=======================================================================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 CHANGEVIRGIN *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 feedbackVIRGIN *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 structureVIRGIN using SUBROUTINE GROPE is identical VIRGIN for GROUPIE and VIRGIN. VIRGIN *All floating point parameters changedVIRGIN 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 VERS. 2020-1 (Feb. 2020) *Identical to 2019-1. VIRGIN VERS. 2023-1 (Feb. 2023) *Decreasee page size from 1,500,000 VIRGIN TO 120,000 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 INTEGRALVIRGIN 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 MEVVIRGIN =-17 SAND-II 755 GROUPS..1.0D-5 eV TO 150 MEVVIRGIN =-18 SAND-II 765 GROUPS..1.0D-5 eV TO 200 MEVVIRGIN =-19 UKAEA 1102 GROUPS..1.0D-5 eV to 1 GeVVIRGIN 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 THISVIRGIN 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+00VIRGIN 3.00000+00 3.50000+00 4.00000+00 4.50000+00 5.00000+00 5.50000+00VIRGIN 6.00000+00 6.50000+00 7.00000+00 7.50000+00 8.00000+00 8.50000+00VIRGIN 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