======================================================================= Virgin
Virgin
PROGRAM VIRGIN Virgin
VERSION 76-1 (NOVEMBER 1976) Virgin
VERSION 84-1 (JUNE 1984) *DOUBLE PRECISION ENERGY Virgin
VERSION 86-1 (JANUARY 1986)*FORTRAN-77/H VERSION Virgin
VERSION 88-1 (JULY 1988) *OPTION...INTERNALLY DEFINE ALL I/O Virgin
FILE NAMES (SEE, SUBROUTINE FILEIO Virgin
FOR DETAILS). Virgin
*IMPROVED BASED ON USER COMMENTS. Virgin
VERSION 89-1 (JANUARY 1989)*PSYCHOANALYZED BY PROGRAM FREUD TO Virgin
INSURE PROGRAM WILL NOT DO ANYTHING Virgin
CRAZY. Virgin
*UPDATED TO USE NEW PROGRAM CONVERT Virgin
KEYWORDS. Virgin
*ADDED LIVERMORE CIVIC COMPILER Virgin
CONVENTIONS. Virgin
VERSION 92-1 (JANUARY 1992)*COMPLETE RE-WRITE Virgin
*OUTPUT IN PLOTTAB FORMAT Virgin
*UP TO 2000 THICKNESSES Virgin
*INCREASED INCORE PAGE SIZE TO 6000 Virgin
CROSS SECTION POINTS Virgin
*ADDED PHOTON CALCULATIONS Virgin
*ADDED BLACKBODY SPECTRUM Virgin
*ADDED MULTIPLE LAYERS Virgin
*ADDED SPATIALLY DEPENDENT DENSITY Virgin
*ADDED FORTRAN SAVE OPTION Virgin
*COMPLETELY CONSISTENT I/O ROUTINES - Virgin
TO MINIMIZE COMPUTER DEPENDENCE. Virgin
VERSION 92-2 (MAY 1992) *CORRECTED TO HANDLE MULTIGROUP CROSS Virgin
SECTIONS AS INPUT IN ENDF/B FORMAT. Virgin
VERSION 96-1 (JANUARY 1996) *COMPLETE RE-WRITE Virgin
*IMPROVED COMPUTER INDEPENDENCE Virgin
*ALL DOUBLE PRECISION Virgin
*ON SCREEN OUTPUT Virgin
*UNIFORM TREATMENT OF ENDF/B I/O Virgin
*IMPROVED OUTPUT PRECISION Virgin
*DEFINED SCRATCH FILE NAMES Virgin
VERSION 99-1 (MARCH 1999) *CORRECTED CHARACTER TO FLOATING Virgin
POINT READ FOR MORE DIGITS Virgin
*UPDATED TEST FOR ENDF/B FORMAT Virgin
VERSION BASED ON RECENT FORMAT CHANGE Virgin
*GENERAL IMPROVEMENTS BASED ON Virgin
USER FEEDBACK Virgin
VERS. 2000-1 (FEBRUARY 2000)*GENERAL IMPROVEMENTS BASED ON Virgin
USER FEEDBACK Virgin
VERS. 2002-1 (MAY 2002) *OPTIONAL INPUT PARAMETERS Virgin
VERS. 2004-1 (MARCH 2004) *ADDED INCLUDE FOR COMMON Virgin
*UP TO 2000 THICKNESSES Virgin
*INCREASED INCORE PAGE SIZE TO 60,000 Virgin
VERS. 2007-1 (JAN. 2007) *CHECKED AGAINST ALL ENDF/B-VII. Virgin
*INCREASED INCORE PAGE SIZE TO Virgin
240,000 FROM 60,000. Virgin
VERS. 2007-2 (DEC. 2007) *72 CHARACTER FILE NAME. Virgin
VERS. 2010-1 (Apr. 2010) *General update based on user feedback Virgin
*INCREASED INCORE PAGE SIZE TO Virgin
600,000 FROM 240,000. Virgin
VERS. 2012-1 (Aug. 2012) *Added CODENAME Virgin
*32 and 64 bit Compatible Virgin
*Added ERROR stop Virgin
VERS. 2015-1 (Jan. 2015) *Extended OUT9. Virgin
*Replaced ALL 3 way IF Statements. Virgin
*Generalized TART Group Structures. Virgin
*Generalized SAND-II Group Structures. Virgin
*Extended SAND-II to 60, 150, 200 MeV. Virgin
VERS. 2015-2 (Apr. 2015) *Changed ALL data to "D" instead of Virgin
"E" to insure it is REAL*8 and avoid Virgin
Truncation ERRORS. Virgin
VERS. 2017-1 (May 2017) *Added UKAEA 1102 Group Structure. Virgin
*Increased points to 3,000,000 Virgin
*Increased groupd to 30,000 Virgin
*Updated based on user feedback Virgin
*Defintion of built-in group structure Virgin
using SUBROUTINE GROPE is identical Virgin
for GROUPIE and VIRGIN. Virgin
*All floating point parameters changed Virgin
to character inout + IN9 conversion. Virgin
VERS. 2018-1 (Jan. 2018) *Decreased PAGE size from 3,000,000 Virgin
to 1,500,000 Virgin
*On-line output for ALL ENDERROR Virgin
VERS. 2019-1 (June 2019) *Additional Interpolation Law Tests Virgin
*Checked Maximum Tabulated Energy to Virgin
insure it is the same for all MTs - Virgin
if not, print WARNING messages. Virgin
Virgin
2015-2 Acknowledgment Virgin
===================== Virgin
I thank Andrej Trkov (NDS, IAEA) for finding the problem with Virgin
the "E" formatted DATA (this effected both VIRGIN and GROUPIE). Virgin
I also thank Andrej for overseeing the entire PREPRO project Virgin
at IAEA, Vienna; he is part of a truly International team who Virgin
worked together to produce PREPRO-2015-2, and to make it Virgin
available Internationally on-line for FREE to ALL users. Virgin
Virgin
OWNED, MAINTAINED AND DISTRIBUTED BY Virgin
------------------------------------ Virgin
THE NUCLEAR DATA SECTION Virgin
INTERNATIONAL ATOMIC ENERGY AGENCY Virgin
P.O. BOX 100 Virgin
A-1400, VIENNA, AUSTRIA Virgin
EUROPE Virgin
Virgin
ORIGINALLY WRITTEN BY Virgin
------------------------------------ Virgin
Dermott E. Cullen Virgin
Virgin
PRESENT CONTACT INFORMATION Virgin
--------------------------- Virgin
Dermott E. Cullen Virgin
1466 Hudson Way Virgin
Livermore, CA 94550 Virgin
U.S.A. Virgin
Telephone 925-443-1911 Virgin
E. Mail RedCullen1@Comcast.net Virgin
Website RedCullen1.net/HOMEPAGE.NEW Virgin
Virgin
PURPOSE Virgin
------- Virgin
THIS PROGRAM IS DESIGNED TO CALCULATE UNCOLLIDED (I.E. VIRGIN) Virgin
FLUX AND REACTIONS DUE TO TRANSMISSION OF A MONODIRECTIONAL Virgin
BEAM OF NEUTRONS THROUGH ANY THICKNESS OF MATERIAL. IN ORDER Virgin
TO SIMULATE AN EXPERIMENTAL MEASUREMENT THE RESULTS ARE GIVEN Virgin
AS INTEGRALS OVER ENERGY TALLY GROUPS (AS OPPOSED TO POINTWISE Virgin
IN ENERGY). BY TAKING THE RATIO OF REACTIONS TO FLUX IN EACH Virgin
GROUP AN EQUIVALENT SPATIALLY DEPENDENT GROUP AVERAGED CROSS Virgin
SECTION IS CALCULATED BY THE PROGRAM. Virgin
Virgin
EVALUATED DATA Virgin
-------------- Virgin
THE EVALUATED DATA MUST BE IN THE ENDF/B FORMAT. HOWEVER IT Virgin
MUST BE LINEAR-LINEAR INTERPOLABLE IN ENERGY-CROSS SECTION Virgin
BETWEEN TABULATED POINTS. SINCE ONLY CROSS SECTIONS (FILE 3 OR 23) Virgin
ARE USED, THIS PROGRAM WILL WORK ON ANY VERSION OF ENDF/B Virgin
(I.E. ENDF/B-I, II, III, IV, V OR VI). Virgin
Virgin
RELATED COMPUTER CODES Virgin
---------------------- Virgin
IN ORDER TO CONVERT ENDF/B DATA TO THE FORM REQUIRED BY THIS CODE Virgin
THE FOLLOWING COMPUTER CODES MAY BE USED, Virgin
Virgin
LINEAR - CONVERT FROM GENERAL ENDF/B INTERPOLATION TO LINEAR- Virgin
LINEAR INTERPOLATION. Virgin
RECENT - ADD THE RESONANCE CONTRIBUTION TO TABULATED BACKGROUND Virgin
CROSS SECTIONS TO OBTAIN LINEAR-LINEAR INTERPOLABLE Virgin
RESULTS. Virgin
SIGMA1 - DOPPLER BROADEN CROSS SECTION TO OBTAIN LINEAR-LINEAR Virgin
INTERPOLABLE RESULTS. Virgin
MIXER - MIX INDIVIDUAL MATERIALS TOGETHER TO DEFINE COMPOSITE Virgin
MIXTURES, E.G., COMBINE MATERIALS TO DEFINE STAINLESS Virgin
STELL. Virgin
Virgin
IN ORDER TO PLOT THE OUTPUT RESULTS OF THIS CODE USE PROGRAM Virgin
PLOTTAB. Virgin
Virgin
COPIES OF ANY OR ALL OF THESE CODES MAY BE OBTAINED FROM D.E. Virgin
CULLEN AT THE ABOVE ADDRESS. Virgin
Virgin
OUTPUT FORMAT Virgin
------------- Virgin
FOR ALL VERSIONS OF THIS PROGRAM PRIOR TO VERSION 92-1 OUTPUT WAS Virgin
IN TABULAR FORM. Virgin
Virgin
FOR VERSION 92-1 AND LATER VERSIONS OF THIS CODE ALL OUTPUT IS IN Virgin
THE PROGRAM PLOTTAB FORMAT TO ALLOW RESULTS TO BE EASILY PLOTTED. Virgin
FOR A COPY OF PROGRAM PLOTTAB CONTACT D.E. CULLEN AT THE ABOVE Virgin
ADDRESS. Virgin
Virgin
TALLY GROUPS Virgin
------------ Virgin
THE TALLY GROUP STRUCTURE MAY BE ANY SET OF MONONTONICALLY Virgin
INCREASING ENERGY BOUNDARIES. THERE MAY BE UP TO 2000 TALLY Virgin
GROUPS. BY USING THE INPUT PARAMETERS THE USER MAY SPECIFY ANY Virgin
ARBITRARY TALLY GROUP STRUCTURE OR SELECT ONE OF THE FOLLOWING Virgin
BUILT-IN GROUP STRUCTURES. Virgin
Virgin
(0) TART 175 GROUPS Virgin
(1) ORNL 50 GROUPS Virgin
(2) ORNL 126 GROUPS Virgin
(3) ORNL 171 GROUPS Virgin
(4) SAND-II 620 GROUPS - 1.0D-4 eV UP TO 18 MEV Virgin
(5) SAND-II 640 GROUPS - 1.0D-4 eV UP TO 20 MEV Virgin
(6) WIMS 69 GROUPS Virgin
(7) GAM-I 68 GROUPS Virgin
(8) GAM-II 99 GROUPS Virgin
(9) MUFT 54 GROUPS Virgin
(10) ABBN 28 GROUPS Virgin
(11) TART 616 GROUPS TO 20 MeV Virgin
(12) TART 700 GROUPS To 1 GeV Virgin
(13) SAND-II 665 GROUPS - 1.0D-5 eV UP TO 18 MEV Virgin
(14) SAND-II 685 GROUPS - 1.0D-5 eV UP TO 20 MEV Virgin
(15) TART 666 GROUPS TO 200 MeV Virgin
(16) SAND-II 725 GROUPS - 1.0D-5 eV UP TO 60 MEV Virgin
(17) SAND-II 755 GROUPS - 1.0D-5 eV UP TO 150 MEV Virgin
(18) SAND-II 765 GROUPS - 1.0D-5 eV UP TO 200 MEV Virgin
(19) UKAEA 1102 GROUPS - 1.0D-5 eV UP TO 1 GeV Virgin
Virgin
INCIDENT SPECTRUM Virgin
----------------- Virgin
THE INCIDENT SPECTRUM MAY BE ANY TABULATED FUNCTION THAT IS Virgin
GIVEN BY A SET OF POINTS THAT IS MONOTONICALLY INCREASING IN Virgin
ENERGY AND LINEAR-LINEAR INTERPOLABLE IN ENERGY-SPECTRUM Virgin
BETWEEN TABULATED POINTS. THERE IS NO LIMIT TO THE NUMBER OF Virgin
POINTS USED TO DESCRIBE THE SPECTRUM. THERE ARE FIVE BUILT-IN Virgin
OPTIONS FOR THE SPECTRUM. Virgin
Virgin
(1) CONSTANT...ENERGY INDEPENDENT (INPUT 0) Virgin
(2) 1/E (INPUT 1) Virgin
(3) BLACKBODY - PHOTON SPECTRUM Virgin
(4) BLACKBODY - ENERGY SPECTRUM (E TIMES THE PHOTON SPECTRUM) Virgin
(5) TRANSMITTED SPECTRUM FROM PREVIOUS CASE Virgin
Virgin
NORMALIZATION OF SPECTRUM Virgin
------------------------- Virgin
ANY INCIDENT SPECTRUM, EITHER READ AS INPUT OR ONE OF THE Virgin
BUILT-IN SPECTRA, WILL BE NORMALIZED TO UNITY WHEN INTEGRATED Virgin
OVER THEIR ENTIRE ENERGY RANGE. Virgin
Virgin
TRANSMITTED SPECTRA WILL NOT BE RE-NORMALIZED, SINCE IT ALREADY Virgin
INCLUDES THE NORMALIZATION OF THE INCIDENT SPECTRUM. Virgin
Virgin
NOTE, INCIDENT SPECTRA IS NORMALIZED TO UNITY OVER THEIR ENTIRE Virgin
ENERGY RANGE - NOT OVER THE ENERGY RANGE OF THE GROUPS. IF THE Virgin
ENERGY RANGE OF THE GROUPS IS LESS THAN THAT OF THE SPECTRUM Virgin
ONLY THAT PORTION OF THE SPECTRUM WILL BE USED AND THIS WILL Virgin
NOT BE RE-NORMALIZED TO UNITY. Virgin
Virgin
COMPOSITION OF A LAYER Virgin
---------------------- Virgin
YOU MAY RUN PROBLEMS INVOLVING Virgin
1) A LAYER OF UNIFORM DENSITY - DENSITY FOR ATTENUATION IS THAT Virgin
OF THE TOTAL. DENSITY FOR REACTIONS IS THAT OF THE REACTION. Virgin
2) A LAYER OF UNIFORM DENSITY - DENSITY IS THE SUM OF THE TOTAL Virgin
AND REACTION DENSITIES - THE SUM OF THE CROSS SECTIONS IS Virgin
USED FOR ATTENUATION AND REACTIONS. Virgin
3) A LAYER OF VARYING DENSITY BASED ON A UNIFORM TOTAL DENSITY Virgin
PLUS A VARIATION BETWEEN 0 AND A MAXIMUM BASED ON THE Virgin
REACTION DENSITY - 0 AT 0 THICKNESS AND MAXIMUM AT MAXIMUM Virgin
THICKNESS. IN THIS CASE THE AVERAGE REACTION DENSITY IS EQUAL Virgin
TO THE INPUT REACTION DENSITY. THE VARIATION IN REACTION Virgin
DENSITY CAN BE LINEAR, SQUARE OR CUBIC. Virgin
4) A LAYER OF VARYING DENSITY BASED ON A TOTAL DENSITY WHICH Virgin
VARYING FROM MAXIMUM AT 0 THICKNESS TO 0 AT MAXIMUM THICKNESS Virgin
PLUS A REACTION DENSITY WHICH VARIES FROM 0 AT 0 THICKNESS Virgin
TO MAXIMUM AT MAXIMUM THICKNESS. IN THIS CASE THE AVERAGE Virgin
DENSITY OF THE TOTAL AND REACTION WILL BOTH BE EQUAL TO THE Virgin
INPUT TOTAL AND REACTION DENSITIES. THE VARIATION IN TOTAL Virgin
AND REACTION DENSITY CAN BE LINEAR, SQUARE OR CUBIC. Virgin
Virgin
IN THE FIRST CASE THE TWO REQUESTED CROSS SECTIONS ARE CONSIDERED Virgin
TO BE INDEPENDENT - THE TOTAL CROSS SECTION IS USED TO CALCULATE Virgin
ATTENUATION AND THE REACTION CROSS SECTION IS USED TO CALCULATE Virgin
REACTIONS, E.G., TRANSMISSION THROUGH NATURAL URANIUM (THE TOTAL Virgin
CROSS SECTION SHOULD BE THAT OF NATURAL URANIUM) AND REACTIONS Virgin
IN A U-235 DETECTOR (THE REACTION CROSS SECTION SHOULD BE THAT OF Virgin
U-235). Virgin
Virgin
IN THE OTHER THREE CASES THE TWO REQUESTED CROSS SECTIONS ARE Virgin
TREATED AS TWO CONSTITUENTS OF A MIXTURE OF TWO MATERIALS AND Virgin
THE TWO CROSS SECTIONS ARE USED BOTH TO DEFINE A TOTAL CROSS Virgin
SECTION FOR ATTENUATION AND A REACTION CROSS SECTION TO DEFINE Virgin
REACTIONS. IN THESE CASES THE MIXTURE WILL VARY CONTINUOUSLY, Virgin
E.G., IN CASE 4) HALF WAY THROUGH THE LAYER THE COMPOSITION WILL Virgin
BE 1/2 THE MATERIAL DEFINED BY THE TOTAL AND 1/2 THE MATERIAL Virgin
BASED ON THE REACTION. IN THESE CASES RATHER THAN THINKING OF Virgin
THE TWO CROSS SECTIONS AS A TOTAL AND REACTION CROSS SECTION, Virgin
IT IS BETTER TO THINK OF THEM AS THE TOTAL CROSS SECTIONS FOR Virgin
MATERIALS A AND B AND THE CALCULATED REACTIONS WILL BE BASED Virgin
ON THESE TWO TOTAL CROSS SECTIONS. Virgin
Virgin
MULTIPLE LAYERS Virgin
--------------- Virgin
THIS CODE MAY BE USED TO RUN EITHER A NUMBER OF INDEPENDENT Virgin
PROBLEMS, EACH INVOLVING TRANSMISSION THROUGH A SINGLE LAYER OF Virgin
MATERIAL, OR TRANSMISSION THROUGH A NUMBER OF LAYERS ONE AFTER Virgin
THE OTHER. Virgin
Virgin
IN THE CASE OF MULTIPLE LAYERS, ONE LAYER AFTER ANOTHER, THE Virgin
TRANSMITTED ENERGY DEPENDENT SPECTRUM IS USED AS THE INCIDENT Virgin
SPECTRUM FOR THE NEXT LAYER. THERE IS NO LIMIT TO THE NUMBER Virgin
OF LAYERS WHICH MAY BE USED - EACH LAYER IS TREATED AS A Virgin
COMPLETELY INDEPENDENT PROBLEM WITH A DEFINED INCIDENT SOURCE, Virgin
AND AS SUCH THE CYCLE OF TRANSMISSION THROUGH EACH LAYER AND Virgin
USING THE TRANSMITTED SPECTRUM AS THE INCIDENT SPECTRUM FOR THE Virgin
NEXT LAYER MAY BE REPEATED ANY NUMBER OF TIMES. Virgin
Virgin
REMEMBER - THE INCIDENT SPECTRUM IS ASSUMED TO BE LINEARLY Virgin
INTERPOLABLE IN ENERGY AND SPECTRUM BETWEEN THE ENERGIES AT Virgin
WHICH IT IS TABULATED. THE TRANSMITTED SPECTRUM WILL BE TABULATED Virgin
AT THE UNION OF ALL ENERGIES OF THE INCIDENT SPECTRUM AND CROSS Virgin
SECTIONS (TOTAL AND REACTION). IN ORDER TO INSURE THE ACCURACY Virgin
OF THE RESULT WHEN PERFORMING MULTIPLE LAYER CALCULATION BE SURE Virgin
TO SPECIFY THE INCIDENT SPECTRUM ON THE FIRST LAYER TO SUFFICIENT Virgin
DETAIL (ENOUGH ENERGY POINTS CLOSELY SPACED TOGETHER) IN ORDER TO Virgin
ALLOW THE TRANSMITTED SPECTRUM TO BE ACCURATELY REPRESENTED BY Virgin
LINEAR INTERPOLATION BETWEEN SUCCESSIVE ENERGY POINTS - THERE IS Virgin
NO LIMIT TO THE NUMBER OF POINTS ALLOWED IN THE INCIDENT SPECTRUM, Virgin
SO IF YOU ARE IN DOUBT, SIMPLY USE MORE ENERGY POINTS TO SPECIFY Virgin
THE INCIDENT SPECTRUM. Virgin
Virgin
RESULT OUTPUT UNITS Virgin
------------------- Virgin
FLUX = EXACTLY AS CALCULATED Virgin
REACTIONS = 1/CM OR 1/GRAM Virgin
AVERAGE = 1/CM - MACROSCOPIC UNITS Virgin
CROSS Virgin
SECTION Virgin
Virgin
THICKNESS AND DENSITY Virgin
--------------------- Virgin
THE UNCOLLIDED CALCULATION ONLY DEPENDS ON THE PRODUCT OF Virgin
THICKNESS AND DENSITY (I.E. GRAMS PER CM SQUARED). THIS FACT Virgin
MAY BE USED TO SIMPLIFY INPUT BY ALLOWING THE THICKNESS AND Virgin
DENSITY TO BE GIVEN EITHER AS CM AND GRAMS/CC RESPECTIVELY Virgin
OR ELSE TO GIVE THICKNESS IN GRAMS/(CM*CM) AND INPUT A Virgin
DENSITY OF 1.0 - OR IN ANY OTHER CONVENIENT UNITS AS LONG AS Virgin
THE PRODUCT OF THICKNESS AND DENSITY IS IN THE CORRECT GRAMS Virgin
PER CENTIMETER SQUARED. Virgin
Virgin
GRAMS/(CM*CM) ARE RELATED TO ATOMS/BARN THROUGH THE RELATIONSHIP Virgin
Virgin
GRAMS/(CM*CM)=(ATOMS/BARN)*(GRAMS/MOLE)*(MOLE/ATOM) Virgin
Virgin
OR... Virgin
Virgin
GRAMS/(CM*CM)=(ATOMS/BARN)*(ATOMIC WEIGHT)/0.602 Virgin
Virgin
CROSS SECTIONS AT A SPACE POINT AND OPTICAL THICKNESS Virgin
----------------------------------------------------- Virgin
THIS PROGRAM ALLOWS LAYERS OF EITHER UNIFORM DENSITY OR Virgin
CONTINUOUSLY VARYING DENSITY. THE DENSITY CAN BE ONE OF THE Virgin
FOLLOWING FORMS, Virgin
1) C = UNIFORM DENSITY Virgin
2) C*2*(X/T) = LINEAR VARIATION FROM 0 TO C Virgin
3) C*(2-2*(X/T)) = LINEAR VARIATION FROM C TO 0 Virgin
4) C*3*(X/T)**2 = SQUARE VARIATION FROM 0 TO C Virgin
5) C*(3-3*(X/T)**2)/2 = SQUARE VARIATION FROM C TO 0 Virgin
6) C*4*(X/T)**3 = CUBIC VARIATION FROM 0 TO C Virgin
7) C*(4-4*(X/T)**3)/3 = CUBIC VARIATION FROM C TO 0 Virgin
Virgin
IN ORDER TO CALCULATE REACTIONS AT A POINT THE MICROSCOPIC Virgin
REACTION CROSS SECTION NEED MERELY BE SCALED BY THESE DENSITIES. Virgin
Virgin
IN ORDER TO CALCULATE TRANSMISSION WE MUST DEFINE THE OPTICAL Virgin
PATH LENGTH WHICH MAY BE DEFINED BY INTEGRATING EACH OF THE Virgin
ABOVE DENSITY FORMS TO FIND, Virgin
1) C*X Virgin
2) C*X*(X/T) Virgin
3) C*X*(2-(X/T)) Virgin
4) C*X*(X/T)**2 Virgin
5) C*X*(3-(X/T)**2)/2 Virgin
6) C*X*(X/T)**3 Virgin
7) C*X*(4-(X/T)**3))/3 Virgin
Virgin
IN ORDER TO CALCULATE TRANSMISSION TO A POINT THE MICROSCOPIC Virgin
TOTAL CROSS SECTION NEED MERELY BE SCALED BY THESE DENSITIES Virgin
TO DEFINE THE OPTICAL PATH LENGTH. Virgin
Virgin
THE VARIATION OF THE DENSITY THROUGH THE LAYER MAY BE DEFINED Virgin
BY SETTING X = 0 OR X = T TO FIND, Virgin
X = 0 X = T Virgin
----- ----- Virgin
1) C C Virgin
2) 0 2*C Virgin
3) 2*C 0 Virgin
4) 0 3*C Virgin
5) 3*C/2 0 Virgin
6) 0 4*C Virgin
7) 4*C/3 0 Virgin
Virgin
THE OPTICAL PATH THROUGH A LAYER OF THICKNESS T MAY BE DEFINED Virgin
FROM THE ABOVE EXPRESSIONS BY SETTING X=T TO FIND THAT IN ALL Virgin
CASES THE ANSWER WILL BY C*T. THE CONSTANTS IN THE ABOVE Virgin
EXPRESSIONS HAVE BEEN INTRODUCED IN ORDER TO FORCE THIS RESULT. Virgin
WITH THESE FACTORS THE OPTICAL PATH LENGTH THROUGH THE LAYER Virgin
WILL EXACTLY CORRESPOND TO AN AVERAGE DENSITY CORRESPONDING TO Virgin
THAT INPUT FOR THE TOTAL AND/OR REACTION, I.E., C CORRESPONDS Virgin
TO THE INPUT DENSITY. Virgin
Virgin
NOTE - FOR THE SAME OPTICAL PATH LENGTHS THROUGH THE LAYER THE Virgin
TRANSMISSION WILL BE EXACTLY THE SAME. HOWEVER, VARYING THE Virgin
DENSITY WILL ALLOW YOU TO MODIFY THE REACTION RATES AT SPECIFIC Virgin
DEPTHS INTO THE LAYER. Virgin
Virgin
COMPUTATION OF INTEGRALS Virgin
------------------------ Virgin
STARTING FROM TOTAL CROSS SECTIONS, REACTION CROSS SECTIONS AND Virgin
A SOURCE SPECTRUM ALL OF WHICH ARE GIVEN IN TABULAR FORM WITH Virgin
LINEAR INTERPOLATION BETWEEN TABULATED POINTS ALL REQUIRED Virgin
INTEGRALS CAN BE DEFINED BY ANALYTICAL EXPRESSIONS INVOLVING Virgin
NOTHING MORE COMPLICATED THAN EXPONENTIALS. THE INTEGRALS THAT Virgin
MUST BE EVALUATED ARE OF THE FORM... Virgin
Virgin
FLUX Virgin
---- Virgin
(INTEGRAL EK TO EK+1) (S(E)* EXP(-XCT(E)*Z)*DE) Virgin
Virgin
REACTIONS Virgin
--------- Virgin
(INTEGRAL EK TO EK+1) (S(E)*XCR(E)*EXP(-XCT(E)*Z)*DE) Virgin
Virgin
WHERE.. Virgin
EK TO EK+1 = LONGEST ENERGY INTERVAL OVER WHICH S(E), XCT(E) AND Virgin
XCR(E) ARE ALL LINEARLY INTERPOLABLE. Virgin
S(E) = ENERGY DEPENDENT WEIGHTING SPECTRUM Virgin
XCR(E) = REACTION CROSS SECTION Virgin
XCT(E) = OPTICAL PATH LENGTH (BASED ON TOTAL CROSS SECTION) Virgin
Z = MATERIAL THICKNESS Virgin
Virgin
S(E), XCR(E) AND XCT(E) ARE ALL ASSUMED TO BE GIVEN IN TABULAR Virgin
FORM WITH LINEAR INTERPOLATION USED BETWEEN TABULATED POINTS. Virgin
IN OTHER WORDS BETWEEN TABULATED POINTS EACH OF THESE THREE IS Virgin
DEFINED BY A FUNCTION OF THE FORM... Virgin
Virgin
F(E)=((E - EK)*FK+1 + (EK+1 - E)*FK)/(EK+1 - EK) Virgin
Virgin
EACH OF THESE THREE CAN BE CONVERTED TO NORMAL FORM BY THE Virgin
CHANGE OF VARIABLES.... Virgin
Virgin
X=(E - 0.5*(EK+1 + EK))/(EK+1 - EK) Virgin
Virgin
IN WHICH CASE X WILL VARY FROM -1 (AT EK) TO +1 (AT EK+1) AND Virgin
EACH FUNCTION REDUCES TO THE NORMAL FORM... Virgin
Virgin
F(X)=0.5*(FK*(1 - X) + FK+1*(1 + X)) Virgin
=0.5*(FK+1 + FK) + 0.5*(FK+1 - FK)*X Virgin
Virgin
BY DEFINING THE AVERAGE VALUE AND 1/2 THE CHANGE ACROSS THE Virgin
INTERVAL. Virgin
Virgin
AVF=0.5*(FK+1 + FK) Virgin
DF= 0.5*(FK+1 - FK) Virgin
DE= 0.5*(EK+1 - EK) Virgin
Virgin
EACH OF THE THREE FUNCTIONS REDUCES TO THE SIMPLE FORM... Virgin
Virgin
F(X)=AVF+DF*X Virgin
Virgin
AND THE TWO REQUIRED INTEGRALS REDUCE TO... Virgin
Virgin
FLUX Virgin
---- Virgin
DE*EXP(-AVXCT*Z) * (INTEGRAL -1 TO +1) Virgin
((AVS+DS*X)*EXP(-DXCT*Z*X)*DX) Virgin
Virgin
REACTION Virgin
-------- Virgin
DE*EXP(-AVXCT*Z) * (INTEGRAL -1 TO +1) Virgin
((AVS*AVXCR+(AVS*DXCR+AVXCR*DS)*X+DS*DXCR*X*X)*EXP(-DXCT*Z*X)*DX) Virgin
Virgin
WHERE Virgin
Virgin
AVXCT = AVERAGE VALUE OF THE TOTAL CROSS SECTION Virgin
AVXCR = AVERAGE VALUE OF THE REACTION CROSS SECTION Virgin
AVS = AVERAGE VALUE OF THE SOURCE Virgin
DXCT = 1/2 THE CHANGE IN THE TOTAL CROSS SECTION Virgin
DXCR = 1/2 THE CHANGE IN THE REACTION CROSS SECTION Virgin
DS = 1/2 THE CHANGE IN THE SOURCE Virgin
DE = 1/2 THE CHANGE IN THE ENERGY Virgin
Virgin
NOTE THAT IN THIS FORM THE ENERGY ONLY APPEARS IN FRONT OF THE Virgin
INTEGRALS AND THE INTEGRALS ARE EXPRESSED ONLY IN TERMS OF THE Virgin
TABULATED VALUES OF S(E), XCT(E) AND XCR(E). IN PARTICULAR NO Virgin
DERIVATIVES ARE USED, SO THAT THERE ARE NO NUMERICAL INSTABILITY Virgin
PROBLEMS IN THE VACINITY OF DISCONTINUITIES IN S(E), XCT(E) OR Virgin
XCR(E). INDEED, SINCE (EK+1 - EK) APPEARS IN FRONT OF THE INTEGRAL Virgin
POINTS OF DISCONTINUITY AUTOMATICALLY MAKE ZERO CONTRIBUTION TO Virgin
THE INTEGRALS. Virgin
Virgin
THE REQUIRED INTEGRALS CAN BE EXPRESSED IN TERMS OF THE THREE Virgin
INTEGRALS IN NORMAL FORM.... Virgin
Virgin
F(A,N) = (INTEGRAL -1 TO 1) (X**N*EXP(-A*X)*DX), N=0,1 AND 2. Virgin
Virgin
THESE THREE INTEGRALS CAN BE EVALUATED TO FIND... Virgin
Virgin
N=0 Virgin
--- Virgin
F(A,0) = (EXP(A)-EXP(-A))/A Virgin
Virgin
N=1 Virgin
--- Virgin
F(A,1) = ((1-A)*EXP(A)-(1+A)*EXP(-A))/(A*A) Virgin
Virgin
N=2 Virgin
--- Virgin
F(A,2) = ((2-2*A+A*A)*EXP(A)-(2+2*A+A*A)*EXP(-A))/(A*A*A) Virgin
Virgin
HOWEVER THESE EXPRESSIONS ARE NUMERICALLY UNSTABLE FOR SMALL Virgin
VALUES OF A. THEREFORE FOR SMALL A THE EXPONENTIAL IN THE Virgin
INTEGRALS ARE EXPANDED IN A POWER SERIES... Virgin
Virgin
EXP(-AX)=1.0-(AX)+(AX)**2/2-(AX)**3/6+(AX)**4/24-........ Virgin
=(SUM K=0 TO INFINITY) (-AX)**K/(K FACTORIAL) Virgin
Virgin
AND THE INTEGRAL REDUCES TO THE FORM.... Virgin
Virgin
(SUM K=0 TO INFINITY) ((-A)**K/(K FACTORIAL)) * Virgin
(INTEGRAL -1 TO 1) (X**(N+K))*DX Virgin
Virgin
WHICH CAN BE ANALYTICALLY EVAULATED TO FIND.... Virgin
(K(N) = K FACTORIAL) Virgin
Virgin
N=0 Virgin
--- Virgin
F(A,0) = 2*(1+(A**2)/K(3)+(A**4)/K(5)+(A**6)/K(7)+.... Virgin
Virgin
N=1 Virgin
--- Virgin
F(A,1) = -2*A*(2/K(3)+4*(A**2)/K(5)+6*(A**4)/K(7)+8*(A**6)/K(9)+.. Virgin
Virgin
N=2 Virgin
--- Virgin
F(A,2) = 2*(2/K(3)+3*4*(A**2)/K(5)+5*6*(A**4)/K(7)+ Virgin
7*8*(A**6)/K(9)+.... Virgin
Virgin
THESE EXPANSIONS ARE USED WHEN THE ABSOLUTE VALUE OF A IS LESS Virgin
THAN 0.1. BY TRUNCATING THE ABOVE SERIES BEFORE A**8 THE ERROR Virgin
RELATIVE TO THE LEADING TERM OF THE SERIES WILL BE 10**(-10), Virgin
YIELDING 10 DIGIT ACCURACY. Virgin
Virgin
AFTER EVALUATING THE ABOVE FUNCTIONS, EITHER DIRECTLY OR BY USING Virgin
THE EXPANSION THE TWO REQUIRED INTEGRALS CAN BE WRITTEN AS... Virgin
Virgin
FLUX Virgin
---- Virgin
DE*EXP(-AVXCT*Z)*(AVS*F(A,0) + DS*F(A,1)) Virgin
Virgin
REACTIONS Virgin
--------- Virgin
DE*EXP(-AVXCT*Z)* Virgin
(AVS*AVXCR*F(A,0) + (AVS*DXCR+AVXCR*DS)*F(A,1) + DS*DXCR*F(A,2)) Virgin
Virgin
INPUT FILES Virgin
----------- Virgin
FILENAME UNIT DESCRIPTION Virgin
-------- ---- ----------- Virgin
INPUT 2 INPUT LINES Virgin
ENDFIN 10 EVALUATED DATA IN ENDF/B FORMAT Virgin
Virgin
OUTPUT FILES Virgin
------------ Virgin
FILENAME UNIT DESCRIPTION Virgin
-------- ---- ----------- Virgin
OUTPUT 3 OUTPUT LISTING Virgin
Virgin
SCRATCH FILES Virgin
------------- Virgin
FILENAME UNIT DESCRIPTION Virgin
-------- ---- ----------- Virgin
SCR1 12 REACTION, FLUX AND CROSS SECTION RESULTS (BCD) Virgin
(SORTED AT END OF RUN AND OUTPUT SEPARATELY) Virgin
SCR2 13 TALLY GROUP ENERGY BOUNDARIES (BINARY) Virgin
SCR3 14 SOURCE SPECTRUM (BINARY) Virgin
SCR4 15 TOTAL CROSS SECTION (BINARY) Virgin
SCR5 16 REACTION CROSS SECTION (BINARY) Virgin
Virgin
OPTIONAL STANDARD FILE NAMES (SEE SUBROUTINE FILIO1 AND FILEIO2) Virgin
---------------------------------------------------------------- Virgin
UNIT FILE NAME FORMAT Virgin
---- ---------- ------ Virgin
2 VIRGIN.INP BCD Virgin
3 VIRGIN.LST BCD Virgin
10 ENDFB.IN BCD Virgin
11-15 (SCRATCH) BINARY Virgin
16 PLOTTAB.CUR PLOTTAB OUTPUT FORMAT DATA Virgin
Virgin
INPUT LINES Virgin
----------- Virgin
ANY NUMBER OF CASES MAY BE RUN ONE AFTER THE OTHER. AFTER THE Virgin
FIRST CASE HAS BEEN RUN THE FOLLOWING CASES MAY USE THE SAME Virgin
THICKNESSES, GROUP STRUCTURE AND SPECTRUM AS THE PRECEDING CASE. Virgin
IN ADDITION THE TRANSMITTED SPECTRUM FROM ONE CASE MAY BE USED Virgin
AS THE INCIDENT SPECTRUM IN THE NEXT CASE, TO ALLOW MULTIPLE Virgin
LAYERS OF DIFFERENT MATERIALS. Virgin
Virgin
LINE COLS. FORMAT DESCRIPTION Virgin
---- ----- ------ ---------- Virgin
1 1-60 ENDF/B INPUT DATA FILENAME Virgin
(STANDARD OPTION = ENDFB.IN) Virgin
Virgin
LEAVE THE DEFINITION OF THE FILENAMES BLANK - THE PROGRAM WILL Virgin
THEN USE STANDARD FILENAMES. Virgin
Virgin
2-3 1-72 18A4 TWO LINE TITLE DESCRIBING PROBLEM Virgin
4 1- 6 I6 ZA (1000*Z+A) OF TARGET FOR TOTAL Virgin
7-11 I5 MT OF TOTAL Virgin
12-22 E11.4 DENSITY FOR TOTAL Virgin
23-28 I6 ZA (1000*Z+A) OF TARGET FOR REACTION Virgin
29-33 I5 MT OF REACTION Virgin
= 0 - NO REACTION CALCULATION (ONLY FLUX). Virgin
= GREATER THAN 0 - CALCULATE REACTIONS. Virgin
34-44 E11.4 DENSITY FOR REACTION Virgin
45-50 I6 NUMBER OF TARGET THICKNESSES Virgin
= GREATER THAN 0 = READ FROM INPUT Virgin
(1 TO 2000 ALLOWED) Virgin
= 0 = SAME AS LAST CASE Virgin
51-55 I5 NUMBER OF TALLY GROUPS Virgin
(REMEMBER NUMBER OF GROUP BOUNDARIES Virgin
IS ONE MORE THAN THE NUMBER OF GROUPS) Virgin
UP TO 2000 GROUPS ARE ALLOWED Virgin
BUILT-IN GROUP STRUCTURES. Virgin
= GREATER THAN 0 = READ FROM INPUT Virgin
= 0 TART 175 GROUPS Virgin
= -1 ORNL 50 GROUPS Virgin
= -2 ORNL 126 GROUPS Virgin
= -3 ORNL 171 GROUPS Virgin
= -4 SAND-II 620 GROUPS..1.0D-4 eV TO 18 MEV Virgin
= -5 SAND-II 640 GROUPS..1.0D-4 eV TO 20 MEV Virgin
= -6 WIMS 69 GROUPS Virgin
= -7 GAM-I 68 GROUPS Virgin
= -8 GAM-II 99 GROUPS Virgin
= -9 MUFT 54 GROUPS Virgin
=-10 ABBN 28 GROUPS Virgin
=-11 TART 616 GROUPS TO 20 MeV Virgin
=-12 TART 700 GROUPS TO 1 GeV Virgin
=-13 SAND-II 665 GROUPS..1.0D-5 eV TO 18 MEV Virgin
=-14 SAND-II 685 GROUPS..1.0D-5 eV TO 20 MEV Virgin
=-15 TART 666 GROUPS TO 200 MeV Virgin
=-16 SAND-II 725 GROUPS..1.0D-5 eV TO 60 MEV Virgin
=-17 SAND-II 755 GROUPS..1.0D-5 eV TO 150 MEV Virgin
=-18 SAND-II 765 GROUPS..1.0D-5 eV TO 200 MEV Virgin
=-19 UKAEA 1102 GROUPS..1.0D-5 eV to 1 GeV Virgin
56-60 I5 NUMBER OF POINTS IN SOURCE SPECTRUM Virgin
(MUST BE AT LEAST TWO POINTS) Virgin
= GREATER THAN 1 = READ FROM INPUT Virgin
= 0 = SAME AS LAST CASE Virgin
= -1 = CONSTANT (ENERGY INDEPENDENT) Virgin
= -2 = 1/E Virgin
= -3 = BLACKBODY - PHOTON SPECTRUM Virgin
= -4 = BLACKBODY - ENERGY SPECTRUM Virgin
= -5 = TRANSMITTED SPECTRUM FROM LAST CASE Virgin
NOTE, ALL SPECTRA, EXCEPT THE TRANSMITTED Virgin
SPECTRUM FROM THE LAST CASE, WILL BE Virgin
NORMALIZED SUCH THAT ITS INTEGRAL OVER Virgin
ENERGY WILL BE UNITY. Virgin
61-64 1X,3I1 SPATIALLY DEPENDENT OUTOUT Virgin
= 0 = NO Virgin
= 1 = YES Virgin
FOR THE 3 QUANTITIES Virgin
COLUMN 67 FLUX Virgin
68 REACTIONS Virgin
69 AVERAGE CROSS SECTION Virgin
65-65 I1 ENERGY DEPENDENT OUTOUT Virgin
= 0 = NONE Virgin
= 1 = INCIDENT SPECTRUM Virgin
= 2 = TRANSMITTED SPECTRUM Virgin
= 3 = INCIDENT REACTIONS Virgin
= 4 = TRANSMIITED REACTIONS Virgin
= 5 = TOTAL CROSS SECTION Virgin
= 6 = REACTION CROSS SECTION Virgin
5 1-11 E11.4 BLACKBODY TEMPERATURE IN eV Virgin
12-22 E11.4 FLUX NORMALIZATION Virgin
23-33 E11.4 REACTION NORMALIZATION Virgin
CALCULATIONS WILL BE BASED ON THE SPECTRUM Virgin
AND CROSS SECTIONS AS READ. AT OUTPUT THE Virgin
RESULTS WILL BE MULTIPLIED BY THESE Virgin
NORMALIZATION FACTORS. Virgin
34-44 I11 DENSITY PROFILE Virgin
= 0 - UNIFORM - BASED ON TOTAL DENSITY Virgin
= 1 - UNIFORM - TOTAL + REACTION DENSITY Virgin
= 2 - TOTAL + LINEAR REACTION Virgin
= 3 - LINEAR (TOTAL + REACTION) Virgin
= 4 - TOTAL + SQUARE REACTION Virgin
= 5 - SQUARE (TOTAL + REACTION) Virgin
= 6 - TOTAL + CUBIC REACTION Virgin
= 7 - CUBIC (TOTAL + REACTION) Virgin
6-N 1-66 6E11.4 TARGET THICKNESSES IN CM Virgin
IF SAME AS LAST CASE THIS SECTION IS NOT Virgin
INCLUDED IN THE INPUT. Virgin
VARY 1-66 6E11.4 TALLY GROUP ENERGY BOUNDARIES Virgin
(NUMBER OF BOUNDARIES IS ONE MORE THAN Virgin
THE NUMBER OF TALLY GROUPS) Virgin
IF THE STANDARD OPTION (-14 TO 0) IS Virgin
SELECTED THIS SECTION IS NOT INCLUDED Virgin
IN THE INPUT Virgin
VARY 1-66 6E11.4 SOURCE SPECTRUM IN ENERGY (eV)-SOURCE PAIRS Virgin
(MUST BE AT LEAST TWO POINTS) Virgin
IF STANDARD OPTION (-5 TO 0) IS SELECTED THIS Virgin
SECTION IS NOT INCLUDED IN THE INPUT Virgin
Virgin
ANY NUMBER OF CASES MAY BE RUN ONE AFTER ANOTHER. Virgin
Virgin
EXAMPLE INPUT NO. 1 Virgin
------------------- Virgin
CALCULATE THE UNCOLLIDED FLUX AND CAPTURE (MT=102) THROUGH Virgin
30 CM OF IRON (DENSITY 7.87 G/CC). TALLY THE RESULTS USING Virgin
THE TART 175 GROUP STRUCTURE. THE SOURCE WILL BE CONSTANT Virgin
FROM 1 KEV TO 20 MEV. USE THE STANDARD ENDF/B INPUT DATA Virgin
FILENAME. Virgin
Virgin
ENDFB.IN Virgin
IRON 0 TO 30 CM THICK. Virgin
CONSTANT SOURCE FROM 1 KEV TO 20 MEV. Virgin
26000 1 7.8700D+ 0 26000 102 7.8700D+ 0 2 0 2 1100 Virgin
0.0000D+ 0 1.0000D+ 0 1.0000D+ 0 0 0.0000D+00 Virgin
0.0000D+00 3.0000D+01 Virgin
1.0000D+03 1.0000D+00 2.0000D+07 1.0000D+00 Virgin
Virgin
EXAMPLE INPUT NO. 2 Virgin
------------------- Virgin
CALCULATE THE UNCOLLIDED PHOTON FLUX THROUGH A MIXTURE OF SILICON Virgin
AND IRON FOR 100 MEV PHOTONS INCIDENT. THE TRANSMISSION WILL BE Virgin
CALCULATED FOR 21 THICKNESSES VARYING BETWEEN 0 AND 1 CM. THERE Virgin
WILL BE ONLY 1 TALLY GROUP SPANNING A VERY NARROW ENERGY RANGE Virgin
NEAR 100 MEV, AND THE SOURCE SPECTRUM WILL BE CONSTANT OVER THE Virgin
SAME ENERGY RANGE. USE THE STANDARD ENDF/B INPUT DATA FILENAME Virgin
BY LEAVING THE FIRST INPUT LINE BLANK. Virgin
Virgin
(THIS IS A BLANK LINE TO USE THE STANDARD INPUT FILENAME) Virgin
100 MEV PHOTONS Virgin
SILICON + 5 % IRON Virgin
14000 521 2.30000+ 0 26000 521 1.15000- 1 21 1 2 1000 Virgin
0.00000+ 0 1.00000+ 0 1.00000+ 0 1 0.00000+00 Virgin
0.00000+00 5.00000-01 1.00000+00 1.50000+00 2.00000+00 2.50000+00 Virgin
3.00000+00 3.50000+00 4.00000+00 4.50000+00 5.00000+00 5.50000+00 Virgin
6.00000+00 6.50000+00 7.00000+00 7.50000+00 8.00000+00 8.50000+00 Virgin
9.00000+00 9.50000+00 1.00000+01 Virgin
9.99000+ 7 1.00100+ 8 Virgin
9.99000+ 7 1.00000+ 4 1.00100+ 8 1.00000+ 4 Virgin
Virgin
======================================================================= Virgin