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PSR-0171 NJOY91.

NJOY91, General ENDF/B Processing System for Reactor Design Problems

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1. NAME OR DESIGNATION OF PROGRAM:  NJOY.
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2. COMPUTERS
To submit a request, click below on the link of the version you wish to order. Only liaison officers are authorised to submit online requests. Rules for requesters are available here.
Program name Package id Status Status date
NJOY91.91 PSR-0171/19 Tested 08-MAR-1994

Machines used:

Package ID Orig. computer Test computer
PSR-0171/19 Many Computers DEC VAX 6000
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3. DESCRIPTION OF PROBLEM OR FUNCTION

The NJOY nuclear data processing system is a comprehensive computer code package for producing pointwise and multigroup neutron, photon, and charged particle cross sections from ENDF/B evaluated nuclear data.
NJOY-89 is a substantial upgrade of the previous release. It includes photon production and photon interaction capabilities, heating calculations, covariance processing, and thermal scattering  capabilities. It is capable of processing data in ENDF/B-4, ENDF/B-5, and ENDF/B-6 formats for evaluated data (to the extent that the latter have been frozen at the time of this release).
NJOY-91.118: This is the last in the NJOY-91 series. It uses the same module structure as the earlier versions and its graphics options depend on DISSPLA. NJOY91.118 includes bug fixes, improvements in several modules, and some new capabilities. Information on the changes is included in the README file. A new test problem was added to test some ENDF/B-6 features, including Reich-Moore resonance reconstruction, energy-angle matrices in GROUPR, and energy-angle distributions in ACER. The 91.118 release is basically configured for UNIX.
Short descriptions of the different modules follow:

RECONR  Reconstructs  pointwise (energy-dependent)  cross  sections      from ENDF/B resonance parameters and interpolation schemes.
BROADR  Doppler broadens and thins pointwise cross sections.

UNRESR  Computes  effective  self-shielded pointwise cross sections in the unresolved-resonance region.

HEATR   Generates  pointwise heat production cross sections (KERMA factors) and radiation-damage-energy production cross
        sections.

THERMR  Produces incoherent inelastic energy-to-energy matrices for free  or bound scatterers, coherent elastic cross  sections for  hexagonal materials, and incoherent elastic cross
        sections.

GROUPR  Generates  self-shielded multigroup  cross sections, group-      to-group neutron scattering matrices, and photon production matrices from pointwise input.

GAMINR  Calculates multigroup photon interaction cross sections and      KERMA factors and group-to-group photon scattering
        matrices.

ERRORR  Produces  multigroup covariance matrices from ENDF/B
        uncertainties.

COVR    Reads the output of ERRORR and performs covariance plotting      and output-formatting operations.

DTFR    Formats multigroup  data for transport codes such as DTF-IV      (5) and ANISN (6).

CCCCR   Formats multigroup  data  for  the CCCC standard  interface      files ISOTXS, BRKOXS, and DLAYXS.

MATXSR  Formats multigroup data for the  MATXS cross section
        interface file.

ACER    Prepares  libraries  for  the  Los Alamos continuous-energy      Monte Carlo code MCNP (8).

POWR    Prepares libraries for the EPRI-CELL and EPRI-CPM codes

MODER   Changes  ENDF/B "tapes" and other ENDF-like  NJOY interface      files back and forth between formatted (i.e., BCD or ASCII) and blocked-binary modes.

PLOTR   Plots 2-d graphs of ENDF, PENDF, or GENDF data.
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4. METHOD OF SOLUTION

RECONR Reconstructs pointwise (energy-dependent) cross sections from ENDF/B resonance parameters and interpolation schemes.

BROADR Doppler broadens and thins pointwise cross sections.

UNRESR Computes effective self-shielded pointwise cross sections in the unresolved-resonance region.

HEATR Generates pointwise heat production cross sections (KERMA factors) and radiation-damage-energy production cross sections.

THERMR Produces incoherent inelastic energy-to-energy matrices for free or bound scatterers, coherent elastic cross sections for hexagonal materials, and incoherent elastic cross sections.

GROUPR Generates self-shielded multigroup cross sections, group-to-group neutron scattering matrices, and photon production matrices from pointwise input.

GAMINR Calculates multigroup photon interaction cross sections and KERMA factors and group-to-group photon scattering matrices.

ERRORR Produces multigroup covariance matrices from ENDF/B uncertainties.

COVR Reads the output of ERRORR and performs covariance plotting and output-formatting operations.

DTFR Formats multigroup data for transport codes such as DTF-IV (5) and ANISN (6).

CCCCR Formats multigroup data for the CCCC standard interface files ISOTXS, BRKOXS, and DLAYXS.

MATXSR Formats multigroup data for the MATXS cross section interface file.

ACER  Prepares libraries for the Los Alamos continuous-energy Monte Carlo code MCNP (8).

POWR  Prepares libraries for the EPRI-CELL and EPRI-CPM codes

MODER Changes ENDF/B "tapes" and other ENDF-like NJOY interface files back and forth between formatted (i.e., BCD or ASCII) and blocked-binary modes.

PLOTR Plots 2-d graphs of ENDF, PENDF, or GENDF data.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Storage allocation parameters have been chosen for efficient use of about 150,000 octal 60-bit words (not counting input/output buffers). This results in a  complex set of limitations on the size of the ENDF/B input files (such as fewer than 100 discrete photons), but all current ENDF/B-IV and V evaluations can be processed within these limitations. Other current limits include 620 groups, 10 temperatures, and 10 sigma- zero values in GROUPR. Dynamic storage allocation also results in some tradeoffs, such as storage versus speed in BROADR and number of groups versus Legendre order in GROUPR. Diagnostic messages are provided when any limits are exceeded. The current allocations have  been adequate for all practical problems attempted to date.
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6. TYPICAL RUNNING TIME

NJOY-89: Typical times are difficult to quote for such a complex system. The samples below, which list CDC-7600 central- processor time plus approximately a 30% surcharge for memory and I/O are limited to a small number of practical problems.
Carbon PENDF with graphite thermal data. Used MODER, RECONR (0.5%),  BROADR (6 temperatures), THERMR (twice), and HEATR. 15.7 min.
Sodium PENDF. Used RECONR (0.5%), BROADR (6 temperatures), THERMR, and HEATR. 9.2 min.
U-238 PENDF with unresolved. Used RECONR (0.5%), BROADR
(7 temperatures), UNRESR, THERMR, and HEATR.             52.0 min.
Carbon GENDF with 70 neutron groups, 12 gamma-ray groups,
6 temperatures, 5 sigma zeros. (Starting from PENDF.)     6.3 min.
Sodium GENDF with 70 neutron groups, 12 gamma-ray groups,
6 temperatures, 5 sigma zeroes. (Starting from PENDF.)    7.1 min.
U-238 GENDF with 70 neutron groups, 12 gamma-ray groups,
7 temperatures, 6 sigma zeroes. (Starting from PENDF.)   46.1 min.
24-group photon interaction library in DTF-IV format for
87 materials. Used RECONR, GAMINR, and DTFR.             87.4 min.
The test problems provided with the package require the following CP time on the CDC-7600:
- Natural carbon problem: 183 secs
- Pu-238 problem: 157 secs
- H and U photon interaction cross section problem: 75 secs
- U-235 error file test problem: 23 secs
on IBM 3084 (sec) on CYBER 740 (sec):
- Natural carbon problem 204 3511
- Pu-238 problem 167 2530
- H and U photon interaction 172 1668
- U-235 error file test problem 20 266
The processing of the complete ENDF/B-V dosimetry file by the RECONR module requires about one hour of CPU time at a 0.1 % tolerance.
NJOY-91.118: Sample problem execution times follow:
                             CRAY       SunSparcStation 2
IN1: natural carbon:         118sec     430.9sec
IN2: Pu-238:                 125sec     349.5sec
IN3: H, U photon interaction  44sec     141.2sec
IN4: U-235 uncertainty file   10sec      44.9sec
IN5:                         153awx     424.2sec
IN6:                          59sec     231.9sec.
PSR-0171/19
NEA-DB compiled and executed the 7 sample problems included in this package on a DEC VAX-6000 computer. For execution,  the following CPU times were found:
   Prob 01           668.8 sec
   Prob 02           552.1 sec
   Prob 03           292.9 sec
   Prob 04           265.1 sec
   Prob 05           646.6 sec
   Prob 06            34.0 sec
   Prob 07           696.1 sec
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7. UNUSUAL FEATURES OF THE PROGRAM

NJOY uses free form input through- out (a simple routine FREE is provided). Variable dimensioning and dynamic storage allocations are used extensively to provide efficient use of the available core storage; an easy-to-use system of subroutines called STORAG reserves, releases, and retrieves pointers and repacks stored data when necessary. All BCD and binary  input/output (except for printed output) takes place through subroutines in order to make adapting NJOY to other computer systems easier. A special blocked binary mode is provided for ENDF/B tapes and interface files. This allows long sections from PENDF tapes, for example, to be paged through the code in binary mode rather than BCD. NJOY calculations using binary files typically run twice as fast as with BCD files.
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8. RELATED AND AUXILIARY PROGRAMS

NJOY incorporates and improves upon the features of its direct ancestor, MINX (10). It also includes and extends the photon production capabilities of LAPHANO (11), the  photon interaction capabilities of GAMLEG (12), the heating capabil- ities of MACK (13), the covariance capabilities of PUFF (14), and the thermal capabilities of FLANGE-II (15) and HEXSCAT (16). The IBM version runs under the control of the ATLAS system (26).

CCCC-IV output from NJOY is compatible with updated versions of CCCC utilities such as LINX (24), BINX (24), AND CINX (25). MATXS output  from NJOY can be further manipulated using programs such as TRANSX,  now under development at Los Alamos. TRANSX can be used to produce sophisticated transport tables (including coupled sets), adjoint data, mixtures, heterogeneous self-shielded data, specially-weighted fission chi vectors, and flexible response edits (including KERMA and DPA), and to perform collapses to sub-set group structures.

TRANSX-CTR reads nuclear data from a library in MATXS format and produces transport tables compatible with many discrete-ordinates (Sn) and diffusion codes. Tables can be produced for neutron photon, or coupled transport.
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9. STATUS
Package ID Status date Status
PSR-0171/19 08-MAR-1994 Tested at NEADB
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10. REFERENCES

(1) R.E. MacFarlane and R.M. Boicourt, "NJOY: A Neutron and Photon Cross Section Processing System", Trans. Am. Nucl. Soc. 22, 720 (1975).

(2) R.E. MacFarlane, D.W. Muir and R.J. Barrett, "Advanced Nuclear   Data Processing Methods for the Fusion Power Program", Trans.
     Am. Nucl. Soc. 23, 16 (1976).

(3) R.E. MacFarlane, R.J. Barrett, D.W. Muir and R.M. Boicourt,
     "NJOY: A Comprehensive ENDF/B Processing System", Proc. Sem-
     inar Workshop on Multigroup Cross Section Processing, Oak
     Ridge, TN, March 14-16, 1978, Oak Ridge National Laboratory,
     Report ORNL/RSIC-41 (October 1978).

(4) R. Kinsey, "ENDF-102, Data Formats and Procedures for the Eval-  uated Nuclear Data File, ENDF", Brookhaven National Laboratory,      Report BNL-NCS-50496 (ENDF-102) (October 1979).

(5) K.D. Lathrop, "DTF-IV, A FORTRAN Program for Solving the Multi-      group Transport Equation with Anisotropic Scattering", Los
     Alamos Scientific Laboratory, Report LA-3373 (1965).

(6) W.W. Engle, Jr., "A User's Manual for ANISN:
A One-Dimensional Discrete Ordinates Transport Code with Anisotropic Scattering", Oak Ridge Gaseous Diffusion Plant Computing Technology Center, Report K-1693 (1967).

(7) R.D. O'Dell, "Standard Interface Files and Procedures for Re-
     actor Physics Codes, Version IV", Los Alamos Scientific Lab-
     oratory, Report LA-6941-MS (September 1977).

(8) "MCNP - A General Monte Carlo Code for Neutron and Photon
     Transport", Los Alamos National Laboratory, Report LA-7396-M,
     Revised (November 1979).

(9) EPRI-CELL and EPRI-CPM are proprietary codes.  Additional in-
     formation may be obtained from the Electric Power Research In-   stitute, 3412 Hillview Ave., Palo Alto, CA 94304.

(10) C.R. Weisbin, P.D. Soran, R.E. MacFarlane, D.R. Harris,
     R.J. LaBauve, J.S. Hendricks, J.E. White and R.B. Kidman,
     "MINX, A Multigroup Interpretation of Nuclear X-Sections from
     ENDF/B", Los AlamosScientific Laboratory, Report LA-6486-MS
     (ENDF-237) (1976).

(11) D.J. Dudziak, R.E. Seamon and D.V. Susco, "LAPHANO: A Multi-
     group Photon-Production Matrix and Source Code for ENDF",
     Los Alamos Scientific Laboratory, Report LA-4750-MS (ENDF-156)   (1967).

(12) K.D. LATHROP, "GAMLEG - A FORTRAN Code to Produce Multigroup
     Cross Sections for Photon Transport Calculations", Los Alamos
     Scientific Laboratory, Report LA-3267 (1965).

(13) M.A. Abdou, C.W. Maynard and R.Q. Wright, "MACK: A Computer
     Program to Calculate Neutron Energy Release Parameters (Flu-
     ence-to-Kerma Factors) and Multigroup Neutron Reaction Cross
     Sections from Nuclear Data in ENDF Format", Oak Ridge National   Laboratory, Report ORNL-TM-3994 (1973).

(14) C.R. Weisbin, E.M. Oblow, J. Ching, J.E. White, R.Q. Wright
     and J. Drischler, "Cross Section and Method Uncertainties:
     The Application of Sensitivity Analysis to Study Their Re-
     lationship in Radiation Transport Benchmark Problems", Oak
     Ridge National Laboratory, Report ORNL-TM-4847 (ENDF-218)
     (1975).

(15) H.C. Honeck and D.R. Finch, "FLANGE-II (Version 71-1), A
     Code to Process Thermal Neutron Data from an ENDF/B Tape",
     E.I. DuPont de Nemours and Co., Savannah River Laboratory,
     Report DP-1278 (1971).

(16) Y.D. Naliboff and J.U. Koppel, "HEXSCAT, Coherent Elastic
     Scattering of Neutrons by Hexagonal Lattices", General Atomic,   Report GA-6026 (1964).

(17) O. Ozer, "RESEND: A Program to Preprocess ENDF/B Materials
     with Resonance Files into a Pointwise Form", Brookhaven
     National Laboratory, Report BNL-17134 (1972).

(18) D.E. Cullen and C.R. Weisbin, "Exact Doppler Broadening of
     Tabulated Cross Sections", Nucl. Sci. Eng. 60, 199 (1976).

(19) R.E. Schenter, J.L. Baker and R.B. Kidman, "ETOX, A Code to
     Calculate GroupConstants for Nuclear Reactor Calculations",
     Battelle Northwest Laboratory, Report BNWL-1002 (1962).

(20) I.I. Bondarenko (ed.), Group Constants for Nuclear Reactor
     Calculations (Consultants Bureau, New York, 1964).

(21) J.H. Hubbell, William J. Veigele, E.A. Briggs, R.T. Brown,
D.T. Cromer and R.J. Howerton, "Atomic Form Factors, Incoherent      Scattering Functions, and Photon Scattering Cross Sections",
     J. Phys. Chem. Ref. Data 4, 471 (1975).

(22) DISSPLA is a proprietary plotting software package.  Inform-
     ation can be obtained from Integrated Software systems Corp.,
     4186 Sorrento Valley Blvd., San Diego, CA 92121.

(23) D.W. Muir and R.J. LaBauve, "COVFILS, A 30-Group Covariance
     Library Based on ENDF/B-V", Los Alamos National Laboratory
     Report LA-8733-MS (ENDF-306) (March 1981).

(24) R.E. MacFarlane and R.B. Kidman, "LINX and BINX: CCCC Utility
     Codes for the MINX Processing Code", Los Alamos Scientific
     Laboratory, Report LA-6219-MS (1976).

(25) R.B. Kidman and R.E. MacFarlane, "CINX: Collapsed Interpreta-
     tion of Nuclear X-Sections", Los Alamos Scientific Laboratory,   Report LA-6287-MS (1976).

(26) Jaime Anaf and E.S. Chalhoub, "Avaliacao dos codigos ETOG-3Q,
     ETOG-3, FLANGE-II, XLACS, NJOY e LINEAR/RECENT/GROUPIE no que
     tange a contribuicao de ressonancias e secoes de choque de
referencia", Relatoria de Pesquisa IEAv- 065/88 (December 1988)      (in Portuguese)
PSR-0171/19, included references:
- R.E. McFarlane:
  Introducing NJOY 89
  LA-UR 89-2057 (June 1989).
- R.E. McFarlane and D.W. Muir:
  NJOY 87.0
  LANL Memo T-2-L-10991 (June 1987).
- R.E. McFarlane, D.W. Muir and R.M. Boicourt:
  The NJOY Nuclear Data Processing System
  Volume I: User's Manual
  Appendix A: Input Instructions
  Appendix B: Definition of ENDF/B Reaction Numbers Code Conversion
  Appendix C: * (Omitted from the document, on RSIC tapes)
  Appendix D: Preprocessing Program for IBM/CDC Code Conversion
  LA-9303-M, Vol. I (ENDF-324) (May 1982).
- R.E. McFarlane, D.W. Muir and R.M. Boicourt:
  The NJOY Nuclear Data Processing System
  Volume II: The NJOY, RECONR, BROADR, HEATR and THERMR Modules
  LA-9303-M, Vol. II (ENDF-324) (May 1982).
- R.E. McFarlane, D.W. Muir:
  The NJOY Nuclear Data Processing System
  Volume III: The GROUPR, GAMINR and MODER Modules
  LA-9303-M, Vol. III (ENDF-324) (October 1987).
- R.E. McFarlane, D.W. Muir:
  The NJOY Nuclear Data Processing System
  Volume IV: The ERROR and COVR Modules
  LA-9303-M, Vol. IV (ENDF-324) (December 1985).
- LANL README file -NJOY91 Modifications (March 1991).
- R.E. McFarlane:
  The NJOY Nuclear Data Processing System, Version 91.0
  Unpublished document (February 7, 1991).
- R.E. McFarlane and D.C. George:
  UPD - A Portable Version-Control Program
  LA-12057-MS UC-705 (April 1991).
- Cover Sheet Only - Proceedings of the Meetings held at OECD NEA
  Data Bank, Saclay, France (20-21 June 1989).
  Proc. of Seminar on NJOY & THEMIS (1989).
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11. MACHINE REQUIREMENTS

NJOY-89: On CDC-7600 140,000 octal words of SCM are sufficient. The  modules GROUPR and ACER used in addition 142,000 octal words of LCM. On IBM 3084 at least 636K bytes of main storage are required and sufficient buffer space should be provided for external files. Normally 700K bytes are sufficient. On CYBER 740 approximately 250,000 octal words are required.
NJOY-91: NJOY-91 runs in Cray computers. Specialized updates are included for VAX, Sun workstations, and IBM RS/6000.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
PSR-0171/19 FORTRAN-77
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13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED

NJOY (6/83) was developed using the LTSS and CTSS time-sharing systems in use at Los Alamos and Livermore, the FTN and CFT compilers, and the mathematical subroutine and plotting packages available at Los Alamos. System dependent functions such as input/output, time, and date have been localized in low-level subroutines for easy replacement. The DISSPLA routines in COVR are available at many other installations; the SC- 4020 routines in DTFR are not, but they have been left in place as a guide for conversion to other graphics  software. Conversion to other operating systems has proven relatively easy.
NJOY-91: A Fortran-77 compiler is required. The CFT77 compiler was used under UNICOS. RSIC tested this release on a Sun running SUN OS  4.1.1 using the Fortran 1.4 compiler. NJOY-91 uses DISSPLA graphics  software available from ISSCO. Omit the '*set diss' upd command if DISSPLA is not available on your system. This system runs on Cray under either UNICOS or CTSS, on the VAX under VMS, on the Sun under  Sun OS4 o5 OS5, and on IBM RS/6000 under AIX 3.2.5.
PSR-0171/19
The test runs at NEA-DB were done under VAX/VMS V.5.5-2. The compiler VAX FORTRAN V.5.5-98 was employed.
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14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

The CDC version consists of about 400 subroutines on 48000 source cards including 9000 comment cards. The reference version uses a two- level overlay structure which can easily be decomposed into 15 in- dependent programs (processing modules) and a user library.
In the CYBER 740 version, segmentation instead of overlay is used. The IBM version is structured in an overlay tree where each module is a branch. The routines and data COMMONs shared by the modules are placed in the main segment.
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15. NAME AND ESTABLISHMENT OF AUTHOR

Contributed by: Radiation Safety Information Computational Center
                Oak Ridge National Laboratory
                Oak Ridge, Tennessee, U. S. A.

Developed by:   R.E. MacFarlane, R.J. Barrett, D.W. Muir and
                R.M. Boicourt
                Los Alamos Scientific Laboratory
                University of California
                P.O. Box 1663
                Los Alamos, NM 87545, USA
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16. MATERIAL AVAILABLE
PSR-0171/19
File name File description Records
PSR0171_19.001 Information file 244
PSR0171_19.002 Comment and installation file 1179
PSR0171_19.003 UNIX script for initial install 22
PSR0171_19.004 Input for UNICOS 71
PSR0171_19.005 Input file 24
PSR0171_19.006 Makefile for SUN 216
PSR0171_19.007 Makefile for UNIX 220
PSR0171_19.008 NJOY91.91 source for UPD 60632
PSR0171_19.009 Version update 91 6172
PSR0171_19.010 Update program UPD 1064
PSR0171_19.011 Update file (UNICOS at NERSC) 41
PSR0171_19.012 Update file for SUN 39
PSR0171_19.013 Update file for Cray (UNICOS / Los Alamos) 33
PSR0171_19.014 Update file for Cray (UNICOS / San Diego) 48
PSR0171_19.015 User input summary from SRC 156
PSR0171_19.016 Update for VAX/VMS 86
PSR0171_19.017 Input summary extracted from SRC 2104
PSR0171_19.018 Updates for Cray under CTSS 107
PSR0171_19.019 Updates for IBM Mainframes 38
PSR0171_19.020 Correction for VAX at NEADB 54
PSR0171_19.021 Sample input 1 85
PSR0171_19.022 Sample input 2 83
PSR0171_19.023 Sample input 3 54
PSR0171_19.024 Sample input 4 41
PSR0171_19.025 Sample input 5 28
PSR0171_19.026 Sample input 6 97
PSR0171_19.027 Sample input 7 48
PSR0171_19.028 Output 1 (Cray) 1983
PSR0171_19.029 Output 2 (Cray) 7714
PSR0171_19.030 Output 3 (Cray) 996
PSR0171_19.031 Output 4 (Cray) 558
PSR0171_19.032 Output 7 (Cray) 18710
PSR0171_19.033 Output 1 NEA/VAX 1985
PSR0171_19.034 Output 2 NEA/VAX 7716
PSR0171_19.035 Output 3 NEA/VAX 1009
PSR0171_19.036 Output 4 NEA/VAX 558
PSR0171_19.037 Output 5 NEA/VAX 25967
PSR0171_19.038 Output 6 NEA/VAX 390
PSR0171_19.039 Output 7 NEA/VAX 19106
PSR0171_19.040 Differences s.p. 1 (Cray/VAX) 168
PSR0171_19.041 differences s.p. 2 (Cray/VAX) 1340
PSR0171_19.042 Differences s.p. 3 (Cray/VAX) 88
PSR0171_19.043 differences s.p. 4 (Cray/VAX) 114
PSR0171_19.044 differences s.p. 7 (Cray/VAX) 462
PSR0171_19.045 Input data file 21769
PSR0171_19.046 Uran data file 17490
PSR0171_19.047 Graphite data 15284
PSR0171_19.048 phot. data 9930
PSR0171_19.049 phot. data 5222
PSR0171_19.050 Output file from s.p. 7 13336
PSR0171_19.051 PENDF output from s.p. 1 18093
PSR0171_19.052 Plot output s.p. 3 0
PSR0171_19.053 Plot output s.p. 5 0
PSR0171_19.054 Plot output s.p. 6 0
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17. CATEGORIES
  • B. Spectrum Calculations, Generation of Group Constants and Cell Problems
  • C. Static Design Studies
  • J. Gamma Heating and Shield Design
  • K. Reactor Systems Analysis

Keywords: Doppler broadening, Monte Carlo method, charged particles, covariance matrices, cross sections, data uncertainties, discrete ordinate method, errors, gamma radiation, kerma factors, kernels, neutrons, photon interaction, resonance integrals, scattering, self-shielding, thermal neutrons, thermal scattering, transport theory, unresolved region.