======================================================================= 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 

                                                                         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    CULLEN1@LLNL.GOV                                        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 (2004-1) ***************          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.                                            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