DATA FORMATS AND PROCEDURES

FOR THE EVALUATED NUCLEAR DATA FILE

0. ENDF-6 PREFACE

This update to revision 4/01 of "Data Formats and Procedures for the Evaluated Nuclear Data File, ENDF" pertains to the version 6 of the ENDF formats. The seventh version of the ENDF/B library, ENDF/B-VII, uses these formats.

Below is a list of changes to the formats and procedures that appear in this edition. In addition, some typographical error corrections are included. Users of this manual who note deficiencies or have suggestions are encouraged to contact the National Nuclear Data Center.

Major updates to Manual for Revision June 2005

Section Page Update

0.7.3 New record type: INTG (N. Larson)

2. Replacement of LRF=5 and 6 with LRF=7 format for R-Matrix parameters. Miscellaneous corrections. (N. Larson)

32. Addition of LCOMP=2 format for resonance-parameter covariance matrices (N. Larson)

Appendix D Addition of D.1.7, Equations for LRF=7 format. Deletion of Sections D.1.5 and D.1.6. Other miscellaneous corrections. (N. Larson)

Major updates to Manual for Revision 2004

Section Page Update

0. 0.5 Added table of library numbers (NLIB)

0.23-.25 Recommended two-dimensional interpolation procedures (M. Greene)

1. 1.7-.8 Energy dependent delayed-group constants added.

2. Miscellaneous corrections and updates (C. Lubitz).

Updates for 2 channel spins (N. Larson, C. Lubitz).

4. 4.1-.4 Removed elastic transformation matrix (C. Dunford)

Increase to 2000, the number of energies for which angular distributions are given (JEFF)

Increase to 201, the number of angles at which a tabular distribution can be given for an incident energy. (JEFF)

6. 6.3-.4 Allow NA=2 for Kalbach-Mann parameterization (JEFF)

6.6 Equation 6.4 corrected (JENDL)

6.10 Add LTP=15 interpolation for ratio to Rutherford scattering (JENDL)

6.12 Revised equation in laboratory frame for LAW=6 (M. Greene)

7. 7.2,7.4 Corrected incoherent inelastic scattering equations (C. Lubitz)

8. 8.9 Added section for stable nucleus (JEFF)

9. 9.1-.2 Added final product identifier, IZAP (JEFF)

10. 10.1-.2 Added final product identifier, IZAP (JEFF)

Appendix D Replaced Section D.3.1 (C. Lubitz).

Appendix F Corrected limit on number of Legendre coefficients

Appendix G Increased limits of number of incident energies and number of angles per incident energy in File 4, 6 and 14

Increased the number of allowed subsections in File 6

0.1. Introduction to the ENDF-6 Format

The ENDF formats and libraries are decided by the Cross Section Evaluation Working Group (CSEWG), a cooperative effort of national laboratories, industry, and universities in the U.S. and Canada,¹ and are maintained by the National Nuclear Data Center (NNDC).

Earlier versions of the ENDF format provided representations for neutron cross sections and distributions, photon production from neutron reactions, a limited amount of charged-particle production from neutron reactions, photo-atomic interaction data, thermal neutron scattering data, and radionuclide production and decay data (including fission products). Version 6 (ENDF-6) allows higher incident energies, adds more complete descriptions of the distributions of emitted particles, and provides for incident charged particles and photonuclear data by partitioning the ENDF library into sub-libraries. Decay data, fission product yield data, thermal scattering data, and photo-atomic data have also been formally placed in sub-libraries. In addition, this rewrite represents an extensive update to the Version V manual.²

0.2. Philosophy of the ENDF System

The ENDF system was developed for the storage and retrieval of evaluated nuclear data to be used for applications of nuclear technology. These applications control many features of the system including the choice of materials to be included, the data used, the formats used, and the testing required before a library is released. An important consequence of this is that each evaluation must be complete for its intended application. If required data are not available for particular reactions, the evaluator should supply them by using systematics or nuclear models.

The ENDF system is logically divided into formats and procedures. Formats describe how the data are arranged in the libraries and give the formulas needed to reconstruct physical quantities such as cross sections and angular distributions from the parameters in the library. Procedures are the more restrictive rules that specify what data types must be included, which format can be used in particular circumstances, and so on. Procedures are, generally, imposed by a particular organization, and the library sanctioned by the Cross Section Evaluation Working Group (CSEWG) is referred to as ENDF/B. Other organizations may use somewhat different procedures, if necessary, but they face the risk that their libraries will not work with processing codes sanctioned by CSEWG.

0.2.1. Evaluated data

An evaluation is the process of analyzing experimentally measured cross-section data, combining them with the predictions of nuclear model calculations, and attempting to extract the true value of a cross section. Parameterization and reduction of the data to tabular form produces an evaluated data set. If a written description of the preparation of a unique data set from the data sources is available, the data set is referred to as a documented evaluation.

0.2.2. ENDF/B Library

The ENDF/B library maintained at the National Nuclear Data Center (NNDC) contains the recommended evaluation for each material. Each material is as complete as possible; however, completeness depends on the intended application. For example, when a user is interested in performing a reactor physics calculation or in doing a shielding analysis, he needs evaluated data for all neutron-induced reactions, covering the full range of incident neutron energies, for each material in the system that he is analyzing. Also, the user expects that the file will contain information such as the angular and energy distributions for secondary neutrons. For another calculation, the user may only need a minor isotope for determining activation, and would then be satisfied by an evaluation that contains only reaction cross sections.

ENDF/B data sets are revised or replaced only after extensive review and testing. This allows them to be used as standard reference data during the lifetime of the particular ENDF/B version.

0.2.3. Choices of Data

The data sets contained on the ENDF/B library are those chosen by CSEWG from evaluations submitted for review. The choice is made on the basis of requirements for applications, conformance of the evaluation to the formats and procedures, and performance in testing. The data set that represents a particular material may change when (1) new significant experimental results become available, (2) integral tests show that the data give erroneous results, or (3) user's requirements indicate a need for more accurate data and/or better representations of the data for a particular material. New or revised data sets are included in new releases of the ENDF/B library.

0.2.4. Experimental Data Libraries

NNDC maintains a library for experimentally measured nuclear reaction data (CSISRS). In addition to the data, the CSISRS library contains bibliographic information, as well as details about the experiment (standard, renormalization, corrections, etc.).

At the beginning of the evaluation process the evaluator may retrieve the available experimental data for a particular material by direct access to the CSISRS database via the World Wide Web or using the NNDC Online Data Service.³ Alternately, the data may be requested from the NNDC, and transmitted in the form of listings, plots, and/or files, which may be formatted to satisfy most needs.

0.2.5. Processing Codes

Once the evaluated data sets have been prepared in ENDF format, they can be converted to forms appropriate for testing and actual applications using processing codes. Processing codes that generate group-averaged cross sections for use in neutronics calculations from the ENDF library have been written. These codes⁴ include such functions as resonance reconstruction, Doppler broadening, multigroup averaging, and/or rearrangement into specified interface formats.

The basic data formats for the ENDF library have been developed in such a manner that few constraints are placed on using the data as input to the codes that generate any of the secondary libraries.

0.2.6. Testing

All ENDF/B evaluations go through at least some testing before being released as a part of a library. Phase 1 testing uses a set of utility codes⁵ maintained by NNDC and visual inspection by a reviewer to assure that the evaluation conforms to the current formats and procedures, takes advantage of the best recent data, and chooses format options suited to the physics being represented. Phase 2 uses calculations of data testing "benchmarks," when available, to evaluate the usefulness of the evaluation for actual applications.⁶ This checking and testing process is a critically important part of the ENDF system.

0.2.7. Documentation

The system is documented by a set of ENDF reports (see Section 0.8) published by the National Nuclear Data Center at Brookhaven National Laboratory. In addition, the current status of the formats, procedures, evaluation process, and testing program is contained in the Summary of the Meetings of the Cross Section Evaluation Working Group.

0.3. General Description of the ENDF System

The ENDF libraries are a collection of documented data evaluations stored in a defined computer-readable format that can be used as the main input to nuclear data processing programs. For this reason, the ENDF format has been constructed with the processing codes in mind. The ENDF format uses 80-character records. Parameters are written in the form of FORTRAN variables (that is, integers start with the letters I, J, K, L, M, or N, and parameters starting with other letters represent real numbers). A complete list of all the parameters defined for the ENDF-6 format will be found in Appendix A (Glossary).

0.3.1. Library Organization

Each ENDF evaluation is identified by a set of key parameters organized into a hierarchy. Following is a list of these parameters and their definitions.

Library	NLIB	a collection of evaluations from a specific evaluation group (e.g., NLIB 0=ENDF/B).
Version	NVER	one of the periodic updates to a library in ENDF format (e.g., NVER 6=ENDF/B-VI). A change of version usually implies a change in format, standards, and procedures. A revision number is appended to the library/version name for each succeeding revision of the data set; for example, ENDF/B-VI.2. There is no parameter for the revision number in the format.

Sublibrary	NSUB	set of evaluations for a particular data type, (e.g., 4=radioactive decay data, 10=incident-neutron data, 12=thermal neutron scattering data). (See Table 0.1 for the complete list of sub-libraries).
Format	NFOR	format in which the data is tabulated; tells the processing codes how to read the subsequent data records (e.g., NFOR 6 = ENDF-6).
Material	MAT	the target in a reaction sub-library, or the radioactive (parent) nuclide in a decay sub-library; see Section 0.3.2.
Mod	NMOD	"modification" flag; see Section 0.3.3.
File	MF	subdivision of a material (MAT); each file contains data for a certain class of information (e.g., MF=3 contains reaction cross sections, MF=4 contains angular distributions). MF runs from 1 to 99. (See Table 0.2 for a complete list of assigned MF numbers).
Section	MT	subdivision of a file (MF) ; each section describes a particular reaction or a particular type of auxiliary data (e.g., MT=102 contains capture data). MT runs from 1 to 999. (See Appendix B for a complete list of assigned MT numbers).

0.3.2. Library (NLIB)

A library is a collection of material evaluations from a recognized evaluation group. Each of these collections is identified by an NLIB number. Currently defined NLIB numbers are given in the table below.

NLIB	Library Definition
0	ENDF/B - United States Evaluated Nuclear Data File
1	ENDF/A - United States Evaluated Nuclear Data File
2	JEFF - NEA Joint Evaluated File (formerly JEF)
3	EFF - European Fusion File (now part of JEFF)
4	ENDF/B High Energy File
5	CENDL – China Evaluated Nuclear Data Library
6	JENDL – Japan Evaluated Nuclear Data Library
31	INDL/V – IAEA Evaluated Neutron Data Library
32	INDL/A – IAEA Nuclear Data Activation Library
33	FENDL – IAEA Fusion Evaluated Nuclear Data Library
34	IRDF – IAEA International Reactor Dosimetry File
35	BROND – Russian Evaluated Nuclear Data File (IAEA version)
36	INGDB-90 – Geophysics Data
37	FENDL/A – FENDL activation evaluations
41	BROND – Russian Evaluated Nuclear Data File (original version)

0.3.3. Material (MAT)

A material is defined as either an isotope or a collection of isotopes. It may be a single nuclide, a natural element containing several isotopes, or a mixture of several elements (compound, alloy, molecule, etc.). A single isotope can be in an excited or isomeric state. Each material in an ENDF library is assigned a unique identification number, designated by the symbol MAT, which ranges from 1 to 9999.⁷

The assignment of MAT numbers for ENDF/B-VI is made on a systematic basis assuming uniqueness of the four digit MAT number for a material. A material will have the same MAT number in each sub-library (decay data, incident neutrons, incident charged particles, etc.).

One hundred MAT numbers (Z01-Z99) have been allocated to each element Z, through Z = 98. Natural elements have MAT numbers Z00. The MAT numbers for isotopes of an element are assigned on the basis of increasing mass in steps of three, allowing for the ground state and two metastable states.⁸ In the ENDF/B files, which are application oriented, the evaluations of neutron excess nuclides are of importance, since this category of nuclide is required for decay heat applications. Therefore, the lightest stable isotope is assigned the MAT number Z25 so that the formulation can easily accommodate all the neutron excess nuclides.

For the special cases of elements from einsteinium to lawrencium (Z≥99) MAT numbers 99xx are assigned, where xx = 20, 25, 20, l5, and l2 for elements 99 to 103 respectively, one covers the known nuclides with allowance for expansion.

For mixtures, compounds, alloys, and molecules, MAT numbers between 0001 and 0099 are assigned on a special basis (see Appendix C).

0.3.4. Material modification (MOD)

All versions of a data set (i.e., the initial release, revisions, or total re-evaluations) are indicated using the material "modification" flags. For the initial release of ENDF/B-VI, the modification flag for each material (MAT) and section (MT) carried over from previous versions is set to zero (MOD 0); for new evaluations they are set to one (MOD 1). Each time a change is made to a material, the modification flag for the material is incremented by one. The modification flag for each section changed in the revised evaluation is set equal to the new material modification number. If a complete re-evaluation is performed, the modification flag for every section is changed to equal the new material "modification" number.

As an example, consider the following. Evaluator X evaluates a set of data for 235U. After checking and testing, the evaluator feels that the data set is satisfactory and transmits it to the NNDC. The Center assigns the data set a MAT number of 9228 subject to CSEWG's approval of the evaluation. This evaluation has "modification" flags equal to 1 for the material and for all sections. After the file is released, user Y retrieves MAT 9228 from the Center's files, adds it to his ENDF library as material 9228, and refers to it in later processing programs by this number. Should the evaluation of material 9228 subsequently be revised and released with CSEWG's approval, the material will have a MOD flag of 2. This material would have MOD flags of 2 on each revised section, but the unchanged sections will have MOD flags of 1.

0.4. Contents of an ENDF Evaluation

As described above, sub-library (NSUB) and material (MAT) specify the target and projectile for a reaction evaluation or the radioactive nuclide for a decay evaluation. MF and MT indicate the type of data represented by a section and the products being defined.

The sub-library distinguishes between different types of data using NSUB = 10*IPART+ITYPE. In this formula, IPART=1000*Z+A defines the incident particle; use IPART=0 for incident photons or no incident particle (decay data), use IPART=11 for incident electrons, and IPART=0 for photo-atomic or electro-atomic data. The sub-libraries allowed for ENDF-6 are listed in Table 0.1.

Table 0.1

Sub-library Numbers and Names

NSUB	IPART	ITYPE	Sub-library Names
NSUB	IPART	ITYPE	Sub-library Names
0	0	0	Photo-Nuclear Data
1	0	1	Photo-Induced Fission Product Yields
3	0	3	Photo-Atomic Interaction Data
4	0	4	Radioactive Decay Data
5	0	5	Spontaneous Fission Product Yields
6	0	6	Atomic Relaxation Data
10	1	0	Incident-Neutron Data
11	1	1	Neutron-Induced Fission Product Yields
12	1	2	Thermal Neutron Scattering Data
113	11	3	Electro-Atomic Interaction Data
10010	1001	0	Incident-Proton Data
10011	1001	1	Proton-Induced Fission Product Yields
10020	1002	0	Incident-Deuteron Data
...
20040	2004	0	Incident-Alpha data

The files (MF) allowed are summarized in Table 0.2, and their use in the different sub-libraries is discussed following.

Table 0.2 Definitions of File Types (MF)
MF	Description
1	General information
2	Resonance parameter data
3	Reaction cross sections
4	Angular distributions for emitted particles
5	Energy distributions for emitted particles
6	Energy-angle distributions for emitted particles
7	Thermal neutron scattering law data
8	Radioactivity and fission-product yield data
9	Multiplicities for radioactive nuclide production
10	Cross sections for radioactive nuclide production
12	Multiplicities for photon production
13	Cross sections for photon production
14	Angular distributions for photon production
15	Energy distributions for photon production
23	Photo- or electro-atomic interaction cross sections
26	Electro-atomic angle and energy distribution
27	Atomic form factors or scattering functions for photo-atomic interactions
28	Atomic relaxation data
30	Data covariances obtained from parameter covariances and sensitivities
31	Data covariances for nu(bar)
32	Data covariances for resonance parameters
33	Data covariances for reaction cross sections
34	Data covariances for angular distributions
35	Data covariances for energy distributions
39	Data covariances for radionuclide production yields
40	Data covariances for radionuclide production cross sections

The following MF numbers have been retired: 16, 17, 18, 19, 20, 21, 22, 24, and 25.

0.4.1. Incident-Neutron Data (NSUB 10)

The procedures for describing neutron-induced reactions for ENDF/B-VI have been kept similar to the procedures used for previous versions so that current evaluations can be carried over, and in order to protect existing processing capabilities. The new features have most of their impact at high energies (above 5-10 MeV) or low atomic weight (²H, ⁹Be), and include improved energy-angle distributions, improved nuclear heating and damage capabilities, improved charged-particle spectral data, and the use of R-matrix or R-function resonance parameterization.

Each evaluation starts with a descriptive data and directory, File 1 (see Section 1.1). For fissionable isotopes, sections of File 1 can be given to describe the number of neutrons produced per fission and the energy release from fission.

A File 2 is always given. For some materials, it may contain only the effective scattering radius, and for other materials, it may contain complete sets of resolved and/or unresolved resonance parameters.

A File 3 is always given. The required energy range is from the threshold or from 10-5eV to 20 MeV, but higher energies are allowed. There is a section for each important reaction or sum of reactions. The MT numbers for these sections are chosen based on the emitted particles as described in Section 0.5 (Reaction Nomenclature). For resonance materials in the resolved resonance energy range, the cross sections for the elastic, fission, and capture reactions are normally the sums of the values given in File 3 and the resonance contributions computed from the parameters given in File 2. An exception to this rule is allowed for certain derived evaluations (see LRP=2 in Section 1.1). In the unresolved resonance range, the self-shielded cross sections will either be sums of File 2 and File 3 contributions, as above, or File 3 values multiplied by a self-shielding factor computed from File 2. (See Sections 2.3.1 and 2.4.21.)

Distributions for emitted neutrons and other particles or nuclei are given using File 4, Files 4 and 5, or File 6. As described in more detail below, File 4 is used for simple two-body reactions (elastic, discrete inelastic). Files 4 and 5 are used for simple continuum reactions, which are nearly isotropic, have minimal pre-equilibrium component, and emit only one important particle. File 6 is used for more complex reactions that require energy-angle correlation, that are important for heating or damage, or that have several important products, which must be tallied.

If any of the reaction products are radioactive, they should be described further in File 8. This file indicates how the production cross section is to be determined (from File 3, 6, 9, or 10) and gives minimal information on the further decay of the product. Additional decay information can be retrieved from the decay data sub-library when required.

Note that yields of particles and residual nuclei are sometimes implicit; for example, the neutron yield for A(n,2n) is two and the yield of the product A-1 is one. If File 6 is used, all yields are explicit. This is convenient for computing gas production and transmutation cross sections. Explicit yields for radioactive products may be given in File 9, or production cross sections can be given in File 10. In the latter case, it is possible to determine the yield by dividing by the corresponding cross section from File 3. File 9 is used in preference to File 10 when strong resonances are present (e.g., radiative capture).

For compatibility with earlier versions, photon production and photon distributions can be described using File 12 (photon production yields), File 13 (photon production cross sections), File 14 (photon angular distributions), and File 15 (photon energy distributions). Note that File 12 is preferred over File 13 when strong resonances are present (capture, fission). Whenever possible, photons should be given with the individual reaction that produced them using File 12. When this cannot be done, summation MT numbers can be used in Files 12 or 13 as described in Section 0.5.9.

When File 6 is used to represent neutron and charged-particle distributions for a reaction, it should also be used for the corresponding photon distribution. This makes an accurate energy-balance check possible for the reaction. When emitted photons cannot be assigned to a particular reaction, they can be represented using summation MT numbers as described in Section 0.5.9.

Finally, covariance data are given in Files 30-40. Procedures for these files are given in Sections 30-40.

0.4.2. Thermal Neutron Scattering (NSUB 12)⁹

Thermal neutron scattering data are kept in a separate sub-library because the targets are influenced by their binding to surrounding atoms and their thermal motion; therefore, the physics represented¹⁰ requires different formats than other neutron data. The data extend to a few eV for several molecules, liquids, solids, and gases. As usual, each evaluation starts with descriptive data and directory file (see Section 1.1). The remaining data is included in File 7. Either the cross sections for elastic coherent scattering, if important, are derived from Bragg edges and structure factors, or cross sections for incoherent elastic scattering are derived from the bound cross section and Debye-Waller integral. Finally, scattering law data for inelastic incoherent scattering are given, using the S(α,β) formalism and the short-collision-time approximation.

0.4.3. Fission Product Yield Data

Data for the production of fission products are given in different sub-libraries according to the mechanism inducing fission. Currently, sub-libraries are defined for neutron-induced fission product yields, and for yields from spontaneous fission. The format also allows for future photon- and charged-particle-induced fission. Each material starts with a descriptive data and directory file (see Section 1.1). The remaining data is given in File 8, which contains two sections: independent yields, and cumulative yields. As described in Section 8.2, the format for these two sections is identical. Covariance data for File 8 are self-contained.

0.4.4. Radioactive Decay Data (NSUB=4)

Evaluations of decay data for radioactive nuclides are grouped together into a sub-library. This sub-library contains decay data for all radioactive products (e.g., fission products and activation products). Fission product yields and activation cross sections will be found elsewhere. Each material contains two, three, or four files, and starts with a descriptive data and directory file (see Section 1.1). For materials undergoing spontaneous fission, additional sections in File 1 give the total, delayed, and prompt fission neutron yields. In addition, the spectra of the delayed and prompt neutrons are given in File 5. The File 5 formats are the same as for induced fission (see Section 5), and the distributions are assumed to be isotropic in the laboratory system. File 8 contains half-lives, decay modes, decay energies, and radiation spectra (see Section 8.3). Finally, covariance data for the spectra in File 5 may be given in File 35; covariance data for File 8 are self-contained.

0.4.5. Photo-Nuclear (NSUB=0) and Charged-Particle (NSUB≥10010) Sub-libraries

Evaluations for incident charged-particle and photo-nuclear reactions are grouped together into sub-libraries by projectile. As usual, each evaluation starts with a descriptive data and directory file (see Section 1.1). For particle-induced fission or photo-fission, File 1 can also contain sections giving the total, delayed, and prompt number of neutrons per fission, and the energy released in fission. Resonance parameter data (File 2) may be omitted entirely (see LRP=-1 in Section 1.1).

Cross sections are given in File 3. The MT numbers used are based upon the particles emitted in the reaction as described in Section 0.5. Explicit yields for all products (including photons) must be given in File 6. In addition, the charged-particle stopping power should be given. If any of the products described by a section of File 6 are radioactive, they should be described further in a corresponding section of File 8. This section will give half-life, minimum information about the decay chain, and decay energies for the radioactive product. Further details, if required, can be found in the decay data sub-library.

Angular distributions or correlated energy-angle distributions can be given for all particles, recoil nuclei, and photons in File 6. It is also possible to give only the average particle energy for less important reactions, or even to mark the distribution "unknown." (See 6.2.1.)

Finally, Files 30 to 40 might be used to describe the covariances for charged-particle and photo-nuclear reactions.

0.4.6. Photo-Atomic Interaction Data (NSUB 3)

Incident photon reactions with the atomic electrons¹¹ are kept in a separate sub-library. These data are associated with elements rather than isotopes. Each material starts with a descriptive data and directory file (see Section 1.1), as usual. In addition, the material may contain a File 23 for photon interaction cross sections, and File 27 for atomic form factors.

0.4.7. Electro-Atomic Interaction Data (NSUB=113)

Incident electron reactions with the atomic electrons are also kept in a separate sublibrary. These data are again associated with elements rather than isotopes. Each material starts with a descriptive data and directory file (see Section 1.1), as usual. In addition, File 23 is given for the elastic, ionization, bremsstrahlung, and excitation cross sections, and File 26 is given for the elastic angular distribution, the bremsstrahlung photon spectra and energy loss, the excitation energy transfer, and the spectra of the scattered and recoil electrons associated with subshell ionization.

0.4.8. Atomic Relaxation Data (NSUB=6)

The target atom can be left in an ionized state due to a variety of different types of interaction, such as photon or electron induced ionization, internal conversion, etc. This section provides the data needed to describe the relaxation of an ionized atom back to neutrality. This includes subshell energies, transition energies, transition probabilities, and other parameters needed to compute the X-ray and electron spectra due to atomic relaxation.

The materials are elements. Each material starts with a descriptive data and directory file (see Section 1.1), as usual. In addition, a File 28 is given containing the relaxation data for all the subshells defined in the photo-atomic or electro-atomic sublibraries.

0.4.9. Energy and Angular Distributions of Reaction Products (Files 4, 5, and 6)

Several different options are available in the ENDF-6 format to describe the distribution in energy and angle of reaction products. In most cases, the double differential cross section of the emitted particle in barns/(eV-sr) is represented by

(0.1)

where µ is the cosine of the emission angle,

E is the energy of the incident particle,

E′ is the energy of the emitted particle,

σ(E) is the reaction cross section,

y(E) is the yield or multiplicity of the emitted particle, and

f(µ,E,E′) is the normalized distribution function in (eV-unit cosine)-1.

For simple two-body reactions, the energy of the emitted particle can be determined from kinematics (see Appendix E); therefore,

(0.2)

where ξ is defined by Eq. (E.5) in Appendix E.

The distribution function f(µ,E) can be given as a section of File 4 with no corresponding section in File 5, or as a section of File 6 with no corresponding sections in Files 4 or 5. For simple continuum reactions, the full distribution is sometimes given as a product of an angular distribution and an energy distribution:

(0.3)

The angular function is given in File 4, and g(E,E′) is given in File 5. This simple continuum format does not allow adequate description of energy-angle correlations, and it can only describe one emitted particle. Emitted photons can be described by this scheme also, but the files used are 14 and 15.

For the more complex reactions, the full distribution function is given in File 6. This file allows for all reaction products to be described, and it allows for energy-angle correlation of the emitted particles.

0.5. Reaction Nomenclature - MT

The following paragraphs explain how to choose MT numbers for particle-induced and photo-nuclear reactions for ENDF-6. A complete list of the definitions of the MT numbers will be found in Appendix B.

0.5.1. Elastic Scattering

Elastic scattering is a two-body reaction that obeys the kinematic equations given in Appendix E. The sections are labeled by MT=2 (except for photo-atomic data, see Section 23). For incident neutrons, the elastic scattering cross section is determined from File 3 together with resonance contributions, if any, from File 2. The angular distribution of scattered neutrons is given in File 4.

For incident charged particles, the Coulomb scattering makes it impossible to define an integrated cross section, and File 3, MT=2 contains either a dummy value of 1.0 or a "nuclear plus interference" cross section defined by a particular cutoff angle. The rest of the differential cross section for the scattered particle is computed from parameters given in File 6, MT=2 (see Section 6.2.6).

0.5.2. Simple Single Particle Reactions

Many reactions have only a single particle and a residual nucleus (and possibly photons) in the final state. These reactions are associated with well-defined discrete states or a continuum of levels in the residual nucleus, or they may proceed through a set of broad levels that may be treated as a continuum. The MT numbers to be used are:

Discrete	Continuum	Discrete+Continuum	Emitted Particle
50-90	91	4	n
600-648	649	103	p
650-698	699	104	d
700-748	749	105	t
750-798	799	106	3He
800-848	849	107	α

By definition, the emitted particle is the lighter of the two particles in the final state.

If the reaction is associated with a discrete state in the residual nucleus, use the first column of numbers. In a typical range, MT=50 leaves the residual nucleus in the ground state, MT=51 leaves it in the first excited state, MT=52 in the second, and so on. The elastic reaction uses MT=2 as described above; therefore, do not use MT=50 for incident neutrons, do not use MT=600 for incident protons, and so on. For incident neutrons, the discrete reactions are assumed to obey two-body kinematics (see Appendix E), and the angular distribution for the particle is given in File 4 or File 6 (except for MT=2). If possible, the emitted photons associated with discrete levels should be represented in full detail using the corresponding MT numbers in File 6 or File 12. For incident charged particles, the emitted particle must be described in File 6. A two-body law can be used for narrow levels, but broader levels can also be represented using energy-angle correlation. Photons associated with the particle should be given in the same section (MT) of File 6 when possible.

If the reaction is associated with a range of levels in the residual nucleus (i.e., continuum), use the second column of MT numbers. For incident neutrons, Files 4 and 5 are allowed for compatibility with previous versions, but it may be necessary to use File 6 to obtain the desired accuracy. When Files 4 and 5 are used, photons should be given in File 12 using the same MT number if possible. For more complicated neutron reactions or incident charged particles, File 6 must be used for the particle and the photons.

The "sum" MT numbers are used in File 3 for the sum of all the other reactions in that row, but they are not allowed for describing particle distributions in Files 4, 5, or 6. As an example, a neutron evaluation might contain sections with MF/MT=3/4, 3/51, 3/91, 4/51, and 6/91. A deuteron evaluation might contain sections with 3/103, 3/600, and 6/600 (the two sections in File 3 would be identical). For a neutron evaluation with no 600-series distributions or partial reactions given, MT=103-107 can appear by themselves; they are simply components of the absorption cross section.

In some cases, it is difficult to assign all the photons associated with a particular particle to the reactions used to describe the particle. In such cases, these photons can be described using the "sum" MT numbers in File 12 or 13 (for neutrons) or in File 6 (for other projectiles).

Some examples of simple single-particle reactions follow.

Reaction	MT
9Be(α,n0)12C	50
Fe(n,nc)Fe	91
2H(d,p0)3He	600
6Li(t,d0)7Li	650
6