=======================================================================
Sixpak

Sixpak

PROGRAM
SIXPAK
Sixpak

==================================================================
Sixpak

VERSION 92-1
(JANUARY 1992)
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VERSION 92-2
(FEBRUARY 1992)*INCREASED CORE ALLOCATION TO
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ACCOMMODATE
JEF AND EFF EVALUATIONS.
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VERSION 92-3
(APRIL 1992)   *ADDED
ADDITIONAL DATA TESTS.
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VERSION 92-4
(SEPT. 1992)   *CORRECTED
KALBACH-MANN CALCULATIONS.  Sixpak

*FOR
PHOTON PRODUCTION OUTPUT MF=12
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(MULTIPLICITY), MF=14 (ISOTROPIC      Sixpak

ANGULAR DISTRIBUTIONS) AND MF=15      Sixpak

(SPECTRA) - PREVIOUSLY ONLY MF=15.    Sixpak

*FIRST ORDER CORRECTIONS TRANSFORMING  Sixpak

CENTER-OF-MASS SPECTRA TO LAB SYSTEM  Sixpak

FOR OUTPUT IN MF=5
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*CORRECTED ISOTROPIC ANGULAR
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DISTRIBUTION FLAG (LI)
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VERSION 94-1
(JANUARY 1994) *VARIABLE ENDF/B INPUT DATA FILENAME   Sixpak

TO ALLOW ACCESS TO FILE STRUCTURES    Sixpak

(WARNING - INPUT PARAMETER FORMAT     Sixpak

HAS BEEN CHANGED)
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*CLOSE ALL FILES BEFORE TERMINATING    Sixpak

(SEE, SUBROUTINE ENDIT)
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*INCREASED MAXIMUM TABLE SIZE FROM     Sixpak

2000 TO 6000.
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VERSION 96-1
(JANUARY 1996) *COMPLETE RE-WRITE
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*IMPROVED COMPUTER INDEPENDENCE
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*ALL
DOUBLE PRECISION
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*ON SCREEN OUTPUT
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*UNIFORM TREATMENT OF ENDF/B I/O
Sixpak

*IMPROVED
OUTPUT PRECISION
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VERSION 99-1
(MARCH 1999)   *CORRECTED
CHARACTER TO FLOATING       Sixpak

POINT READ FOR MORE DIGITS
Sixpak

*UPDATED
TEST FOR ENDF/B FORMAT
Sixpak

VERSION BASED ON RECENT FORMAT CHANGE Sixpak

*GENERAL IMPROVEMENTS BASED ON
Sixpak

USER FEEDBACK
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VERSION 99-2
(JUNE 1999)    *ASSUME
ENDF/B-VI, NOT V, IF MISSING
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MF=1, MT-451.
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VERS. 2000-1
(FEBRUARY 2000)*GENERAL IMPROVEMENTS BASED ON
Sixpak

USER FEEDBACK
Sixpak

VERS. 2002-1
(JANUARY 2002) *CORRECTED ANGULAR DISTRIBUTION (MF=4) Sixpak

OUTPUT TO INSURE USED FIELDS ARE 0    Sixpak

(MAY 2002)
*OPTIONAL INPUT PARAMETERS
Sixpak

(NOV. 2002)
*EXTENDED TO ALLOW CHARGED PARTICLE    Sixpak

ANGULAR DISTRIBUTION IN MF=4 -        Sixpak

WARNING - STRICTLY SPEAKING THIS IS   Sixpak

NOT LEGAL, SINCE MF=4 IS SUPPOSED TO  Sixpak

BE USED ONLY FOR NEUTRON ANGULAR      Sixpak

DISTRIBUTIONS - BUT WHERE MT MAKES    Sixpak

IT OBVIOUS THAT THE OUTGOING PARTICLE Sixpak

IS NOT A NEUTRON HOPEFULLY IT WILL    Sixpak

NOT
CAUSE A PROBLEM IF MF=4 IS USED
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FOR CHARGED PARTICLES.
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VERS. 2004-1
(MARCH 2004)   *ADDED INCLUDE
FOR COMMON
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*INCREASED
MAXIMUM TABLE SIZE FROM
Sixpak

6,000 TO 12,000.
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*ADDED DUMMY A FOR ELEMENTS
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*CORRECTED
OUTPUT INTERPOLATON LAWS
Sixpak

VERS. 2007-1
(JAN.  2007)   *CHECKED AGAINST ALL ENDF/B-VII.
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*INCREASED MAXIMUM TABLE SIZE FROM     Sixpak

12,000 TO 120,000.
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Sixpak

OWNED,
MAINTAINED AND DISTRIBUTED BY
Sixpak

------------------------------------                               Sixpak

THE NUCLEAR DATA
SECTION
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INTERNATIONAL
ATOMIC ENERGY AGENCY
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P.O. BOX
100
Sixpak

A-1400, VIENNA,
AUSTRIA
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EUROPE
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ORIGINALLY
WRITTEN BY
Sixpak

------------------------------------
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DERMOTT E.
CULLEN
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UNIVERSITY OF
CALIFORNIA
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LAWRENCE
LIVERMORE NATIONAL LABORATORY
Sixpak

L-159
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P.O. BOX 808
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LIVERMORE, CA
94550
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U.S.A.
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TELEPHONE  925-423-7359
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E. MAIL    [email-masked]
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WEBSITE
HTTP://WWW.LLNL.GOV/CULLEN1
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COLLABORATION
Sixpak

==================================================================
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DEVELOPED IN
COLLABORATION WITH,
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*THE NATIONAL
NUCLEAR DATA CENTER, BROOKHAVEN NATIONAL LAB
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*THE NUCLEAR
DATA SECTION, IAEA, VIENNA, AUSTRIA
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*CENTRO TECNICO
AEROSPACIAL, SAO JOSE DOS CAMPOS, BRAZIL
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AS A PART OF AN
INTERNATIONAL PROJECT ON THE EXCHANGE OF
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NUCLEAR
DATA
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ACKNOWLEDGEMENT
(VERSION 92-1)
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================================================================== Sixpak

THE AUTHOR
THANKS SOL PEARLSTEIN (BROOKHAVEN NATIONAL LAB) FOR     Sixpak

SIGNIFICANTLY
CONTRIBUTING TOWARD IMPROVING THE ACCURACY AND
Sixpak

COMPUTER
INDEPENDENCE OF THIS CODE - THANKS, SOL
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Sixpak

ACKNOWLEDGEMENT
(VERSION 92-4)
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==================================================================
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THE AUTHOR
THANKS BOB MACFARLANE (LOS ALAMOS) FOR SUGGESTING HOW   Sixpak

TO PROPERLY
OUTPUT THE PHOTON PRODUCTION DATA TO PUT IT INTO
Sixpak

EXACTLY THE FORM
NEEDED FOR USE IN PROCESSING CODES.
Sixpak

Sixpak

THE AUTHOR
THANKS CHRIS DEAN (WINFRITH) FOR POINTING OUT ERRORS    Sixpak

IN THE EARLIER
TREATMENT OF THE KALBACH-MANN FORMALISM AND IN      Sixpak

THE DEFINITION
OF THE ISOTROPIC ANGULAR DISTRIBUTION FLAG (LI).    Sixpak

Sixpak

AUTHORS
MESSAGE
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==================================================================
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THE COMMENTS
BELOW SHOULD BE CONSIDERED THE LATEST DOCUMENTATION   Sixpak

INCLUDING ALL
RECENT IMPROVEMENTS. PLEASE READ ALL OF THESE
Sixpak

COMMENTS BEFORE
IMPLEMENTING AND USING THESE CODES.
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Sixpak

AT THE PRESENT
TIME WE ARE ATTEMPTING TO DEVELOP A SET OF COMPUTER Sixpak

INDEPENDENT
PROGRAMS THAT CAN EASILY BE IMPLEMENTED ON ANY ONE     Sixpak

OF A WIDE
VARIETY OF COMPUTERS. IN ORDER TO ASSIST IN THIS PROJECT Sixpak

IT WOULD BE
APPECIATED IF YOU WOULD NOTIFY THE AUTHOR OF ANY
Sixpak

COMPILER
DIAGNOSTICS, OPERATING PROBLEMS OR SUGGESTIONS ON HOW TO  Sixpak

IMPROVE THIS
PROGRAM. HOPEFULLY, IN THIS WAY FUTURE VERSIONS OF    Sixpak

THIS PROGRAM
WILL BE COMPLETELY COMPATIBLE FOR USE ON YOUR
Sixpak

COMPUTER.
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PURPOSE
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==================================================================
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1) CHECK ALL
DOUBLE-DIFFERENTIAL DATA (MF=6)
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2) OUTPUT
EQUIVALENT MF = 4, 5, 12, 14 AND 15 DATA.
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DATA
CHECKING
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==================================================================
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ALL OF THE
ENDF/B-VI MF=6 DATA IS CHECKED - FOR DETAILS SEE BELOW. Sixpak

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THE MF=6 DATA IS
NOT CORRECTED AND OUTPUT IN THE ENDF/B FORMAT.    Sixpak

IT IS MERELY
CHECKED. IF ERRORS ARE FOUND IT IS UP TO THE USER     Sixpak

TO TAKE
CORRECTIVE ACTION ON THE MF=6 DATA.
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Sixpak

IN CONTRAST WHEN
PROBLEMS ARE FOUND IN DATA WHICH WILL BE OUTPUT   Sixpak

IN THE ENDF/B
FORMAT (MF=4, 5, 12, 14 AND 15), WHENEVER POSSIBLE   Sixpak

CORRECTIVE
ACTION WILL BE TAKEN.
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FURTHER CHECKS
AND CORRECTIONS
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==================================================================
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ONCE THE DATA
HAS BEEN OUTPUT IN MF = 4, 5, 12, 14 AND 15 FORMATS  Sixpak

FURTHER
CORRECTIVE ACTION CAN BE TAKEN AS FOLLOWS,
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Sixpak

PROGRAM
LEGEND
Sixpak

==============
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CAN BE USED TO
CORRECT ANGULAR DISTRIBUTIONS WHICH ARE NEGATIVE,   Sixpak

TO CONVERT FROM
LEGENDRE COEFFICIENTS TO TABULATED ANGULAR
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DISTRIBUTIONS
AND GENERALLY PERFORM MORE EXTENSIVE TESTS OF
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ALL MF=4
DATA.
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Sixpak

PROGRAM EVALPLOT
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================
Sixpak

VERSION 92-1 AND
LATER VERSIONS CAN PLOT ALL OF THE MF=4, 5 AND 15 Sixpak

DATA OUTPUT BY
THIS CODE. EARLIER VERSIONS CAN PLOT MF=4 AND 5.    Sixpak

GRAPHICS IS AN
EXCELLENT WAY TO CHECK THIS DATA.
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Sixpak

PROGRAM
PLOTTAB
Sixpak

===============
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THIS IS A
GENERAL PLOTTING PROGRAM AND THERE IS AN INTERFACE IN    Sixpak

THIS CODE TO
PRODUCE OUTPUT FOR ANY MF=6 DATA IN THE PLOTTAB
Sixpak

INPUT FORMAT.
THIS PROGRAM CAN BE USED TO CHECK ALL OF THE MF=6    Sixpak

DATA AS WELL AS
THE EQUIVALENT MF=4, 5, 12, 14 AND 15 DATA - AS    Sixpak

WELL AS
COMPARING THE ORIGINAL MF=6 AND EQUIVALENT DATA.
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Sixpak

DATA OUTPUT
Sixpak

==================================================================
Sixpak

THE ENDF/B MF=4,
5, 12, 14 AND 15 FORMATS ONLY ALLOW FOR NEUTRONS  Sixpak

INCIDENTS
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Sixpak

THE ENDF/B MF=4
AND 5 FORMATS ONLY ALLOW FOR NEUTRONS OUTGOING.    Sixpak

Sixpak

THE ENDF/B
MF=12, 14 AND 15 ONLY ALLOWS FOR PHOTONS OUTGOING.      Sixpak

Sixpak

THESE ARE THE
ONLY COMBINATIONS OF DATA OUTPUT BY THIS CODE.
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Sixpak

ALL OTHER COMBINATIONS
OF INCIDENT AND OUTGOING PARTICLES ARE      Sixpak

CHECKED, BUT THE
RESULTS CANNOT BE OUTPUT IN THE ENDF/B FORMAT.    Sixpak

HOWEVER, USING
THE PLOTTAB INTERFACE BUILT INTO THIS CODE THIS     Sixpak

DATA CAN, AND
HAS BEEN, OUTPUT AND CHECKED.
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Sixpak

THE NEUTRON DATA
IN MF=4 CAN BE IN THE FORM OF EITHER TABULATED    Sixpak

ANGULAR
DISTRIBUTIONS OR LEGENDRE COEFFICIENTS.
Sixpak

Sixpak

THE NEUTRON
(MF=5) OR PHOTON (MF=15) SPECTRA ARE BOTH IN EXACTLY   Sixpak

THE SAME FORMAT
= ARBITRARY TABULATED FUNCTIONS - ENDF/B OPTION    Sixpak

LF=1.
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Sixpak

ENDF/B DATA
OUTPUT ORDER
Sixpak

==================================================================
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ENDF/B DATA IS
OUTPUT IN ASCENDING MAT, MF, MT ORDER. IN ORDER TO  Sixpak

ALLOW THIS
PROGRAM TO PRODUCE ALL OUTPUT IN A SINGLE PASS THROUGH  Sixpak

THE MF=6 DATA,
OUTPUT FOR EACH (MAT, MT) IS OUTPUT TO SEPERATE     Sixpak

FILES FOR MF=4,
5, 12, 14 AND 15.
Sixpak

Sixpak

FOR SUBSEQUENT
USE THE ENDF/B FORMATTED DATA OUTPUT BY THIS CODE   Sixpak

CAN BE MERGED
TOGETHER USING PROGRAM MERGER (CONTAIN THE AUTHOR    Sixpak

OF THIS CODE FOR
A COPY OF MERGER), E.G., MERGE MF=12, 14 AND 15   Sixpak

DATA IN ORDER TO THEN CALCULATE
PHOTON PRODUCTION DATA OR MF=4     Sixpak

AND 5 CAN BE
MERGED TOGETHER TO CALCULATE NEUTRON TRANSFER - OR    Sixpak

ALL OF THEM CAN
BE MERGED TOGETHER TO PERFORM NEUTRON AND PHOTON   Sixpak

CALCULATIONS.
Sixpak

Sixpak

CORRELATED
(MF=6) VS. UNCORRELATED (MF=4 AND 5) DATA
Sixpak

==================================================================
Sixpak

THE ENDF/B
DOUBLE DIFFERENTAL = CORRELATED - DATA IN MF=6
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REPRESENTS DATA
IN THE FORM,
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Sixpak

F(E,EP,COS) =
SIG(E)*Y(E)*G0(E,EP)*F(E,EP,COS)
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Sixpak

SIG(E)      = MF=3 CROSS
SECTIONS                                  Sixpak

Y(E)        =
YIELD (MULTIPLICITY)
Sixpak

G0(E,EP)    = ENERGY SPECTRUM
Sixpak

F(E,EP,COS) =
ANGULAR DISTRIBUTION
Sixpak

Sixpak

IN A SITUATION
WHERE YOU HAVE MONOENERGETIC AND MONODIRECTIONAL    Sixpak

NEUTRONS
INCIDENT YOU WILL BE ABLE TO OBSERVE CORRELATION EFFECTS  Sixpak

IN THE NEUTRON
SPECTRUM AND ANGULAR DISTRIBUTION.
Sixpak

Sixpak

EVEN IN
SITUATIONS WHERE YOU HAVE A NARROW SPECTRUM OF NEUTRONS    Sixpak

THAT ARE HIGHLY
DIRECTIONALLY ORIENTED YOU MAY BE ABLE TO OBSERVE  Sixpak

THESE
CORRELATION EFFECTS, E.G., A NARROW 14 MEV FUSION SOURCE     Sixpak

INCIDENT ON THE
FIRST WALL OF A CTR DEVICE.
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Sixpak

FOR SUCH
SITUATIONS USE OF THE CORRELATED (MF=6) DATA IS REQUIRED  Sixpak

IN
CALCULATIONS.
Sixpak

Sixpak

HOWEVER, IN MANY
APPLICATIONS WHERE THERE IS A BROAD SPECTRUM OF   Sixpak

NEUTRONS AND THE
NEUTRON FLUX IS NOT HIGHLY DIRECTIONALLY
Sixpak

ORIENTED, THE NEUTRON
MULTIPLICATION, SPECTRUM AND ORIENTATION     Sixpak

CAN BE FAIRLY
ACCURATELY CALCULATED WITHOUT CONSIDERING
Sixpak

CORRELATION
EFFECTS.
Sixpak

Sixpak

THE UNCORRELATED
DATA PRODUCED BY THIS CODE REPLACES THE
Sixpak

CORRELATED
DATA,
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Sixpak

F(E,EP,COS) =
SIG(E)*Y(E)*G0(E,EP)*F(E,EP,COS)
Sixpak

Sixpak

BY THE
UNCORRELATED DATA,
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Sixpak

F(E,EP,COS) =
SIG(E)*Y(E)*G0(E,EP)*F0(E,COS)
Sixpak

Sixpak

BY INTEGRATING
G0(E,EP)*F(E,EP,COS) OVER SECONDARY ENERGY (EP)     Sixpak

TO DEFINE AN
AVERAGE ANGULAR DISTRIBUTION, F0(E,COS).
Sixpak

Sixpak

WHAT IS LOST IN
THIS PROCESS IS THE CORRELATION BETWEEN EP AND COS Sixpak

SO THAT IN A
TRANSPORT CALCULATION ALL MOMENTS OF THE FLUX WILL    Sixpak

HAVE THE SAME
SPECTRUM, G0(E,EP) AND EACH WILL BE EFFECTED BY THE  Sixpak

AVERAGE ANGULAR
DISTRIBUTION.
Sixpak

Sixpak

FOR APPLICATIONS
TO HIGH ENERGY FUSION APPLICATIONS CORRELATED     Sixpak

DATA SHOULD BE
USED. HOWEVER, FOR LOWER ENERGY APPLICATIONS,
Sixpak

SUCH AS FISSION
REACTORS, IT SHOULD BE ADEQUATE TO USE THE
Sixpak

UNCORRELATED
DATA - IN THIS CASE THE MOST IMPORTANT EFFECT
Sixpak

WILL BE THE OVERALL
NEUTRON MULTIPLICATION AND SPECTRUM.
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Sixpak

AN IMPORTANT
CONSIDERATION IN DESIGNING THIS PROGRAM IS THAT
Sixpak

MANY COMPUTER
CODES - DATA PROCESSING AND TRANSPORT CODES -
Sixpak

CANNOT USE THE
CORRELATED (MF=6) DATA - NOR ARE THEY INTENDED      Sixpak

FOR HIGH ENERGY
USE. FOR THESE CODES THE UNCORRELATED DATA
Sixpak

PRODUCED BY THIS
CODE SHOULD BE ADEQUATE TO MEET THEIR NEEDS.      Sixpak

Sixpak

WARNING - IT
CANNOT BE STRESSED ENOUGH THAT THE OUTPUT OF THIS     Sixpak

CODE SHOULD ONLY
BE USED FOR LOW ENERGY APPLICATIONS - FAILURE     Sixpak

TO HEED THIS
WARNING CAN LEAD TO COMPLETELY UNRELIABLE RESULTS.    Sixpak

Sixpak

ENDF/B
FORMAT
Sixpak

==================================================================
Sixpak

THIS PROGRAM
ONLY USES THE ENDF/B BCD OR CARD IMAGE FORMAT (AS     Sixpak

OPPOSED TO THE
BINARY FORMAT) AND CAN HANDLE DATA IN ANY VERSION   Sixpak

OF THE ENDF/B
FORMAT (I.E., ENDF/B-I, II,III, IV, V OR VI FORMAT). Sixpak

Sixpak

IT IS ASSUMED
THAT THE DATA IS CORRECTLY CODED IN THE ENDF/B       Sixpak

FORMAT AND NO
ERROR CHECKING IS PERFORMED. IN PARTICULAR IT IS     Sixpak

ASSUMED THAT THE
MAT, MF AND MT ON EACH LINE IS CORRECT. SEQUENCE  Sixpak

NUMBERS (COLUMNS
76-80) ARE IGNORED ON INPUT, BUT WILL BE
Sixpak

CORRECTLY OUTPUT
ON ALL LINES. THE FORMAT OF SECTION MF=1, MT=451  Sixpak

AND ALL SECTIONS
OF MF=6 MUST BE CORRECT. THE PROGRAM SKIPS ALL    Sixpak

OTHER SECTIONS
OF DATA AND AS SUCH IS INSENSITIVE TO THE FORMAT    Sixpak

OF ALL OTHER
SECTIONS.
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Sixpak

CONTENTS OF
OUTPUT
Sixpak

==================================================================
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5 ENDF/B
FORMATTED OUTPUT FILES ARE PRODUCED FOR NEUTRON INCIDENT  Sixpak

DATA,
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Sixpak

1) ENDFB.MF4 -
ANGULAR DISTRIBUTIONS AND LEGENDRE COEFFICIENTS     Sixpak

FOR NEUTRONS
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2) ENDFB.MF5 -
TABULATED NEUTRON ENERGY SPECTRA
Sixpak

3) ENDFB.M12 -
PHOTON EMISSION MULTIPLICITY
Sixpak

4) ENDFB.M14 -
PHOTON EMISSION ANGULAR DISTRIBUTIONS (ALWAYS
Sixpak

ISOTROPIC)
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5) ENDFB.M15 -
TABULATED PHOTON EMISSION SPECTRA
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EMITTED PARTICLE
YIELD
Sixpak

==================================================================
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NEUTRONS
Sixpak

========
Sixpak

IN MF=6 THE
YIELD FOR EACH REACTION IS THE ACTUAL MULTIPLICITY OF  Sixpak

THE REACTION,
E.G., (N,2N) = 2. IN USING MF=4 AND 5 DATA THE
Sixpak

ENDF/B
CONVENTION IS THAT THE MULTIPLICITY IS IMPLIED BY THE
Sixpak

MT NUMBER, E.G., MT=16 = (N,2N) = 2.
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Sixpak

THE ONLY EXCEPT
IN ENDF/B-VI IS MT=201 = TOTAL NEUTRON PRODUCTION  Sixpak

WHERE AN ACTUAL
ENERGY DEPENDENT YIELD IS INCLUDED IN MF=6.
Sixpak

HOWEVER, IN THIS
CASE THE MF=3 CROSS SECTION INCLUDES THE
Sixpak

MULTIPLICITY (S.
PEARLSTEIN, PRIVATE COMMUNICATION, JAN. 1992),    Sixpak

SIG(MT=201) =
2*SIG(N,2N)+3*SIG(N,3N).....ETC.
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Sixpak

SO THAT FOR ALL
ENDF/B-VI DATA AS OF JANUARY 1992 THE MF=4 AND 5   Sixpak

DATA OUTPUT BY
THIS CODE CAN BE USED IN CONJUNCTION WITH THE MF=3  Sixpak

CROSS SECTIONS -
WITHOUT ANY REFERENCE TO THE MF=6 YIELD.
Sixpak

Sixpak

PHOTONS
Sixpak

=======
Sixpak

UNLIKE THE
NEUTRONS WHERE WITH ONLY ONE EXCEPTION (MT=201) THE     Sixpak

MF=6 YIELD IS
ENERGY INDEPENDENT, IN THE CASE OF PHOTON EMISSION   Sixpak

ALMOST ALL OF
THE PHOTONS HAVE AN ENERGY DEPENDENT YIELD.
Sixpak

Sixpak

THIS PROGRAM
WILL OUTPUT THE PHOTON MULTIPLICITY IN MF=12 AND      Sixpak

INDICATE THAT
THERE IS A NORMALIZED DISTRIBUTION IN MF=15
Sixpak

(LF=1 IN
MF=12).
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Sixpak

THIS PROGRAM
WILL OUTPUT THE NORMALIZED PHOTON SPECTRA IN MF=15.   Sixpak

CONTINUOUS
ENERGY SPECTRA AND DISCRETE PHOTONS WILL ALL BE OUTPUT  Sixpak

AS NORMALIZED
SPECTRA.
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Sixpak

THIS PROGRAM
WILL ALSO OUTPUT MF=14 PHOTON ANGULAR DISTRIBUTION    Sixpak

DATA, ALWAYS
USING THE ISOTROPIC FLAG TO MINIMIZE OUTPUT.
Sixpak

Sixpak

WARNING OF
ENERGY DEPENDENT YIELD
Sixpak

=================================
Sixpak

THIS PROGRAM
WILL PRINT A WARNING MESSAGE IF A SECTION OF DATA     Sixpak

BEING OUTPUT IN
THE ENDF/B FORMAT HAS AN ENERGY DEPENDENT MF=6     Sixpak

YIELD AND THE
EMITTED PARTICLE IS A NEUTRON - SINCE THE ENDF/B     Sixpak

CONVENTION IS
THAT FOR EACH MT NUMBER THE MULTIPLICITY IS IMPLIED  Sixpak

WE DO NOT EXPECT
AN ENERGY DEPENDENT MULTIPLICITY FOR NEUTRON      Sixpak

EMISSION.
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Sixpak

USING THE
OUTPUT
Sixpak

==================================================================
Sixpak

NOTE, THAT IN
USING THIS DATA, STARTING FROM THE RELATIONSHIP,     Sixpak

Sixpak

F(E,EP,COS) =
SIG(E)*Y(E)*G0(E,EP)*F0(E,COS)
Sixpak

Sixpak

USING THE ENDF/B
CONVENTION THAT THE MULTIPLICITY IS EITHER
Sixpak

IMPLIED BY THE
MT NUMBER (E.G., MT=16 = N,2N - MULTIPLICITY = 2)   Sixpak

OR INCLUDED IN
THE CROSS SECTION (E.G., MT=201 = TOTAL NEUTRON     Sixpak

PRODUCTION) ALL
THE INFORMATION REQUIRED FOR A CALCULATION IS      Sixpak

AVAILABLE
IN,
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Sixpak

MF=3       -
SIG(E)
Sixpak

MF=4       -
F0(E,COS) - FOR OUTGOING NEUTRONS
Sixpak

MF=5       -
G0(E,EP)  - FOR OUTGOING NEUTRONS
Sixpak

MF=12      - Y(E)      - FOR OUTGOING
PHOTONS
Sixpak

MF=14      - F0(E,COS) -
FOR OUTGOING PHOTONS (ALWAYS ISOTROPIC)   Sixpak

MF=15      - G0(E,EP)  - FOR OUTGOING PHOTONS
Sixpak

Sixpak

DOCUMENTATION
Sixpak

==================================================================
Sixpak

ONLY SECTIONS OF
MF=4, 5, 12, 14, 15 ARE OUTPUT ON A ENDF/B FILE.  Sixpak

THE ONLY
DOCUMENTATION IS THE ENDF/B TAPE LABEL (FIRST RECORD OF   Sixpak

EACH FILE) WHICH
IDENTIFIES THE DATA AS SIXPAK OUTPUT.
Sixpak

Sixpak

REACTION
INDEX
Sixpak

==================================================================
Sixpak

THIS PROGRAM
DOES NOT USE THE REACTION INDEX WHICH IS GIVEN IN     Sixpak

SECTION MF=1,
MT=451 OF EACH EVALUATION.
Sixpak

Sixpak

SECTION
SIZE
Sixpak

==================================================================
Sixpak

ALL OF THE DATA
IN ENDF/B-VI, MF=6 ARE QUITE SMALL TABLES. AS SUCH Sixpak

THIS PROGRAM
ONLY ALLOWS TABLES OF UP TO 12000 POINTS (12,000 X,   Sixpak

Y VALUES). THIS
SIZE IS MORE THAN ADEQUATE TO HANDLE ALL OF THE    Sixpak

CURRENT
ENDF/B-VI DATA, AND IT CAN BE EASILY INCREASED TO HANDLE   Sixpak

ANY NEWER DATA
AS IT BECOMES AVAILABLE.
Sixpak

Sixpak

PLEASE CONTACT
THE AUTHOR IF YOU HAVE AN EVALUATION WHICH EXCEEDS  Sixpak

THIS LIMIT.
Sixpak

Sixpak

SELECTION OF
DATA
Sixpak

==================================================================
Sixpak

THE PROGRAM SELECTS
DATA TO BE PROCESSED BASED ON MAT/MT RANGES    Sixpak

(MF=6 ASSUMED).
THIS PROGRAM ALLOWS UP TO 100 MAT/MT RANGES TO BE  Sixpak

SPECIFIED BY
INPUT PARAMETERS. THE PROGRAM WILL ASSUME THAT THE    Sixpak

ENDF/B TAPE IS
IN MAT ORDER. THE PROGRAM WILL TERMINATE EXECUTION  Sixpak

WHEN A MAT IS
FOUND THAT IS ABOVE ALL REQUESTED MAT RANGES.
Sixpak

Sixpak

PROGRAM
OPERATION
Sixpak

==================================================================
Sixpak

EACH SECTION
(MT) OF MF=6 DATA IS SUBDIVIDED INTO SUBSECTIONS -    Sixpak

ONE SUBSECTION
FOR EACH EMITTED PARTICLE.                          Sixpak

Sixpak

EACH SUBSECTION
OF DATA IS CONSIDERED SEPARATELY. EACH SUBSECTION  Sixpak

OF ENDF/B MF=6
DATA TO PROCESS IS IN THE FORM,                     Sixpak

Sixpak

F(E,EP,COS) =
SIG(E)*Y(E)*G0(E,EP)*F(E,EP,COS)
Sixpak

Sixpak

SIG(E)      = MF=3 CROSS
SECTIONS
Sixpak

Y(E)        =
YIELD (MULTIPLICITY)
Sixpak

G0(E,EP)    = ENERGY SPECTRUM
Sixpak

F(E,EP,COS) =
ANGULAR DISTRIBUTION
Sixpak

Sixpak

G0(E,EP) = 1
WHEN INTEGRATED OVER EP (SECONDARY ENERGY)
Sixpak

G0(E,EP)*F(E,EP,COS)
= 1 WHEN INTEGRATED OVER EP AND COS
Sixpak

Sixpak

THIS PROGRAM
WILL DEFINE THE ZEROTH ORDER MOMENTS OF THE
Sixpak

ENERGY AND ANGULAR
DISTRIBUTIONS,
Sixpak

Sixpak

G0(E,EP)  = G0(E,EP)*F(E,EP,COS) INTEGRATED OVER
COS
Sixpak

F0(E,COS) =
G0(E,EP)*F(E,EP,COS) INTEGRATED OVER EP
Sixpak

Sixpak

FOR NEUTRON
INDUCED REACTIONS THE ENDF/B FORMATTED OUTPUT WILL BE  Sixpak

Sixpak

F0(E,COS)- IN
ENDFB.MF4 FOR NEUTRONS OUT OF A REACTION
Sixpak

G0(E,EP) - IN
ENDFB.MF5 FOR NEUTRONS OUT OF A REACTION
Sixpak

- IN ENDFB.M15 FOR PHOTONS OUT OF A REACTION
Sixpak

Sixpak

FOR NEUTRONS
INCIDENT AND NEUTRONS EMITTED THIS DATA WILL BE
Sixpak

OUTPUT IN MF=4
AND 5 FORMATS.
Sixpak

Sixpak

FOR NEUTRONS
INCIDENT AND PHOTONS EMITTED THIS DATA WILL BE
Sixpak

OUTPUT IN MF=15
FORMAT - THE SPECTRA ARE OUTPUT AND THE            Sixpak

ANGULAR
DISTRIBUTION IS IGNORED.
Sixpak

Sixpak

ALL PHOTON
EMISSION IN THE ENDF/B-VI LIBRARY AS OF JANUARY 1992    Sixpak

IS ISOTROPIC AND
AS SUCH NO DISTRIBUTION OF PHOTON ANGULAR
Sixpak

DISTRIBUTIONS
NEED BE OUTPUT - IT IS ALWAYS ISOTROPIC.
Sixpak

Sixpak

FOR ALL OTHER COMBINATIONS INCIDENT AND
EMITTED PARTICLES
Sixpak

THERE WILL BE NO
ENDF/B FORMATTED OUTPUT.
Sixpak

Sixpak

VARIATIONS FROM
ENDF/B MANUAL
Sixpak

==================================================================
Sixpak

LAW=1, LANG=2 =
KALBACH-MANN
Sixpak

============================
Sixpak

FOR THE
DISTRIBUTIONS,
Sixpak

Sixpak

F(MU,E,EP) =
G0(E,EP)*A*(COSH(MU*A)+R(E,EP)*SINH(MU*A))
Sixpak

Sixpak

G0(E,EP) = 1 -
WHEN INTEGRATED OVER EP.
Sixpak

Sixpak

A*(COSH(MU*A)+R(E,EP)*SINH(MU*A)) = 2 - WHEN INTEGRATD OVER MU     Sixpak

Sixpak

THIS MEANS AS
DEFINED IN THE ENDF/B MANUAL THE DISTRIBUTIONS
Sixpak

ARE NORMALIZED
TO 2, INSTEAD OF 1. IN ORDER TO OBTAIN CORRECTLY    Sixpak

NORMALIZED
DISTRIBUTIONS THE DISTRIBUTION SHOULD BE DEFINED
Sixpak

TO INCLUDE A
FACTOR OF 1/2 MULTIPLYING THE ANGULAR PART OF         Sixpak

THE
DISTRIBUTION.
Sixpak

Sixpak

F(MU,E,EP) =
G0(E,EP)*0.5*A*(COSH(MU*A)+R(E,EP)*SINH(MU*A))        Sixpak

Sixpak

THIS IS THE FORM
USED IN THIS CODE
Sixpak

Sixpak

LAW=1, ND NOT 0 = DISCRETE
SECONDARY ENERGY DISTRIBUTION
Sixpak

========================================================
Sixpak

THE ENDF/B
MANUAL SAYS THESE ARE FLAGGED WITH NEGATIVE ENERGIES.   Sixpak

IN ENDF/B-VI ALL
OF THESE HAVE POSITIVE ENERGY. THIS CODE DOES     Sixpak

NOT CONSIDER THE
ENDF/B-VI DATA TO BE IN ERROR.
Sixpak

Sixpak

WITH THE
CONVENTION ACTUALLY USED IN ENDF/B-VI ALL SECONDARY
Sixpak

ENERGIES SHOULD
BE NON-NEGATIVE AND IN ASCENDING ENERGY ORDER      Sixpak

FOR EACH
INCIDENT ENERGY.
Sixpak

Sixpak

FROM THE ENDF/B
MANUAL IT IS NOT OBVIOUS WHAT G0(E,EP) SHOULD BE   Sixpak

FOR DISCRETE
PHOTONS - PHYSICALLY THIS IS A DELTA FUNCTION. IN     Sixpak

ENDF/B-VI IT IS
ENTERED AS 1.0 = INTERPRETING IT AS INTEGRATED     Sixpak

OVER SECONDARY
ENERGY - IN WHICH CASE THE DELTA FUNCTION = 1.0.    Sixpak

Sixpak

LIMITATIONS
Sixpak

==================================================================
Sixpak

CHECKING
DATA
Sixpak

==================================================================
Sixpak

THIS PROGRAM
CHECKS ALL ENDF/B-VI MF=6 DATA. THE FOLLOWING CHECKS  Sixpak

ARE
PERFORMED.
Sixpak

Sixpak

PARAMETERS
Sixpak

==========
Sixpak

ALL PARAMETERS
ARE CHECKED FOR CONSISTENCY. IF PARAMETERS ARE      Sixpak

NOT CONSISTENT
THE PROGRAM MAY NOT BE ABLE TO PERFORM THE
Sixpak

FOLLOWING TESTS
AND WILL MERELY SKIP A SECTION OF DATA.
Sixpak

Sixpak

INTERPOLATION
LAWS
Sixpak

==================
Sixpak

ALL INTEGRATIONS
ARE PERFORMED USING THE INTERPOLATION LAW GIVEN   Sixpak

FOR SECONDARY ENERGY
AND/OR COSINE. INTEGRATIONS ARE NOT
Sixpak

PERFORMED OVER
INCIDENT - ONLY INTEGRATION OVER SECONDARY ENERGY   Sixpak

AND/OR COSINE
ARE PERFORMED AT EACH INCIDENT ENERGY. THEREFORE     Sixpak

THE
INTERPOLATION LAW FOR INCIDENT ENERGY IS NOT USED BY THIS      Sixpak

CODE.
Sixpak

Sixpak

ALL
INTERPOLATION LAWS ARE CHECKED. ALL DATA ASSOCIATED WITH
Sixpak

INTERPOLATION
LAWS ARE CHECKED, E.G., NO NON-NEGATIVE VALUES
Sixpak

REQUIRING LOG
INTERPOLATION. IN ORDER TO PERFORM REQUIRED
Sixpak

INTEGRALS OVER
COS AND EP IT IS IMPERATIVE THAT THE INTERPOLATION  Sixpak

LAWS BE
COMPATIBLE WITH THE DATA.
Sixpak

Sixpak

ENDF/B-VI ALLOWS
NEW INTERPOLATION LAWS FOR CORRESPONDING POINT    Sixpak

AND UNIT BASE
TRANSFORMATION INTERPOLATION. NONE OF THESE NEW      Sixpak

INTERPOLATION
LAWS ARE USED IN THE ENDF/B-VI LIBRARY AS OF
Sixpak

JANUARY 1992 TO
INTERPOLATE IN SECONDARY ENERGY OR COSINE.         Sixpak

THEREFORE THIS
PROGRAM CAN PERFORM ALL OF THE REQUIRED INTEGRALS   Sixpak

OVER SECONDARY
ENERGY AND/OR COSINE USING ONLY THE OLDER
Sixpak

INTERPOLATION
CODES. THIS PROGRAM ONLY PERFORMS INTEGRALS FOR      Sixpak

EACH INCIDENT
ENERGY, SO THAT INTERPOLATION IN INCIDENT ENERGY     Sixpak

IS NOT PERFORMED
BY THIS PROGRAM.
Sixpak

Sixpak

NEW
INTERPOLATION SCHEMES ARE USED FOR INCIDENT ENERGY - FOR
Sixpak

EXAMPLE,
CORRESPONDING POINT INTERPOLATION IS SPECIFIED TO ALLOW   Sixpak

INTERPOLATION IN
G0(E,EP) TO SIMULATE CASES WHERE THE INPUT ENERGY Sixpak

LIMIT IS DEFINED
BY E-EP = A DIAGONAL CURVE ACROSS (E,EP) SPACE.   Sixpak

THIS
INTERPOLATION CODE CANNOT BE SPECIFIED IN THE MF=5 OUTPUT     Sixpak

OF THIS CODE -
MF=5 ONLY ALLOWS THE OLDER INTERPOLATION LAWS
Sixpak

INT=1 THROUGH 5.
THEREFORE THIS PROGRAM WILL USE THE CLOSEST
Sixpak

CORRESPONDING
INTERPOLATION CODE FOR OUTPUT TO MF=5. FOR USE
Sixpak

WHERE THE OUTPUT
OF THIS CODE = LOW ENERGY APPLICATIONS - THIS     Sixpak

SHOULD HAVE
LITTLE EFFECT ON RESULTS.
Sixpak

Sixpak

FOR CONSISTENCY
WITH EARLIER VERSIONS OF ENDF/B IN CREATING THE    Sixpak

ENDF/B OUTPUT,
IF ANY INPUT INTERPOLATION LAW IS NOT IN THE
Sixpak

RANGE 1-5, IT
WILL FIRST BE TESTED TO SEE IF MOD(10) IT IS
Sixpak

IN THIS RANGE,
FINALLY IF EVEN THIS DOESN'T WORK IT IS SET
Sixpak

EQUAL TO 2
(LINEARLY INTERPOLATION). THIS METHOD WILL EFFECTIVELY  Sixpak

REPLACE
CORRESPONDING POINT AND UNIT BASE TRANSFORMATION BY THE    Sixpak

CLOSEST RELATED
INTERPOLATION LAW 1 THROUGH 5 - AGAIN NOTE, AS     Sixpak

OF JANUARY 1992
NONE OF THESE NEW LAWS ARE USED IN ENDF/B-VI. IF   Sixpak

THIS MUST BE
DONE FOR INTERPOLATION IN SECONDARY ENERGY OR COSINE  Sixpak

AN ERROR MESSAGE
WILL BE PRINTED - SINCE THIS WOULD EFFECT THE     Sixpak

ACCURACY OF THE
INTEGRALS PERFORMED BY THIS PROGRAM. IF THIS MUST  Sixpak

BE DONE FOR
INCIDENT ENERGY NO MESSAGE IS PRINTED - SINCE THIS     Sixpak

WILL NOT EFFECT
THE ACCURACY OF THE INTEGRALS PERFORMED BY THIS    Sixpak

PROGRAM.
Sixpak

Sixpak

SPECTRA AND
ANGULAR DISTRIBUTIONS
Sixpak

=================================
Sixpak

ALL SPECTRA AND
ANGULAR DISTRIBUTIONS ARE CHECKED TO INSURE
Sixpak

THEY ARE
NORMALIZED AND DO NOT INCLUDE ANY NEGATIVE VALUES.
Sixpak

Sixpak

LEGENDRE
COEFFICIENTS
Sixpak

=====================
Sixpak

THE
NORMALIZATION, F0, CANNOT BE NEGATIVE.
Sixpak

Sixpak

LEGENDRE
COEFFICIENTS IN NORMAL FORM ARE CHECKED TO INSURE
Sixpak

THEY ARE IN THE
RANGE -1 TO +1 = THE LEGENDRE EXPANSION OF A
Sixpak

DELTA FUNCTION
AT COS=+1 OR -1 - COEFFICIENTS SHOULD NOT
Sixpak

EXCEED WHAT YOU
GET FROM A DELTA FUNCTION.
Sixpak

Sixpak

ANGULAR
DISTRIBUTIONS ARE CHECKED AT COS = -1, 0 AND +1.
Sixpak

Sixpak

CREATING ENDF/B
OUTPUT
Sixpak

==================================================================
Sixpak

THIS PROGRAM CAN
CREATE EQUIVALENT MF =4, 5, 12, 14, 15 DATA FOR   Sixpak

ALL OF THE DATA
INCLUDED IN ENDF/B-VI AS OF JANUARY 1992, EXCEPT   Sixpak

FOR 1 SECTION OF
LAW=6 DATA (SEE DETAILS BELOW).
Sixpak

Sixpak

THIS PROGRAM HAS
NOT BEEN TESTED ON OTHER DATA LIBRARIES, E.G.,    Sixpak

JEF, JENDL,
ETC.
Sixpak

Sixpak

THE PROGRAM HAS
THE FOLLOWING LIMITATION AS FAR AS CREATING
Sixpak

ENDF/B FORMATTED
OUTPUT.
Sixpak

Sixpak

ISOTROPIC PHOTON
EMISSION
Sixpak

=========================
Sixpak

FOR PHOTON
EMISSION THE DISTRIBUTIONS ARE ASSUMED TO BE ISOTROPIC  Sixpak

AND ONLY THE
MULTIPLICITY IS OUTPUT IN MF=12, ISOTROPIC ANGULAR    Sixpak

DISTRIBUTIONS IN
MF=14 AND THE SPECTRA IN MF=15. ALL ENDF/B-VI     Sixpak

MF=6 DATA AS OF
JANUARY 1992 INCLUDE ONLY ISOTROPIC PHOTON
Sixpak

EMISSION - SO
THAT THIS IS NOT A LIMITATION ON TRANSLATING
Sixpak

ENDF/B-VI
DATA.
Sixpak

Sixpak

EITHER TABULATED
OR LEGENDRE COEFFICIENTS
Sixpak

=========================================
Sixpak

FOR LAW=2 THE
REPRESENTATION, EITHER TABULATED OR LEGENDRE
Sixpak

COEFFICIENTS,
CAN BE SPECIFIED FOR EACH INCIDENT ENERGY.
Sixpak

Sixpak

IN ORDER TO
OBTAIN CORRECT ENDF/B OUTPUT THE REPRESENTATION
Sixpak

MUST BE THE SAME
FOR ALL INCIDENT ENERGIES = MF=4 DATA CAN ONLY    Sixpak

BE TABULATED OR
LEGENDRE OVER THE ENTIRE ENERGY RANGE.
Sixpak

Sixpak

YIELD AND OUTPUT
NORMALIZATION
Sixpak

==============================
Sixpak

THE YIELD
INCLUDED WITH EACH SECTION OF DATA IS NOT USED FOR
Sixpak

OUTPUT FOR NEUTRONS,
BUT IS INCLUDED IN THE OUTPUT FOR PHOTONS.    Sixpak

IN ALL CASES THE
ANGULAR DISTRIBUTIONS AND SPECTRA OUTPUT ARE      Sixpak

NORMALIZED TO
UNITY.
Sixpak

Sixpak

LAW=0
Sixpak

=====
Sixpak

NO OUTPUT - INCIDENT
NEUTRON - EMITTED PHOTON OR NEUTRON
Sixpak

REACTIONS ARE NOT EXPECTED.
Sixpak

Sixpak

LAW=1
Sixpak

=====
Sixpak

FOR EACH
INCIDENT ENERGY DISCRETE AND CONTINUOUS EMISSION SPECTRA  Sixpak

CANNOT BE MIXED
TOGETHER - THEY MUST BE ALL EITHER DISCRETE OR     Sixpak

CONTINUOUS. IF
DISCRETE EMISSION IS GIVEN ONLY 1 SECONDARY
Sixpak

ENERGY (NEP=1)
MAY BE GIVEN = A NORMALIZED DISTRIBUTION FOR A      Sixpak

SINGLE DISCRETE
EMISSION ENERGY. ALL OF THE ENDF/B-VI DATA AS      Sixpak

OF JANUARY 1992
CONFORM TO THESE LIMITATIONS.
Sixpak

Sixpak

SINCE THE FLAG
NA, TO INDICATE ISOTROPIC DISTRIBUTIONS, IS ONLY    Sixpak

GIVEN FOR EACH
SECONDARY ENERGY (EP) THE PROGRAM CANNOT DECIDE     Sixpak

IN ADVANCE
WHETHER OR NOT THE DISTRIBUTION WILL BE ISOTROPIC
Sixpak

AT ALL INCIDENT
ENERGIES. THEREFORE ISOTROPIC DISTRIBUTIONS        Sixpak

WILL BE OUTPUT
EITHER: LANG = 1 - AS 1 LEGENDRE COEFFICIENT = 0.0  Sixpak

OR LANG = NOT 1
- AS A 2 POINT ANGULAR DISTRIBUTION AT COS = -1.0  Sixpak

AND +1.0 WITH
BOTH VALUES EQUAL TO 0.5 (A NORMALIZED ISOTROPIC     Sixpak

DISTRIBUTION).
Sixpak

Sixpak

DISCRETE PHOTONS
ARE OUTPUT IN MF=15 AS 3 POINT DISTRIBUTIONS      Sixpak

WITH SECONDARY
ENERGY POINTS AT EP-DEP, EP, EP+DEP, WHERE
Sixpak

DEP=0.001*EP.
THE VALUES AT EP-DEP AND EP+DEP ARE 0.0, AND
Sixpak

AT EP THE VALUE
IS 1000.0/EP TO NORMALIZE THE DISTRIBUTION.
Sixpak

Sixpak

LAW=2
Sixpak

=====
Sixpak

NO LIMITATION ON
REPRESENTATIONS.
Sixpak

Sixpak

LAW=3
Sixpak

=====
Sixpak

NO LIMITATION ON
REPRESENTATIONS.
Sixpak

Sixpak

LAW=4
Sixpak

=====
Sixpak

NO OUTPUT -
INCIDENT NEUTRON - EMITTED PHOTON OR NEUTRON
Sixpak

REACTIONS ARE NOT EXPECTED.
Sixpak

Sixpak

LAW=5
Sixpak

=====
Sixpak

NO OUTPUT -
INCIDENT NEUTRON - EMITTED PHOTON OR NEUTRON
Sixpak

REACTIONS ARE NOT EXPECTED.
Sixpak

Sixpak

LAW=6
Sixpak

=====
Sixpak

NO OUTPUT -
ENDF/B-VI ONLY INCLUDES 1 SECTION OF THIS TYPE OF DATA Sixpak

FOR
(N,D) 2N,P.
Sixpak

Sixpak

LAW=7
Sixpak

=====                                                              Sixpak

FOR EACH
INCIDENT ENERGY THE REPRESENTATION MUST BE EITHER,
Sixpak

Sixpak

1) SQUARE = FOR
EACH INCIDENT COSINE EXACTLY THE SAME SECONDARY    Sixpak

ENERGIES.
Sixpak

Sixpak

2) LINEAR = FOR
EACH INCIDENT COSINE THE INTERPOLATION LAW
Sixpak

BETWEEN SECONDARY ENERGIES MUST BE LINEAR.
Sixpak

Sixpak

THESE 2
PRESENTATIONS ARE THE ONLY ONES PRESENTED IN ENDF/B-VI     Sixpak

AS OF JANUARY
1992 - SO THIS PROGRAM CAN TRANSLATED ALL LAW=7      Sixpak

DATA FOR
ENDF/B-VI.
Sixpak

Sixpak

LABORATORY VS.
CENTER-OF-MASS SYSTEM
Sixpak

==================================================================
Sixpak

IN MANY CASES
PEOPLE ASSUME THAT FOR HEAVY (HIGH ATOMIC WEIGHT)    Sixpak

MATERIALS THE
CENTER-OF-MASS AND LAB SYSTEMS ARE ALMOST IDENTICAL, Sixpak

SINCE IN THIS
CASE THE CENTER-OF-MASS ENERGY WILL BE MUCH SMALLER  Sixpak

THAN THE
INCIDENT ENERGY. FOR A PROCESS SUCH AS ELASTIC SCATTERING Sixpak

WHERE FOR HEAVY
MATERIALS THE SECONDARY ENERGY, EP, WILL ALWAYS    Sixpak

BE A LARGE
FRACTION OF THE INCIDENT ENERGY, THIS ASSUMPTION IS     Sixpak

VALID. HOWEVER,
FOR THE TYPICAL REACTIONS INCLUDED IN MF=6 THIS    Sixpak

IS NOT ALWAYS
TRUE - IN MANY OF THESE CASES THE SECONDARY ENERGY   Sixpak

CAN EXTEND ALL
THE WAY DOWN TO ZERO, AND IN PARTICULAR IT CAN      Sixpak

BE SMALL
COMPARED TO THE CENTER-OF-MASS ENERGY - WHICH MAKES THE   Sixpak

TRANSFORMATION
FROM CENTER-OF-MASS TO LAB IMPORTANT. THEREFORE     Sixpak

GENERALLY TO
TREAT MF=6 DATA WE MUST CONSIDER THIS TRANSFORMATION. Sixpak

Sixpak

THE FOLLOWING
DISCUSSING ONLY APPLIES TO SPECTRA THAT MAY BE
Sixpak

OUTPUT IN MF=5 =
ONLY DATA FOR NEUTRONS INCIDENT AND EMITTED -     Sixpak

IN PARTICULAR
THE FOLLOWING DEFINITIONS ARE NOT GENERAL - THEY     Sixpak

ARE ONLY VALID
FOR INCIDENT AND EMITTED NEUTRONS.
Sixpak

Sixpak

DOUBLE
DIFFERENTIAL DATA IN MF=6 MAY BE GIVEN IN EITHER THE LAB    Sixpak

OR C.M. SYSTEM.
SIMILARLY ANGULAR DISTRIBUTIONS IN MF=4 MAY BE     Sixpak

GIVEN IN EITHER
THE LAB OR C.M. SYSTEM. IN CONTRAST ENERGY
Sixpak

SPECTRA IN MF=5
CAN ONLY BE GIVEN IN THE LABORATORY SYSTEM.
Sixpak

Sixpak

THE ANGULAR
DISTRIBUTIONS OUTPUT BY THIS CODE IN MF=4 ARE IN THE   Sixpak

SAME SYSTEM IN
WHICH THEY ARE GIVEN IN MF=6 - EITHER LAB OR
Sixpak

CENTER-OF-MASS
SYSTEM.
Sixpak

Sixpak

THE ENERGY
SPECTRA OUTPUT BY THIS CODE IN MF=5 MUST BE IN THE LAB  Sixpak

SYSTEM - THIS IS
THE ONLY ALLOWED FORM FOR MF=5 DATA.
Sixpak

Sixpak

FOR MF=6 SPECTRA
GIVEN IN THE LAB SYSTEM THIS MERELY REQUIRES      Sixpak

COPYING THE
GIVEN SPECTRA TO MF=5 OUTPUT.
Sixpak

Sixpak

FOR MF=6 SPECTRA
GIVEN IN THE CENTER-OF-MASS SYSTEM ONLY FIRST     Sixpak

ORDER
CORRECTIONS IN THE SPECTRA AND USED AND THEY ARE THEN
Sixpak

OUTPUT IN MF=5
AS IN THE LAB SYSTEM - THE FIRST ORDER CORRECTIONS  Sixpak

ARE DESCRIBED
BELOW.
Sixpak

Sixpak

DEFINING,
Sixpak

MM      = CENTER OF MASS
MOTION
Sixpak

CM      = OUTGOING
(EMITTED) PARTICLE IN CENTER OF MASS
Sixpak

LAB     = OUTGOING (EMITTED)
PARTICLE IN LAB
Sixpak

THETA   = CM SCATTERING ANGLE RELATIVE TO
INCIDENT DIRECTION       Sixpak

COS(CM) = COSINE
OF THE CM SCATTERING ANGLE
Sixpak

Sixpak

FOR NEUTRONS
INCIDENT WITH AN ENERGY, E, AND THEREFORE A SPEED,    Sixpak

Sixpak

VN(E) =
2*SQRT(E)/MASS(IN)
Sixpak

Sixpak

THE
CENTER-OF-MASS SPEED IS GIVEN BY,
Sixpak

Sixpak

V(MM) = VN(E)/(1
+ A)
Sixpak

Sixpak

AND THE CENTER
OF MASS ENERGY BY,
Sixpak

Sixpak

E(MM) =
1/2*MASS(IN)*V(MM)**2
Sixpak

= 1/2*MASS(IN)*VN(E)**2/(1 + A)**2
Sixpak

=
E/(1 + A)**2
Sixpak

Sixpak

FOR
DISTRIBUTIONS GIVEN IN MF=6 IN THE CM, THE SPEED, V(CM),
Sixpak

SHOULD BE
VECTORIALLY ADDED TO THAT OF OUTGOING PARTICLES TO
Sixpak

DEFINE THE
OUTGOING PARTICLES LAB VELOCITY, AND IN TURN IT'S
Sixpak

ENERGY,
Sixpak

Sixpak

V(LAB)*COS(LAB)
= V(MM) + V(CM)*COS(CM)
Sixpak

V(LAB)*SIN(LAB)
=
V(CM)*SIN(CM)
Sixpak

Sixpak

V(LAB)**2 =
V(MM)**2 + V(CM)**2 + 2*COS(CM)*V(MM)*V(CM)
Sixpak

Sixpak

EP(LAB)   = 0.5*MASS(OUT)*V(LAB)**2                                Sixpak

Sixpak

= E(MM) + EP(CM) + 2*COS(CM)*SQRT(E(MM)*EP(CM))
Sixpak

Sixpak

WE CAN ALSO
DEFINE THE REVERSE TRANSFORMATION USING,
Sixpak

Sixpak

V(CM)*COS(CM) =
V(LAB)*COS(LAB) - V(MM)
Sixpak

V(CM)*SIN(CM) =
V(LAB)*SIN(LAB)
Sixpak

Sixpak

V(CM)**2 =
V(MM)**2 + V(LAB)**2 - 2*COS(LAB)*V(MM)*V(LAB)          Sixpak

Sixpak

EP(CM)   = 0.5*MASS(OUT)*V(CM)**2
Sixpak

Sixpak

= E(MM) + EP(LAB) - 2*COS(LAB)*SQRT(E(MM)*EP(LAB))       Sixpak

Sixpak

WE CAN DEFINE
COS(LAB) FROM THE RELATIONSHIP,
Sixpak

Sixpak

V(LAB)*COS(LAB)
= V(MM) + V(CM)*COS(CM)
Sixpak

Sixpak

COS(LAB)        =[V(MM) +
V(CM)*COS(CM)]/V(LAB)
Sixpak

Sixpak

[V(MM) + V(CM)*COS(CM)]
Sixpak

COS(LAB)
=---------------------------------------------     Sixpak

SQRT[V(MM)**2+V(CM)**2+2*COS(CM)*V(MM)*V(CM)]     Sixpak

Sixpak

OR COS(CM) FROM
THE RELATIONSHIP,
Sixpak

Sixpak

V(CM)*COS(CM)  =
V(LAB)*COS(LAB) - V(MM)
Sixpak

Sixpak

COS(CM)
=[V(LAB)*COS(LAB) - V(MM)]/V(CM)
Sixpak

Sixpak

[V(LAB)*COS(LAB) - V(MM)]
Sixpak

COS(CM)
=------------------------------------------------  Sixpak

SQRT[V(LAB)**2+V(CM)**2-2*COS(LAB)*V(LAB)*V(MM)]  Sixpak

Sixpak

THE JACOBIAN CAN
BE DEFINED FROM,
Sixpak

Sixpak

V(LAB)*COS(LAB)
= V(MM) + V(CM)*COS(CM)
Sixpak

Sixpak

J =
D[COS(CM)]/D[COS(LAB)] = V(LAB)/V(CM)
Sixpak

= SQRT[EP(LAB)/EP(CM)]
Sixpak

Sixpak

WITH THESE
DEFINITIONS OF EP(LAB) AND COS(LAB) IN TERMS OF E(MM),  Sixpak

EP(CM) AND
COS(CM) IT IS POSSIBLE TO PERFORM A POINT-BY-POINT      Sixpak

TRANSFORMATION
OF DISTRIBUTIONS FROM THE CM TO LAB SYSTEM USING    Sixpak

THESE
DEFINITIONS - OR IF WE WISHED WE COULD PERFORM THE REVERSE   Sixpak

TRANSFORMATION
USING THE ABOVE RELATIONSHIPS AND THE IDENTITY,     Sixpak

Sixpak

F(E,EP(LAB),COS(LAB))*D(COS(LAB))=F(E,EP(CM),COS(CM))*D(COS(CM))   Sixpak

Sixpak

THIS IS NOT WHAT
WILL BE DONE HERE, SINCE WE WILL ONLY BE
Sixpak

INTERESTED IN
THE ZEROTH ORDER MOMENTS OF THESE DISTRIBUTIONS,     Sixpak

BUT WE WILL BE
INTERESTED IN DEFINING THOSE MOMENTS IN THE
Sixpak

LAB SYSTEM IN
TERMS OF MF=6 SPECTRA GIVEN IN THE CM SYSTEM USING,  Sixpak

Sixpak

F(E,EP(LAB),COS(LAB)) = F(E,EP(CM),COS(CM))*J
Sixpak

Sixpak

THE LIMITS OF
EP(LAB) ARE DEFINED BY SETTING COS(CM) = +1 OR -1,   Sixpak

Sixpak

EP(LAB)   = (SQRT(EP(CM)) +
SQRT(E(MM)))**2  FOR COS(CM) = +1      Sixpak

= (SQRT(EP(CM)) - SQRT(E(MM)))**2
FOR COS(CM) = -1      Sixpak

Sixpak

IN THIS FORM WE
CAN SEE THAT AS LONG AS THE SECONDARY ENERGY IN    Sixpak

THE
CENTER-OF-MASS SYSTEM, EP(CM), IS MUCH LARGER THAN THE
Sixpak

ENERGY OF THE
CENTER-OF-MASS, E(MM), THE CENTER-OF-MASS AND LAB    Sixpak

ENERGIES WILL BE
ALMOST EQUAL - SIMILARLY FOR THE COSINE, IN
Sixpak

THIS CASE COS(LAB) AND COS(CM) WILL BE
ALMOST EQUAL - HOWEVER,
Sixpak

FOR THE MF=6
DATA WE CANNOT ASSUME THAT THIS IS TRUE.
Sixpak

Sixpak

TO FIRST ORDER
THE ANGULAR DEPENDENCE CAN BE IGNORED,
Sixpak

Sixpak

EP(LAB)   = E(MM) + EP(CM)
Sixpak

Sixpak

ALL THIS SAYS IS
THAT TO FIRST ORDER THE EFFECT OF TRANSFORMING    Sixpak

FROM THE CM TO
LAB SYSTEM IS TO INCREASE THE ENERGY OF THE
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EMITTED PARTICLE
IN THE CENTER-OF-MASS SYSTEM BY THE ENERGY OF     Sixpak

THE
CENTER-OF-MASS TO DEFINE THE LAB ENERGY.
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NOT ONLY THE
ENERGY, BUT ALSO THE SPECTRA MUST BE TRANSFORMED.     Sixpak

STARTING FROM
THE DOUBLE DIFFERENTIAL DATA IN THE LAB SYSTEM,      Sixpak

F(E,EP,COS(LAB)), WE CAN DEFINE THE LAB SCALAR SPECTRUM AS,
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G0(E,EP) =
INTEGRAL F(E,EP,COS(LAB))*D(COS(LAB))
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THIS IS THE
NORMAL CALCULATION DEFINED ABOVE AND USED FOR DATA     Sixpak

GIVEN IN THE LAB
SYSTEM.
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STARTING FROM
DATA IN THE CENTER OF MASS SYSTEM F(E,EP,COS(CM)),   Sixpak

WE CAN USE THE
RELATIONSHIP,
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F(E,EP,COS(LAB))*D(COS(LAB)) = F(E,EP,COS(CM))*J*D(COS(LAB))
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J
= SQRT(EP(LAB)/EP(CM)) - THE JACOBIAN
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= E(MM)/EP(CM) +
1 + 2*COS(CM)*SQRT(E(MM)/EP(CM))
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AS IN THE CASE
OF THE ENERGY, IN THIS FORM WE CAN SEE THAT AS      Sixpak

LONG AS THE
SECONDARY ENERGY IN THE CENTER-OF-MASS SYSTEM,
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EP(CM), IS LARGE
COMPARED TO THE CENTER-OF-MASS ENERGY, E(MM),     Sixpak

THE JACOBIAN IS
ESSENTIALLY UNITY AND THE CENTER-OF-MASS AND LAB   Sixpak

SPECTRA WILL BE
VERY SIMILAR - AGAIN, GENERALLY WE CANNOT
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ASSUME THAT THIS
IS TRUE FOR THE MF=6 SPECTRA.
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THEREFORE WE CAN
ALSO DEFINE THE LAB SCALAR SPECTRUM IN TERMS OF   Sixpak

THE CM SPECTRUM
IN THE FORM,
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G0(E,EP) =
INTEGRAL F(E,EP,COS(CM))*J*D(COS(LAB))
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CONSISTENT WITH
THE ABOVE ASSUMPTION THAT THE ANGULAR DEPENDENCE   Sixpak

OF EP(LAB) CAN
BE IGNORED THE JACOBIAN WILL NOT BE USED IN
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PERFORMING THESE
INTEGRALS - IN WHICH CASE THE INTEGRAL REDUCES    Sixpak

TO EXACTLY THE
SAME FORM AS IF THE DATA WERE IN THE LAB SYSTEM.    Sixpak

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IT SHOULD BE
NOTED THAT SINCE IN THIS CASE THE MF=4 ANGULAR
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DISTRIBUTIONS
ARE GIVEN IN THE CM SYSTEM AND WHEN USED IN ANY      Sixpak

APPLICATION THEY
WILL BE TRANSFORMED TO THE LAB SYSTEM - WHEN      Sixpak

THIS IS DONE THE
JACOBIAN WILL BE APPLIED.
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IN THIS CODE
WHERE WE ARE MOSTLY CONCERNED WITH CONSERVING THE     Sixpak

NUMBER OF
EMITTED PARTICLES AND AVERAGE ENERGIES THE NEUTRON
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SPECTRA OUTPUT
IN MF=5 WILL NOT BE COMPLETELY CONVERTED TO THE     Sixpak

LAB SYSTEM -
ONLY FIRST ORDER CORRECTIONS WILL BE INCLUDED BY      Sixpak

INCREASING THE EMITTED
PARTICLE ENERGY BY THE CENTER OF MASS
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ENERGY, I.E.,
FOR A CENTER OF MASS SPECTRUM TABULATED AT CENTER    Sixpak

OF MASS ENERGIES
EP(CM) THESE WILL ALL BE UNIFORMLY INCREASED      Sixpak

BY E(MM) TO
ACCOUNT FOR THE CENTER OF MASS MOTION - THE SPECTRA    Sixpak

WILL NOT BE
MODIFIED BY THE JACOBIAN FACTOR SQRT(EP(LAB)/EP(CM))   Sixpak

SINCE THIS WOULD
REQUIRE A DETAILED TRANSFORMATION IN ENERGY AND   Sixpak

COS(THETA) SPACE
- WHICH IS JUDGED NOT TO BE WORTH PERFORMING      Sixpak

WITHIN THE
LIMITS OF WHERE THE OUTPUT FROM THIS CODE IS INTENDED   Sixpak

TO BE USED.
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SINCE THE
ANGULAR DISTRIBUTION IS ALWAYS OUTPUT IN THE SAME
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SYSTEM AS WHICH
IT IS GIVEN IN MF=6, NO TRANSFORMATION IS
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REQUIRED FOR THE
MF=4 OUTPUT.
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WHEN USED IN LOW
ENERGY APPLICATIONS (E.G., FISSION REACTORS) THE  Sixpak

HIGH ENERGY
SPECTRA PRESENTED IN MF=6 WILL BE MOSTLY IMPORTANT     Sixpak

SIMPLY IN
CONSERVING PARTICLES, (E.G., AS IN (N,2N)) AND ENERGY    Sixpak

AND THE DETAILS
OF THE CORRELATION AND GROSS ENERGY SPECTRA WILL   Sixpak

NOTE PLAY THAT
IMPORTANT A ROLE. IN THIS CASE THE SPECTRA OUTPUT   Sixpak

BY THIS PROGRAM
IN MF=5 SHOULD BE ADEQUATE.
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PLOTTAB
FORMATTED OUTPUT
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==================================================================
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THIS PROGRAM
CONTAINS ROUTINES TO PRODUCE OUTPUT THAT CAN BE USED  Sixpak

AS INPUT TO THE
PLOTTAB CODE TO OBTAIN GRAPHIC RESULTS.
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THESE ROUTINES
ARE DESIGNED ONLY FOR USE BY THE AUTHOR TO CHECK    Sixpak

THIS CODE. USERS
ARE ASKED NOT TO ACTIVATE OR TRY TO USE THESE     Sixpak

ROUTINES. UNLESS
YOU COMPLETELY UNDERSTAND THIS CODE THE RESULTS   Sixpak

CAN BE
UNRELIABLE IF YOU ACTIVATE THESE ROUTINES.
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INPUT FILES
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==================================================================
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UNIT  DESCRIPTION
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----  -----------
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2  INPUT LINES (BCD - 80
CHARACTERS/RECORD)
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10  ORIGINAL ENDF/B DATA (BCD
- 80 CHARACTERS/RECORD)
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OUTPUT
FILES
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==================================================================
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UNIT  DESCRIPTION
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----  -----------
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3  OUTPUT REPORT (BCD - 120
CHARACTERS/RECORD)
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11  ENDF/B DATA MF=4 (BCD -
80 CHARACTERS/RECORD)
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12  ENDF/B DATA MF=5 (BCD -
80 CHARACTERS/RECORD)
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14  ENDF/B DATA MF=15 (BCD -
80 CHARACTERS/RECORD)
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17  ENDF/B DATA MF=12 (BCD -
80 CHARACTERS/RECORD)
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18
ENDF/B DATA MF=14 (BCD - 80 CHARACTERS/RECORD)
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15  PLOTTAB INPUT PARAMETERS
(BCD - 80 CHARACTERS/RECORD)
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16  PLOTTAB FORMATTED OUTPUT
(BCD - 80 CHARACTERS/RECORD)
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SCRATCH
FILES
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==================================================================
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NONE
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OPTIONAL
STANDARD FILE NAMES (SEE SUBROUTINE FILIO1 AND FILIO2)    Sixpak

==================================================================
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UNIT  FILE NAME
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----  ----------
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2   SIXPAK.INP
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3   SIXPAK.LST
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10   ENDFB.IN
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11   ENDFB.MF4
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12   ENDFB.MF5
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14   ENDFB.M15
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17   ENDFB.M12
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18   ENDFB.M14
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15   PLOTTAB.INP
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16   PLOTTAB.CUR
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INPUT
PARAMETERS
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==================================================================
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LINE  COLS.  DESCRIPTION
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----  -----  -----------
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1   1-60  ENDF/B INPUT DATA FILENAME
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(STANDARD OPTION = ENDFB.IN)
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2-N   1-6   MINIMUM MAT FOR REQUESTED
RANGE
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9-11  MINIMUM MT FOR
REQUESTED RANGE
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12-17  MAXIMUM MAT FOR
REQUESTED RANGE
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20-22  MAXIMUM MT FOR
REQUESTED RANGE
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LEAVE THE
DEFINITION OF THE FILENAME BLANK - THE PROGRAM WILL      Sixpak

THEN USE THE
STANDARD FILENAME (ENDFB.IN).
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UP TO 100 MAT/MT
RANGES MAY BE SPECIFIED. THE LIST OF RANGES IS    Sixpak

TERMINATED BY A
BLANK LINE. IF THE FIRST INPUT LINE IS COMPLETELY  Sixpak

BLANK ALL DATA
WILL BE PROCESSED.
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EXAMPLE INPUT
NO. 1
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-------------------
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PROCESS ALL MF=6
DATA ON AN ENDF/B TAPE. USE THE STANDARD INPUT    Sixpak

DATA FILENAME
ENDFB.IN IN THIS CASE THE USER CAN EITHER EXPLICITLY Sixpak

SPECIFY THE
FILENAME AND MAT/MT RANGE BY THE FOLLOWING
2 INPUT    Sixpak

LINES,
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ENDFB.IN
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1    1  9999  999
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(BLANK LINE, TERMINATES REQUEST LIST)
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OR BY INPUTTING
2 BLANK LINE = PROCESS EVERYTHING.
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EXAMPLE INPUT
NO. 2
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-------------------
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PROCESS BE-9,
MAT=425, MT=16. READ THE DATA FROM ENDFB6\BE9.
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IN THIS CASE THE
FOLLOWING 3 INPUT LINES ARE REQUIRED,
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ENDFBB6\BE9
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425   16   425   16
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(BLANK LINE, TERMINATES REQUEST LIST)
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EXAMPLE INPUT
NO. 3
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-------------------
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PROCESS ALL
MT=16 (N,2N) DATA. THIS CAN BE DONE BY SPECIFYING THE  Sixpak

MAXIMUM MAT
RANGE = 1 TO 9999, AND MT=16 FOR THE MINIMUM AND
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MAXIMUM MT
RANGE. READ THE DATA FROM ENDFB6\K300. IN THIS CASE     Sixpak

CASE THE
FOLLOWING 3 INPUT LINES ARE REQUIRED,
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ENDFB6\K300
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1   16  9999   16
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(BLANK LINE, TERMINATES REQUEST LIST)
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=======================================================================
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