ORNL/M-6620

LETTER REPORT

Computational Physics and Engineering Division

To: C. W. Nilsen

Subject of Document: Prototypic Testing of Codes to Process All Scattering and Production Reactions and Produce Multigroup Cross-Section Libraries

Type of Document: Letter Report

Author: N. M. Greene

Date Published: November 1998

Prepared for

U.S. Nuclear Regulatory Commission

under Contract JCN W6479

with Oak Ridge National Laboratory

Prepared by the

OAK RIDGE NATIONAL LABORATORY

P.O. Box 2008

Oak Ridge, Tennessee 37831-6370

managed by

LOCKHEED MARTIN ENERGY RESEARCH CORP.

for the

U.S. DEPARTMENT OF ENERGY

under contract DE-AC05-96OR22464

LETTER REPORT

CONTENTS

LIST OF FIGURES

LIST OF TABLES

1. INTRODUCTION

A large number of nuclear analysis and design tasks require cross-sections in order to perform the required studies. In particular, many of these situations require multigroup cross sections. For example, every computer code that performs particle transport calculations in the SCALE¹ system needs multigroup data.

These multigroup data are generated by processing basic cross-section data, that invariably are taken from libraries that use the Evaluated Nuclear Data File (ENDF/B²) formats. These files were designed in the early 1960's by Henry C. Honeck and were initially released as Version 1. Subsequent releases (Version 6 was made available around 1985) have become progressively more complicated in the kinds of data that are included and have required the computer codes that use these data to be modified in order to make use of the data.

The changes that were made in going from Version 5 to Version 6 were the most revolutionary in this evolution, and include many changes that make the new evaluations completely unusable by the codes that had previously been used to prepare multigroup cross-section libraries. It is the impression of the author that the NJOY³ code system developed at LANL is the only processing code system that has maintained compatibility with the evolution of the formats. Because of this, NJOY is used throughout the world for producing multigroup libraries with the latest files. It is felt that an alternate method for producing libraries is highly desirable to provide an independent check on the procedures used in a single processing system.

At ORNL, the in-house computer code system most often used to produce multigroup libraries is called AMPX⁴. AMPX is a reasonably comprehensive cross-section processor for Version 5 and earlier versions of ENDF/B; however, several new situations could not be handled by its codes in the last major distribution of this code system that was made in 1992. In particular, many Version 6 evaluations use the Reich-Moore formalism for representing resolved resonance data. Many reactions have their kinematics described in a new and very general manner in a place called "File 6" in the data files. In addition to these two major changes, several other comparatively minor changes were introduced throughout the files.

For several years, we have recognized the need for extending our processing capabilities to allow using the latest cross-section files. A review of the new formats was made and consideration was given to starting with the existing AMPX processing codes and making the requisite changes that would allow them to process the new formats. However, it was decided that these changes would be major and would yield codes that would be patched up so much that they would be very hard to maintain and extend. Furthermore, it was recognized that the existing collection of codes had been written by many individuals at different times using different approaches for performing common operations, such as the methods used to integrate functions. It was felt that initiating a developmental task that would produce new codes afforded the chance to unify our codes and procedures, a very desirable situation that would probably never present itself again.

The procedures described in Section 3 of this report were developed to position our AMPX system to be a comprehensive processor of Version 6 and future versions of ENDF/B. The major codes that are described are all completely new codes, and make little use of coding that existed at the initiation of this effort. Certainly, many of the procedures picked for inclusion in the new codes were based on knowledge gained from developing the earlier AMPX processing codes, and the new codes were written in a manner that allow them to make use of much of the pre-existing software, but the primary processing procedures are new, and, to the knowledge of the author, have not been used in any previous code that prepares multigroup cross-section libraries. As such, they offer a very independent capability that other processing codes can use for comparison purposes. They have been written with future processing needs uppermost in mind, and, because of this, have included capabilities that are not used in the present implementation, but can be easily activated when new needs are encountered.

The processing discussed in this report all relate to neutron cross-section libraries. The processing of gamma ray data will be covered by tasks scheduled for future development.

2. GROUP-AVERAGING REQUIREMENTS

The needs of the codes that use multigroup data at ORNL fit into the following categories:

1.parameters that are averaged over the "flux" in the energy groups,

2.multiplicities, such as ,

3., the fission spectrum, and

4.group-to-group transfer cross-sections.

2.1. GROUP-AVERAGED CROSS SECTIONS

The first of these categories is the simplest and involves the calculation of an averaged cross section according to the following expression:

Almost every process included in a cross-section library requires this operation (e.g., elastic scattering, total, etc.).

2.2. MULTIPLICITIES

This is a very specialized need and affects most neutron cross-section libraries in one parameter; namely, , the average number of neutrons produced from fission. A parameter, such as this one, is obtained from the following expression:

2.3. ONE-DIMENSIONAL FISSION SPECTRUM

Because of the manner in which the fission source is included in a typical implementation of a diffusion, a discrete ordinates, or a Monte Carlo program, a parameter, _g, which is the fraction of the fission neutrons that are produced within an energy group, is required.

The data that are given in an ENDF/B library are given in a manner that allows one to calculate a more correct group-to-group value for this parameter; namely (gg), or the fraction of the neutrons that are produced in group g that will end up in group g. Our codes calculate these parameters, which must be reduced to a more approximate form using the following expression:

2.4. GROUP-TO-GROUP TRANSFER CROSS-SECTIONS

One of the more complicated and time-consuming operations involved in producing multigroup cross-sections is that of generating transfer matrices. In multigroup methods that solve the transport equation, such as discrete ordinates codes or Monte Carlo codes, these transfer matrices generally are given in a form that describes the transfer from group g to a group g as a function of scattering angle. This is accomplished by using matrices of the elements of a Legendre fit to the group-to-group values. Recall that using a Legendre fit involves the following expression for a function, f:

For our group-to-group values, we need values of _n(gg) that are calculated by the following expression:

The scattering probability, f(EE,µ), can have two forms. For two-body reactions where the kinematics are known, it is a "delta" function; namely, (EE,µ); however, for multi-body processes where the kinematics are intractable, it is given on an ENDF/B library in a large variety of tabular and analytic expressions. Some of the analytic forms are rooted in nuclear theory while others are convenient expressions that approximately fit experimental observations.

The determination of a transfer matrix can be done in a large number of ways. For example, the AMPX codes that existed prior to the methods described in this report used at least eight or nine very different procedures for generating scattering matrices. In this work, we have developed a new approach that we feel is able to generate transfer matrices for all of the situations covered by the independent coding described above. This will certainly make the new system easier to maintain, since all maintenance is focused on one set of coding, and should also make it easier to ensure that quality assurance needs are satisfied.

3. NEW AMPX PROCEDURES AND CODES

In our new procedures, the generation of a set of multigroup cross-sections involves three steps:

1. Generate a tabular file that contains data that describes the variation of the cross sections for each process as a function of energy.

2. Generate a tabular file that contains data that describes the kinematics for each process that produces secondary particles (neutrons in this case). This tabular file describes the kinematics as a function of temperature, incident neutron energy, outgoing neutron energy, and scattering angle.

3. Use the tabular data files from steps 1 and 2 along with a tabular file which contains a weighting function (flux) to generate averaged data, multiplicities, transfer matrices, etc., as described in Section 2 of this report. These multigroup values are written on an AMPX master cross-section library.

These three procedures are handled by three separate computer codes described in the following sections.

3.1 POLIDENT -- CODE TO GENERATE POINT CROSS-SECTION DATA

POLIDENT scans the ENDF/B library to locate the information it needs to make point cross-sections for a nuclide.

The most complicated operations performed in POLIDENT involve using resonance parameters to determine point cross-sections. Resonance parameters occur in two classes: resolved resonance data and unresolved resonance data.

Resolved resonance data are presented in four different formalisms in Version 6:

1. Single-Level Breit Wigner (SLBW),

2. Multi-Level Breit Wigner (MLBW),

3. Adler-Adler (AA), or

4. Reich-Moore (RM).

In using each of these kinds of data, the code looks at the parameters to see where the resonances are located and their sizes and uses these in a complicated procedure that generates an energy mesh on which the cross-sections are then calculated. The energy mesh is carefully selected in a manner that yields a cross-section array that can be linearly interpolated to within a user specified tolerance. Cross-section values are generated for (n,), fission, elastic scattering, and the total cross section. The cross sections are written to a scratch file that will be combined later with point data for other energy ranges to produce single arrays for each process.

Unresolved resonance data can be given according to three different structures, all based on the SLBW approximation. Once this structure is known, a procedure developed by Dick Hwang at ANL is used to generate point infinite-dilution values for (n,), fission, elastic scattering and total cross-section. These values are written to a scratch file for combining with other data.

The last information that POLIDENT accesses is energy-value pairs for all of the reactions in the ENDF/B evaluation. For resonance nuclides, these files can contain "background" data that is intended to correct data in the resonance fits. Additionally, all nuclides will contain data outside the resonance ranges that must be combined to produce a single array spanning all energy regions.

Nuclides that do not have resonance data are passed through POLIDENT. For these non-resonance nuclides, the purpose is to produce energy-value pairs that can be linearly interpolated to get intermediate values to a specified accuracy.

The cross-sections from POLIDENT are written to a file that can be saved.

3.2. YYYYYYYYYYYY (Y12) -- MODULE TO GENERATE TABULAR KINEMATICS DATA

Y12 looks at the ENDF/B file to locate information related to the kinematics of all reactions described in the evaluation. This program contains a few thousands of lines of FORTRAN coding to cover the myriad of situations that can be used in ENDF/B evaluations.

Kinematics data describes particle interactions at a specified temperature, incident energy, and scattering angle.

Y12 writes a tabular file that describes kinematics data in the following record structure:

Record type 1--MT,NTEMP, where MT is the process identifier, and NTEMP is the number of temperature at which data are given.

Record type 2--T, NSUB, where T is the temperature in Kelvin for the data which follow, and NSUB is the number of subsections it takes to describe the data. (There are NTEMP of these Record type 2's and the structure that falls under it).

Record type 3--MM,(GMU(M),WMU(M),M=1,MM), where MM is the number of angles at which data are given for the subsection, and the GMU and WMU are the cosines of the angles-of-scatter in the LAB system and the integration weights associated with these angles in a Gaussian or Lobatto quadrature. (There are NSUB of these Record type 3's and the structure that falls under it).

Record type 4--GMU,WMU,NE, where GMU is the cosine and WMU is the weight of the angle for which the data are given and NE is the number of source energies at which

data are given. (There are MM of the Record type 4's and the structure that falls under it).

Record type 5--E,NEF, where E is the incident energy and NEF is the number of "final" energies at which the process produces particles. (There are NE of these Record type 5's and the record that falls under it).

Record type 6--(EF(I),I=1,NEF),(F(I),I=1,NEF),(PF(I),I=1,NEF), where EF are the final energies of the particles that are produced, the F's contain the fraction of the particles that are produced at the EF's. The PF's are the powers associated with an integration scheme⁵, developed for use in other AMPX modules. There is one Record type 6, for a single temperature, a single subsection, a single scattering angle, and a single source energy. (It will contain only one point for "delta" function reactions, such as elastic scattering).

The above structure defines a five level loop structure, and no uniformity is required concerning the length of the loops. For example, under a particular angle, one may use 25 source energies and 50 source energies under the next angle, etc.

Schematically the structure is shown below:

Record type 1--NTEMP

Loop over NTEMP Temperatures

| Record type 2--NSUB

| Loop over NSUB subsections

| |

| | Record type 3--MM

| | Loop over MM angles

| | |

| | | Record type 4--NE

| | | Loop over NE source energies

| | | |

| | | | Record type 5--NEF

| | | | Give Record type 6

| | | | |

| | | | Record type 6

| | | | The Stuff

This same loop structure is used for all processes. If there is no temperature dependence, NTEMP is set to 1, and if there is only one subsection, NSUB is one, and if there is no angular dependence, MM is set to one, etc., etc. The data for all processes are simply stacked on a single tabular kinematics file.

The simple requirement for a uniform structure makes this scheme very attractive from a data processing standpoint, because it helps to eliminate "options," that many of us consider the bane of a good computer program. By requiring any reaction that needs to have kinematics treated to use the same structure, we have forced a uniformity that allows us to write a post-processing code that only works one way. This, of course, is making us process the "simplest" situation in our most complicated data structure, but, the extra data storage and handling are more than compensated for by the quality assurance benefits provided.

As mentioned earlier, there are a large number of ways that kinematics data can be presented in an ENDF/B evaluation. Some reactions, primarily the two-body reactions, require that the user know the physical expressions that specify the kinematics. For example, for elastic and discrete level inelastic scattering, one must know the expressions that tell where a sink neutron will emerge for scattering at a particular energy and through a particular angle. Furthermore, the procedures must know how to accept data in either the CM or LAB system, and how to make the transforms between these two systems. For processes like these, the scattering distribution may be given in either the CM or LAB system in Legendre polynomial fits or in tabular distributions.

For multi-body reactions, many more options are provided. In the simpler situations, secondary energy scattering distributions may be specified as a function of incident energy. The distributions may be simple analytic expressions, such as a fission spectrum, or may be given as tabular distributions. In this case, the process can be specified to be isotropic in the LAB system, or differential data may be given in a separate file that needs to be multiplied by the "isotropic" data, in order to specify angular dependence.

The most general and complicated situations are encountered in the "File 6" part of the evaluation. In this case, there are seven possible representations that include a full tabular description of kinematics, a very complicated combination of analytical procedures with tabular data (the Kalbach-Mann procedures), and many simpler situations. In several cases, data that were located elsewhere in earlier versions of ENDF/B are now stored in File 6. To further generalize the situation, for reactions that yield multiple exit particles, data for each exit particle may be given in this file. For example, two body discrete level inelastic scattering produce an exit neutron, a gamma ray, and the residual nucleus. Data for each of these "particles" can be included in an evaluation.

Other new data formats are used for thermal scattering, and these employ a mixture of analytic and tabular data formats.

In summary, Y12 has been programmed to produce the tabular kinematics file mentioned above for neutron-producing reactions.

The tabular file produced by Y12 is saved for use in later calculations. (Note that there is nothing associated with an energy group structure in either the file written by POLIDENT or the one from Y12; they can both be used to generate libraries in many group structures.)

3.3 XXXXXXXXXX (X10) -- CODE TO PRODUCE MULTIGROUP CROSS-SECTIONS FROM TABULATED POINT CROSS-SECTIONS AND TABULATED KINEMATICS DATA

Thus far, we have discussed the procedures used in POLIDENT and Y12 for producing their own respective tabular-formatted files based on an ENDF/B evaluation.

X10 only accepts tabular functions and does not read ENDF/B files. The flux used to produce averaged cross-sections must be supplied in tabular format. All cross-sections for all reactions must be input on a tabular-formatted file, and all kinematics data must be supplied in the tabular structure described above.

X10 does not know anything about the "physics" of the reactions for which it makes averaged cross-sections. Everything pertaining to these data must be included in the input tabular files.

X10 has few options, and, hopefully, will never have many. The user specifies the location of the three kinds of input tabular data and tells how these data are identified. A group structure is selected, along with the order of scattering to which the data will be processed. The two other pieces of required input tell where the group averaged cross-sections are to be written, and what identifier is to be associated with the data.

A run of X10 uses the following flow pattern:

1. Input data are read and listed to identify the code's interpretation of the input.

2. The code searches for the weighting spectrum and aborts if the function cannot be found.

3. The tabulated data produced by POLIDENT are read and an internal directory of these data is constructed.

4. The tabulated kinematics data produced by Y12 are read and a directory of these data is constructed.

5. X10 loops over the reactions in the point data directory, and looks at the kinematics directory to see if it needs to produce transfer matrices.

6. A set of subroutines under the general heading, X2D6, is called to either produce group-averaged cross-sections or group-averaged cross-sections and associated transfer arrays. (X2D6 is described in a separate section below). X2D6 writes the group-averaged data onto a scratch file, along with transfer matrices, if these are produced. The code knows which reaction identifiers indicate that they are "multiplicities," and performs the operations necessary to properly group average these data, which are then written to the same scratch file mentioned earlier. Special coding is included to calculate _g as described in Section 2.3.

7. When all reactions have been processed, X10 looks at the scratch file mentioned in step 6 and produces an internal directory of the data written on it.

This scan is used to determine the maximum order of scattering, the maximum array sizes, the number of records required to write the data on an AMPX master library, and to prepare a directory of the scattering data, which will later be written on the AMPX master library.

8. Using the information just collected, the header part of the AMPX master library is written, after which the scratch file is reread to collect the group-averaged data, so that they can be written to the master library. If scattering matrices have been produced, the directory for these data is written to the AMPX master library, after which the scratch file is read again to locate and read the scattering matrix data and write it on the AMPX master library.

NOTE: The user does not have to specify anything about which processes are treated, how many, or, in fact, anything about the make-up of any file. X10 looks at the files, finds what it can process, and processes what it finds. The output is written in an AMPX master library that can be saved for use in later applications.

3.3.1 Characteristics of the X2D6 Processing Routines

The X2D6 routines were written to provide a set of capabilities that make it usable for practically any group-averaging operation that we have encountered in our multigroup applications at ORNL. As such, it has been programmed with the "hooks" necessary to allow the replacement and retirement of some of the older AMPX modules, that will not process the latest ENDF/B formats. The two most obvious codes that should be replaced are LAPHNGAS, that is used to produce gamma-production matrices for neutron reactions, and SMUG, that is used to produce group-averaged gamma ray cross-section libraries. The XLACS module that was written to generate multigroup neutron cross-sections is effectively replaced by the POLIDENT, Y12, and X10 modules described above.

A difference of X2D6 and most other routines that calculate averaged cross sections and transfer matrices is that the same routines are used to calculate average cross-sections or averaged cross-sections and transfer matrices. The integrations required are all collected together in a procedure that ensure that the precision of the averaged parameters is the same as that of the elements of a scattering transfer matrix. The program starts at the bottom energy, looks at the points in all the other functions it uses in order to find the next highest energy, and processes this panel. Subsequently, the next higher panel is processed, etc. This is equivalent to forming a union energy mesh of all functions, sorting them, and processing the panels. As a panel is processed (integrated), it is added to the appropriate energy group. Furthermore, if a transfer matrix is to be calculated, this panel can be further subdivided by locating the piece(s) that scatter to a particular sink group. These sub-pieces are added to the appropriate transfer array bin, etc. Thus, the procedure is inherently conservative. The same integration procedure calculates the transfer matrix elements that are used to calculate the averaged cross-sections.

Another significant difference in X2D6 and the usual scattering matrix calculator is that it always requires a "source" energy group structure and a "sink" energy group structure, even when they are identical. This is very useful, since the same coding can be used to calculate neutron-to-neutron scattering arrays that are used to calculate neutron-to-gamma ray scattering arrays, etc. X2D6 does not know what the source particle is or what the sink particle is.

In typical calculations of group-averaged parameters, one is calculating a reaction rate that is the integral of a flux times a cross section for an energy group that is, subsequently, divided by the integral of a flux to obtain the averaged value. X2D6 is programmed to handle this most common and usual situation, but it also can handle other special weightings, such as "cell" weighting, which is used to produce group-averaged parameters for homogenized representations of lattice structures, etc. This is accomplished by allowing the independent input of a flux to use in the numerator calculation (the reaction rate), and another flux to use in the denominator (the integral of the flux over the system). Even the simple case described at the beginning of this paragraph requires two fluxes to be specified. In this case, the same flux is used in both places. As a result, the "options" are removed from X2D6. The options are accommodated by the manner in which a program communicates with X2D6.

The present implementation of X2D6 allows up to five point functions that vary with energy to be specified. Nonexistent functions are designated by telling the code that the function has zero (0) points. Thus, if one wants an averaged cross-section, a numerator flux and a denominator flux and a cross-section array are specified, and this allows the averaged values to be calculated. By default, X2D6 calculates the integrals of products of functions. Provisions are included for more complicated situations, however. When Bondarenko functions are desired, the integration involves four separate functions in the numerator, a cross section, a flux, a total cross section and a constant background value. These are not simply multiplied, but involve a product of the first two functions divided by the sum of the last two functions. The denominator integral is similar but only involves three functions. X2D6 provides three arrays that can be used to specify very general combinations involving multiple functions that can handle situations such as needed to calculate Bondarenko factors. The three arrays are very simple "assembly language" like commands, and allow one to raise functions to powers, multiply, divide, etc., as needed. As a result, X2D6 can not only calculate Bondarenko functions for a group structure, but can also calculate Bondarenko factors for the transfer matrix elements of any process.

When X2D6 sees that two functions, in addition to the fluxes, are specified, it automatically produces a flux-weighted value for the first function, and weights the second function over the product of the first function times the flux, such as is needed to weight a multiplicity.

In summary, we have tried to include all of the calculational capabilities in a single coding package which eliminates internal options. Rather, a wide variety of options are provided, depending on how a computer code communicates with X2D6.

If additional options are needed, a concerted attempt will be made to make the changes in a manner that follows the programming philosophy just described, so that we can have a single set of basic processing routines to maintain.

3.3.2. Simple Procedure for Preparing Calculational Sequences

The preparation of the input for a series of computer codes, such as POLIDENT, Y-12, and X-10, and other AMPX utility programs, is a labor intensive and error-prone process. Those who approach this task by preparing a "master" set of input data, and then editing and reediting this file are simply asking for the troubles that are sure to follow.

To make it easier to perform this task and to circumvent the error-causing data transcription problems, a series of computer programs and procedures were developed.

All of the ENDF/B-VI data that have been distributed by the National Nuclear Data Center (NNDC) at Brookhaven National Laboratory are written in a single directory on a workstation at ORNL.

A program was written that scans all of these separate files and locates all evaluations, the version numbers, ZA-numbers, release dates, revision numbers, etc., and creates a directory file containing this information. This file can be listed, read, and/or sorted to make reports that tell where particular evaluations are located and how they are identified. The most important function of such a directory is to make it easy to locate the latest evaluation for a nuclide, since this is expected to be the most correct data evaluation.

While the directories just described give one the information needed to prepare input for the three codes mentioned above, it is the errors that invariably occur when one specifies these data to the computer codes that we want to avoid.

Another computer program was written that can read and search the directory file and extract the requisite data that is needed to prepare input files for the necessary codes, and write these to computer files. This procedure makes only two requirements of the user. The code first prompts the user for the symbol of the nuclide for which processing is desired, for example, U235 for ²³⁵U. The code then scans the directory file and writes out the directory lines (numbered 1 through N) for the N collections it locates. It then asks,"Which Set Do You Wish to Process?" The user enters, for example, 2 for the second evaluation listed. The code then looks at the information associated with this directory line and extracts all the parameters it needs to create the execution sequence to make group averaged cross-sections for the evaluation, after which it writes the input data to a computer file. Included with the input data are the instructions about which files to access to find the evaluation, and the information about where the output from the different computer codes should be written. (Note that the user only specifies U235 and 2). The energy group structure is presently hard-coded into the computer program that creates the execution sequence.

To run the job that was just set up, a special script called SUBMASTER was written that requires only that the user say SUBMASTER U235 to make a run for ²³⁵U. In a simple extension of this technique, a user could collect a group of these "SUBMASTER" commands together into a single script called, for example, MASTER238 as follows:

SUBMASTER U235

SUBMASTER U238

SUBMASTER AL27

SUBMASTER BE9

and then execute MASTER238 overnight or on a weekend or whenever convenient to make a library for the desired number of nuclides.

Figure 1 shows the execution sequences that were created for ²⁷Al and ²³⁵U:

=shell

ln -fs /home/nmg/x2d6/y12 y12

ln -fs /home/nmg/x2d6/master x10

ln -fs /home/nmg/ampxjobs/rade rade

ln -fs /home/nmg/polident/polident polident

ln -fs /rsicws/endf/rev3/tape.134 ft11f001

=jergens

0$$ 11 30 18 1$$ 1 t

3$$ 1099 0 2 t

=polident

0$$ 31 25 1$$ 1 t

2$$ 1325 11 2 6 t

=y12

0$$ 32 11 1$$ 1325 2$$ 2 6 3$$ 32 8 8 8 8 t

=x10

0$$ 1 30 31 32 1$$ 13027 238 5 2$$ 99 1099 1325 1325 t

AL27 1325 13027 ENDFB V6 REL0 REV0 MOD1 AMPX 09/19/98 rev3/tape.134

=rade

1$$ 1 e t

=shell

cp ft31f001 /home/nmg/x2d6/multigroup/v6/238group.point/al27

cp ft32f001 /home/nmg/x2d6/multigroup/v6/238group.kinematics/al27

=shell

ln -fs /home/nmg/x2d6/y12 y12

ln -fs /home/nmg/x2d6/master x10

ln -fs /home/nmg/ampxjobs/rade rade

ln -fs /home/nmg/polident/polident polident

ln -fs /rsicws/endf/rev3/tape.135 ft11f001

=jergens

0$$ 11 30 18 1$$ 1 t

3$$ 1099 0 2 t

=polident

0$$ 31 25 1$$ 1 t

2$$ 9228 11 2 6 t

=y12

0$$ 32 11 1$$ 9228 2$$ 2 6 3$$ 32 8 8 8 8 t

=x10

0$$ 1 30 31 32 1$$ 92235 238 5 2$$ 99 1099 9228 9228 t

U235 9228 92235 ENDFB V6 REL0 REV3 MOD4 AMPX 09/19/98 rev3/tape.135

=rade

1$$ 1 e t

=shell

cp ft31f001 /home/nmg/x2d6/multigroup/v6/238group.point/u235

cp ft32f001 /home/nmg/x2d6/multigroup/v6/238group.kinematics/u235

Figure 1. Input data required to create multigroup data for ²⁷Al and ²³⁵U.

4. RESULTS OF PROCESSING AL-27

To demonstrate the processing capability for Version 6 of ENDF/B, the nuclide ²⁷Al was selected, because it represents a nuclide that implements many of the new format changes.

To limit the number of values that would have to be examined, the 16 group Hanson-Roach structure was selected. To facilitate comparisons, a "flat" weighting spectrum was selected. A 5^th order Legendre fit for the scattering matrices was selected.

Even though it was recognized that our primary neutron cross-section production module XLACS would ignore the new formats in the evaluation, it will still produce a cross-section file that contains averaged values for all processes, will generate scattering matrices for elastic scattering and discrete-level inelastic scattering, and has been extensively tested by having its libraries used in a very large number of benchmarking calculations. Therefore, it was used to check the results from the new procedure.

Table 1 shows the group parameters produced by XLACS which we have used to

produce multigroup libraries for Versions 5 and earlier. Table 2 shows the same parameters produced by the X10 module. With the exception of the group 1 "inelastic" value, all numbers agree to within one digit in six digits. This agreement is to be expected, since the integration procedures in both codes that produce these numbers are using the same numerical procedure. The difference in the first group inelastic value is almost certainly due to the fact that XLACS gets its inelastic values by averaging "point cross-sections" that are the sum of 39 inelastic levels and so-called evaporation values. X10, on the other hand, calculates the averages of the 39 levels and the evaporation values and adds these to get the inelastic values. Even here, the difference is only one out of 5 digits, which is very acceptable.

Table 3 gives typical elastic scattering matrix values produced by XLACS, while Table 4 gives the corresponding values produced by X10. Considering that XLACS produces its values by dealing with expressions that are associated with the kinematics of elastic scattering, while X10 accepts tabulations of differential cross-sections that are based on these kinematics, the observed agreement is very gratifying, when one considers just how much the calculational procedures used in XLACS and X10 differ from one another.

Table 5 gives the scattering matrix terms for the first inelastic level produced by the XLACS program, while Table 6 gives values produced by X10. The P₀ terms compare well with one another, while the higher order terms do not agree as well. In both cases, the fact that the agreement is not as good as that observed for elastic scattering is due to the angular variation of these cross sections being stored in a new format and location in Version 6. When XLACS does not find these data in the place used in earlier versions of ENDF/B, it automatically assumes that the angular variation is isotropic in the CM. An examination of the X10 results, shows that the anisotropic data that are given in Version 6 do produce larger values than are observed in the XLACS results, which is as expected, since an isotropic cross-section in the CM transforms into a linearly-anisotropic cross-section in the LAB, which is the system in which our values are reported.

Table 1. Group averaged cross-sections from XLACS

Neutron Group Parameters

MT= 1 MT= 2 MT= 4 MT= 16 MT= 22

Group Total Elastic Inelastic n2n n,na

----- ----------- ----------- ----------- ----------- -----------

1 1.90208E+00 9.82617E-01 7.10585E-01 1.48422E-03 1.65797E-03

2 2.96575E+00 2.57234E+00 3.92794E-01 0.00000E+00 0.00000E+00

3 3.16376E+00 3.02840E+00 1.34721E-01 0.00000E+00 0.00000E+00

4 4.03609E+00 4.03495E+00 2.86450E-04 0.00000E+00 0.00000E+00

5 4.25416E+00 4.25295E+00 0.00000E+00 0.00000E+00 0.00000E+00

6 6.16879E+00 6.16486E+00 0.00000E+00 0.00000E+00 0.00000E+00

7 1.37879E+00 1.37153E+00 0.00000E+00 0.00000E+00 0.00000E+00

8 1.34848E+00 1.34581E+00 0.00000E+00 0.00000E+00 0.00000E+00

9 1.35050E+00 1.34728E+00 0.00000E+00 0.00000E+00 0.00000E+00

10 1.35411E+00 1.34731E+00 0.00000E+00 0.00000E+00 0.00000E+00

11 1.35811E+00 1.34730E+00 0.00000E+00 0.00000E+00 0.00000E+00

12 1.36872E+00 1.34722E+00 0.00000E+00 0.00000E+00 0.00000E+00

13 1.38122E+00 1.34712E+00 0.00000E+00 0.00000E+00 0.00000E+00

14 1.41067E+00 1.34707E+00 0.00000E+00 0.00000E+00 0.00000E+00

15 1.45067E+00 1.34702E+00 0.00000E+00 0.00000E+00 0.00000E+00

16 1.59555E+00 1.34762E+00 0.00000E+00 0.00000E+00 0.00000E+00

Neutron Group Parameters

MT= 28 MT= 51 MT= 52 MT= 53 MT= 54

Group n,np Level 01 Level 02 Level 03 Level 04

----- ----------- ----------- ----------- ----------- -----------

1 7.69269E-02 2.77287E-02 5.69248E-02 8.80104E-02 4.30939E-02

2 0.00000E+00 9.91749E-02 2.19231E-01 7.20181E-02 2.36998E-03

3 0.00000E+00 6.97120E-02 6.50092E-02 0.00000E+00 0.00000E+00

4 0.00000E+00 2.86450E-04 0.00000E+00 0.00000E+00 0.00000E+00

5 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

Group 6 to Group 15 are identical to Group 5

16 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

Neutron Group Parameters

MT= 55 MT= 56 MT= 57 MT= 58 MT= 59

Group Level 05 Level 06 Level 07 Level 08 Level 09

----- ----------- ----------- ----------- ----------- -----------

1 2.15068E-02 7.04921E-02 9.71722E-03 9.42156E-03 6.49650E-03

2 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

Group 3 to Group 15 are identical to Group 2

16 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00 0.00000E+00

Table 1 (continued)

Neutron Group Parameters

MT= 60 MT= 91 MT= 102 MT= 103 MT= 104

Group Level 10 Evaporation n,g n,p n,d

----- ----------- ----------- ----------- ----------- -----------

1 1.17846E-02 1.45548E-01 4.65869E-04 6.18259E-02 4.07007E-03

2 0.00000E+00 0.00000E+00 4.92925E-04 1.24612E-04 0.00000E+00

3 0.00000E+00 0.00000E+00 6.38241E-04 0.00000E+00 0.00000E+00

4 0.00000E+00 0.00000E+00 8.56640E-04 0.00000E+00 0.00000E+00

5 0.00000E+00 0.00000E+00 1.20967E-03 0.00000E+00 0.00000E+00

6 0.00000E+00 0.00000E+00 3.92892E-03 0.00000E+00 0.00000E+00

7 0.00000E+00 0.00000E+00 7.25750E-03 0.00000E+00 0.00000E+00

8 0.00000E+00 0.00000E+00 2.66686E-03 0.00000E+00 0.00000E+00

9 0.00000E+00 0.00000E+00 3.21750E-03 0.00000E+00 0.00000E+00

10 0.00000E+00 0.00000E+00 6.80500E-03 0.00000E+00 0.00000E+00

11 0.00000E+00 0.00000E+00 1.08100E-02 0.00000E+00 0.00000E+00

12 0.00000E+00 0.00000E+00 2.15000E-02 0.00000E+00 0.00000E+00

13 0.00000E+00 0.00000E+00 3.41000E-02 0.00000E+00 0.00000E+00

14 0.00000E+00 0.00000E+00 6.36000E-02 0.00000E+00 0.00000E+00

15 0.00000E+00 0.00000E+00 1.03650E-01 0.00000E+00 0.00000E+00

16 0.00000E+00 0.00000E+00 2.47927E-01 0.00000E+00 0.00000E+00

Neutron Group Parameters

MT= 105 MT= 107 MT= 1099

Group n,t n,a Flux

----- ----------- ----------- -----------

1 3.29588E-04 6.21208E-02 8.00000E-01

2 0.00000E+00 0.00000E+00 1.06667E-01

3 0.00000E+00 0.00000E+00 3.33333E-02

Group 4 is identical to Group 3

5 0.00000E+00 0.00000E+00 2.00000E-02

6 0.00000E+00 0.00000E+00 5.53333E-03

7 0.00000E+00 0.00000E+00 9.33333E-04

8 0.00000E+00 0.00000E+00 1.63333E-04

9 0.00000E+00 0.00000E+00 3.00000E-05

10 0.00000E+00 0.00000E+00 4.66667E-06

11 0.00000E+00 0.00000E+00 1.33333E-06

12 0.00000E+00 0.00000E+00 4.66667E-07

13 0.00000E+00 0.00000E+00 1.33333E-07

14 0.00000E+00 0.00000E+00 4.00000E-08

15 0.00000E+00 0.00000E+00 2.00000E-08

16 0.00000E+00 0.00000E+00 6.60000E-09

Table 2. Group averaged cross-sections from X10

Neutron Group Parameters

MT= 1 MT= 2 MT= 4 MT= 16 MT= 22

Group Total Elastic Inelastic n2n n,na

----- ----------- ----------- ----------- ----------- -----------

1 1.90207E+00 9.82616E-01 7.10569E-01 1.48422E-03 1.65797E-03

2 2.96575E+00 2.57234E+00 3.92794E-01 0.00000E+00 0.00000E+00

3 3.16376E+00 3.02840E+00 1.34721E-01 0.00000E+00 0.00000E+00

4 4.03609E+00 4.03495E+00 2.86450E-04 0.00000E+00 0.00000E+00

5 4.25416E+00 4.25295E+00 0.00000E+00 0.00000E+00 0.00000E+00

6 6.16878E+00 6.16485E+00 0.00000E+00 0.00000E+00 0.00000E+00