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

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    [email-masked]
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-........
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=(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

--------  ----  -----------
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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

----  ----------  ------
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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

----  -----  ------  ----------
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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)
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= GREATER THAN 1 = READ FROM INPUT
Virgin

=  0 = SAME AS LAST CASE
Virgin

=
-1 = CONSTANT (ENERGY INDEPENDENT)
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= -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
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= 4 = TRANSMIITED REACTIONS
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=
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