=======================================================================
Sigma1

Sigma1

PROGRAM
SIGMA1
Sigma1

==============
Sigma1

VERSION 73-1
(MARCH 1973)
Sigma1

VERSION 76-1
(FEBRUARY 1976)
Sigma1

VERSION 76-2 (OCTOBER
1976)
Sigma1

VERSION 77-1
(JANUARY 1977)
Sigma1

VERSION 78-1
(JULY 1978)
Sigma1

VERSION 79-1
(JULY 1979)    CDC-7600
AND CRAY-1 VERSION.
Sigma1

VERSION 80-1
(MAY 1980)     IBM,
CDC AND CRAY VERSION
Sigma1

VERSION 80-2
(DECEMBER 1980)IMPROVED BASED ON USER COMMENTS.
Sigma1

VERSION 81-1
(MARCH 1981)   DOUBLE PRECISION
IBM VERSION
Sigma1

VERSION 81-2
(AUGUST 1981)  IMPROVED IBM SPEED
AND STABILITY       Sigma1

VERSION 82-1
(JANUARY 1982) IMPROVED COMPUTER COMPATIBILITY
Sigma1

VERSION 83-1
(JANUARY 1983)*MAJOR RE-DESIGN.
Sigma1

*PAGE SIZE INCREASED - 1002 TO 2004.    Sigma1

*ELIMINATED COMPUTER DEPENDENT CODING.  Sigma1

*NEW, MORE COMPATIBLE I/O UNIT NUMBER.  Sigma1

*ADDED STANDARD ALLOWABLE ERROR OPTION  Sigma1

(CURRENTLY 0.1 PER-CENT).
Sigma1

*UNRESOLVED RESONANCE REGION COPIED.    Sigma1

*1/V EXTENSION OF CROSS SECTIONS
Sigma1

OUTSIDE OF TABULATED ENERGY
RANGE AND  Sigma1

INTO UNRESOLVED ENERGY
RANGE.
Sigma1

VERSION 83-2
(OCTOBER 1983)*IMPROVED BASED ON USER COMMENTS.
Sigma1

VERSION 84-1
(APRIL 1984)  *IMPROVED NUMERICAL
STABILITY.
Sigma1

*PARTIAL EVALUATION TREATMENT.
Sigma1

VERSION 85-1
(APRIL 1985)  *ITERATE TO
CONVERGENCE (USING THE SAME Sigma1

ENERGY GRID FOR HOT CROSS SECTION AS   Sigma1

COLD CROSS SECTIONS WAS FOUND TO BE    Sigma1

INACCURATE).
Sigma1

*NEW FASTER HIGH ENERGY BROADENING.     Sigma1

*UPDATED FOR ENDF/B-VI FORMATS.
Sigma1

*SPECIAL I/O
ROUTINES TO GUARANTEE      Sigma1

ACCURACY OF ENERGY.
Sigma1

*DOUBLE PRECISION TREATMENT OF ENERGY   Sigma1

(REQUIRED FOR NARROW RESONANCES).      Sigma1

VERSION 85-2
(AUGUST 1985) *FORTRAN-77/H VERSION
Sigma1

VERSION 86-1
(JANUARY 1986)*ENERGY DEPENDENT SCATTERING RADIUS     Sigma1

VERSION 88-1
(JULY 1988)   *OPTION...INTERNALLY
DEFINE ALL I/O
Sigma1

FILE NAMES (SEE, SUBROUTINE FILEIO     Sigma1

FOR DETAILS).
Sigma1

*IMPROVED BASED ON USER COMMENTS.
Sigma1

VERSION 89-1
(JANUARY 1989)*PSYCHOANALYZED BY PROGRAM FREUD TO     Sigma1

INSURE PROGRAM WILL NOT DO ANYTHING    Sigma1

CRAZY.
Sigma1

*UPDATED TO USE NEW PROGRAM CONVERT     Sigma1

KEYWORDS.
Sigma1

*ADDED LIVERMORE
CIVIC COMPILER
Sigma1

CONVENTIONS.
Sigma1

VERSION 90-1
(JUNE 1990)   *UPDATED BASED ON
USER COMMENTS
Sigma1

*ADDED FORTRAN SAVE OPTION
Sigma1

*NEW
MORE CONSISTENT ENERGY OUTPUT      Sigma1

ROUTINES
Sigma1

VERSION 91-1
(JULY 1991)   *WARNING...INPUT
PARAMETER FORMAT       Sigma1

HAS
BEEN CHANGED - SEE BELOW FOR       Sigma1

DETAILS.
Sigma1

*ADDED CHARGED PARTICLE PROJECTILES     Sigma1

*OUTPUT
ENERGY RANGE IS ALWAYS AT
Sigma1

LEAST AS LARGE AS INPUT ENERGY RANGE.  Sigma1

*NO 1/V EXTENSION OF CROSS SECTIONS     Sigma1

FROM UNRESOLVED ENERGY RANGE.
Sigma1

VERSION 92-1
(JANUARY 1992)*INSURE MINIMUM AND MAXIMUM CROSS
Sigma1

SECTIONS ARE ALWAYS KEPT (NOT THINNED) Sigma1

*MT=19 (FIRST CHANCE FISSION) TREATED   Sigma1

THE SAME AS FISSION.
Sigma1

*VARIABLE MINIMUM CROSS SECTION OF      Sigma1

INTEREST - TO ALLOW SMALL CROSS
Sigma1

SECTIONS NEAR THRESHOLDS TO BE
Sigma1

TREATED PROPERLY.
Sigma1

*ALL ENERGIES INTERNALLY ROUNDED PRIOR  Sigma1

TO CALCULATIONS.
Sigma1

*COMPLETELY CONSISTENT I/O AND ROUNDING Sigma1

ROUTINES - TO MINIMIZE COMPUTER        Sigma1

DEPENDENCE.
Sigma1

VERSION 92-2
(JULY 1992)   *CORRECTED BUG
ASSOCIATED WITH
Sigma1

THRESHOLD REACTIONS.
Sigma1

*UNRESOLVED
REGION COPIED WITHOUT
Sigma1

THINNING (IT SHOULD BE EXACTLY THE     Sigma1

SAME AT ALL TEMPERATURES).
Sigma1

*NO
THINNING OF REACTIONS (MT) THAT     Sigma1

WERE NOT BROADENED.
Sigma1

VERSION 93-1
(APRIL 1993)  *INCREASED PAGE SIZE
FROM 2004
Sigma1

TO
24000 ENERGY PONTS.
Sigma1

VERSION 94-1
(JANUARY 1994)*VARIABLE ENDF/B DATA FILENAMES
Sigma1

TO ALLOW ACCESS TO FILE STRUCTURES     Sigma1

(WARNING - INPUT PARAMETER FORMAT      Sigma1

HAS BEEN CHANGED)
Sigma1

*CLOSE ALL FILES BEFORE TERMINATING     Sigma1

(SEE, SUBROUTINE ENDIT)
Sigma1

VERSION 96-1
(JANUARY 1996) *COMPLETE RE-WRITE
Sigma1

*IMPROVED COMPUTER INDEPENDENCE
Sigma1

*ALL DOUBLE PRECISION
Sigma1

*ON SCREEN OUTPUT
Sigma1

*UNIFORM TREATMENT OF ENDF/B I/O
Sigma1

*IMPROVED OUTPUT PRECISION             Sigma1

*DEFINED SCRATCH FILE NAMES
Sigma1

*ALWAYS INCLUDE THERMAL VALUE
Sigma1

VERSION 97-1
(APRIL 1997)   *OPTIONALLY SET
NEGATIVE CROSS
Sigma1

SECTIONS = 0 ON INPUT AND
Sigma1

OUTPUT.
Sigma1

*INCREASED PAGE SIZE FROM 24000
Sigma1

TO
60000 ENERGY POINTS.
Sigma1

VERSION 99-1
(MARCH 1999)   *CORRECTED
CHARACTER TO FLOATING       Sigma1

POINT READ FOR MORE DIGITS
Sigma1

*UPDATED
TEST FOR ENDF/B FORMAT
Sigma1

VERSION BASED ON RECENT FORMAT CHANGE Sigma1

*TREAT LOW ENERGY INITIAL CROSS
Sigma1

SECTIONS
AS LOG-LOG INTERPOLABLE      Sigma1

*CONSTANT (RATHER THAN 1/V) EXTENSION  Sigma1

TO HIGHER ENERGY.
Sigma1

*UPDATED CONSTANTS
BASED ON CSEWG
Sigma1

SUBCOMMITTEE RECOMMENDATIONS
Sigma1

*GENERAL IMPROVEMENTS BASED ON
Sigma1

USER FEEDBACK
Sigma1

VERSION 99-2
(JUNE 1999)    *EXTENDED
RANGE OF INTEGRALS FROM 4
Sigma1

TO 5 UNITS ON EACH SIDE OF ENERGY     Sigma1

POINT TO ALLOW FOR LARGER VARIATION   Sigma1

IN THE LOCAL CROSS SECTION
Sigma1

*ASSUME ENDF/B-VI, NOT V, IF MISSING   Sigma1

MF=1, MT-451.
Sigma1

VERSION 99-3
(OCTOBER 1999))*IMPROVED ERFC FUNCTION DEFINITION.    Sigma1

I THANK BOB MACFARLANE (LANL) FOR     Sigma1

SUPPLYING A MORE ACCURATE ERFC        Sigma1

FUNCTION.
Sigma1

VERS. 2000-1
(FEBRUARY 2000)*CORRECTED LOW ENERGY INTERPOLATION    Sigma1

FOR NON-POSITIVE CROSS SECTIONS
Sigma1

*GENERAL IMPROVEMENTS BASED ON
Sigma1

USER FEEDBACK
Sigma1

VERS. 2002-1
(MAY 2002)
*OPTIONAL INPUT PARAMETERS
Sigma1

VERS. 2004-1
(JAN. 2004)    *OPTIONALLY
IGNORE UNRESOLVED REGION
Sigma1

*CORRECTED PROBLEM AT THE RESOLVED/    Sigma1

UNRESOLVED ENERGY BOUNDARY.
Sigma1

*CORRECTED
HIGH ENERGY CONSTANT CROSS
Sigma1

SECTION EXTENSION.
Sigma1

*TIGHTER CRITERIA FOR INITIAL ENERGY   Sigma1

POINT
SPACING
Sigma1

*TEMPERATURE DEPENDENT ENERGY POINT    Sigma1

SPACING.
Sigma1

*ADDED NEW REICH-MOORE (LRF=7) TO      Sigma1

FILE2 TO ALLOW COPY TO FIND ANY
Sigma1

FOLLOWING UNRESOLVED PARAMETERS
Sigma1

VERS. 2005-1
(JUNE 2005)    *CORRECTED
ERROR IN EHOT3 EQUIVALENCE
Sigma1

TO EHOT - THIS ONLY EFFECTS VERY BIG  Sigma1

OUTPUT FILES.
Sigma1

VERS. 2007-1
(JAN. 2007)    *CHECKED
AGAINST ALL ENDF/B-VII.
Sigma1

*INCREASED PAGE SIZE FROM 60,000
Sigma1

TO 360,000 ENERGY POINTS.
Sigma1

Sigma1

Acknowledgement
2004
Sigma1

--------------------
Sigma1

Currently almost
all improvements to this code are based upon      Sigma1

feedback from
code users who report problems. This feedback
Sigma1

benefits ALL
users of this code, and ALL users are encouraged      Sigma1

to report
problems.
Sigma1

Sigma1

Improvements on
the 2004 version of this code based on user
Sigma1

feedback
including,
Sigma1

1) Bret Beck  - reported a problem at the
resolved/unresolved      Sigma1

energy boundary.
Sigma1

2) S. Ganesan -
reported a problem for small temperature changes.  Sigma1

Sigma1

OWNED,
MAINTAINED AND DISTRIBUTED BY
Sigma1

------------------------------------
Sigma1

THE NUCLEAR DATA
SECTION                                           Sigma1

INTERNATIONAL
ATOMIC ENERGY AGENCY
Sigma1

P.O. BOX
100
Sigma1

A-1400, VIENNA,
AUSTRIA
Sigma1

EUROPE
Sigma1

Sigma1

ORIGINALLY
WRITTEN BY
Sigma1

------------------------------------
Sigma1

DERMOTT E.
CULLEN
Sigma1

UNIVERSITY OF
CALIFORNIA
Sigma1

LAWRENCE
LIVERMORE NATIONAL LABORATORY
Sigma1

L-159
Sigma1

P.O. BOX
808
Sigma1

LIVERMORE, CA
94550
Sigma1

U.S.A.
Sigma1

TELEPHONE  925-423-7359
Sigma1

E. MAIL    [email-masked]
Sigma1

WEBSITE
HTTP://WWW.LLNL.GOV/CULLEN1
Sigma1

Sigma1

AUTHORS MESSAGE
Sigma1

---------------
Sigma1

THE REPORT
DESCRIBED ABOVE IS THE LATEST PUBLISHED DOCUMENTATION   Sigma1

FOR THIS
PROGRAM. HOWEVER, THE COMMENTS BELOW SHOULD BE CONSIDERED Sigma1

THE LATEST
DOCUMENTATION INCLUDING ALL RECENT IMPROVEMENTS. PLEASE Sigma1

READ ALL OF
THESE COMMENTS BEFORE IMPLEMENTATION, PARTICULARLY     Sigma1

THE COMMENTS
CONCERNING MACHINE DEPENDENT CODING.
Sigma1

Sigma1

AT THE PRESENT
TIME WE ARE ATTEMPTING TO DEVELOP A SET OF COMPUTER Sigma1

INDEPENDENT
PROGRAMS THAT CAN EASILY BE IMPLEMENTED ON ANY ONE     Sigma1

OF A WIDE
VARIETY OF COMPUTERS. IN ORDER TO ASSIST IN THIS PROJECT Sigma1

IT WOULD BE
APPECIATED IF YOU WOULD NOTIFY THE AUTHOR OF ANY
Sigma1

COMPILER
DIAGNOSTICS, OPERATING PROBLEMS OR SUGGESTIONS ON HOW TO  Sigma1

IMPROVE THIS
PROGRAM. HOPEFULLY, IN THIS WAY FUTURE VERSIONS OF    Sigma1

THIS PROGRAM
WILL BE COMPLETELY COMPATIBLE FOR USE ON YOUR
Sigma1

COMPUTER.
Sigma1

Sigma1

PURPOSE
Sigma1

-------
Sigma1

THIS PROGRAM IS
DESIGNED TO DOPPLER BROADEN NEUTRON INDUCED
Sigma1

CROSS SECTIONS.
EACH SECTION OF CROSS SECTIONS (FILE 3) IS READ    Sigma1

FROM THE ENDF/B
FORMAT. THE DATA IS DOPPLER BROADENED, THINNED     Sigma1

AND OUTPUT IN THE ENDF/B
FORMAT.
Sigma1

Sigma1

IN THE FOLLOWING
DISCUSSION FOR SIMPLICITY THE ENDF/B TERMINOLOGY  Sigma1

---ENDF/B
TAPE---WILL BE USED. IN FACT THE ACTUAL MEDIUM MAY BE    Sigma1

TAPE, CARDS,
DISK OR ANY OTHER MEDIUM.
Sigma1

Sigma1

ENDF/B
FORMAT                                                      Sigma1

-------------
Sigma1

THIS PROGRAM
ONLY USES THE ENDF/B BCD OR CARD IMAGE FORMAT (AS     Sigma1

OPPOSED TO THE
BINARY FORMAT) AND CAN HANDLE DATA IN ANY VERSION   Sigma1

OF THE ENDF/B
FORMAT (I.E., ENDF/B-I, II, III, IV OR V FORMAT).    Sigma1

Sigma1

IT IS ASSUMED
THAT THE DATA IS CORRECTLY CODED IN THE ENDF/B
Sigma1

FORMAT AND NO
ERROR CHECKING IS PERFORMED. IN PARTICULAR IT IS     Sigma1

ASSUMED THAT THE
MAT, MF AND MT ON EACH CARD IS CORRECT. SEQUENCE  Sigma1

NUMBERS (COLUMNS
76-80) ARE IGNORED ON INPUT, BUT WILL BE
Sigma1

CORRECTLY OUTPUT
ON ALL CARDS. THE FORMAT OF SECTION MF=1, MT=451  Sigma1

AND ALL SECTIONS
OF MF=3 MUST BE CORRECT. THE PROGRAM COPIES ALL   Sigma1

OTHER SECTION OF
DATA AS HOLLERITH AND AS SUCH IS INSENSITIVE TO   Sigma1

THE CORRECTNESS
OR INCORRECTNESS OF ALL OTHER SECTIONS.
Sigma1

Sigma1

ALL CROSS
SECTIONS THAT ARE USED BY THIS PROGRAM MUST BE TABULATED Sigma1

AND LINEARLY
INTERPOLABLE IN ENERGY AND CROSS SECTION (ENDF/B      Sigma1

INTERPOLATION
LAW 2). FILE 3 CROSS SECTIONS MAY BE MADE LINEARLY   Sigma1

INTERPOLABLE BY
USING PROGRAM LINEAR (UCRL-50400, VOL.17, PART A). Sigma1

FILE 2 RESONANCE
PARAMETERS MAY BE USED TO RECONSTRUCT ENERGY      Sigma1

DEPENDENT CROSS
SECTIONS AND ADD IN FILE 3 BACKGROUND CROSS
Sigma1

SECTIONS TO
DEFINE LINEARLY INTERPOLABLE CROSS SECTIONS BY USING   Sigma1

PROGRAM RECENT
(UCRL-50400, VOL. 17, PART C). IF THIS PROGRAM      Sigma1

FINDS THAT THE
FILE 3 CROSS SECTIONS ARE NOT LINEARLY INTERPOLABLE Sigma1

THIS PROGRAM
WILL TERMINATE EXECUTION.
Sigma1

Sigma1

UNRESOLVED
RESONANCE REGION
Sigma1

---------------------------
Sigma1

IN THE
UNRESOLVED RESONANCE REGION IT IS NOT POSSIBLE TO EXACTLY   Sigma1

DEFINE THE
ENERGY DEPENDENCE OF THE CROSS SECTIONS. THE AVERAGE    Sigma1

WIDTHS AND
SPACINGS GIVEN IN ENDF/B ARE ONLY ADEQUATE TO DEFINE    Sigma1

AVERAGE VALUES
OF THE CROSS SECTIONS. THEREFORE ALL CROSS SECTIONS Sigma1

IN THE ENDF/B
FORMAT FOR THE UNRESOLVED REGION ARE REALLY AVERAGE  Sigma1

VALUES WHICH
CANNOT BE DOPPLER BROADENED USING THE SIGMA1 METHOD   Sigma1

(WHICH REQUIRES
TABULATED, LINEARLY INTERPOLABLE, ENERGY DEPENDENT Sigma1

CROSS
SECTIONS.
Sigma1

Sigma1

THEREFORE,
Sigma1

(1) ALL
TABULATED POINTS WITHIN THE UNRESOLVED RESONANCE REGION    Sigma1

WILL BE COPIED,
WITHOUT MODIFICATION OR BROADENING. ADOPTION OF    Sigma1

THIS CONVENTION
WILL ALLOW SUBSEQUENT PROGRAMS TO PROPERLY DEFINE  Sigma1

SELF-SHIELDED,
DOPPLER BROADENED CROSS SECTIONS IN THE UNRESOLVED  Sigma1

RESONANCE
REGION.
Sigma1

(2) CROSS
SECTIONS WILL BE EXTENDED AS 1/V ABOVE THE UPPER ENERGY  Sigma1

LIMIT OF THE
RESOLVED RESONANCE REGION AND BELOW THE LOWER ENERGY  Sigma1

LIMIT OF THE
CONTINUUUM REGION (I.E. INTO THE UNRESOLVED
Sigma1

RESONANCE
REGION). THIS CONVENTION WILL GUARANTEE A SMOOTH
Sigma1

BEHAVIOR CLOSE
TO THE UNRESOLVED RESONANCE REGION BOUNDARIES.      Sigma1

Sigma1

OUTPUT
FORMAT
Sigma1

-------------
Sigma1

IN THIS VERSION
OF SIGMA1 ALL FILE 3 ENERGIES WILL BE OUTPUT IN    Sigma1

F (INSTEAD OF E)
FORMAT IN ORDER TO ALLOW ENERGIES TO BE WRITTEN   Sigma1

WITH UP TO 9
DIGITS OF ACCURACY. IN PREVIOUS VERSIONS THIS WAS AN  Sigma1

OUTPUT OPTION.
HOWEVER USE OF THIS OPTION TO COMPARE THE RESULTS   Sigma1

OF ENERGIES
WRITTEN IN THE NORMAL ENDF/B CONVENTION OF 6 DIGITS    Sigma1

TO THE 9 DIGIT
OUTPUT FROM THIS PROGRAM DEMONSTRATED THAT FAILURE  Sigma1

TO USE THE 9
DIGIT OUTPUT CAN LEAD TO LARGE ERRORS IN THE DATA     Sigma1

JUST DUE TO
TRANSLATION OF THE ENERGIES TO THE ENDF/B FORMAT.      Sigma1

Sigma1

CONTENTS OF
OUTPUT
Sigma1

------------------
Sigma1

ENTIRE
EVALUATIONS ARE OUTPUT, NOT JUST THE BROADENED FILE 3
Sigma1

CROSS SECTIONS,
E.G. ANGULAR AND ENERGY DISTRIBUTIONS ARE ALSO     Sigma1

INCLUDED.
Sigma1

Sigma1

DOCUMENTATION
Sigma1

-------------
Sigma1

THE FACT THAT
THIS PROGRAM HAS OPERATED ON THE DATA IS DOCUMENTED  Sigma1

BY THE ADDITION
OF THREE COMMENTS CARDS AT THE END OF EACH
Sigma1

HOLLERITH
SECTION IN THE FORM
Sigma1

Sigma1

*****************
PROGRAM SIGMA1 (2007-1) ***************
Sigma1

DATA DOPPLER
BROADENED TO 300.0   KELVIN
AND
Sigma1

DATA THINNED TO
WITHIN AN ACCURACY OF  0.1
PER-CENT
Sigma1

Sigma1

THE ORDER OF ALL
SIMILAR COMMENTS (FROM LINEAR,RECENT AND GROUPY)  Sigma1

REPRESENTS A
COMPLETE HISTORY OF ALL OPERATIONS PERFORMED ON
Sigma1

THE DATA.
Sigma1

Sigma1

THESE COMMENT
CARDS ARE ONLY ADDED TO EXISTING HOLLERITH SECTIONS, Sigma1

I.E., THIS
PROGRAM WILL NOT CREATE A HOLLERITH SECTION. THE FORMAT Sigma1

OF THE HOLLERITH
SECTION IN ENDF/B-V DIFFERS FROM THE THAT OF      Sigma1

EARLIER VERSIONS
OF ENDF/B. BY READING AN EXISTING MF=1, MT=451    Sigma1

IT IS POSSIBLE
FOR THIS PROGRAM TO DETERMINE WHICH VERSION OF      Sigma1

THE ENDF/B
FORMAT THE DATA IS IN. WITHOUT HAVING A SECTION OF      Sigma1

MF=1, MT=451
PRESENT IT IS IMPOSSIBLE FOR THIS PROGRAM TO
Sigma1

DETERMINE WHICH
VERSION OF THE ENDF/B FORMAT THE DATA IS IN, AND   Sigma1

AS SUCH IT IS
IMPOSSIBLE FOR THE PROGRAM TO DETERMINE WHAT FORMAT  Sigma1

SHOULD BE USED
TO CREATE A HOLLERITH SECTION.
Sigma1

Sigma1

REACTION
INDEX
Sigma1

--------------
Sigma1

THIS PROGRAM
DOES NOT USE THE REACTION INDEX WHICH IS GIVEN IN     Sigma1

SECTION MF=1,
MT=451 OF EACH EVALUATION.
Sigma1

Sigma1

THIS PROGRAM
DOES NOT UPDATE THE REACTION INDEX IN MF=1, MT=451.   Sigma1

THIS CONVENTION HAS BEEN ADOPTED BECAUSE
MOST USERS DO NOT
Sigma1

REQUIRE A
CORRECT REACTION INDEX FOR THEIR APPLICATIONS AND IT WAS Sigma1

NOT CONSIDERED
WORTHWHILE TO INCLUDE THE OVERHEAD OF CONSTRUCTING  Sigma1

A CORRECT
REACTION INDEX IN THIS PROGRAM. HOWEVER, IF YOU REQUIRE  Sigma1

A REACTION INDEX
FOR YOUR APPLICATIONS, AFTER RUNNING THIS PROGRAM Sigma1

YOU MAY USE
PROGRAM DICTIN TO CREATE A CORRECT REACTION INDEX.     Sigma1

Sigma1

SECTION
SIZE
Sigma1

------------
Sigma1

SINCE THIS
PROGRAM USES A LOGICAL PAGING SYSTEM THERE IS NO LIMIT  Sigma1

TO THE NUMBER OF
POINTS IN ANY SECTION, E.G., THE TOTAL CROSS      Sigma1

SECTION MAY BE
REPRESENTED BY 200,000 DATA POINTS.
Sigma1

Sigma1

SELECTION OF
DATA
Sigma1

-----------------
Sigma1

THE PROGRAM
SELECTS MATERIALS TO BE BROADENED BASED EITHER ON      Sigma1

MAT (ENDF/B MAT
NO.) OR ZA. THE PROGRAM ALLOWS UP TO 100 MAT OR    Sigma1

ZA RANGES TO BE
SPECIFIED. THE PROGRAM WILL ASSUME THAT THE
Sigma1

ENDF/B TAPE IS
IN EITHER MAT OR ZA ORDER, WHICHEVER CRITERIA IS    Sigma1

USED TO SELECT
MATERIALS, AND WILL TERMINATE WHEN A MAT OR ZA      Sigma1

IS FOUND THAT IS
ABOVE THE RANGE OF ALL REQUESTS.
Sigma1

Sigma1

ENERGY GRID OF
BROADENED DATA
Sigma1

-----------------------------
Sigma1

THE ENERGY GRID
FOR THE DOPPLER BROADENED CROSS SECTIONS IS
Sigma1

SELECTED TO INSURE THAT THE
BROADENED DATA IS LINEAR-LINEAR
Sigma1

INTERPOLABLE. AS
SUCH THE ENERGY GRID FOR THE BROADENED DATA
Sigma1

MAY NOT BE THE
SAME AS THE ENERGY GRID FOR THE ORIGINAL
Sigma1

UNBROADENED
DATA. GENERALLY AFTER BROADENING THERE WILL BE
Sigma1

FEWER DATA
POINTS IN THE RESONANCE REGION, BUT AT LOW ENERGY
Sigma1

THERE MAY BE
MORE POINTS, DUE TO THE 1/V LOW ENERGY EFFECT
Sigma1

CREATED BY
DOPPLER BROADENING.
Sigma1

Sigma1

EFFECTIVE
TEMERATURE INCREASE
Sigma1

-----------------------------
Sigma1

IF THE ORIGINAL
DATA IS NOT AT ZERO KELVIN THE PROGRAM WILL
Sigma1

BROADEN THE DATA
BY THE EFFECTIVE TEMPERATURE DIFFENCE TO THE      Sigma1

FINAL
TEMPERATURE. IF THE DATA IS ALREADY AT A TEMPERATURE THAT    Sigma1

IS HIGHER THAN
THE FINAL TEMPERATURE DOPPLER BROADENING IS
Sigma1

NATURALLY NOT
PERFORMED AND THE TEMPERATURE IN THE SECTION IS LEFT Sigma1

AT ITS ORIGINAL
VALUE.
Sigma1

Sigma1

MULTIPLE FINAL
TEMPERATURES
Sigma1

---------------------------
Sigma1

THE PRESENT
VERSION ONLY DOPPLER BROADENS TO ONE FINAL TEMPERATURE Sigma1

(IF THERE IS
SUFFICIENT INTEREST EXPRESSED BY USERS FUTURE
Sigma1

VERSION MAY
BROADEN TO MULTIPLE TEMPERATURES. PLEASE
Sigma1

CONTACT THE
AUTHOR IF YOU ARE INTERESTED IN A MULTIPLE
Sigma1

TEMPERATURE
OPTION).
Sigma1

Sigma1

PROGRAM OPERATION
Sigma1

-----------------
Sigma1

EACH SECTION OF
FILE 3 DATA IS CONSIDERED SEPERATELY. THE DATA     Sigma1

IS READ AND
DOPPLER BROADENED A PAGE AT A TIME (ONE PAGE IS
Sigma1

60000 DATA
POINTS). UP TO THREE PAGES OF DATA MAY BE IN THE CORE   Sigma1

AT ANY GIVEN
TIME, THE PAGE BEING BROADENED, THE PAGE BELOW IT     Sigma1

IN ENERGY AND THE
PAGE ABOVE IT IN ENERGY. AFTER A PAGE HAS BEEN   Sigma1

BROADENED IT IS
THINNED, IF THE ENTIRE SECTION CONTAINS ONLY
Sigma1

ONE PAGE OR
LESS, IT WILL STILL BE CORE RESIDENT AND WILL BE
Sigma1

WRITTEN DIRECTLY
FROM CORE TO THE OUTPUT TAPE. IF THE BROADENED,   Sigma1

THINNED SECTION
IS LARGER THAN A PAGE, AFTER A PAGE HAS BEEN
Sigma1

BROADENED AND
THINNED IT IS WRITTEN TO A SCRATCH FILE. AFTER THE   Sigma1

ENTIRE SECTION
HAS BEEN BROADENED AND THINNED THE DATA IS READ     Sigma1

FROM SCRATCH TO
CORE, ONE PAGE AT A TIME, THE OUTPUT TO THE OUTPUT Sigma1

TAPE.
Sigma1

Sigma1

ALLOWABLE
ERROR
Sigma1

---------------
Sigma1

AFTER DOPPLER
BROADENING THE CROSS SECTION IN THE RESONANCE REGION Sigma1

WILL GENERALLY
BE MUCH SMOOTHER THAN THE UNBROADENED DATA AND CAN  Sigma1

BE REPRESENTED
TO THE SAME ACCURACY BY A SMALLER NUMBER OF ENERGY  Sigma1

POINTS.
THEREFORE AFTER DOPPLER BROADENING THE DATA CAN BE THINNED Sigma1

WITH ESSENTIALLY
NO LOSE OF INFORMATION.
Sigma1

Sigma1

THE ALLOWABLE
ERROR MAY BE ENERGY INDEPENDENT (CONSTANT) OR ENERGY Sigma1

DEPENDENT. THE
ALLOWABLE ERROR IS DESCRIBED BY A TABULATED
Sigma1

FUNCTION OF UP
TO 20 (ENERGY,ERROR) PAIRS AND LINEAR INTERPOLATION Sigma1

BETWEEN
TABULATED POINTS. IF ONLY ONE TABULATED POINT IS GIVEN THE Sigma1

ERROR WILL BE
CONSIDERED CONSTANT OVER THE ENTIRE ENERGY RANGE.    Sigma1

WITH THIS ENERGY
DEPENDENT ERROR ONE MAY OPTIMIZE THE OUTPUT FOR   Sigma1

ANY GIVEN
APPLICATION BY USING A SMALL ERROR IN THE ENERGY RANGE   Sigma1

OF INTEREST AND
A LESS STRINGENT ERROR IN OTHER ENERGY RANGES.     Sigma1

Sigma1

INPUT FILES
Sigma1

-----------
Sigma1

UNIT  DESCRIPTION
Sigma1

----  -----------
Sigma1

2  INPUT CARDS (BCD - 80
CHARACTERS/RECORD)
Sigma1

10  ORIGINAL ENDF/B DATA (BCD
- 80 CHARACTERS/RECORD)
Sigma1

Sigma1

OUTPUT
FILES
Sigma1

------------
Sigma1

UNIT  DESCRIPTION
Sigma1

----  -----------
Sigma1

3  OUTPUT REPORT (BCD - 120
CHARACTERS/RECORD)
Sigma1

11  FINAL ENDF/B DATA (BCD -
80 CHARACTERS/RECORD)
Sigma1

Sigma1

SCRATCH
FILES
Sigma1

-------------
Sigma1

UNIT  DESCRIPTION
Sigma1

----  -----------
Sigma1

12  SCRATCH FILE FOR
BROADENED DATA
Sigma1

(BINARY - 180000 WORDS/RECORD - DOUBLE PRECISION/
Sigma1

42000
WORDS/RECORD - SINLGE PRECISION)
Sigma1

Sigma1

OPTIONAL
STANDARD FILE NAMES (SEE SUBROUTINE FILEIO)
Sigma1

----------------------------------------------------
Sigma1

UNIT  FILE NAME
Sigma1

----  ----------
Sigma1

2   SIGMA1.INP                                                   Sigma1

3   SIGMA1.LST
Sigma1

10   ENDFB.IN
Sigma1

11   ENDFB.OUT
Sigma1

12   (SCRATCH)
Sigma1

Sigma1

INPUT CARDS
Sigma1

-----------
Sigma1

CARD  COLS.  DESCRIPTION
Sigma1

----  -----  -----------
Sigma1

1   1-11  SELECTION CRITERIA (0=MAT, 1=ZA)
Sigma1

12-22  MONITOR MODE
SELECTOR
Sigma1

= 0 - NORMAL OPERATION
Sigma1

= 1 - MONITOR PROGRESS OF DOPPLER BROADENING OF DATA. Sigma1

EACH TIME A PAGE OF DATA POINTS IS WRITTEN TO   Sigma1

THE SCRATCH FILE PRINT OUT THE TOTAL NUMBER OF  Sigma1

POINTS ON SCRATCH AND THE LOWER AND UPPER
Sigma1

ENERGY LIMITS OF THE PAGE (THIS OPTION MAY BE   Sigma1

USED IN ORDER TO MONITOR THE EXECUTION SPEED    Sigma1

OF
LONG RUNNING JOBS).
Sigma1

23-33  KELVIN
TEMPERATURE
Sigma1

34-44  MINIMUM CROSS SECTION
OF INTEREST
Sigma1

(DEFAULT
VALUE = 1.0E-10 BARNS).
Sigma1

45-55  NEGATIVE CROSS SECTION
TREATMENT
Sigma1

= 0 - O.K. - NO CHANGE
Sigma1

= 1 - SET = 0
Sigma1

56-66  UNRESOLVED RESONANCE
REGION TREATMENT
Sigma1

= 0 - COPY (NO BROADENING)
Sigma1

= 1 - IGNORE (BROADEN)
Sigma1

2   1-60  ENDF/B INPUT DATA FILENAME
Sigma1

(STANDARD OPTION = ENDFB.IN)
Sigma1

3   1-60  ENDF/B OUTPUT DATA FILENAME
Sigma1

(STANDARD OPTION = ENDFB.OUT)
Sigma1

4-N   1-11  LOWER MAT OR ZA LIMIT
Sigma1

12-22  UPPER MAT OR ZA
LIMIT
Sigma1

UP TO 100 MAT OR ZA RANGES MAY BE SPECIFIED, ONE      Sigma1

RANGE PER CARD. THE LIST OF RANGES IS TERMINATED BY   Sigma1

A BLANK CARD. IF THE UPPER LIMIT IS LESS THAN THE     Sigma1

LOWER LIMIT THE UPPER LIMIT WILL BE SET EQUAL TO THE  Sigma1

LOWER LIMIT. IF THE FIRST REQUEST CARD IS BLANK IT    Sigma1

WILL TERMINATE THE LIST OF REQUESTS AND CAUSE ALL     Sigma1

DATA TO BE RETRIEVED (SEE EXAMPLE INPUT).
Sigma1

VARY  1-11  ENERGY FOR ERROR LAW
Sigma1

12-22  ERROR FOR ERROR
LAW
Sigma1

THE
ACCEPTABLE LINEARIZING ERROR CAN BE GIVEN AS AN   Sigma1

ENERGY DEPENDENT FUNCTION SPECIFIED BY UP TO 20
Sigma1

(ENERGY,ERROR) PAIRS AND LINEAR INTERPOLATION
Sigma1

TABULATE
POINTS. ENERGIES MUST BE IN ASCENDING ORDER. Sigma1

THE ERROR LAW IS TERMINATED BY A BLANK CARD. IF THE   Sigma1

FIRST ERROR LAW CARD IS BLANK IT WILL TERMINATE THE   Sigma1

ERROR LAW AND THE ERROR WILL BE TREATED AS ENERGY     Sigma1

INDEPENDENT, EQUAL TO ZERO, WHICH INDICATES THAT THE  Sigma1

BROADENED DATA SHOULD NOT BE THINNED.
Sigma1

Sigma1

EXAMPLE INPUT
NO. 1
Sigma1

-------------------
Sigma1

BROADEN ALL
URANIUM ISOTOPES AND THORIUM-232 TO 300 KELVIN. FROM   Sigma1

0 TO 100 EV THIN
OUTPUT DATA TO 0.1 PER-CENT ACCURACY. FROM 100 EV Sigma1

TO 1 KEV VARY
THE ERROR BETWEEN 0.1 AND 1 PER-CENT. ABOVE 1 KEV    Sigma1

USE 1 PER-CENT
ACCURACY.
Sigma1

Sigma1

EXPLICITLY
SPECIFY THE STANDARD FILENAMES.
Sigma1

Sigma1

THE FOLLOWING 11
CARDS ARE REQUIRED
Sigma1

Sigma1

1
0 3.00000+ 2
Sigma1

ENDFB.IN
Sigma1

ENDFB.OUT
Sigma1

92000      92999
Sigma1

90232
(UPPER LIMIT WILL AUTOMATICALLY BE DEFINED)   Sigma1

(BLANK CARD INDICATES END OF REQUEST LIST)    Sigma1

0.00000+ 0 1.00000-03
Sigma1

1.00000+ 2 1.00000-03
Sigma1

1.00000+ 3 1.00000-02
Sigma1

1.00000+ 9 1.00000-02
Sigma1

(BLANK
CARD INDICATES END OF ERROR LAW)
Sigma1

Sigma1

EXAMPLE INPUT
NO. 2
Sigma1

-------------------                                                Sigma1

BROADEN ALL DATA
TO 300 KELVIN AND DO NOT THIN THE BROADEN DATA.   Sigma1

ALL OF THE
STANDARD OPTION MAY BE INVOKED MERELY BY SPECIFYING     Sigma1

THE KELVIN
TEMPERATURE ON THE FIRST CARD. ALL OTHER FIELDS MAY     Sigma1

BE LEFT
BLANK.
Sigma1

Sigma1

LEAVE THE
DEFINITION OF THE FILENAMES BLANK - THE PROGRAM WILL     Sigma1

THEN USE
STANDARD FILENAMES.
Sigma1

Sigma1

THE FOLLOWING 5
CARDS ARE REQUIRED
Sigma1

Sigma1

3.00000+ 2
Sigma1

(USE STANDARD FILENAME = ENDFB.IN)
Sigma1

(USE STANDARD FILENAME = ENDFB.OUT)
Sigma1

(RETRIEVE ALL DATA, TERMINATE REQUEST LIST)      Sigma1

(0.0 ALLOWABLE ERROR, TERMINATE ERROR LAW)       Sigma1

Sigma1

EXAMPLE INPUT
NO. 3
Sigma1

-------------------
Sigma1

THE SAME AS
ABOVE, ONLY DEFINE THE MINIMUM CROSS SECTION OF
Sigma1

INTEREST TO BE
1.0E-30 BARNS (INSTEAD OF THE DEFAULT VALUE OF      Sigma1

1.0E-10).
Sigma1

Sigma1

READ ENDF/B DATA
FROM \ENDFB6\RECENT\ZA092238 AND WRITE ENDF/B     Sigma1

DATA TO
\ENDFB\SIGMA1\ZA092238
Sigma1

Sigma1

THE FOLLOWING 5
CARDS ARE REQUIRED
Sigma1

Sigma1

3.00000+ 2 1.00000-30
Sigma1

\ENDFB6\RECENT\ZA092238
Sigma1

\ENDFB6\SIGMA1\ZA092238
Sigma1

(RETRIEVE ALL DATA, TERMINATE REQUEST LIST)      Sigma1

(0.0 ALLOWABLE ERROR, TERMINATE ERROR LAW)
Sigma1

Sigma1

=======================================================================
Sigma1