=======================================================================
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
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
UNIVERSITY OF CALIFORNIA
Virgin
LAWRENCE LIVERMORE
NATIONAL LABORATORY
Virgin
L-159
Virgin
P.O. BOX 808 Virgin
LIVERMORE, CA
94550 Virgin
U.S.A.
Virgin
TELEPHONE 925-423-7359 Virgin
E. MAIL CULLEN1@LLNL.GOV Virgin
WEBSITE HTTP://WWW.LLNL.GOV/CULLEN1 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
(1) TART 175 GROUPS
(INPUT 0) Virgin
(2) ORNL 50 GROUPS (INPUT -1)
Virgin
(3) ORNL 126 GROUPS
(INPUT -2)
Virgin
(4) ORNL 171 GROUPS
(INPUT -3)
Virgin
(5) SAND-II 620
GROUPS...UP TO 18 MEV (INPUT -4) Virgin
(6) SAND-II 640
GROUPS...UP TO 20 MEV (INPUT -5) Virgin
(7) WIMS 69 GROUPS
(INPUT -6)
Virgin
(8) GAM-I 68 GROUPS
(INPUT -7)
Virgin
(9) GAM-II 99 GROUPS
(INPUT -8)
Virgin
(10) MUFT 54 GROUPS
(INPUT -9)
Virgin
(11) ABBN 28 GROUPS
(INPUT -10)
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
SAME AS LAST CASE
Virgin
= -1 TART 175 GROUPS Virgin
= -2 ORNL 50 GROUPS Virgin
= -3 ORNL 126 GROUPS Virgin
= -4 ORNL 171 GROUPS Virgin
= -5 SAND-II 620 GROUPS..UP TO 18 MEV. Virgin
= -6 SAND-II 640 GROUPS..UP TO 20 MEV. Virgin
= -7 WIMS 69 GROUPS Virgin
= -8 GAM-I 68 GROUPS Virgin
= -9 GAM-II 99 GROUPS Virgin
=-10 MUFT 54 GROUPS Virgin
=-11 ABBN 28 GROUPS 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 (-11 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 7.87000+ 0 26000 102 7.87000+ 0 2 0 2 1100
Virgin
0.00000+ 0 1.00000+
0 1.00000+ 0 0 0.00000+00 Virgin
0.00000+00
3.00000+01 Virgin
1.0000E+03
1.0000E+00 2.0000E+07 1.0000E+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