1

Generation of thermal neutron
scattering cross section fromevaluated nuclear data
Kenichi Tada
Nuclear Science and Engineering Center
Japan Atomic Energy Agency

2Outline• Overview of evaluated nuclear data library• Thermal neutron scattering data in evaluated nuclear

data• Coherent elastic scattering• For crystalline materials （Bragg diffraction)• Incoherent elastic scattering• For non-crystalline materials• Incoherent inelastic scattering• Using thermal scattering law data : S(α, β)• Processing flow to generate cross section (XS) libraries• Overview of nuclear data processing• Processing of thermal neutron scattering data
• Generation of XS library3Evaluated nuclear data
• Containing many physical quantities for nucleus• Cross section, energy and angular distribution ofemitted particle, fission yield, half-life, …
• Major evaluated nuclear data library• JENDL (JAEA, Japan)• Japanese Evaluated Nuclear Data Library• ENDF/B (CSEWG, USA)• Evaluated Nuclear Data File
• JEFF (OECD/NEA)• Joint Evaluated Fission and Fusion File
• Others• TENDL (PSI, IAEA), BROND (Russia), CENDL (China)

4Physical quantities in evaluated nuclear data
For neutronics
calculation• Resonance parameter• Number of neutrons per fission• Fission spectrum• Cross section• Angular distribution of emitted particle• Energy distribution of emitted particle

For thermal
neutronscattering• Thermal neutron scattering data
• Fission yield• Decay data
• γ-ray data

（half-life, transition probability）（Intensity, Energy）…

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Data format for evaluated nuclear data
• The current format is ENDF-6 format• Formatted for ENDF/B library• Maintained by the cross section evaluation working group(CSEWG) in USA• Ref: A. Trkov, et. al., “ENDF-6 Format Manual,” BNL-203218-2018-INRE• The new format GNDS is defined in OECD/NEA• GNDS：Generalized Nuclear Data Structure• XML format• The format manual will be released in 2019
• Ref: Nuclear Data Sheets, 113, pp.3145-3171,(2012).

6Data structure of ENDF-6 format• ENDF-6 format consists mainly three stages• material ： One nucleus or material
Distinguished by MAT number• file： Physical quantities (XS, energy and angulardistributions, …)
Distinguished by MF number• section： Reaction type and data typeDistinguished by MT number

MT=1

MF=2

MT=2

MF=3

MT=3…

…

MAT

MF=1

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Data representation of ENDF-6 format• One or two dimensional tabulated functions• Tabulated pairs of x(n) and y(n) are provided• 𝐸𝐸1 , 𝜎𝜎1 , 𝐸𝐸2 , 𝜎𝜎2 , 𝐸𝐸3 , 𝜎𝜎3 , ⋯ , 𝐸𝐸𝑛𝑛 , 𝜎𝜎𝑛𝑛

• Available interpolation scheme• Constant (histogram), linear-linear, linear-log, log-linear, log-log• Parameters of function• Ex) resonance formula, polynomial representation,Legendre polynomials, …

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Typical file (MF) number• MF= 1: Comments, number ofImportant forthermal neutronscattering

neutrons per fission• MF= 2: Resonance parameters• MF= 3: Reaction cross sections• MF= 4: Angular distributions ofemitted particle• MF= 5: Energy distributions ofemitted particle• MF= 6: Angular and energy distributionsof emitted particle• MF= 7: Thermal neutron scattering data
• MF= 8: Fission yield and decay data
• MF= 9: Multiplicities of radioactiveproducts• MF=10: Production cross sections forradio nuclides• MF=11-15: Photon production• MF=30-40: Covariance data

Ref： BNL-203218-2018-INRE

9Example of evaluated nuclear data(n,2n) XS of Fe-56 from JENDL-4.0MFMATMT
2.605600+4 5.545440+100002631 3 16
1 HEAD-1.120270+7-1.120270+7001112631 3 16211200002631 3 16
31.140470+7 0.000000+0 1.170000+7 1.622410-2 1.200000+7 4.800450-22631 3 16
4TAB11.300000+7 2.138200-1 1.400000+7 3.891650-1 1.500000+7 5.134000-12631 3 1651.600000+7 5.817500-1 1.700000+7 6.107500-1 1.800000+7 6.118000-12631 3 1661.900000+7 5.977000-1 2.000000+7 5.759000-1
2631 3 1672631 3 099999 SEND

66 letters (11 data)

4 2 3

5 letters[MAT, 3, MT/ ZA, AWR, 0, 0, 0, 0] HEAD
[MAT, 3, MT/ QM, QI, 0, LR, NR, NP/ Eint/ σ(E)] TAB1
[MAT, 3, 0/ 0.0, 0.0, 0, 0, 0, 0] SENDZA, AWR : 1000.0×Z＋A, mass quantities for materials
QM：Mass-difference Q value (eV)QI : Reaction Q value
LR : Complex or “breakup” reaction flag

10Thermal neutron scattering data in nuclear data
• Evaluated nuclear data library contained in MF=7
• Three scattering reactions are available• Coherent elastic scattering (MF=7, MT=2)• For crystalline materials （Bragg diffraction)• Incoherent elastic scattering (MF=7, MT=2)• For non-crystalline materials• Incoherent inelastic scattering (MF=7, MT=4)• Using thermal scattering law data : S(α, β)• ENDF-6 format cannot contain both the parameters ofcoherent and incoherent elastic scattering cross sections• The new nuclear data format GNDS will be able to contain bothcross sections• Covariance data of thermal neutron scattering is not formatted and it
will be formatted in GNDS

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Overview of nuclear data processing
Evaluated Nuclear Data File(JENDL、ENDF、JEFF)• Generating cross section (XS)

• Not just a converter• Many processes, e.g.,linearization and Doppler
broadening, are required• NJOY of LANL is widely usedin the world

Cross Section (b)library from evaluated nuclear
data library

105

Nuclear Data Processing

Total XS of 235U (293.6 K)
104103102
101
100 10-4 10-2 100 102 104 106
Incident Neutron Energy (eV)• Development of domestic nuclear

data processing code wasrequired• We started to develop a newnuclear data processing code
FRENDY in 2013

Flux Distribution
Cross Section
library

Transport codes
MVP, PHITS,
MCNP

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Processing flow to
generate XS libraries

Evaluated nuclear
data file• Linearization and Doppler

broadening are required before
processing thermal neutron
scattering data
• ACE is a cross section data libraryformat for continuous-energy Monte
Carlo calculation code
• For MCNP, PHITS and Serpent

Resonance reconstruction(Linearization)
Doppler broadening
Processing thermal
neutron scattering data

Generation of thermal
multi group XS library

Generation of thermal
ACE file

Multi-group XSlibrary

ACE file13Sample input of NJOY reconr/ command
20 21/ input(tape20), output(tape21)'pendf tape for JENDL-4.0 H001‘ / identifier for PENDF(H in H2O)
125/ mat• Input file of NJOY isso difficult• Input data cannot bemade if user cannot
read the evaluatednuclear data file
• FRENDY can easilygenerate ACE file withsimple input• Evaluated nuclear data

file name andtemperature are only
required

1.00e-03 0.00
/ err, temp0/broadr/ command
20 21 22/ input(tape20), output(tape21)
125 1/ mat
1.00e-03
/ err
296.0
/ temp0/
thermr/ command
23 22 25
/ endf, pendf(in), pendf(out)
1 125 8 1 4 1 2 229 0 / mat_e, mat_p, bin no, temp no,
inela opt, ela opt, principal atom no,mtref, pri opt
296.0/ temp1.0E-3 5.0/ err, max eneacer/ command
23 25 0 30 31/ nendf, npend, ngend, nace, ndir
2 1 1 0.20
/ iopt(fast), iprint(max), itype, suffix'ACE file for 01_h_in_h2o' / identifier for ACE file125 296.0 'lwtr'/ matd, tempd, tname
1001 0 0/ moderator component za value229 64 230 0 1 1000.0 0 / mti, nbint, mte, ielas,nmix, emax, iwt
stop/

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Sample input of FRENDY (H in H2O)
• Simple input file
• Nuclear data file name (1H and H2O), ACE file nameand temperature are only required• Comment line is similar to C/C++• //~ or /* ~ */< Sample input of FRENDY (H in H2O) >ace_therm_mode //process TSL data
nucl_file_name
H001.dat
nucl_file_name_tsl H_in_H2O.txt
ace_file_name
H_in_H2O.ace
temp /* temp data */ 296.0 // [K]Ref. K. Tada, et. al., “Development and verification of a new nuclear data processing system FRENDY,” J. Nucl. Sci. Technol.,
54 [7], pp.806-817 (2017).
K. Tada, “Comparison of the processing results between FRENDY and NJOY”, Technical Meeting on the Nuclear Data
Processing (2017).
(https://www-nds.iaea.org/index-meeting-crp/TM_NDP/)

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Processing of thermal neutron scattering data
• Calculates scattering cross sections and angular andenergy distributions for secondary neutron• Neutronics calculation codes cannot treat the parameters ofthermal neutron scattering data
• Converting MF=7 into MF=3 (cross section) and MF=6 (angular andenergy distributions of emitted particle) is required• To reduce the data size of evaluated nuclear data file,parameters of thermal neutron scattering data are contained• The large amount of data size is required to storage XS and angularand energy distributions for secondary neutronE’E

μ=cosθlab16

Evaluated nuclear data (coherent elastic)• Temperature• Number of Bragg edge
• Bragg edges andstructure factors
σ𝑐𝑐𝑐𝑐𝑐 𝐸𝐸, 𝐸𝐸 ′ , 𝜇𝜇

Cross-section [b]

10.0

1.0

Coherent elastic scattering XS(Graphite, 296K, JENDL-4.0)
0.1

1.0×10-4𝐸𝐸𝑖𝑖 <𝐸𝐸

1.0×10-2
1.0×100
Incident neutron energy [eV]1= � 𝑠𝑠𝑖𝑖 𝛿𝛿 𝜇𝜇 − 𝜇𝜇𝑖𝑖 𝛿𝛿 𝐸𝐸 − 𝐸𝐸 ′𝐸𝐸𝑖𝑖• 𝑠𝑠𝑖𝑖 : structure factors• 𝐸𝐸𝑖𝑖 : energy of Bragg edge
• 𝐸𝐸 : incident energy• 𝜇𝜇 : scattering cosine in laboratory system

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Evaluated nuclear data (incoherent elastic)• Temperature• Bound scattering XS• Debye-Waller factor

Cross-section [b]

100.0
10.0

1.00.1𝑖𝑖𝑖𝑖𝑖𝑖

σIncoherent elastic scattering XS(Hin ZrH, 296K, JENDL-4.0)
1.0×10-4
1.0×10-2
1.0×100
Incident neutron energy [eV]𝜎𝜎𝑏𝑏 −2𝑊𝑊𝐸𝐸 1−𝜇𝜇𝐸𝐸, 𝐸𝐸 , 𝜇𝜇 = 𝑒𝑒𝛿𝛿 𝐸𝐸 − 𝐸𝐸 ′2′• 𝜎𝜎𝑏𝑏 : Characteristics bound scattering XS• 𝑊𝑊 : Debye-Waller integral divided by the atomic mass(eV−1) as a function of temperature (K)18

Evaluated nuclear data (incoherent inelastic)• Temperature• S(α,β), α, and β• Free atom scattering XS

Cross section [b]• Number of atoms

10000
1000

Incoherent inelastic scattering XS(Hin H2O, 296K, JENDL-4.0)

10010𝑁𝑁𝑠𝑠

𝑀𝑀𝑛𝑛
𝐴𝐴𝑛𝑛 + 1𝑖𝑖𝑖𝑖𝑖𝑖′
𝜎𝜎𝐸𝐸, 𝐸𝐸 , 𝜇𝜇 = �𝜎𝜎𝑓𝑓𝑓𝑓
2k B 𝑇𝑇𝐴𝐴𝑛𝑛
𝑛𝑛=0

1.0×10-4
1.0×10-2
1.0×100
Incident neutron energy [eV]2𝐸𝐸 ′ −𝛽𝛽𝑒𝑒 2 𝑆𝑆𝑛𝑛 𝛼𝛼𝑛𝑛 , 𝛽𝛽𝐸𝐸

• 𝑁𝑁𝑠𝑠 : Number of non-principal scattering atom types• 𝑀𝑀𝑛𝑛 : Number of n-th type atoms• 𝜎𝜎𝑓𝑓𝑓𝑓 : Characteristics free atom scattering cross section

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Generation of ACE file
• Continuous energyMonte Carlo calculation 0.15
0.10
codes use cumulative
probability distribution 0.050.00(PDF/CDF)• Cross section, angularand energy distributions
are converted tocumulative probability
distribution• PDF: Probability DensityFunction• CDF : Cumulative
Density Function【Example of PDF and CDF】
PDF
CDF

1.00.50.00246810 12 14 16

From linear-linear to PDF/CDF
0.15

PDF

0.10

CDF

1.00.50.05

0.00.00
02468

10 12 14 16

From histogram to PDF/CDF

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Required data to generate XS library• Two types of data are available to generate ACE file
• Parameters of thermal neutron scattering data (MF=7)• Scattering cross section (MF=3) and angular and energy
distributions for secondary neutron (MF=6)• The unified energy grid is used to generate ACE file
• These data must be calculated in specified incident energy (10-5 ~ 10eV) using linear-linear, linear-log, log-linear or log-log interpolation• If users generate XS library from the latter type,modification of nuclear data processing code is required• FRENDY is a good tool to generate XS library from it!!

E’E

μ=cosθlab

Cross section [b]

10000
1000

Incoherent inelastic scattering XS(Hin H2O, 296K, JENDL-4.0)

100
10

1.0×10-4
1.0×10-2
1.0×100
Incident neutron energy [eV]

21Conclusions• Overview of evaluated nuclear data library• Thermal neutron scattering data in evaluatednuclear data
• Coherent and incoherent elastic scattering• Incoherent inelastic scattering• Processing flow to generate XS libraries• Two types of data are available to generate ACE file
• Parameters of thermal neutron scattering data
• Scattering cross section and angular and energy distributions forsecondary neutron• FRENDY is a good tool to generate XS library fromthese data