,n)16O cross section measurement of Bair and Haas[120] at roughly their original normalization scale (0.94),a consequence of the unitarity imposed by an R-matrixdescription. The resulting 16O(n, α)13C cross sections areshown in Fig. 25. They agree with the measurements andevaluation done at JRC-Geel by Giorginis [121], which are30 – 50% higher than the ENDF/B VII.1 cross sections,

and with the normalization (0.95) of the Bair and Haas[120] data determined independently by Giorginis.A post-analysis check of the evaluated total cross sec-

tion was provided by measurements of Danon et al. [122]at RPI. This is shown at energies below 9 MeV in Fig. 26.The resolution and scatter of the measurement are not asgood as those of the other data we fit, but the normal-ization was determined in a novel way, by using a watertarget and normalizing to the total cross section for hydro-gen scattering in the oxygen window at 2.35 MeV. Whenthe evaluated total cross section and the RPI measure-ment are binned in the same way (2-3 MeV widths), theC/E ratios in those bins deviate from unity by 1 % orless at energies up to 9 MeV, confirming that the averagenormalization and shape of the evaluation is correct.

3.6

3.65

3.7

3.75

3.8

3.85

3.9

0.01 0.1 1 10 102 103 104 105

n+16O Elastic Scattering Cross Section

ENDF/B-VII.1CIELO 7/14ENDF VIII.0=CIELOKopecky-PlompenSchneider `76

Dilg `71Koester `90Block `75OhkuboJohnson X 0.98

recommended value ofKopecky and Plompen

Cro

ss S

ection (

b)

Incident Neutron Energy (eV)

FIG. 23. (Color online) The neutron elastic cross section on16O at low energies as a function of the incident neutron energy(MeV) for the current ENDF/B-VIII.0 analysis is comparedwith data and previous evaluations of ENDF/B-VII.1 (greencurve) and data [115, 123–128]. Figure taken from Fig. 1 ofRef. [109].

Another goal of the analysis was to obtain more rea-sonable capture cross sections for 16O. This was doneby including the 90-degree excitation function for the17O(γ, n0)

16O reaction measured by Holt et al. [129], aswell as the low-energy measurements of the n+16O to-tal capture cross section by Firestone [72] and by theJapanese groups [130, 131]. The value of the Holt datais that they cover a wide enough energy range to revealthe resonant structure of the photo-disintegration crosssection over the first 6–7 resonances above the neutronthreshold in 17O. Therefore, we were able to extend the en-ergy range in which resonance effects on the capture crosssection are taken into account (typically this has beendone only over the first resonance). The fits to these dataare shown in Figs. 27 and 28. At energies above 2 MeV,the R-matrix calculation was joined to a direct-capturecalculation by Kawano.Above the range of the R-matrix analysis (7 MeV),

14


FIG. 24. (Color online) The total neutron cross section (barn)on 16O as a function of the incident neutron energy (MeV) forthe current ENDF/B-VIII.0 analysis is compared with data.The inset shows the fit to the 13C(α, n) data of Bair and Haas[120], normalized by 0.94. Figure adapted from Fig. 2 of Ref.[109].

FIG. 25. (Color online) 16O(n, α0) reaction cross section (inbarn) as a function of the incident neutron energy (MeV). TheENDF/B-VII.1 evaluation (green curve) is compared to thedata of Bair and Haas and the current ENDF/B-VIII.0 (redcurve). Also displayed is the reevaluation of the JRC-Geel data(green triangles; JRC-Geel) [121]. Figure adapted from Fig. 3of Ref. [109].

the cross sections were matched smoothly to the existingevaluation, taking into account the experimental data, sothat, except for capture (MT=102), VIII.0 is identical toVII.1 at energies above 9 MeV.

11. 18O

The 2005 evaluation of 18O from M.N. Nikolaev wasadopted from ROSFOND [23, 24] in part because it wasthe only 18O evaluation available. This evaluation usesresonances from the Atlas of Neutron resonances [132]

FIG. 26. (Color online) The total neutron cross section for16O as a function of the incident neutron energy (MeV) forthe current ENDF/B-VIII.0 analysis is compared with datafrom Danon et al. [122].

FIG. 27. (Color online) The differential cross section for the17O(γ, n0)

16O reaction at 90◦ (lab). The measurements (bluepoints) are from Holt et al. [129], and the solid red curve isthe R-matrix calculation, with the indicated Jπ values of theresonances.

below 5 MeV. Above 5 MeV, the evaluation is mostlytaken from the J. Kopecky and D. Nierop evaluation inEAF-3. To supplement these cross sections, the inelasticscattering cross section is taken from 16O and the elasticcross section is the difference of the total and reactioncross sections. Elastic angular distributions were takenfrom 17O and other secondary angular distributions wereassumed to be isotropic in the center of mass system.Evaporation spectra were used to describe the secondaryneutron energy distributions.

12. 40Ar

The 40Ar evaluation in ENDF/B-VII.1 was taken fromJENDL-3.3 [133], and one of the issues in this file is that

15


1

10

100

1000

10-5 10-3 10-1 101 103

VIII.0VII.1=JENDL-4.0Firestone `16Igashira `95Nagai `99

σn,γ (μb)

En (keV)

Cro

ss s

ectio

n (𝝁

b)

Incident neutron energy (keV)

16O(n,𝛾)

101

102

103

10310110-110-310-5100

10-2 10-2 100 102 104

ENDF/B-VIII.0ENDF/B-VII.1=JENDL-4.0

FIG. 28. (Color online) The total neutron capture cross sectionfor 16O as a function of the incident neutron energy (keV)compared with experimental data [72, 130, 131]. The red line isthe ENDF/B-VIII.0 evaluation, and the green line is ENDF/BVII.1 = JENDL 4.0.

the particle energy spectra and the angular distributionsare given in the MF4 and MF5 sections. In the currentevaluation, they are now in MF6. The evaluation is basedon the partial γ-ray production cross section measurementwith the GErmanium Array for Neutron Induced Excita-tions (GEANIE) detector [134]. The γ-ray productioncross section calculation was performed with the CoH3code [135]. The statistical model calculations in the rela-tively light mass region, such as for argon, require carefulselection of discrete levels included, because the nuclearstructure and the γ-ray decay scheme significantly impactthe calculated γ-ray production cross sections. The dis-crete states up to 4.43 MeV are included in the calculation,and the continuum state is assumed above that energy. Athigher energies the direct (non-compound) population ofcollective levels is very important for the γ-ray productioncross section calculation. The discrete levels of 2.52, 3.21,3.92, 3.68, 4.08, and 4.32 MeV were included as collectivestates and the DWBA calculation was performed. Finallythe (n,p) cross section was slightly adjusted to reproduceavailable experimental data near 14 MeV.

13. 40Ca

BackgroundA resonance parameter evaluation of 40Ca in the neutronenergy range of thermal up to 1.5 MeV was performedwith support from the US Nuclear Criticality Safety Pro-gram (NCSP) in an effort to provide improved calciumcross section and covariance data for the Hanford Plu-tonium Finishing plant and Hanford Tank Farms in theDOE complex. Calcium is present in structural materialssuch as concrete and admixed materials in waste streams,but it is also a neutron-absorbing element that can influ-ence the reactivity of systems with fissionable material.The evaluation methodology used the Reich-Moore

approximation of the R-matrix formalism to fit high-resolution transmission and capture measurements per-formed between 2012 and 2014 at the GEel LINear Ac-celerator facility (GELINA) [136], as well as other experi-mental data sets on natural and isotopic calcium availablein the EXFOR library [137–140]. Table IX presents anoverview of the experimental data sets used in the fittingprocedure, as well as some of their features, such as samplethickness and average uncertainty.

TABLE IX. n+40Ca experimental data overview.

SampleAuthor Energy range

Type Δσ(%)Facility/Year Thick.(at/b)

natCaCierjacks [137] 0.5–31 MeV

Totala 1.5KIT/1968 0.21326

natCaPerey [138] 0.2–29 MeV

Totala 16.4ORNL/1972 0.7028

40CaJohnson [139] 40 keV–6 MeV

Totala 3.8ORNL/1973 0.0656

natCaSingh [140] 1.6 keV–0.5 MeV

Totala 10.0bNSC/1974 0.029762

natCaGuber [136] 20 eV–1 MeV

Trans. 2.6GEEL/2014 0.10971

natCaGuber [136] 10 eV–0.6 MeV

Capture 14.8GEEL/2014 0.01674

natCaGuber [136] 10 eV–0.6 MeV

Capture 17.2GEEL/2015 0.10971

a Fitted as transmission data.b Assumed uncertainty since no error analysis was reported.

Along with the elastic and capture channels, thereare two additional energetically possible channels forthe n+40Ca reaction system in the neutron range up to1.5 MeV. Table X shows that the (n,α) reaction channel,having a positive Q-value, is defined over the wholeneutron energy range, and the (n,p) reaction channel hasan energy threshold at about 0.5 MeV. Even though,

TABLE X. Reaction Q-values and thresholds for n+40Ca.

Reaction products Q-valuea (keV) Thresholda (keV)

41Ca+γ 8362.82 037Ar+α 1747.66 040K+p -528.55 541.89

a Calculated by mass values from the 2012 Atomic MassEvaluation [141].

in the analyzed energy range, these channels can be ofa small magnitude (� 10−4–10−3 b), it is important toinclude them within the R-matrix formalism. By usingbuilt-in capabilities of the SAMMY code [142, 143] forfitting resonant cross sections in the ingoing and outgoingcharged particle channels, the present ENDF/B-VIII.0set of evaluated resonance parameters considered not onlythe neutron and gamma exit channels, but also α-particleand proton exit channels for three incident neutron

16


partial waves. The level energies Eλ, the probabilityamplitudes (γλc ), and the related partial widths (Γ

λc )

were defined within a comprehensive set of reactionchannels c. Thanks to the I = 0+ ground state spin of40Ca, the total spin Jπ of a given resonance implicitlydefines the l-value of that resonance. The analysis of theexperimental data used the SAMMY code that performeda multi-level multi-channel R-matrix fit to neutron datausing experimental conditions such as resolution function,finite size of the sample, and nonuniform thickness.Nuclide abundances of the samples, multiple scattering,self-shielding, normalization, background, and Dopplerbroadening were also taken into account.

Previous EvaluationsIn both previous ENDF/B-VII.0 and -VII.1 libraries,the evaluated set of neutron resonance parameterswas reported over the energy range from thermal upto 0.5 MeV and adopted from JEFF-3.1 (released in2005), which in turn adopted the resonance evaluationfrom JENDL-3.3 (released in 2002). The original setof resonance parameters was based on the analysis ofMughabghab [132] and defined in terms of the MultiLevel Breit Wigner formula. In the libraries mentionedabove, no covariance information was available.

ResultsThe results of the evaluated cross sections and relateduncertainties at thermal energy are displayed for three re-action channels in Table XI. No significant discrepanciesbetween the evaluated values and the values reported inthe ATLAS are present. The conservatively large uncer-tainty for the (n,α) reaction channel is justified by the lackof recent experimental data and by the difficulty in accu-rately measuring these reaction cross sections partly dueto their modest magnitudes. In this regard, the only (n,α)measurement found in the EXFOR library was performedby Münnich in the late fifties [144].

TABLE XI. 40Ca thermal cross sections (in barn) calculatedat T=293.6 K compared to the values found in the Atlas ofNeutron Resonances.

40Ca (n,el) (n,γ) (n,α)

ENDF/B-VIII.0 2.66±2.6% 0.41±4.6% 2.48·10−3±83%ATLAS 2.73±2.2% 0.41±4.8% 2.50·10−3±44%

In Fig. 29, the total (solid black line) and capture (solidred line) cross sections calculated from the ENDF/B-VIII.0 R-matrix resonance parameters in the Reich-Moore approximation are compared with the experimen-tal data [136]. They are also compared to the cross sec-tions reconstructed from ENDF/B-VII.1 R-matrix reso-nance parameters (dashed lines) in the Multi Level BreitWigner formula. As shown in the figure, the improved setof transmission and capture experimental data made itpossible to obtain reasonable values of the neutron andcapture widths in the specified energy range.

10−4

10−3

10−2

10−1

10+0

10+1

10+2

10+3

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Cro

ssse

ctio

n(b

)


(n,tot)×10

(n,γ)

40Ca

FIG. 29. (Color online) 40Ca(n,γ) and total cross sectionsin the energy range up to 0.35 MeV calculated from theENDF/B-VIII.0 (solid lines) and ENDF/B-VII.1 (dashed lines)resonance parameters are compared with the experimentaldata [136].

0

20

40

60

80

100

120

140

160

180

200

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Cum

ul.N

umbe

rof

Obs

erve

dLe

vels

Neutron incident energy (MeV)

〈D0〉 = 46.5±0.51〈D1〉 = 14.7±0.12〈D2〉 = 15.6±0.13

× 2n+40Ca cumulative

level distribution

FIG. 30. (Color online) Plot of the ENDF/B-VIII.0 cumulativenumber of observed s- (red dots), p- (blue triangles) and d-levels (black diamonds) vs energy for n+40Ca. The values ofaverage s-level spacings 〈D0〉, p-level spacings 〈D1〉, and d-levelspacings 〈D2〉 shown in the plot represent the inverse of theslope of a straight line fitted to the data (red, blue, black lines)for the given channel radius ac.

In Figs. 30–31, the average level spacings 〈D0〉, 〈D1〉,〈D2〉 and the strength functions S0, S1, S2 (in units of10+4) for the observed s- (red dots), p- (blue triangle)and d-levels (black diamonds) are displayed with the fittedcurves (solid lines). Except for s-wave, the level spacingsand the strength functions are displayed for two mixedpopulations of levels for which the weak dependence of thetotal spin Jπ was neglected. In the neutron energy regionup to 0.6 MeV, the average level spacing 〈D2〉 seems togrow more rapidly than the average level spacings for s-and p-wave for which their behavior is close to linear. Thedeparture from linearity of 〈D2〉 and partly 〈D1〉, mightbe attributed to the tendency of the level densities to

17


0.0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800 1000 1200 1400

∑ ig iΓ

l ni/[

(2l+

1)V

l](k

eV)

Incident Neutron Energy (keV)

S0 · 10+4 = 2.349±0.085, N1/2+= 28S1 · 10+4 = 0.275±0.009, N1/2−= 51, N3/2−= 48S2 · 10+4 = 0.871±0.072, N3/2+= 53, N5/2+= 43

ac=4.99 fm

n+40Ca cumulative

reduced neutron widths

FIG. 31. (Color online) Plot of cumulative reduced neutron-widths

∑i giΓ

0i vs energy for n+

40Ca for three partial wavesl. The slopes of the straight lines give the strength functionsS0, S1, S2 (in 10

+4 unit) for the given channel radius ac. Forpartial waves l ≥ 1 the reduced neutron-widths are defined interms of the square well potential Vl.

grow exponentially. This can be more evident for popula-tions with high fractional density due to their total spinaccording to the 2J + 1 rule.Figure 31 shows results of the strength functions up

to 1.5 MeV, which is a small slice of excitation energy inthe compound nucleus 41Ca. To some extent, the impactof levels outside this energy region are seen, as in thelow value of the p-wave strength function S1. This canbe attributed to a hierarchy of more complicated config-urations such as centroids of single-particle states [145]for p-levels above 2 MeV. This is also consistent with thelarge negative value found for the R∞1J parameter indicat-ing centroids of the 2p1/2 and 2p3/2 levels.

B. Z=21-60

1. 56Fe

BackgroundIron is an extremely common structural material,leading to its inclusion in the CIELO project. 56Feis the dominant isotope with a natural abundance of91.8%. This isotope is therefore the main focus ofthe CIELO iron project and is the main subject ofthe iron evaluation summary paper also included inthis volume [19]. We summarize this 56Fe evaluation here.

Resolved Resonance RegionAfter careful performance studies, it was decided to adoptfor the resolved resonance range (up to the incident energyof 850 keV) the evaluated resonances from JENDL-4.0 [4],which originates from the Froehner evaluation [146] forJEF-2.2 [147] with corrections. A resonance energy waschanged from 767.240 keV to 766.724 keV and the spu-rious resonance at 59.9 keV was deleted in this new file.

The background near 800 keV was reduced by 40 percent.An artificial “background” was added to capture around24.5 keV, since previous estimates of capture in the regionwhere a dip in the elastic cross section is observed seemedto be low and certain critical assembly benchmarks aresensitive to this quantity. It was thought that the previousENDF/B-VII.1’s broad minimum in capture in this energyregion was caused by inappropriately-placed bound states.The adjusted capture cross section now nearly follows the1/v behavior. More details on such corrections and reason-ing of the choices made can be found in Ref. [19]. Fig. 32shows the 56Fe neutron capture cross section comparedwith ENDF/B-VII.1 and experimental data, where theimpact of the increased background can be clearly seen.

10-4

10-2

100

102

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

Cro

ss S

ection (

b)


56Fe(n,γ)

H.Pomerance, 1952

B.J.Allen, 1976

Huang Zheng-De, 1980

O.A.Shcherbakov, 1977

O.A.Shcherbakov, 1977

ENDF/B-VII.1

ENDF/B-VIII.0

FIG. 32. (Color online) Evaluated 56Fe(n,γ) cross section com-pared with data retrieved from EXFOR and with the previousevaluation.

The choice, based on validation, for capture cross sec-tions above 860 keV was the one from the RPI data pre-sented by Y. Danon in Ref. [148].The elastic angular distributions in the resolved reso-

nance range are chosen from resolution-broadened Pereydata [149]. Sample plots of angular distributions areshown in Fig. 33 for two different incident energies. Itwas found that the data from Kinney et al. [150] presentnoticeable anisotropy relative to forward and backwarddata, as can be clearly seen in Fig. 33, upper panel. Suchanisotropic behavior of the elastic angular distributiondata from Kinney fades as neutron incident energy pro-gresses to higher values, as can be seen in Fig. 33, bottompanel.While Froehner’s evaluation for the 56Fe resonances

was effectively adopted, the covariance on these param-eters have since been lost. Rather than re-evaluatingthe resonance region, a more pragmatic approachwas adopted. Resonances from the Atlas of NeutronResonances [132] were matched with those in the ENDFfile and, after matching, both the parameters and theiruncertainties were used to generate covariances with theresonance module of the EMPIRE code. For missingresonance uncertainties, an educated guess based onaverage parameter uncertainties was used. The uncertain-

18


ties of the negative resonance parameters were chosento reproduce uncertainties of the thermal constantsand the uncertainty of the scattering radius was takeninto account. With this input, the EMPIRE resonancemodule produced a MF=32 file with covariances for theresonance parameters.

10-2

10-1

100

dσ

/dΩ

(b/s

rad)

56Fe(n,elas)

Einc = 504 keV

C.M.Perey, 1991

W.E.Kinney, 1976

ENDF/B-VII.1

ENDF/B-VIII.0

10-2

10-1

100

0 20 40 60 80 100 120 140 160

dσ

/dΩ

(b/s

rad)

Angle (degree)

56Fe(n,elas)

Einc = 734 keV

C.M.Perey, 1991

W.E.Kinney, 1976

ENDF/B-VII.1

ENDF/B-VIII.0

FIG. 33. (Color online) Elastic angular distributions for neu-tron incident energies of 504 and 734 keV, compared toENDF/B-VII.1. By comparing the different datasets of bothpanels one can observe the anisotropic behavior of Kinney dataat lower incident energies.

Fast RegionThe JEFF-3.2 [151] evaluation contains inelastic cross sec-tions measured by Dupont et al. [152], even though theauthors have discovered normalization concerns and theresults were not published. New measurements were per-formed by Negret et al. [153], but with a lower resolution.The Dupont and Negret data were binned over a suitableenergy mesh and a piecewise linear scaling parameter wasconstructed to adjust Dupont data such that they agreeon average with the Negret data. It was also found thatthe energy calibration of the Negret data did not matchthe resonances of the total cross section. For this reason, acorrection was made to the energy scale which amountedto 2.5 keV at 1.8 MeV. The adopted inelastic cross sec-tions between 850 keV and 3.5 MeV are the ones fromJEFF-3.2 [151]. In addition, the inelastic cross section be-low 1 MeV was reduced by 15% to approximately agreewith Perey data [149]. The total inelastic cross section isshown in Fig. 34.

Level-density parameters for compound, target and the

different residual nuclides were fitted to achieve a reason-ably good agreement with the IRDFF evaluation [12, 13]for the (n, p) reaction. Even though this reaction waseventually replaced by IRDFF in the final file (with thedifference put into the elastic channel), the fit allowedconsistency between all other reactions. The (n, p) partialcross sections are re-scaled to match the total (n, p) crosssection in the IRDFF-v1.05 file.

Considering the reasoning detailed in Ref. [19], the totalcross sections adopted above the resonance range werefrom JEFF-3.2 [151], which originates from the Vonach-Tagesen evaluation [154] with superimposed fluctuationsthat correspond to the Berthold measurements [155] onnatFe. The contribution of the minor isotopes was takeninto account.The elastic cross section is defined as the difference

between the total and the remaining partial cross sections.To test the consistency, the cross section was resolution-broadened to 0.3 percent, achieving good agreement withKinney data.

0.5

1

1.5

2

1 2 3 4 5 6 7 8

Cro

ss S

ection (

b)


56Fe (n,inel)

Nelson*, 2004

Negret, 2013

ENDF/B-VII.1

ENDF/B-VIII.0

FIG. 34. (Color online) Evaluated 56Fe(n, n′) neutron inelasticcross section compared with data retrieved from EXFOR andwith the previous evaluation. The asterisk on the Nelson dataindicates that they are renormalized as described in Ref. [19].

Above the resonance range and up to 2.5 MeV theangular distributions correspond to re-fitted Kinney data[150] with some adjustments based on the comparisonwith Perey data [149] in the overlapping region. In therange 2.5-4.0 MeV the angular distributions are takenfrom Smith [156] while above said incident-energy regionthe EMPIRE [157] calculations are adopted.For the 56Fe fast region, covariances were computed

for the major reaction channels represented in the evalu-ations i.e., total, elastic, inelastic, capture, (n, 2n), and(n, p). Inelastic scattering to individual discrete levels(MT=51,...,90) and to the continuum (MT=91) were com-bined together into MT=4. Additionally, covariances forthe sum of all the remaining channels (MT=5) were pro-vided as well as cross-correlations among all reactions men-tioned above. These covariances were determined usingKalman filter-inspired Bayesian update procedure origi-nally coded by Kawano and Shibata in the KALMAN code

19


and included in EMPIRE [157]. The KALMAN methodol-ogy combines experimental uncertainties with the modelconstraints imposed through the sensitivity profiles pro-vided by the EMPIRE code. With it, EMPIRE modelparameters are sequentially adjusted to each experimentconsidered and cross section covariances are obtained bypropagating covariances of the model parameters. There-fore, all physical constraints and correlations are includedin the cross section covariances by construction in ad-dition to the correlations imposed by the experimentalcovariance.IRDFF recommendations [12, 13] were given special

treatment in the 56Fe evaluation. As discussed above,IRDFF cross sections were used in the evaluation pro-cedure in place of the experimental datasets and, afterfitting, EMPIRE calculated cross sections were replacedwith the IRDFF values. Therefore, it was desirable to alsoretain IRDFF covariances. This was achieved by adjust-ing the weights of the IRDFF cross sections to reproduceoriginal IRDFF uncertainties. The resulting off-diagonalpart of the covariance matrix necessarily differs from theIRDFF since the IRDFF covariance is purely based on56Fe(n, p) experimental data while the CIELO 56Fe in-cludes also physics constraints and the correlations withother reactions. The CIELO 56Fe(n, p) uncertainties areshown in Fig. 35.

5 10 15 20 25 30 35 40 45 50Incident Neutron Energy (MeV)

0

5

10

15

Un

ce

rta

inty

(%

)

ENDF/B-VIII.0 56

Fe(n,p)

IRDFF 56

Fe(n,p)

56Fe(n,p) Uncertainties

FIG. 35. (Color online) Evaluated 56Fe(n, p) neutron crosssection uncertainty, compared with IRDFF.

2. 54Fe, 57Fe and 58Fe

Although 56Fe is the dominant iron isotope, there is asignificant contribution from the minor isotopes in anynaturally occurring iron sample. Therefore, as part ofthe CIELO iron project, 54Fe, 57Fe and 58Fe were alsoevaluated. As their evaluations are covered in detail inthe iron evaluation summary paper also included in thisissue of Nuclear Data Sheets [19], we do not discuss themhere.

3. 59Co, 58−62,64Ni

LANL updated the reaction cross sections (above theresonance range) of several isotopes in the structural mate-rial region, 59Co and 58,59,60,61,62,64Ni based on the CoH3calculations. The MF6 representation is consistently usedfor the continuum energy and angular distributions foremitted particles as well as the γ-ray production, sinceMF6 is suitable for radiation shielding and γ heating cal-culations. This was especially important for 59Co, becauseisotropic angular distributions were given to many reac-tions in the previous evaluation and no proton and α-particle angular distributions were given.In the evaluation procedure, particular attention was

paid to the radiative capture, (n,p), (n,α), and (n,2n) crosssections by comparing with available experimental data.When experimental data from different laboratories wereinconsistent with each other, we revisited the nuclear dataused in the data analysis, and looked for a possible sys-tematic bias prior to performing the model calculations.Although the evaluation includes the 2H, 3H, 3He emissionchannels too, they tend to be purely theoretical predic-tions since few experimental data exit.

The α-particle production cross section for these nucleiwas calculated with an improved Iwamoto-Harada model[158], which reproduces the measured data at LANSCE.

4. 63,65Cu

Background & Previous EvaluationsOver the past decade, discrepancies between the computedand measured keff of criticality safety benchmark experi-ments containing copper were noticed by the nuclear dataand criticality safety community [159]. The most notableof these benchmarks is the set of highly enriched uraniummetal fuel systems with copper reflectors from the Interna-tional Criticality Safety Benchmark Evaluation Project’s(ICSBEP’s) Zeus experiment [160]. The US Departmentof Energy (DOE) Nuclear Data Advisory Group, whichmaintains and constantly updates lists of materials thatare considered important for applications in nuclear criti-cality safety, identified 63Cu and 65Cu as “important formeasurement and evaluation in the next five years.” Over25 other ICSBEP benchmark evaluations contain signif-icant amounts of copper, so the new evaluation resultsin statistically significant changes in the calculated keff .Therefore, improving the copper evaluation will not onlyallow for more accurate criticality safety calculations in-volving copper as a material, but it will also result inbetter agreement between calculated and measured inte-gral benchmark results.Copper is also commonly used as a minor structural

material in many fission power facilities, and it is an im-portant structural component in Scandinavian spent fuelfinal disposal canisters. Copper is also an important heatsink material for fusion power reactors and is used fordiagnostics, microwave waveguides, and mirrors in the In-

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ternational Thermonuclear Experimental Reactor (ITER).Consistent and correct nuclear data evaluations for theisotopes of copper are a high priority for applicationsto the International Fusion Materials Irradiation Facil-ity (IFMIF), where the equipment must withstand high-energy particle irradiation. The neutron cross section ofthe copper isotopes is also important to the astrophysicscommunity. The two stable copper isotopes lie along thebeta-decay valley of stable isobars involved in the slow-neutron-capture-process (s-process). The s-process occursin stars, is responsible for the creation of approximatelyhalf of the stable isotopes heavier than iron, and plays animportant role in the galactic chemical evolution.The copper resolved resonance region evaluations in

the ENDF/B-VII.1 library are based on the resonanceparameters from Mughabghab [161]. The authors of theprevious copper evaluations contained in the ENDF/B-VII.1 library used these resonance parameters to fit the1977 transmission data of Pandey et al. [162]. The au-thors noted the fit of the experimental data was improvedwhen an additional constant background was added.However, this yielded a total average cross section thatwas too large. In addition, the original authors indicatedthe need to include a capture background from 60 keVto 99.5 keV. The original evaluation for both isotopes ofcopper did not include evaluation of experimental capturedata. In the ENDF/B-VII.1 evaluation, the angulardistribution of neutrons from elastic scattering wasoriginally generated with the GENOA code [163]. Theangular distributions are represented as coefficients ofLegendre polynomials. There are only four energy pointsacross the ENDF/B-VII.1 resolved resonance region(RRR) for the representation of the angular distribution.They are 10−5 eV, 0.0253 eV, 10 keV, and 100 keV.

Resonance RegionTo address the nuclear criticality safety community’s con-cerns about the performance of the copper isotopes inintegral benchmarks, the resolved resonance region of thetwo copper isotopes was reevaluated based on the experi-mental data sets shown in Table XII. Furthermore, experi-

TABLE XII. Experimental data used in the RRR evaluation.Both stable copper isotopes were studied in each experiment.Table taken from Table 1 of Ref. [164].

Reference Energy Range (eV) Facility MeasurementPandey et al. [162] 32–185,000 ORELA Trans. at 78 mPandey et al. [162] 1,000–1,400,000 ORELA Trans. at 78 mGuber et al. [165] 100–300,000 GELINA Cap at 58 mGuber et al. [165] 100–90,000 GELINA Cap at 58 mSobes et al. [166] 0.01–0.1 MITR Trans. at 1.2 m

mental capture cross section measurements were analyzedfor the first time in the resonance evaluation of copper.Analyzing both the capture and transmission experimen-tal data sets allows for the capture-to-scattering ratio tobe set correctly for the entire RRR.

As shown in Table XII, the new resonance evaluation isbased on two sets of transmission data from the Oak RidgeElectron Linear Accelerator (ORELA) [162] and one dataset from the MIT Nuclear Reactor (MITR) [166], plus two

63,65Cu(n,γ) high-resolution measurements performed byGuber et al. [165] at GELINA in 2011. The first ORELAdata set ranges from 32 eV to 185 keV, and the seconddata set is from 1 keV to 1.4 MeV. The first data set hasbetter energy resolution than the second set in the energyregion below 10 keV. The second data set has significantlybetter energy resolution at energies above approximately60 keV. Finally, the third new experimental data set spansthe thermal region of 0.01–0.1 eV and was measured todetermine the low energy shape of the cross section andapproximate the negative-energy resonances.

The new evaluation was done based on the Reich-Mooreapproximation of the R-matrix theory of nuclear reso-nance reactions. The evaluation method used the gener-alized least squares (GLS) method implemented in theSAMMY evaluation code to find the optimum value ofthe resonance parameters.

All sets of experimental data in Table XII were analyzedsimultaneously.The external resonances were determined from fitting

the experimental data above 100 keV. The negative-energy external resonances received additional treatmentin this evaluation because of the availability of crosssection data spanning the thermal energy region (0.01–0.1 eV). The negative-energy external resonances wereadjusted to fit the shape of the total thermal cross sectioninstead of the typical practice of fitting a single value atthermal energy.

The angular distributions of elastic scattering are basedon averaging of angular distributions reconstructed fromresonance parameters following the Blatt and Biedenharnformalism [167]. This technique results in angular distri-butions that are more consistent with the evaluated elasticscattering cross section.A statistical search using the GLS methodology was

performed for the value of the scattering radius for bothisotopes based on the analyzed experimental data. No evi-dence was found to support a change from the 6.7 fm valuereported for both isotopes in Ref. [161]. The Wescott inte-gral calculated from the evaluated resonance parametersis unity, indicating a 1/v neutron capture cross section inthe thermal energy region.The Maxwellian-averaged capture cross sections

(MACS) for 63Cu and 65Cu are presented inFigs. 36 and 37, respectively. The MACS for bothisotopes were calculated from the resonance parametersevaluated based on the differential experimental data inTable XII and the high-energy evaluated cross sectionsdescribed in the section below. The systematically largerMACS value for 63Cu is corroborated by a new measure-ment from Weigand et al. at the Los Alamos NeutronScience Center (LANSCE) Experimental Facility [168].Further, feedback from integral experiments also sug-

gests that the capture cross section of 63Cu may be toolarge to fit the KADoNiS data [169, 170].Resonance parameter covariance matrices were gener-

ated through the GLS methodology in SAMMY. It iswell known that the GLS methodology results in unre-

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