=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PROGRAM SIXPAK = &nb= sp; = &nb= sp; Sixpak

=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Sixpak

VERSION 92= -1 (JANUARY 1992) = &nb= sp; = Sixpak

VERSION 92= -2 (FEBRUARY 1992)*INCREASED CORE ALLOCATION TO = Sixpak

= = ACCOMMODATE JEF AND EFF EVALUATIONS. Sixpak

VERSION 92= -3 (APRIL 1992) *ADDED ADDITIONAL DATA TESTS. = Sixpak

VERSION 92= -4 (SEPT. 1992) *CORRECTED KALBACH-MANN CALCULATIONS. Si= xpak

= &nb= sp; *FOR PHOTON PRODUCTION OUTPUT MF=3D12 &nbs= p; Sixpak

= &nb= sp; = (MULTIPLICITY), MF=3D14 (ISOTROPIC Sixpak

= &nb= sp; = ANGULAR DISTRIBUTIONS) AND MF=3D15 Sixpak

= &nb= sp; = (SPECTRA) - PREVIOUSLY ONLY MF=3D15. Sixpak

= &nb= sp; *FIRST ORDER CORRECTIONS TRANSFORMING Sixpak

= &nb= sp; = CENTER-OF-MASS SPECTRA TO LAB SYSTEM Sixpak

= &nb= sp; = FOR OUTPUT IN MF=3D5 = Sixpak

= &nb= sp; *CORRECTED ISOTROPIC ANGULAR = Sixpak

= &nb= sp; = DISTRIBUTION FLAG (LI) = Sixpak

VERSION 94= -1 (JANUARY 1994) *VARIABLE ENDF/B INPUT DATA FILENAME Sixpak

= &nb= sp; = TO ALLOW ACCESS TO FILE STRUCTURES Sixpak

= &nb= sp; = (WARNING - INPUT PARAMETER FORMAT Sixpak

= &nb= sp; = HAS BEEN CHANGED) = Sixpak

= &nb= sp; *CLOSE ALL FILES BEFORE TERMINATING Sixpak

= &nb= sp; = (SEE, SUBROUTINE ENDIT) = Sixpak

= &nb= sp; *INCREASED MAXIMUM TABLE SIZE FROM Sixpak

= &nb= sp; = 2000 TO 6000. = &nb= sp; Sixpak

VERSION 96= -1 (JANUARY 1996) *COMPLETE RE-WRITE = Sixpak

= &nb= sp; *IMPROVED COMPUTER INDE= PENDENCE Sixpak

= &nb= sp; *ALL DOUBLE PRECISION &n= bsp; Sixpak

= &nb= sp; *ON SCREEN OUTPUT = &nb= sp; Sixpak

= &nb= sp; *UNIFORM TREATMENT OF ENDF/B I/O Sixpak

= = *IMPROVED OUTPUT PRECISION = Sixpak

VERSION 99= -1 (MARCH 1999) *CORRECTED CHARACTER TO FLOATING Sixp= ak

= &nb= sp; = POINT READ FOR MORE DIGITS = Sixpak

= &nb= sp; *UPDA= TED TEST FOR ENDF/B FORMAT Sixpak

= &nb= sp; = VERSION BASED ON RECENT FORMAT CHANGE Sixpak

= &nb= sp; *GENERAL IMPROVEMENTS BASED ON Sixpak

= &nb= sp; = USER FEEDBACK = &nb= sp; Sixpak

VERSION 99= -2 (JUNE 1999) *ASSU= ME ENDF/B-VI, NOT V, IF MISSING Sixpak

= &nb= sp; = MF=3D1, MT-451. = &nb= sp; Sixpak

VERS. 2000= -1 (FEBRUARY 2000)*GENERAL IMPROVEMENTS BASED ON Sixpak

= &nb= sp; = USER FEEDBACK = &nb= sp; Sixpak

VERS. 2002= -1 (JANUARY 2002) *CORRECTED ANGULAR DISTRIBUTION (MF=3D4) Sixpak

= &nb= sp; = OUTPUT TO INSURE USED FIELDS ARE 0 Sixpak

= (MAY 2002) *OPTIONAL INPUT PARAMETERS = Sixpak

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

= &nb= sp; = ANGULAR DISTRIBUTION IN MF=3D4 - Sixpak

= &nb= sp; = WARNING - STRICTLY SPEAKING THIS IS Sixpak

= &nb= sp; = NOT LEGAL, SINCE MF=3D4 IS SUPPOSED TO Sixpak

= &nb= sp; = BE USED ONLY FOR NEUTRON ANGULAR Sixpak

= &nb= sp; = DISTRIBUTIONS - BUT WHERE MT MAKES Sixpak

= &nb= sp; = IT OBVIOUS THAT THE OUTGOING PARTICLE Sixpak

= &nb= sp; = IS NOT A NEUTRON HOPEFULLY IT WILL Sixpak

= &nb= sp; NOT CAUSE A PROBLEM IF MF=3D4 IS USED &nb= sp; Sixpak

= &nb= sp; = FOR CHARGED PARTICLES. = Sixpak

VERS. 2004= -1 (MARCH 2004) *ADDED INC= LUDE FOR COMMON = Sixpak

= = *INCREAS= ED MAXIMUM TABLE SIZE FROM &= nbsp; Sixpak

= &nb= sp; = 6,000 TO 12,000. = &nb= sp; Sixpak

= &nb= sp; *ADDED DUMMY A FOR ELEMENTS = Sixpak

= &nb= sp; = *CORRECTED OUTPUT INTERPOLATON LAWS Sixpak

VERS. 2007= -1 (JAN. 2007) *CHECKED AGAINST ALL ENDF/B-= VII. Sixpak

= &nb= sp; *INCREASED MAXIMUM TABLE SIZE FROM Sixpak

= &nb= sp; = 12,000 TO 120,000. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

OWNED, MAINTAINED AND DISTRIBUTED BY = &nb= sp; Sixpak

------------------------------------ = &nb= sp; Sixpak

THE NUCLEA= R DATA SECTION = &nb= sp; = Sixpak

INTERNATIO= NAL ATOMIC ENERGY AGENCY = &nb= sp; Sixpak

P.O. BOX 100 = &nb= sp; = = Sixpak

A-1400, VI= ENNA, AUSTRIA = &nb= sp; = Sixpak

EUROPE = &nb= sp; = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = Sixpak

ORIGINALLY WRITTEN BY = &nb= sp; = Sixpak

------------------------------------ = &nb= sp; Sixpak

DERMOTT E. CULLEN = &nb= sp; = &nb= sp; Sixpak

UNIVERSITY= OF CALIFORNIA = &nb= sp; = Sixpak

LAWRENCE LIVERMORE NATIONAL LABORATORY = &nb= sp; Sixpak

L-159 = &nb= sp; = &nb= sp; = Sixpak

P.O. BOX 808 = &nb= sp; = &nb= sp; Sixpak

LIVERMORE,= CA 94550 = &nb= sp; = &nb= sp; Sixpak

U.S.A. = &nb= sp; = &nb= sp; = Sixpak

TELEPHONE<= span style=3D'mso-spacerun:yes'> 925-423-7359 = &nb= sp; = Sixpak

E. MAIL CULLEN1@LLNL.GOV = &nb= sp; = Sixpak

WEBSITE HTTP://WWW.LLNL.GOV/CULLEN1 = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

COLLABORATION = &nb= sp; = &nb= sp; Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D Sixpak

DEVELOPED = IN COLLABORATION WITH, = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

*THE NATIO= NAL NUCLEAR DATA CENTER, BROOKHAVEN NATIONAL LAB Sixpak

= &nb= sp; = = &nb= sp; Sixpak

*THE NUCLE= AR DATA SECTION, IAEA, VIENNA, AUSTRIA = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

*CENTRO TE= CNICO AEROSPACIAL, SAO JOSE DOS CAMPOS, BRAZIL = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

AS A PART = OF AN INTERNATIONAL PROJECT ON THE EXCHANGE OF = Sixpak

NUCLEAR DATA = &nb= sp; = = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

ACKNOWLEDG= EMENT (VERSION 92-1) = &nb= sp; = Sixpak

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

SIGNIFICAN= TLY CONTRIBUTING TOWARD IMPROVING THE ACCURACY AND Sixpak

COMPUTER INDEPENDENCE OF THIS CODE - THANKS, SOL = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp;Sixpak

ACKNOWLEDG= EMENT (VERSION 92-4) = &nb= sp; = Sixpak

THE AUTHOR THANKS BOB MACFARLANE (LOS ALAMOS) FOR SUGGESTING HOW Sixpak

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

EXACTLY TH= E FORM NEEDED FOR USE IN PROCESSING CODES. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

IN THE EAR= LIER TREATMENT OF THE KALBACH-MANN FORMALISM AND IN Sixpak

THE DEFINI= TION OF THE ISOTROPIC ANGULAR DISTRIBUTION FLAG (LI). Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

AUTHORS MESSAGE = &nb= sp; = &nb= sp; Sixpak

THE COMMEN= TS BELOW SHOULD BE CONSIDERED THE LATEST DOCUMENTATION Sixpak

INCLUDING = ALL RECENT IMPROVEMENTS. PLEASE READ ALL OF THESE Sixpak

COMMENTS B= EFORE IMPLEMENTING AND USING THESE CODES. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

AT THE PRE= SENT 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 TH= IS PROGRAM. HOPEFULLY, IN THIS WAY FUTURE VERSIONS OF Sixpak

THIS PROGR= AM WILL BE COMPLETELY COMPATIBLE FOR USE ON YOUR Sixpak

COMPUTER.<= span style=3D'mso-spacerun:yes'> = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PURPOSE = &nb= sp; = &nb= sp; = Sixpak

1) CHECK A= LL DOUBLE-DIFFERENTIAL DATA (MF=3D6) = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

2) OUTPUT EQUIVALENT MF =3D 4, 5, 12, 14 AND 15 DATA. = Sixpak

= = &nb= sp; = &nb= sp; Sixpak

DATA CHECKING = &nb= sp; = &nb= sp; Sixpak

ALL OF THE ENDF/B-VI MF=3D6 DATA IS CHECKED - FOR DETAILS SEE BELOW. Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THE MF=3D6= DATA IS NOT CORRECTED AND OUTPUT IN THE ENDF/B FORMAT. Sixpak

IT IS MERE= LY CHECKED. IF ERRORS ARE FOUND IT IS UP TO THE USER Sixpak

TO TAKE CORRECTIVE ACTION ON THE MF=3D6 DATA. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

IN CONTRAS= T WHEN PROBLEMS ARE FOUND IN DATA WHICH WILL BE OUTPUT Sixpak

IN THE END= F/B FORMAT (MF=3D4, 5, 12, 14 AND 15), WHENEVER POSSIBLE Sixpak

CORRECTIVE ACTION WILL BE TAKEN. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = = Sixpak

FURTHER CH= ECKS AND CORRECTIONS = &nb= sp; = Sixpak

ONCE THE D= ATA HAS BEEN OUTPUT IN MF =3D 4, 5, 12, 14 AND 15 FORMATS Sixpak

FURTHER CORRECTIVE ACTION CAN BE TAKEN AS FOLLOWS, = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PROGRAM LEGEND = &nb= sp; = &nb= sp; Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D = &nb= sp; = &nb= sp; Sixpak

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

TO CONVERT= FROM LEGENDRE COEFFICIENTS TO TABULATED ANGULAR Sixpak

DISTRIBUTI= ONS AND GENERALLY PERFORM MORE EXTENSIVE TESTS OF Sixpak

ALL MF=3D4 DATA. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PROGRAM EV= ALPLOT = &nb= sp; = &nb= sp; Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D = &nb= sp; = &nb= sp; Sixpak

VERSION 92= -1 AND LATER VERSIONS CAN PLOT ALL OF THE MF=3D4, 5 AND 15 Sixpak

DATA OUTPU= T BY THIS CODE. EARLIER VERSIONS CAN PLOT MF=3D4 AND 5. Sixpak

GRAPHICS I= S AN EXCELLENT WAY TO CHECK THIS DATA. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PROGRAM PLOTTAB = = &nb= sp; = Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D = &nb= sp; = &nb= sp; Sixpak

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

THIS CODE = TO PRODUCE OUTPUT FOR ANY MF=3D6 DATA IN THE PLOTTAB Sixpak

INPUT FORM= AT. THIS PROGRAM CAN BE USED TO CHECK ALL OF THE MF=3D6 Sixpak

DATA AS WE= LL AS THE EQUIVALENT MF=3D4, 5, 12, 14 AND 15 DATA - AS Sixpak

WELL AS COMPARING THE ORIGINAL MF=3D6 AND EQUIVALENT DATA. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

DATA OUTPU= T = &nb= sp; = &nb= sp; Sixpak

THE ENDF/B= MF=3D4, 5, 12, 14 AND 15 FORMATS ONLY ALLOW FOR NEUTRONS Sixpak

INCIDENTS<= span style=3D'mso-spacerun:yes'> = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THE ENDF/B= MF=3D4 AND 5 FORMATS ONLY ALLOW FOR NEUTRONS OUTGOING. Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THE ENDF/B MF=3D12, 14 AND 15 ONLY ALLOWS FOR PHOTONS OUTGOING. Sixpak

= &nb= sp; = &nb= sp; = Sixpak

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

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

ALL OTHER = COMBINATIONS OF INCIDENT AND OUTGOING PARTICLES ARE Sixpak

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

HOWEVER, U= SING THE PLOTTAB INTERFACE BUILT INTO THIS CODE THIS Sixpak

DATA CAN, = AND HAS BEEN, OUTPUT AND CHECKED. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THE NEUTRO= N DATA IN MF=3D4 CAN BE IN THE FORM OF EITHER TABULATED Sixpak

ANGULAR DISTRIBUTIONS OR LEGENDRE COEFFICIENTS. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THE NEUTRON (MF=3D5) OR PHOTON (MF=3D15) SPECTRA ARE BOTH IN EXACTLY Sixpak

THE SAME F= ORMAT =3D ARBITRARY TABULATED FUNCTIONS - ENDF/B OPTION Sixpak

LF=3D1. = &nb= sp; = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

ENDF/B DATA OUTPUT ORDER = &nb= sp; = Sixpak

ENDF/B DAT= A 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=3D6= DATA, OUTPUT FOR EACH (MAT, MT) IS OUTPUT TO SEPERATE Sixpak

FILES FOR = MF=3D4, 5, 12, 14 AND 15. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

FOR SUBSEQ= UENT USE THE ENDF/B FORMATTED DATA OUTPUT BY THIS CODE Sixpak

CAN BE MER= GED TOGETHER USING PROGRAM MERGER (CONTAIN THE AUTHOR Sixpak

OF THIS CO= DE FOR A COPY OF MERGER), E.G., MERGE MF=3D12, 14 AND 15 Sixpak

DATA IN ORDER TO THEN CALCULA= TE PHOTON PRODUCTION DATA OR MF=3D4 Sixpak

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

ALL OF THE= M CAN BE MERGED TOGETHER TO PERFORM NEUTRON AND PHOTON Sixpak

CALCULATIO= NS. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

CORRELATED (MF=3D6) VS. UNCORRELATED (MF=3D4 AND 5) DATA = Sixpak

THE ENDF/B DOUBLE DIFFERENTAL =3D CORRELATED - DATA IN MF=3D6 = Sixpak

REPRESENTS= DATA IN THE FORM, = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = Sixpak

F(E,EP,COS= ) =3D SIG(E)*Y(E)*G0(E,EP)*F(E,EP,COS) = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

SIG(E) =3D MF=3D3= CROSS SECTIONS = &nb= sp; Sixpak

<= /p>

Y(E) =3D YIELD (MULTIPLICITY) = &nb= sp; Sixpak

G0(E,EP) =3D ENERGY SPECTRUM = &nb= sp; = Sixpak

F(E,EP,COS= ) =3D ANGULAR DISTRIBUTION = = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

IN A SITUA= TION WHERE YOU HAVE MONOENERGETIC AND MONODIRECTIONAL Sixpak

NEUTRONS INCIDENT YOU WILL BE ABLE TO OBSERVE CORRELATION EFFECTS Sixpak

IN THE NEU= TRON SPECTRUM AND ANGULAR DISTRIBUTION. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

THAT ARE H= IGHLY DIRECTIONALLY ORIENTED YOU MAY BE ABLE TO OBSERVE Sixpak

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

INCIDENT O= N THE FIRST WALL OF A CTR DEVICE. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

FOR SUCH SITUATIONS USE OF THE CORRELATED (MF=3D6) DATA IS REQUIRED Sixpak

IN CALCULATIONS. = &nb= sp; = &nb= sp; Sixpak

= = &nb= sp; = &nb= sp; = Sixpak

HOWEVER, I= N MANY APPLICATIONS WHERE THERE IS A BROAD SPECTRUM OF Sixpak

NEUTRONS A= ND THE NEUTRON FLUX IS NOT HIGHLY DIRECTIONALLY = Sixpak

ORIENTED, = THE NEUTRON MULTIPLICATION, SPECTRUM AND ORIENTATION Sixpak

CAN BE FAI= RLY ACCURATELY CALCULATED WITHOUT CONSIDERING = Sixpak

CORRELATION EFFECTS. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = Sixpak

THE UNCORR= ELATED DATA PRODUCED BY THIS CODE REPLACES THE = Sixpak

CORRELATED DATA, = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = = &nb= sp; Sixpak

F(E,EP,COS= ) =3D SIG(E)*Y(E)*G0(E,EP)*F(E,EP,COS) = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

BY THE UNCORRELATED DATA, = = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

F(E,EP,COS= ) =3D SIG(E)*Y(E)*G0(E,EP)*F0(E,COS) = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = = Sixpak

BY INTEGRA= TING G0(E,EP)*F(E,EP,COS) OVER SECONDARY ENERGY (EP) Sixpak

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

= &nb= sp; = &nb= sp; = Sixpak

WHAT IS LO= ST 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 S= AME SPECTRUM, G0(E,EP) AND EACH WILL BE EFFECTED BY THE Sixpak

AVERAGE AN= GULAR DISTRIBUTION. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

FOR APPLIC= ATIONS TO HIGH ENERGY FUSION APPLICATIONS CORRELATED Sixpak

DATA SHOUL= D BE USED. HOWEVER, FOR LOWER ENERGY APPLICATIONS, Sixpak

SUCH AS FI= SSION REACTORS, IT SHOULD BE ADEQUATE TO USE THE Sixpak

UNCORRELAT= ED DATA - IN THIS CASE THE MOST IMPORTANT EFFECT Sixpak

WILL BE TH= E OVERALL NEUTRON MULTIPLICATION AND SPECTRUM. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

AN IMPORTA= NT CONSIDERATION IN DESIGNING THIS PROGRAM IS THAT Sixpak

MANY COMPU= TER CODES - DATA PROCESSING AND TRANSPORT CODES - Sixpak

CANNOT USE= THE CORRELATED (MF=3D6) DATA - NOR ARE THEY INTENDED Sixpak

FOR HIGH E= NERGY USE. FOR THESE CODES THE UNCORRELATED DATA Sixpak

PRODUCED B= Y THIS CODE SHOULD BE ADEQUATE TO MEET THEIR NEEDS. Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

CODE SHOUL= D ONLY BE USED FOR LOW ENERGY APPLICATIONS - FAILURE Sixpak

TO HEED TH= IS WARNING CAN LEAD TO COMPLETELY UNRELIABLE RESULTS. Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

ENDF/B FORMAT = &nb= sp; = = Sixpak

THIS PROGR= AM 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 END= F/B FORMAT (I.E., ENDF/B-I, II,III, IV, V OR VI FORMAT). Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

IT IS ASSU= MED THAT THE DATA IS CORRECTLY CODED IN THE ENDF/B Sixp= ak

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

ASSUMED TH= AT THE MAT, MF AND MT ON EACH LINE IS CORRECT. SEQUENCE Sixpak

NUMBERS (C= OLUMNS 76-80) ARE IGNORED ON INPUT, BUT WILL BE = Sixpak

CORRECTLY = OUTPUT ON ALL LINES. THE FORMAT OF SECTION MF=3D1, MT=3D451 Sixpak

AND ALL SE= CTIONS OF MF=3D6 MUST BE CORRECT. THE PROGRAM SKIPS ALL Sixpak

OTHER SECT= IONS OF DATA AND AS SUCH IS INSENSITIVE TO THE FORMAT Sixpak

OF ALL OTH= ER SECTIONS. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

CONTENTS OF OUTPUT = &nb= sp; = &nb= sp; Sixpak

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

DATA, = &nb= sp; = &nb= sp; = Sixpak

= &nb= sp; = = &nb= sp; = Sixpak

1) ENDFB.M= F4 - ANGULAR DISTRIBUTIONS AND LEGENDRE COEFFICIENTS Sixpak

= FOR NEUTRONS = &nb= sp; = Sixpak

2) ENDFB.M= F5 - TABULATED NEUTRON ENERGY SPECTRA = Sixpak

3) ENDFB.M= 12 - PHOTON EMISSION MULTIPLICITY = &nb= sp; Sixpak

4) ENDFB.M= 14 - PHOTON EMISSION ANGULAR DISTRIBUTIONS (ALWAYS Sixpak

= ISOTROPIC) = &nb= sp; = Sixpak

5) ENDFB.M= 15 - TABULATED PHOTON EMISSION SPECTRA = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

EMITTED PA= RTICLE YIELD = &nb= sp; = Sixpa= k

NEUTRONS = &nb= sp; = &nb= sp; Sixpak

=3D=3D=3D= =3D=3D=3D=3D=3D = &nb= sp; = &nb= sp; Sixpak

IN MF=3D6 = THE YIELD FOR EACH REACTION IS THE ACTUAL MULTIPLICITY OF Sixpak

THE REACTI= ON, E.G., (N,2N) =3D 2. IN USING MF=3D4 AND 5 DATA THE Sixpak

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

MT NUMBER, E.G., MT=3D16 =3D (N,2N)= =3D 2. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THE ONLY E= XCEPT IN ENDF/B-VI IS MT=3D201 =3D TOTAL NEUTRON PRODUCTION Sixpak

WHERE AN A= CTUAL ENERGY DEPENDENT YIELD IS INCLUDED IN MF=3D6. Sixpak

HOWEVER, I= N THIS CASE THE MF=3D3 CROSS SECTION INCLUDES THE = Sixpak

MULTIPLICI= TY (S. PEARLSTEIN, PRIVATE COMMUNICATION, JAN. 1992), Sixpak

SIG(MT=3D2= 01) =3D 2*SIG(N,2N)+3*SIG(N,3N).....ETC. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

SO THAT FO= R ALL ENDF/B-VI DATA AS OF JANUARY 1992 THE MF=3D4 AND 5 Sixpak

DATA OUTPU= T BY THIS CODE CAN BE USED IN CONJUNCTION WITH THE MF=3D3 Sixpak

CROSS SECT= IONS - WITHOUT ANY REFERENCE TO THE MF=3D6 YIELD. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PHOTONS = &nb= sp; = &nb= sp; Sixpak

=3D=3D=3D= =3D=3D=3D=3D = &nb= sp; = &nb= sp; = Sixpak

UNLIKE THE NEUTRONS WHERE WITH ONLY ONE EXCEPTION (MT=3D201) THE Sixpak

MF=3D6 YIE= LD IS ENERGY INDEPENDENT, IN THE CASE OF PHOTON EMISSION Sixpak

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

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THIS PROGR= AM WILL OUTPUT THE PHOTON MULTIPLICITY IN MF=3D12 AND Sixpak

INDICATE T= HAT THERE IS A NORMALIZED DISTRIBUTION IN MF=3D15 = Sixpak

(LF=3D1 IN MF=3D12). = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THIS PROGR= AM WILL OUTPUT THE NORMALIZED PHOTON SPECTRA IN MF=3D15. Sixpak

CONTINUOUS ENERGY SPECTRA AND DISCRETE PHOTONS WILL ALL BE OUTPUT Sixpak

AS NORMALI= ZED SPECTRA. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = Sixpak

THIS PROGR= AM WILL ALSO OUTPUT MF=3D14 PHOTON ANGULAR DISTRIBUTION Sixpak

DATA, ALWA= YS USING THE ISOTROPIC FLAG TO MINIMIZE OUTPUT. = Sixpak

= = &nb= sp; = &nb= sp; = Sixpak

WARNING OF ENERGY DEPENDENT YIELD = &nb= sp; Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D = &nb= sp; Sixpak

THIS PROGR= AM WILL PRINT A WARNING MESSAGE IF A SECTION OF DATA Sixpak

BEING OUTP= UT IN THE ENDF/B FORMAT HAS AN ENERGY DEPENDENT MF=3D6 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.<= span style=3D'mso-spacerun:yes'> = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = = &nb= sp; Sixpak

USING THE OUTPUT = &nb= sp; = &nb= sp; Sixpak

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

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

F(E,EP,COS= ) =3D SIG(E)*Y(E)*G0(E,EP)*F0(E,COS) = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = = Sixpak

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

IMPLIED BY= THE MT NUMBER (E.G., MT=3D16 =3D N,2N - MULTIPLICITY =3D 2) Sixpak

OR INCLUDE= D IN THE CROSS SECTION (E.G., MT=3D201 =3D TOTAL NEUTRON Sixpak

PRODUCTION= ) ALL THE INFORMATION REQUIRED FOR A CALCULATION IS Sixpak

AVAILABLE IN, = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

MF=3D3 - SIG(E) = &nb= sp; = &nb= sp; Sixpak

MF=3D4 - F0(E,COS) - FOR OUTGOING NEUTRONS = Sixpak

MF=3D5 - G0(E,EP) - FOR OUTGOING NEUTR= ONS = Sixpak

MF=3D12 - Y(E) - FOR OUTG= OING PHOTONS = &nb= sp; Sixpak

MF=3D14 - F0(E,COS= ) - FOR OUTGOING PHOTONS (ALWAYS ISOTROPIC) Sixpak

MF=3D15 - G0(E,EP)= - FOR OUTGOING PHOTONS = &nb= sp; Sixpak

= = &nb= sp; = &nb= sp; Sixpak

DOCUMENTATION = &nb= sp; = &nb= sp; Sixpak

ONLY SECTI= ONS OF MF=3D4, 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

= &nb= sp; = = &nb= sp; Sixpak

REACTION INDEX = &nb= sp; = &nb= sp; Sixpak

THIS PROGR= AM DOES NOT USE THE REACTION INDEX WHICH IS GIVEN IN Sixpak

SECTION MF= =3D1, MT=3D451 OF EACH EVALUATION. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

SECTION SIZE = &nb= sp; = = Sixpak

ALL OF THE= DATA IN ENDF/B-VI, MF=3D6 ARE QUITE SMALL TABLES. AS SUCH Sixpak

THIS PROGR= AM 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. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PLEASE CON= TACT THE AUTHOR IF YOU HAVE AN EVALUATION WHICH EXCEEDS Sixpak

THIS LIMIT= . = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = Sixpak

SELECTION = OF DATA = &nb= sp; = &nb= sp; Sixpak

THE PROGRA= M SELECTS DATA TO BE PROCESSED BASED ON MAT/MT RANGES Sixpak

(MF=3D6 AS= SUMED). 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 TAP= E IS IN MAT ORDER. THE PROGRAM WILL TERMINATE EXECUTION Sixpak

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

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PROGRAM OPERATION = = &nb= sp; = Sixpak

EACH SECTI= ON (MT) OF MF=3D6 DATA IS SUBDIVIDED INTO SUBSECTIONS - Sixpak

ONE SUBSEC= TION FOR EACH EMITTED PARTICLE. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

EACH SUBSE= CTION OF DATA IS CONSIDERED SEPARATELY. EACH SUBSECTION Sixpak

OF ENDF/B = MF=3D6 DATA TO PROCESS IS IN THE FORM, = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

F(E,EP,COS= ) =3D SIG(E)*Y(E)*G0(E,EP)*F(E,EP,COS) = Sixpak

= &nb= sp; = &nb= sp; = Sixpak

SIG(E) =3D MF=3D3= CROSS SECTIONS = &nb= sp; Sixpak

Y(E) =3D YIELD (MULTIPLICITY) = &nb= sp; Sixpak

G0(E,EP) =3D ENERGY SPECTRUM = &nb= sp; = Sixpak

F(E,EP,COS= ) =3D ANGULAR DISTRIBUTION = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

G0(E,EP) = =3D 1 WHEN INTEGRATED OVER EP (SECONDARY ENERGY) = Sixpak

G0(E,EP)*F= (E,EP,COS) =3D 1 WHEN INTEGRATED OVER EP AND COS = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THIS PROGR= AM WILL DEFINE THE ZEROTH ORDER MOMENTS OF THE = Sixpak

ENERGY AND= ANGULAR DISTRIBUTIONS, = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

G0(E,EP) =3D G0(E,EP)*F(E,EP,COS) INTEGRATE= D OVER COS = Sixpak

F0(E,COS) = =3D G0(E,EP)*F(E,EP,COS) INTEGRATED OVER EP = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

= &nb= sp; = = &nb= sp; = 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

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

FOR NEUTRO= NS INCIDENT AND NEUTRONS EMITTED THIS DATA WILL BE Sixpak

OUTPUT IN = MF=3D4 AND 5 FORMATS. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

FOR NEUTRO= NS INCIDENT AND PHOTONS EMITTED THIS DATA WILL BE Sixpak

OUTPUT IN = MF=3D15 FORMAT - THE SPECTRA ARE OUTPUT AND THE Sixpa= k

ANGULAR DISTRIBUTION IS IGNORED. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

IS ISOTROP= IC AND AS SUCH NO DISTRIBUTION OF PHOTON ANGULAR Sixpak

DISTRIBUTI= ONS NEED BE OUTPUT - IT IS ALWAYS ISOTROPIC. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

FOR ALL OTHER COMBINATIONS INCIDENT= AND EMITTED PARTICLES = Sixpak

THERE WILL= BE NO ENDF/B FORMATTED OUTPUT. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

VARIATIONS= FROM ENDF/B MANUAL = &nb= sp; = Sixpak

LAW=3D1, L= ANG=3D2 =3D KALBACH-MANN = &nb= sp; = Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D = &nb= sp; = Sixpak

FOR THE DISTRIBUTIONS, = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

F(MU,E,EP)= =3D G0(E,EP)*A*(COSH(MU*A)+R(E,EP)*SINH(MU*A)) = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

G0(E,EP) = =3D 1 - WHEN INTEGRATED OVER EP. = &nb= sp; Sixpak

= &nb= sp; = = &nb= sp; Sixpak

A*(COSH(MU*A)+R(E,EP)*SINH(MU*A)) =3D 2 - WHEN INTEGRATD OVER MU Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

ARE NORMAL= IZED 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. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

F(MU,E,EP)= =3D G0(E,EP)*0.5*A*(COSH(MU*A)+R(E,EP)*SINH(MU*A)) Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THIS IS TH= E FORM USED IN THIS CODE = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

LAW=3D1, ND NOT 0 =3D D= ISCRETE SECONDARY ENERGY DISTRIBUTION = Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D = 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 CONSID= ER THE ENDF/B-VI DATA TO BE IN ERROR. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

ENERGIES S= HOULD BE NON-NEGATIVE AND IN ASCENDING ENERGY ORDER Sixpak

FOR EACH INCIDENT ENERGY. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = Sixpak

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

FOR DISCRE= TE PHOTONS - PHYSICALLY THIS IS A DELTA FUNCTION. IN Sixpak

ENDF/B-VI = IT IS ENTERED AS 1.0 =3D INTERPRETING IT AS INTEGRATED Sixpak

<= /p>

OVER SECON= DARY ENERGY - IN WHICH CASE THE DELTA FUNCTION =3D 1.0. Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

LIMITATION= S = &nb= sp; = = &nb= sp;Sixpak

CHECKING DATA = &nb= sp; = &nb= sp; Sixpak

THIS PROGR= AM CHECKS ALL ENDF/B-VI MF=3D6 DATA. THE FOLLOWING CHECKS Sixpak

ARE PERFORMED. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PARAMETERS= = &nb= sp; = &nb= sp; Sixpak

=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D = &nb= sp; = &nb= sp; Sixpak

ALL PARAME= TERS ARE CHECKED FOR CONSISTENCY. IF PARAMETERS ARE Sixpak

NOT CONSIS= TENT THE PROGRAM MAY NOT BE ABLE TO PERFORM THE = Sixpak

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

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

INTERPOLAT= ION LAWS = &nb= sp; = &nb= sp; Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D = &nb= sp; = &nb= sp; Sixpak

ALL INTEGR= ATIONS ARE PERFORMED USING THE INTERPOLATION LAW GIVEN Sixpak

FOR SECOND= ARY ENERGY AND/OR COSINE. INTEGRATIONS ARE NOT = Sixpak

PERFORMED = OVER INCIDENT - ONLY INTEGRATION OVER SECONDARY ENERGY Sixpak

AND/OR COS= INE ARE PERFORMED AT EACH INCIDENT ENERGY. THEREFORE Sixpak

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

CODE. = &nb= sp; = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

ALL INTERPOLATION LAWS ARE CHECKED. ALL DATA ASSOCIATED WITH Sixpak

INTERPOLAT= ION 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. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

AND UNIT B= ASE TRANSFORMATION INTERPOLATION. NONE OF THESE NEW Sixpak

INTERPOLAT= ION LAWS ARE USED IN THE ENDF/B-VI LIBRARY AS OF Sixpak

JANUARY 19= 92 TO INTERPOLATE IN SECONDARY ENERGY OR COSINE. Sixpak

THEREFORE = THIS PROGRAM CAN PERFORM ALL OF THE REQUIRED INTEGRALS Sixpak

OVER SECON= DARY ENERGY AND/OR COSINE USING ONLY THE OLDER = Sixpak

INTERPOLAT= ION CODES. THIS PROGRAM ONLY PERFORMS INTEGRALS FOR Sixpak

EACH INCID= ENT ENERGY, SO THAT INTERPOLATION IN INCIDENT ENERGY Sixpak

IS NOT PER= FORMED BY THIS PROGRAM. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

NEW INTERPOLATION SCHEMES ARE USED FOR INCIDENT ENERGY - FOR Sixpak

EXAMPLE, CORRESPONDING POINT INTERPOLATION IS SPECIFIED TO ALLOW Sixpak

INTERPOLAT= ION IN G0(E,EP) TO SIMULATE CASES WHERE THE INPUT ENERGY Sixpak

LIMIT IS D= EFINED BY E-EP =3D A DIAGONAL CURVE ACROSS (E,EP) SPACE. Sixpak

THIS INTERPOLATION CODE CANNOT BE SPECIFIED IN THE MF=3D5 OUTPUT Sixpak

OF THIS CO= DE - MF=3D5 ONLY ALLOWS THE OLDER INTERPOLATION LAWS Sixpak

INT=3D1 TH= ROUGH 5. THEREFORE THIS PROGRAM WILL USE THE CLOSEST Sixpak

CORRESPOND= ING INTERPOLATION CODE FOR OUTPUT TO MF=3D5. FOR USE Sixpak

WHERE THE = OUTPUT OF THIS CODE =3D LOW ENERGY APPLICATIONS - THIS Sixpak

SHOULD HAVE LITTLE EFFECT ON RESULTS. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

FOR CONSIS= TENCY WITH EARLIER VERSIONS OF ENDF/B IN CREATING THE Sixpak

ENDF/B OUT= PUT, 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 RA= NGE, 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 RE= LATED 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 M= ESSAGE WILL BE PRINTED - SINCE THIS WOULD EFFECT THE Sixpak

ACCURACY O= F THE INTEGRALS PERFORMED BY THIS PROGRAM. IF THIS MUST Sixpak

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

WILL NOT E= FFECT THE ACCURACY OF THE INTEGRALS PERFORMED BY THIS Sixpak

PROGRAM. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = Sixpak

SPECTRA AND ANGULAR DISTRIBUTIONS = &nb= sp; Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D = &nb= sp; Sixpak

ALL SPECTR= A AND ANGULAR DISTRIBUTIONS ARE CHECKED TO INSURE Sixpak

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

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

LEGENDRE COEFFICIENTS = &nb= sp; = Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D = &nb= sp; = Sixpak

THE NORMALIZATION, F0, CANNOT BE NEGATIVE. = &nb= sp; Sixpak

= &nb= sp; = = &nb= sp; = Sixpak

LEGENDRE COEFFICIENTS IN NORMAL FORM ARE CHECKED TO INSURE Sixpak

THEY ARE I= N THE RANGE -1 TO +1 =3D THE LEGENDRE EXPANSION OF A Sixpak

DELTA FUNC= TION AT COS=3D+1 OR -1 - COEFFICIENTS SHOULD NOT = Sixpak

EXCEED WHA= T YOU GET FROM A DELTA FUNCTION. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

ANGULAR DISTRIBUTIONS ARE CHECKED AT COS =3D -1, 0 AND +1. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

CREATING E= NDF/B OUTPUT = &nb= sp; = Sixpak

THIS PROGR= AM CAN CREATE EQUIVALENT MF =3D4, 5, 12, 14, 15 DATA FOR Sixpak

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

FOR 1 SECT= ION OF LAW=3D6 DATA (SEE DETAILS BELOW). = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THIS PROGR= AM HAS NOT BEEN TESTED ON OTHER DATA LIBRARIES, E.G., Sixpak

JEF, JENDL, ETC. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = Si= xpak

THE PROGRA= M HAS THE FOLLOWING LIMITATION AS FAR AS CREATING Sixpak

ENDF/B FOR= MATTED OUTPUT. = &nb= sp; = Sixpak

= = &nb= sp; = &nb= sp; = Sixpak

ISOTROPIC = PHOTON EMISSION = &nb= sp; = Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D = &nb= sp; = Sixpak

FOR PHOTON EMISSION THE DISTRIBUTIONS ARE ASSUMED TO BE ISOTROPIC Sixpak

AND ONLY T= HE MULTIPLICITY IS OUTPUT IN MF=3D12, ISOTROPIC ANGULAR Sixpak

DISTRIBUTI= ONS IN MF=3D14 AND THE SPECTRA IN MF=3D15. ALL ENDF/B-VI Sixpak

MF=3D6 DAT= A AS OF JANUARY 1992 INCLUDE ONLY ISOTROPIC PHOTON Sixpak

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

ENDF/B-VI DATA. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = = &nb= sp; Sixpak

EITHER TAB= ULATED OR LEGENDRE COEFFICIENTS = &nb= sp; Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D = &nb= sp; Sixpak

FOR LAW=3D= 2 THE REPRESENTATION, EITHER TABULATED OR LEGENDRE Sixpak

COEFFICIEN= TS, CAN BE SPECIFIED FOR EACH INCIDENT ENERGY. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

MUST BE TH= E SAME FOR ALL INCIDENT ENERGIES =3D MF=3D4 DATA CAN ONLY Sixpak

BE TABULAT= ED OR LEGENDRE OVER THE ENTIRE ENERGY RANGE. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

YIELD AND = OUTPUT NORMALIZATION = &nb= sp; = Sixpak

=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D=3D= =3D=3D=3D=3D=3D=3D=3D=3D = &nb= sp; = Sixpak

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

OUTPUT FOR NEUTRO= NS, BUT IS INCLUDED IN THE OUTPUT FOR PHOTONS. Sixpak

IN ALL CAS= ES THE ANGULAR DISTRIBUTIONS AND SPECTRA OUTPUT ARE Sixpak

NORMALIZED= TO UNITY. = &nb= sp; = &nb= sp; Sixpak

= = &nb= sp; = &nb= sp; = Sixpak

LAW=3D0 = &nb= sp; = &nb= sp; = Sixpak

=3D=3D=3D= =3D=3D = &nb= sp; = &nb= sp; = Sixpak

NO OUTPUT = - INCIDENT NEUTRON - EMITTED PHOTON OR NEUTRON = Sixpak

= REACTIONS ARE NOT EXPECTED. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

LAW=3D1 = = &nb= sp; = Sixpak

=3D=3D=3D= =3D=3D = &nb= sp; = &nb= sp; = 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 (NE= P=3D1) MAY BE GIVEN =3D A NORMALIZED DISTRIBUTION FOR A Sixpak

SINGLE DIS= CRETE EMISSION ENERGY. ALL OF THE ENDF/B-VI DATA AS Sixpak

OF JANUARY= 1992 CONFORM TO THESE LIMITATIONS. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; 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 INC= IDENT ENERGIES. THEREFORE ISOTROPIC DISTRIBUTIONS Sixpak

WILL BE OU= TPUT EITHER: LANG =3D 1 - AS 1 LEGENDRE COEFFICIENT =3D 0.0 Sixpak

OR LANG = =3D NOT 1 - AS A 2 POINT ANGULAR DISTRIBUTION AT COS =3D -1.0 Sixpak

AND +1.0 W= ITH BOTH VALUES EQUAL TO 0.5 (A NORMALIZED ISOTROPIC Sixpak

DISTRIBUTION). = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

DISCRETE P= HOTONS ARE OUTPUT IN MF=3D15 AS 3 POINT DISTRIBUTIONS Sixpak

WITH SECON= DARY ENERGY POINTS AT EP-DEP, EP, EP+DEP, WHERE = Sixpak

DEP=3D0.00= 1*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

= = &nb= sp; = &nb= sp; Sixpak

LAW=3D2 = &nb= sp; = &nb= sp; = Sixpak

=3D=3D=3D= =3D=3D = &nb= sp; = &nb= sp; = Sixpak

NO LIMITAT= ION ON REPRESENTATIONS. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

LAW=3D3 = &nb= sp; = &nb= sp; = Sixpak

=3D=3D=3D= =3D=3D = &nb= sp; = &nb= sp; = Sixpak

NO LIMITAT= ION ON REPRESENTATIONS. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

LAW=3D4 = &nb= sp; = = &nb= sp; Sixpak

=3D=3D=3D= =3D=3D = &nb= sp; = &nb= sp; = Sixpak

NO OUTPUT - INCIDENT NEUTRON - EMITTED PHOTON OR NEUTRON = Sixpak

= REACTIONS ARE NOT EXPECTED. = = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

LAW=3D5 = &nb= sp; = &nb= sp; = Sixpak

=3D=3D=3D= =3D=3D = &nb= sp; = &nb= sp; Sixpak

NO OUTPUT - INCIDENT NEUTRON - EMITTED PHOTON OR NEUTRON = Sixpak

= REACTIONS ARE NOT EXPECTED. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

LAW=3D6 = &nb= sp; = &nb= sp; = Sixpak

=3D=3D=3D= =3D=3D = &nb= sp; = &nb= sp; = Sixpak

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

= FOR (N,D) 2N,P. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

LAW=3D7 = &nb= sp; = &nb= sp; = Sixpak

=3D=3D=3D= =3D=3D = &nb= sp; = &nb= sp; Sixpak

FOR EACH INCIDENT ENERGY THE REPRESENTATION MUST BE EITHER, Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

1) SQUARE = =3D FOR EACH INCIDENT COSINE EXACTLY THE SAME SECONDARY Sixpak

= ENERGIES. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

2) LINEAR = =3D FOR EACH INCIDENT COSINE THE INTERPOLATION LAW Sixpak

= BETWEEN SECONDARY ENERGIES MUST BE LINEAR. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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

AS OF JANU= ARY 1992 - SO THIS PROGRAM CAN TRANSLATED ALL LAW=3D7 Sixpak

DATA FOR ENDF/B-VI. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = Sixpak

LABORATORY= VS. CENTER-OF-MASS SYSTEM = &nb= sp; Sixpak

IN MANY CA= SES PEOPLE ASSUME THAT FOR HEAVY (HIGH ATOMIC WEIGHT) Sixpak

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

SINCE IN T= HIS 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. HOW= EVER, FOR THE TYPICAL REACTIONS INCLUDED IN MF=3D6 THIS Sixpak

IS NOT ALW= AYS 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

TRANSFORMA= TION FROM CENTER-OF-MASS TO LAB IMPORTANT. THEREFORE Sixpak

GENERALLY = TO TREAT MF=3D6 DATA WE MUST CONSIDER THIS TRANSFORMATION. Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THE FOLLOW= ING DISCUSSING ONLY APPLIES TO SPECTRA THAT MAY BE Sixpak

OUTPUT IN = MF=3D5 =3D ONLY DATA FOR NEUTRONS INCIDENT AND EMITTED - Sixpak

IN PARTICU= LAR THE FOLLOWING DEFINITIONS ARE NOT GENERAL - THEY Sixpak

ARE ONLY V= ALID FOR INCIDENT AND EMITTED NEUTRONS. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

DOUBLE DIFFERENTIAL DATA IN MF=3D6 MAY BE GIVEN IN EITHER THE LAB Sixpak

OR C.M. SY= STEM. SIMILARLY ANGULAR DISTRIBUTIONS IN MF=3D4 MAY BE Sixpak

GIVEN IN E= ITHER THE LAB OR C.M. SYSTEM. IN CONTRAST ENERGY Sixpak

SPECTRA IN= MF=3D5 CAN ONLY BE GIVEN IN THE LABORATORY SYSTEM. Sixpak

= &nb= sp; = &nb= sp; = Sixpak

THE ANGULAR DISTRIBUTIONS OUTPUT BY THIS CODE IN MF=3D4 ARE IN THE Sixpak

SAME SYSTE= M IN WHICH THEY ARE GIVEN IN MF=3D6 - EITHER LAB OR Sixpak

CENTER-OF-= MASS SYSTEM. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THE ENERGY SPECTRA OUTPUT BY THIS CODE IN MF=3D5 MUST BE IN THE LAB Sixpak

SYSTEM - T= HIS IS THE ONLY ALLOWED FORM FOR MF=3D5 DATA. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

FOR MF=3D6= SPECTRA GIVEN IN THE LAB SYSTEM THIS MERELY REQUIRES Sixpak

COPYING THE GIVEN SPECTRA TO MF=3D5 OUTPUT. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = Si= xpak

FOR MF=3D6= 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=3D5 AS IN THE LAB SYSTEM - THE FIRST ORDER CORRECTIONS Sixpak

ARE DESCRI= BED BELOW. = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

DEFINING,<= span style=3D'mso-spacerun:yes'> = &nb= sp; = &nb= sp; Sixpak

MM =3D CENTER= OF MASS MOTION = &nb= sp; = Sixpak

CM =3D OUTGOI= NG (EMITTED) PARTICLE IN CENTER OF MASS = Sixpak

LAB =3D OUTGOING (EM= ITTED) PARTICLE IN LAB = &nb= sp; Sixpak

THETA =3D CM SCATTERING ANGLE RELA= TIVE TO INCIDENT DIRECTION Sixp= ak

COS(CM) = =3D COSINE OF THE CM SCATTERING ANGLE = &nb= sp; Sixpak

= &nb= sp; = = &nb= sp; Sixpak

FOR NEUTRO= NS INCIDENT WITH AN ENERGY, E, AND THEREFORE A SPEED, Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

VN(E) =3D 2*SQRT(E)/MASS(IN) = &nb= sp; = Si= xpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THE CENTER-OF-MASS SPEED IS GIVEN BY, = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = = Sixpak

V(MM) =3D = VN(E)/(1 + A) = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

AND THE CE= NTER OF MASS ENERGY BY, = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

E(MM) =3D 1/2*MASS(IN)*V(MM)**2 = &nb= sp; = Sixpak

= =3D 1/2*MASS(IN)*VN(E)**2/(1 + A)**2 = &nb= sp; Sixpak

= =3D E/(1 + A)**2 = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

FOR DISTRIBUTIONS GIVEN IN MF=3D6 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, = &nb= sp; = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

V(LAB)*COS= (LAB) =3D V(MM) + V(CM)*COS(CM) = &nb= sp; Sixpak

V(LAB)*SIN= (LAB) =3D V(CM)*SIN(CM) = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = Sixpak

V(LAB)**2 = =3D V(MM)**2 + V(CM)**2 + 2*COS(CM)*V(MM)*V(CM) = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

EP(LAB) =3D 0.5*MASS(OUT)*V(LAB)**2 = = &nb= sp; Sixpa= k

<= /p>

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

= =3D E(MM) + EP(CM) + 2*COS(CM)*SQRT(E(MM)*EP(CM)) = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

WE CAN ALSO DEFINE THE REVERSE TRANSFORMATION USING, = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

V(CM)*COS(= CM) =3D V(LAB)*COS(LAB) - V(MM) = = Sixpak

V(CM)*SIN(= CM) =3D V(LAB)*SIN(LAB) = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

V(CM)**2 = =3D V(MM)**2 + V(LAB)**2 - 2*COS(LAB)*V(MM)*V(LAB) Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

EP(CM) =3D 0.5*MASS(OUT)*V(CM)**2 = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

= =3D E(MM) + EP(LAB) - 2*COS(LAB)*SQRT(E(MM)*EP(LAB)) Sixp= ak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

WE CAN DEF= INE COS(LAB) FROM THE RELATIONSHIP, = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = Sixpak

V(LAB)*COS= (LAB) =3D V(MM) + V(CM)*COS(CM) = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

COS(LAB) =3D[V(MM) + V(CM)*COS(CM)]/V(LAB) = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; [V(MM) + V(CM)*COS(CM)] = &nb= sp; Sixpak

COS(LAB) =3D--------------------------------------------- Sixpak

= &nb= sp; SQRT[V(MM)**2+V(CM)**2+2*COS(CM)*V(MM)*V(CM)] Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

OR COS(CM)= FROM THE RELATIONSHIP, = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

V(CM)*COS(CM) =3D V(LAB)*COS(LAB) - V(MM) = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

COS(CM) =3D[V(LAB)*COS(LAB) - V(MM)]/V(CM) = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; [V(LAB)*COS(LAB) - V(MM)] = = Sixpak

COS(CM) =3D------------------------------------------------ Sixpak

= &nb= sp; SQRT[V(LAB)**2+V(CM)**2-2*COS(LAB)*V(LAB)*V(MM)] Sixpak

= &nb= sp; = &nb= sp; = Sixpak

THE JACOBI= AN CAN BE DEFINED FROM, = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

V(LAB)*COS= (LAB) =3D V(MM) + V(CM)*COS(CM) = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

J =3D D[COS(CM)]/D[COS(LAB)] =3D V(LAB)/V(CM) = &nb= sp; Sixpak

= &nb= sp; =3D SQRT[EP(LAB)/EP(CM)] = Sixpak

= &nb= sp; = &nb= sp; = 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

TRANSFORMA= TION OF DISTRIBUTIONS FROM THE CM TO LAB SYSTEM USING Sixpak

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

TRANSFORMA= TION USING THE ABOVE RELATIONSHIPS AND THE IDENTITY, Sixpak

= &nb= sp; = &nb= sp; = &nb= sp;Sixpak

F(E,EP(LAB),COS(LAB))*D(COS(LAB))=3DF(E,EP(CM),COS(CM))*D(COS(CM)) Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THIS IS NO= T WHAT WILL BE DONE HERE, SINCE WE WILL ONLY BE = Sixpak

INTERESTED= IN THE ZEROTH ORDER MOMENTS OF THESE DISTRIBUTIONS, Sixpak

BUT WE WIL= L BE INTERESTED IN DEFINING THOSE MOMENTS IN THE Sixpak

LAB SYSTEM= IN TERMS OF MF=3D6 SPECTRA GIVEN IN THE CM SYSTEM USING, Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

F(E,EP(LAB),COS(LAB)) =3D F(E,EP(CM),COS(CM))*J = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = Sixpak

THE LIMITS= OF EP(LAB) ARE DEFINED BY SETTING COS(CM) =3D +1 OR -1, Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

EP(LAB) =3D (SQRT(EP(CM)) + SQRT(E(MM)))**2 FOR COS(CM) = =3D +1 Sixpak

= =3D (SQRT(EP(CM)) - SQRT(E(MM)))**2= FOR COS(CM) =3D -1 Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

IN THIS FO= RM 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 W= ILL BE ALMOST EQUAL - SIMILARLY FOR THE COSINE, IN Sixpak

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

FOR THE MF= =3D6 DATA WE CANNOT ASSUME THAT THIS IS TRUE. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

TO FIRST O= RDER THE ANGULAR DEPENDENCE CAN BE IGNORED, = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

EP(LAB) =3D E(MM) + EP(CM) = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

ALL THIS S= AYS IS THAT TO FIRST ORDER THE EFFECT OF TRANSFORMING Sixpak

FROM THE C= M TO LAB SYSTEM IS TO INCREASE THE ENERGY OF THE Sixpak

EMITTED PA= RTICLE IN THE CENTER-OF-MASS SYSTEM BY THE ENERGY OF Sixpak

THE CENTER-OF-MASS TO DEFINE THE LAB ENERGY. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

NOT ONLY T= HE ENERGY, BUT ALSO THE SPECTRA MUST BE TRANSFORMED. Sixpak

STARTING F= ROM THE DOUBLE DIFFERENTIAL DATA IN THE LAB SYSTEM, Sixpak

F(E,EP,COS(LAB)), WE CAN DEFINE THE LAB SCALAR SPECTRUM AS, Sixpak

= &nb= sp; = &nb= sp; = Sixpak

G0(E,EP) = =3D INTEGRAL F(E,EP,COS(LAB))*D(COS(LAB)) = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THIS IS THE NORMAL CALCULATION DEFINED ABOVE AND USED FOR DATA Sixpak

GIVEN IN T= HE LAB SYSTEM. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

STARTING F= ROM DATA IN THE CENTER OF MASS SYSTEM F(E,EP,COS(CM)), Sixpak

WE CAN USE= THE RELATIONSHIP, = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

F(E,EP,COS(LAB))*D(COS(LAB)) =3D F(E,EP,COS(CM))*J*D(COS(LAB)) Sixpak

= &nb= sp; = &nb= sp; = Sixpak

J =3D SQRT(EP(LAB)/EP(CM)) - THE JACOBIAN = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

= =3D E(MM)/= EP(CM) + 1 + 2*COS(CM)*SQRT(E(MM)/EP(CM)) Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

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, Sixpak

EP(CM), IS= LARGE COMPARED TO THE CENTER-OF-MASS ENERGY, E(MM), Sixpak

THE JACOBI= AN IS ESSENTIALLY UNITY AND THE CENTER-OF-MASS AND LAB Sixpak

SPECTRA WI= LL BE VERY SIMILAR - AGAIN, GENERALLY WE CANNOT = Sixpak

ASSUME THA= T THIS IS TRUE FOR THE MF=3D6 SPECTRA. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

THEREFORE = WE CAN ALSO DEFINE THE LAB SCALAR SPECTRUM IN TERMS OF Sixpak

THE CM SPE= CTRUM IN THE FORM, = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

G0(E,EP) = =3D INTEGRAL F(E,EP,COS(CM))*J*D(COS(LAB)) = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

CONSISTENT= WITH THE ABOVE ASSUMPTION THAT THE ANGULAR DEPENDENCE Sixpak

OF EP(LAB)= CAN BE IGNORED THE JACOBIAN WILL NOT BE USED IN Sixpak

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

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

IT SHOULD = BE NOTED THAT SINCE IN THIS CASE THE MF=3D4 ANGULAR Sixpak

DISTRIBUTI= ONS ARE GIVEN IN THE CM SYSTEM AND WHEN USED IN ANY Sixpak

APPLICATIO= N THEY WILL BE TRANSFORMED TO THE LAB SYSTEM - WHEN Sixpak

THIS IS DONE THE JACOBIAN WILL BE APPLIED. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

IN THIS CO= DE WHERE WE ARE MOSTLY CONCERNED WITH CONSERVING THE Sixpak

NUMBER OF EMITTED PARTICLES AND AVERAGE ENERGIES THE NEUTRON Sixpak

SPECTRA OU= TPUT IN MF=3D5 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 Sixpak

ENERGY, I.= E., FOR A CENTER OF MASS SPECTRUM TABULATED AT CENTER Sixpak

OF MASS EN= ERGIES 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= . = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

SINCE THE ANGULAR DISTRIBUTION IS ALWAYS OUTPUT IN THE SAME Sixpak

SYSTEM AS = WHICH IT IS GIVEN IN MF=3D6, NO TRANSFORMATION IS = Sixpak

REQUIRED F= OR THE MF=3D4 OUTPUT. = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

WHEN USED = IN LOW ENERGY APPLICATIONS (E.G., FISSION REACTORS) THE Sixpak

HIGH ENERGY SPECTRA PRESENTED IN MF=3D6 WILL BE MOSTLY IMPORTANT Sixpak

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

AND THE DE= TAILS OF THE CORRELATION AND GROSS ENERGY SPECTRA WILL Sixpak

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

BY THIS PR= OGRAM IN MF=3D5 SHOULD BE ADEQUATE. = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

PLOTTAB FORMATTED OUTPUT = &nb= sp; = Sixpak

THIS PROGR= AM CONTAINS ROUTINES TO PRODUCE OUTPUT THAT CAN BE USED Sixpak

AS INPUT T= O THE PLOTTAB CODE TO OBTAIN GRAPHIC RESULTS. = Sixpak

= = &nb= sp; = &nb= sp; Sixpak

THESE ROUT= INES 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. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

INPUT FILE= S = &nb= sp; = &nb= sp; = Sixpak

UNIT DESCRIPTION = &nb= sp; = &nb= sp; Sixpak

---- ----------- = &nb= sp; = &nb= sp; Sixpak

2 INPUT LINES (BCD - 80 CHARACTERS/RECORD) = Sixpak

10 ORIGINAL ENDF/B DAT= A (BCD - 80 CHARACTERS/RECORD) = Sixpak

= &nb= sp; = &nb= sp; = Sixpak

OUTPUT FILES = &nb= sp; = &nb= sp; Sixpak

UNIT DESCRIPTION = &nb= sp; = Sixpak

---- ----------- = &nb= sp; = &nb= sp; Sixpak

3 OUTPUT REPORT (BCD -= 120 CHARACTERS/RECORD) = Sixpak

11 ENDF/B DATA MF=3D4 = (BCD - 80 CHARACTERS/RECORD) = Sixpak

12 ENDF/B DATA MF=3D5 = (BCD - 80 CHARACTERS/RECORD) = Sixpak

14 ENDF/B DATA MF=3D15= (BCD - 80 CHARACTERS/RECORD) = Sixpak

17 ENDF/B DATA MF=3D12= (BCD - 80 CHARACTERS/RECORD) = Sixpak

18= ENDF/B DATA MF=3D14 (BCD - 80 CHARACTERS/RECORD) = Sixpak

15 PLOTTAB INPUT PARAM= ETERS (BCD - 80 CHARACTERS/RECORD) Sixpak

16 PLOTTAB FORMATTED O= UTPUT (BCD - 80 CHARACTERS/RECORD) Sixpak

= = &nb= sp; = &nb= sp; Sixpa= k

SCRATCH FILES = &nb= sp; = &nb= sp; Sixpak

NONE = = &nb= sp; = &nb= sp;Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

OPTIONAL STANDARD FILE NAMES (SEE SUBROUTINE FILIO1 AND FILIO2) Sixpak

UNIT FILE NAME = &nb= sp; = &nb= sp; Sixpak

---- ---------- = &nb= sp; = &nb= sp; Sixpak

2 SIXPAK.INP = &nb= sp; = &nb= sp; Sixpak

3 SIXPAK.LST = &nb= sp; = &nb= sp; Sixpak

10 ENDFB.IN = &nb= sp; = &nb= sp; Sixpak

11 ENDFB.MF4 = &nb= sp; = = Sixpak

12 ENDFB.MF5 = &nb= sp; = &nb= sp; Sixpak

14 ENDFB.M15 = &nb= sp; = &nb= sp; Sixpak

17 ENDFB.M12 = &nb= sp; = Sixpa= k

18 ENDFB.M14 = &nb= sp; = &nb= sp; Sixpak

15 PLOTTAB.INP = &nb= sp; = &nb= sp; Sixpak

16 PLOTTAB.CUR = &nb= sp; = &nb= sp; Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

INPUT PARAMETERS = &nb= sp; = &nb= sp; Sixpak

LINE COLS. DESCRIPTION = &nb= sp; = Sixpak

---- ----- ----------- = &nb= sp; = Sixpak

1 1-60 ENDF/B INPUT DATA FILENAME = &nb= sp; Sixpak

= (STANDARD OPTION =3D ENDFB.IN) = &nb= sp; Sixpak

2-N<= span style=3D'mso-spacerun:yes'> 1-6 MINIMUM MAT FOR REQUESTED RANGE &= nbsp; &nbs= p; Sixpak

= 9-11 MINIMUM MT FOR REQUESTED RANGE = &nb= sp; Sixpak

= 12-17 MAXIMUM MAT FOR REQUESTED RANGE = &nb= sp; Sixpak

= 20-22 MAXIMUM MT FOR REQUESTED RANGE = &nb= sp; Sixpak

= &nb= sp; = = &nb= sp; = Sixpak

LEAVE THE DEFINITION OF THE FILENAME BLANK - THE PROGRAM WILL Sixpak

THEN USE T= HE STANDARD FILENAME (ENDFB.IN). = &nb= sp; Sixpak

= &nb= sp; = = &nb= sp; Sixpak

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. = = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

EXAMPLE IN= PUT NO. 1 = &nb= sp; = &nb= sp; Sixpak

------------------- = &nb= sp; = = Sixpak

PROCESS AL= L MF=3D6 DATA ON AN ENDF/B TAPE. USE THE STANDARD INPUT Sixpak

DATA FILEN= AME ENDFB.IN IN THIS CASE THE USER CAN EITHER EXPLICITLY Sixpak

SPECIFY THE FILENAME AND MAT/MT RANGE BY THE FOLLOWING= 2 INPUT Si= xpak

LINES, = &nb= sp; = &nb= sp; = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

ENDFB.IN = &nb= sp; = &nb= sp; Sixpak

= 1 1 9999 999 = &nb= sp; = Sixpak

= &nb= sp; (BLANK LINE, TERMINATES REQUEST LIST) Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

OR BY INPU= TTING 2 BLANK LINE =3D PROCESS EVERYTHING. = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

EXAMPLE IN= PUT NO. 2 = &nb= sp; = &nb= sp; Sixpak

------------------- = &nb= sp; = &nb= sp; Sixpak

PROCESS BE= -9, MAT=3D425, MT=3D16. READ THE DATA FROM ENDFB6\BE9. Sixpak

IN THIS CA= SE THE FOLLOWING 3 INPUT LINES ARE REQUIRED, = Sixpak

= &nb= sp; = &nb= sp; = Sixpak

ENDFBB6\BE= 9 = &nb= sp; = &nb= sp; Sixpak

425 16 425 16 = &nb= sp; = Sixpak

= &nb= sp; (BLANK LINE, TERMINATES REQUEST LIST) Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

EXAMPLE IN= PUT NO. 3 = &nb= sp; = &nb= sp; Sixpak

------------------- = &nb= sp; = Sixpak

PROCESS ALL MT=3D16 (N,2N) DATA. THIS CAN BE DONE BY SPECIFYING THE Sixpak

MAXIMUM MAT RANGE =3D 1 TO 9999, AND MT=3D16 FOR THE MINIMUM AND Sixpak

MAXIMUM MT RANGE. READ THE DATA FROM ENDFB6\K300. IN THIS CASE Sixpak

CASE THE FOLLOWING 3 INPUT LINES ARE REQUIRED, = Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak

ENDFB6\K30= 0 = &nb= sp; = &nb= sp; Sixpak

= 1 16 9999 16 = &nb= sp; = Sixpak

= &nb= sp; (BLANK LINE, TERMINATES REQUEST LIST) Sixpak

= &nb= sp; = &nb= sp; = &nb= sp; Sixpak