CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C This code now modified to run under Linux C (by Scott Dodelson, Oct'01) C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Changes (to run inder DEC unix f77): C ----------------------------------- C ir=1 -> ir=5 ... input unit number C iw=1 -> iw=6 ... output unit number C COMMON /check/ itime -> COMMON /checkcb/ itime C COMMON /time/ -> COMMON /ttime/ C output nuc123.dat -> new123.dat C C========================IDENTIFICATION DIVISION============================== PROGRAM new123 C----------LINKAGES. C CALLED BY - none C CALLS - [subroutine] help, setcom, setmod, run, output C----------REMARKS. C Control program - C Offers user the main menu and channels through to various options. C Implementation - C To run this program, new123.f must be linked with nuccom.f C (containing the computation subroutines), nucrat.f (with the C reaction rates), and newint.f (with an interface subroutine). C *THIS IS DONE THROUGH INCLUDE STATEMENTS AT THE END OF THIS PROGRAMME* C * so just use: f77 new123.f (or similar) * C This program has been written to be compatible with C ANSI FORTRAN-77 with the exception of the END DO statement C used to limit the number of statement labels. C Notes - C The program utilizes Wagoner's code as the core of the computational C routines. C Documentation - C Kawano, L., 1992, Fermilab preprint FERMILAB-PUB-92/04-A, C Kellogg Radiation Lab preprint OAP-714. C Copy - C Version 4.1 (December 1991) C----------PARAMETERS. PARAMETER (ir=5) !Input unit number (previous value = 1). PARAMETER (iw=6) !Output unit number (previous value = 1). PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (nnuc=26) !Number of nuclides in calculation. C----------COMMON AREAS. COMMON /recpr0/ reacpr !Reaction parameter values. COMMON /recpr/ iform,ii,jj,kk,ll,rev,q9 !Reaction parameter names. COMMON /rates/ f,r !Reaction rates. COMMON /compr0/ cy0,ct0,t9i0,t9f0,ytmin0,inc0 !Default comp parameters. COMMON /compr/ cy,ct,t9i,t9f,ytmin,inc !Computation parameters. COMMON /modpr0/ c0,cosmo0,xi0 !Default model parameters. COMMON /modpr/ g,tau,xnu,c,cosmo,xi !Model parameters. COMMON /varpr0/ dt0,eta0 !Default variationl params. COMMON /varpr/ dt1,eta1 !Variational parameters. COMMON /checkcb/ itime !Computation location. COMMON /runopt/ irun,isize,jsize !Run options. COMMON /outopt/ nout,outfile !Output option. C==========================DECLARATION DIVISION================================= C----------REACTION PARAMETERS FROM BLOCK DATA. REAL reacpr(nrec,8) !Reaction parameters. C----------REACTION PARAMETERS. INTEGER iform(nrec) !Reaction type code (1-11). INTEGER ii(nrec) !Incoming nuclide type (1-26). INTEGER jj(nrec) !Incoming light nuclide type (1-6). INTEGER kk(nrec) !Outgoing light nuclide type (1-6). INTEGER ll(nrec) !Outgoing nuclide type (1-26). REAL rev(nrec) !Reverse reaction coefficient. REAL q9(nrec) !Energy released in reaction. C----------REACTION RATES. REAL f(nrec) !Forward reaction rate coefficients. REAL r(nrec) !Reverse reaction rate coefficients. C----------DEFAULT COMPUTATION PARAMETERS. REAL cy0 !Default cy. REAL ct0 !Default ct. REAL t9i0 !Default t9i. REAL t9f0 !Default t9f. REAL ytmin0 !Default ytmin. INTEGER inc0 !Default accumulation increment. C----------COMPUTATIONAL PARAMETERS. REAL cy !Time step limiting constant on abundances. REAL ct !Time step limiting constant on temperature. REAL t9i !Initial temperature (in 10**9 K). REAL t9f !Final temperature (in 10**9 k). REAL ytmin !Smallest abundances allowed. INTEGER inc !Accumulation increment. C----------DEFAULT MODEL PARAMETERS. REAL c0(3) !Default c. REAL cosmo0 !Default cosmological constant. REAL xi0(3) !Default neutrino degeneracy parameters. C----------EARLY UNIVERSE MODEL PARAMETERS. REAL c(3) !c(1) is variation of gravitational constant. | !c(2) is neutron lifetime (sec). | !c(3) is number of neutrino species. REAL cosmo !Cosmological constant. REAL xi(3) !Neutrino degeneracy parameters. C----------DEFAULT VARIATIONAL PARAMETERS. REAL dt0 !Default initial time step. REAL eta0 !Default baryon-to-photon ratio. C----------VARIATIONAL PARAMETERS. REAL dt1 !Initial time step. REAL eta1 !Baryon-to-photon ratio. C----------COMPUTATION LOCATION. INTEGER itime !Time check. C----------RUN OPTION. INTEGER irun !Run network size. INTEGER isize !Number of nuclides in computation. INTEGER jsize !Number of reactions in computation. C----------OUTPUT FILE STATUS. INTEGER nout !Number of output requests. LOGICAL outfile !Indicates if output file used. C----------USER RESPONSE VARIABLES. INTEGER inum !Selection number. C===========================PROCEDURE DIVISION================================== C10--------OPEN FILES AND PRINT GREETING---------------------------------------- OPEN (unit=2, file='new123.dat', status='unknown') !Output file. itime = 1 !Time = beginning of program. CALL check !Check interface subroutine. WRITE (iw,1000) 1000 FORMAT (6(/), | 2(' ',4x,'NN',6x,'NN UU',6x,'UU',4x,8('C'),6x,'11',8x, | 6('2'),6x,6('3'),/), | 2(' ',4x,'NN',6x,'NN UU',6x,'UU CC',12x,'1111',6x, | '22',6x,'22 33',6x,'33',/), | 2(' ',4x,'NNNN NN UU',6x,'UU CC',14x,'11',14x, | '22',10x,'33',/), | 2(' ',4x,'NN NN NN UU',6x,'UU CC',14x,'11',12x, | '22',10x,'33',/), | 2(' ',4x,'NN NNNN UU',6x,'UU CC',14x,'11',10x, | '22',14x,'33',/), | 2(' ',4x,'NN',6x,'NN UU',6x,'UU CC',14x,'11',8x, | '22',8x,'33',6x,'33',/), | 2(' ',4x,'NN',6x,'NN ',10('U'),4x,8('C'),4x,6('1'),4x, | 10('2'),4x,6('3'),/),/, | ' ',26x,'MODIFIED APRIL 1994',///, | ' ','(Press to continue): ',$) C20--------INPUT INITIALIZATION INFORMATION AND PAUSE--------------------------- DO i = 1,nrec C..........READ IN REACTION PARAMETERS. iform(i) = int(reacpr(i,2))!Reaction type. ii(i) = int(reacpr(i,3))!Incoming nuclide type. jj(i) = int(reacpr(i,4))!Incoming nuclide type. kk(i) = int(reacpr(i,5))!Outgoing nuclide type. ll(i) = int(reacpr(i,6))!Outgoing nuclide type. rev(i) = reacpr(i,7) !Reverse reaction coefficient. q9(i) = reacpr(i,8) !Energy released. C..........INITIALIZE REACTION RATES. f(i) = 0. !Forward rate coeff. r(i) = 0. !Reverse rate coeff. C..........SET RUN OPTIONS TO DEFAULT. END DO irun = 1 !Do full run. isize = nnuc !Use all 26 nuclides. jsize = nrec !Use all 88 reactions. C..........SET OUTPUT OPTION TO DEFAULT. nout = 0 !No output requests. outfile = .false. !Output file not used. C..........SET VALUES TO DEFAULT. cy = cy0 !Time step limiting constant on abundances. ct = ct0 !Time step limiting constant on temperature. t9i = t9i0 !Initial temperature. t9f = t9f0 !Final temperature. ytmin = ytmin0 !Smallest abundances allowed. inc = inc0 !Accumulation increment. c(1) = c0(1) !Variation of gravitational constant. c(2) = c0(2) !Neutron lifetime. c(3) = c0(3) !Number of neutrino species. cosmo = cosmo0 !Cosmological constant. xi(1) = xi0(1) !Electron degeneracy parameter. xi(2) = xi0(2) !Muon degeneray parameter. xi(3) = xi0(3) !Tauon degeneracy parameter. dt1 = dt0 !Initial time step. eta1 = eta0 !Baryon-to-photon ratio. C..........ACCEPT RETURN TO CONTINUE. READ (ir,*) !Pause. C30--------PRINT MENU AND AWAIT RESPONSE---------------------------------------- C..........RETURN FROM LOOPING. 300 CONTINUE C..........DISPLAY MENU. WRITE (iw,3000) 3000 FORMAT (8(/), | ' ',32x,'MENU SELECTION',/, | ' ',32x,'---- ---------',//, | ' ',24x,'1. HELP',/, | ' ',24x,'2. SET COMPUTATION PARAMETERS',/, | ' ',24x,'3. SET MODEL PARAMETERS',/, | ' ',24x,'4. RUN',/, | ' ',24x,'5. OUTPUT',/, | ' ',24x,'6. EXIT',8(/), | ' ',24x,'Enter selection (1-6): ',$) C..........READ IN SELECTION NUMBER. READ (ir,3001) inum 3001 FORMAT(i1) C40--------BRANCH TO APPROPRIATE SECTION---------------------------------------- GO TO (410,420,430,440,450,460),inum GO TO 460 !Improper input or . 410 CONTINUE !Help section. CALL help GO TO 500 420 CONTINUE !Set computation parameters section. CALL setcom GO TO 500 430 CONTINUE !Set model parameters section. CALL setmod GO TO 500 440 CONTINUE !Run section. itime = 2 !Time = beginning of run section. CALL check !Check interface subroutine. CALL run itime = 9 !Time = end of run section. CALL check !Check interface subroutine. GO TO 500 450 CONTINUE !Output section. CALL output GO TO 500 460 CONTINUE !Exit section. IF (outfile) THEN CLOSE (unit=2,status='keep') !Close output file. ELSE CLOSE (unit=2,status='delete') !File not used - dispose. END IF itime = 10 !Time = end of program. CALL check !Check interface subroutine. STOP C50---------GO BACK TO MENU----------------------------------------------------- 500 CONTINUE GO TO 300 END C========================IDENTIFICATION DIVISION================================ SUBROUTINE help C----------LINKAGES. C CALLED BY - [program] nuc123 C CALLS - none C----------REMARKS. C Displays description and workings of the program. C----------PARAMETERS. PARAMETER (ir=5) !Input unit number (previous value = 1). PARAMETER (iw=6) !Output unit number (previous value = 1). C==========================DECLARATION DIVISION================================= C----------USER RESPONSE VARIABLES. INTEGER inum !Selection number. C===========================PROCEDURE DIVISION================================== C10--------PRINT HELP SELECTION------------------------------------------------- C..........RETURN FROM LOOPING. 100 CONTINUE C..........DISPLAY MENU. WRITE (iw,1000) 1000 FORMAT (8(/), | ' ',32x,'HELP SELECTION',/, | ' ',32x,'---- ---------',//, | ' ',24x,'1. INTRODUCTION',/, | ' ',24x,'2. SETTING UP A RUN',/, | ' ',24x,'3. RUNNING THE PROGRAM',/, | ' ',24x,'4. OUTPUT OPTIONS',/, | ' ',24x,'5. GENERAL METHOD OF COMPUTATION',/, | ' ',24x,'6. USING THE INTERFACE SUBROUTINE',/, | ' ',24x,'7. EXIT',7(/), | ' ',24x,'Enter selection (1-7): ',$) C..........READ IN SELECTION NUMBER. READ (ir,1001) inum 1001 FORMAT (i1) C20--------BRANCH TO APPROPRIATE SECTION---------------------------------------- GO TO (210,220,230,240,250,260,270),inum GO TO 270 !Improper input or . C21--------INTRODUCTION SECTION------------------------------------------------- 210 CONTINUE !Setting up a run section. WRITE (iw,2100) 2100 FORMAT (/, | ' ',31x,'INTRODUCTION',/, | ' ',31x,'------------',2(/), | ' ','Welcome to the wonderful world of primor', | 'dial nucleosynthesis. NUC123 is a ',/, | ' ','FORTRAN program designed to provide the ', | 'early universe researcher with the tools',/, | ' ','necessary for the investigation of primo', | 'rdial nucleosynthesis. Its menu-driven ',/, | ' ','interface allows the user to first set c', | 'omputation parameters (such as the time ',/, | ' ','step) and model parameters (such as the ', | 'neutron lifetime and number of neutri- ',/, | ' ','nos) before doing single runs or multipl', | 'e runs (in which desired model parame- ',/, | ' ','ters are varied over a desired range.) ', | 'After the run, the user can utilize the ',/, | ' ','menu to either produce an output file or', | ' to view the most recent run on the ',/, | ' ','screen. The program comes with an empty', | ' subroutine CHECK into which the user ',/, | ' ','may wish to put additional code to add t', | 'o the computation in an original manner.',10(/), | ' ','(Enter to go back to help menu): ',$) READ (ir,*) GO TO 300 C22--------SET UP RUN SECTION--------------------------------------------------- 220 CONTINUE !Setting up a run section. WRITE (iw,2200) 2200 FORMAT (/, | ' ',29x,'SETTING UP A RUN',/, | ' ',29x,'------- -- - ---',2(/), | ' ','I. Setting computation parameters. ',/, | ' ',' The accuracy of the computation and t', | 'he relevant temperature region can be ',/, | ' ',' set by the following parameters: ',/, | ' ',' A. Time step limiting constant 1 (d', | 'efault value of 0.03) ',/, | ' ',' B. Time step limiting constant 2 (d', | 'efault value of 0.003) ',/, | ' ',' C. Initial time step (default value', | ' of 10**-4) ',/, | ' ',' D. Initial temperature (default val', | 'ue of 10**2) ',/, | ' ',' This is the temperature at the be', | 'ginning of the run in units of 10**9 K ',/, | ' ',' E. Final temperature (default value', | ' of 10**-2) ',/, | ' ',' This is the termination temperatu', | 're of the run in units of 10**9 K ',/, | ' ',' F. Smallest abundances allowed (def', | 'ault value of 10**-25) ',/, | ' ',' Elemental abundances are not allo', | 'wed to drop below this value ',/, | ' ',' G. # of iterations for each accumula', | 'tion (default value of 300) ',/, | ' ',' This is the number of iterations ', | 'before values are put in an output array',6(/), | ' ','(Enter 1 to continue, to end): ',$) READ (ir,1001) inum IF (inum.eq.1) THEN WRITE (iw,2202) 2202 FORMAT (/, | ' ','II. Setting model parameters. ',/, | ' ',' Default values here give what is know', | 'n as the standard model with best guess ',/, | ' ',' figure on the neutron lifetime of 889', | '.1 seconds. Nonstandard scenarios can',/, | ' ',' be investigated by varying the follow', | 'ing parameters: ',/, | ' ',' A. The gravitational constant ',/, | ' ',' (The default value of one here gi', | 'ves the usual 6.6720e-8 dyne*cm**2/g**2)',/, | ' ',' B. Neutron life-time (default value', | ' of 889.1 seconds) ',/, | ' ',' C. Number of neutrino species (defa', | 'ult value of 3 light neutrinos) ',/, | ' ',' D. Final baryon-to-photon ratio (se', | 't to log(eta) = -9.5) ',/, | ' ',' E. Cosmological constant (default v', | 'alue of 0) ',/, | ' ',' F. Neutrino degeneracy parameters (', | 'default values all 0) ',/, | ' ',' There are 3 separate parameters f', | 'or the electron, muon, and tau neutrinos',11(/), | ' ','(Enter to go back to help menu): ',$) READ (ir,*) GO TO 300 ELSE GO TO 300 END IF !(inum.eq.1) C23--------RUN PROGRAM SECTION-------------------------------------------------- 230 CONTINUE !Running the program section. WRITE (iw,2300) 2300 FORMAT (/, | ' ',28x,'RUNNING THE PROGRAM',/, | ' ',28x,'------- --- -------',2(/), | ' ','I. Setting run speed. ',/, | ' ',' The code can be run at 3 different se', | 'ttings of speed. The running of the ',/, | ' ',' code can be speeded up by reducing th', | 'e number of nuclides and reactions. The',/, | ' ',' complete computation takes into accou', | 'nt the following nuclides: n, p, d, t, ',/, | ' ',' He3, He4, Li6, Li7, Be7, Li8, B8, Be9', | ',B10, B11, C11, B12, C12, N12, C13, N13,',/, | ' ',' C14, N14, O14, N15, O15, and O16. ',/, | ' ',' The given CPU percentages and abundan', | 'ce variations are with regard to a ',/, | ' ',' single run with all default parameter', | ' values. ',/, | ' ',' A. 26 nuclides, 88 reactions (defaul', | 't) ',/, | ' ',' nuclides from n to O16 ',/, | ' ',' B. 18 nuclides, 60 reactions ',/, | ' ',' nuclides from n to N12 ',/, | ' ',' (63% CPU time, variation = .1%) ',/, | ' ',' C. 9 nuclides, 25 reactions ',/, | ' ',' nuclides from n to Be7 ',/, | ' ',' (20% CPU time, variation = .5%) ',4(/), | ' ','(Enter 1 to continue, to end): ',$) READ (ir,1001) inum IF (inum.eq.1) THEN WRITE (iw,2302) 2302 FORMAT (/, | ' ','II. Do single run. ',/, | ' ',' A. Interactive. ',/, | ' ',' In an interactive session, the us', | 'er can readily input the computational ',/, | ' ',' and model parameters and begin th', | 'e computation process. The run itself ',/, | ' ',' is commenced when option 2, "GO",', | ' in the "RUN" section is requested. ',//, | ' ',' B. Batch. ',/, | ' ',' To run the program in a batch mod', | 'e, it must be altered slightly so that ',/, | ' ',' the I/O takes place with files in', | 'stead of a terminal. This is done by ',/, | ' ',' setting different values for the ', | 'input and output unit number parameters ',/, | ' ',' "ir" and "iw" and assigning them ', | 'to different files in NUC123. In the ',/, | ' ',' file assigned the "ir" unit numbe', | 'r, one must place the responses to the ',/, | ' ',' queries of the program. ',10(/), | ' ','(Enter 1 to continue, to end): ',$) READ (ir,1001) inum IF (inum.eq.1) THEN WRITE (iw,2304) 2304 FORMAT (/, | ' ','III. Do multiple runs. ',/, | ' ',' A wide range of early universe model', | 's can be covered by doing many runs ',/, | ' ',' while one or more parameters are var', | 'ied over a range of interest. The ',/, | ' ',' parameters that can be varied are th', | 'e following: ',/, | ' ',' A. Eta ', | ' - Logrithmic variation ',/, | ' ',' B. Gravitational constant ', | ' - Linear variation ',/, | ' ',' C. Neutron lifetime ', | ' - Linear variation ',/, | ' ',' D. Number of neutrino species ', | ' - Linear variation ',/, | ' ',' E. Cosmological constant ', | ' - Linear variation ',/, | ' ',' F. Neutrino degeneracy parameters ', | ' - Linear variation ',/, | ' ',' 1. Electron neutrino ',/, | ' ',' 2. Muon neutrino ',/, | ' ',' 3. Tauon neutrino ',/, | ' ',' At most 3 parameters can be varied. ', | ' The first parameter inputted will be ',/, | ' ',' will be varied in the outermost loop', | ' and the third parameter inputted will ',/, | ' ',' be varied in the innermost loop. ',7(/), | ' ','(Enter to go back to help menu): ',$) READ (ir,*) GO TO 300 ELSE GO TO 300 END IF !(inum.eq.1) ELSE GO TO 300 END IF !(inum.eq.1) C24--------OUTPUT OPTIONS SECTION----------------------------------------------- 240 CONTINUE !Output options section. WRITE (iw,2400) 2400 FORMAT (/, | ' ',30x,'OUTPUT OPTIONS',/, | ' ',30x,'------ -------',2(/), | ' ','I. Request output file. ',/, | ' ',' After a run, the user can request the', | ' program to put the resulting numbers ',/, | ' ',' into an output file. This can be don', | 'e as many times as desired and all the ',/, | ' ',' information will be put in one new fi', | 'le under the name of "NUC123.DAT." If ',/, | ' ',' there is no request during the entire', | ' running of the program, this file is ',/, | ' ',' not created. If an output file is re', | 'quested after a multiple run, only the ',/, | ' ',' information from the very last run wi', | 'll be given. The output file will give ',/, | ' ',' the computational and model parameter', | 's for each run and will contain the ',/, | ' ',' following information: ',/, | ' ',' A. Temperatures in decreasing order ',/, | ' ',' B. Abundances for n, p, d, t, He3, H', | 'e4, Li6, Li7, Be7, and Li8 & up ',/, | ' ',' (p and He4 are in mass fraction, ', | 'the rest in ratios to the p abundance) ',/, | ' ',' C. Time, time interval, chemical pot', | 'ential of the electron ',/, | ' ',' D. Energy densities for photons, ele', | 'ctrons, electron neutrinos, and baryons ',/, | ' ',' E. Baryon-to-photon ratio, expansion', | ' rate of the universe ',5(/), | ' ','(Enter 1 to continue, to end): ',$) READ (ir,1001) inum IF (inum.eq.1) THEN WRITE (iw,2402) 2402 FORMAT (/, | ' ','II. Request output on screen. ',/, | ' ',' Instead of waiting to print out an o', | 'utput file, the user can immediately ',/, | ' ',' access the results of the latest run', | ' by requesting the output on the ',/, | ' ',' screen. There are four screens on e', | 'ach of which are displayed the ',/, | ' ',' computational and model parameters a', | 'nd the temperature: ',/, | ' ',' A. Abundances for d, t, He3, He4, a', | 'nd Li7 ',/, | ' ',' (He4 in mass fraction, rest as a', | ' ratio with the p abundance) ',/, | ' ',' B. Abundances for n, p, Li6, Be7, a', | 'nd Li8 & up ',/, | ' ',' (p in mass fraction, rest as a r', | 'atio with the p abundance) ',/, | ' ',' C. Energy densities for photons, el', | 'ectrons, electron neutrinos, & baryons ',/, | ' ',' D. Time, time interval, chemical po', | 'tential of the electron, ',/, | ' ',' baryon-to-photon ratio, and expa', | 'nsion rate of the universe ',11(/), | ' ','(Enter to go back to help menu): ',$) READ (ir,*) GO TO 300 ELSE GO TO 300 END IF !(inum.eq.1) C25--------METHOD OF COMPUTATION SECTION---------------------------------------- 250 CONTINUE !General method of computation section. WRITE (iw,2500) 2500 FORMAT (/, | ' ',22x,'GENERAL METHOD OF COMPUTATION',/, | ' ',22x,'------- ------ -- -----------',2(/), | ' ','I. Time evolution algorithm. ',/, | ' ',' The program utilizes a 2-point Runge-', | 'Kutta scheme (located in subroutine ',/, | ' ',' DRIVER) to time-evolve the temperatur', | 'e, the quantity hv (the ratio of the ',/, | ' ',' baryon density to T**3), the chemical', | ' potential of the electron, and the ',/, | ' ',' nuclide abundances. In the 2-point R', | 'unge-Kutta routine, a variable v at time',/, | ' ',' t0 (= v0) is evolved to a time t1 by ', | 'adding to v0 the average of the ',/, | ' ',' derivatives evaluated at t0 and at t1', | ' multiplied by dt: ',/, | ' ',' v1 = v0 + 0.5(dvdt(t0)+dvdt(t1)) ',/, | ' ',' where dvdt(t1) is gotten by first fin', | 'ding v1'' = v0 + dvdt(t0). The ',/, | ' ',' derivatives of the nuclide abundances', | ' are first computed and these are used ',/, | ' ',' to find the derivatives of t9, hv, an', | 'd phie (this is done in subroutine ',/, | ' ',' DERIVS). To compute the time derivat', | 'ives of the nuclide abundances, a matrix',/, | ' ',' equation is set up (in subroutine SOL', | ') and is solved (in subroutine EQSLIN) ',/, | ' ',' by gaussian elimination utilizing imp', | 'licit differentiation. ',6(/), | ' ','(Enter 1 to continue, to end): ',$) READ (ir,1001) inum IF (inum.eq.1) THEN WRITE (iw,2502) 2502 FORMAT (/ | ' ','II. Hierarchy of Subroutines. ',/, | ' ',' NUC123 ', | ' Main program (main menu) ',/, | ' ',' HELP ', | ' Help option ',/, | ' ',' SETCOM ', | ' Set computational parameters',/, | ' ',' SETMOD ', | ' Set model parameters ',/, | ' ',' RUN ', | ' Run computation code ',/, | ' ',' DRIVER ', | ' Main routine (Runge-Kutta loop) ',/, | ' ',' START ', | ' Initialization routine ',/, | ' ',' RATE0 ', | ' Computes weak decay rates ',/, | ' ',' DERIVS ', | ' Computes time derivatives ',/, | ' ',' THERM ', | ' Computes energy densities ',/, | ' ',' BESSEL ', | ' Gives functions of Kn ',/, | ' ',' KNUX ', | ' Computes modified Bessel fcn Kn ',/, | ' ',' NUDENS ', | ' Computes neutrino energy density ',/, | ' ',' RATE1-4 ', | ' Computes rates for reactions',/, | ' ',' SOL ', | ' Builds A matrix for eqn dy/dt = Ay ',/, | ' ',' EQSLIN ', | ' Solves dy/dt=Ay by gaussian elim ',/, | ' ',' ACCUM ', | ' Output accumulator ',/, | ' ',' OUTPUT ', | ' Allows user to output result',4(/), | ' ','(Enter to go back to help menu): ',$) READ (ir,*) GO TO 300 ELSE GO TO 300 END IF !(inum.eq.1) C26--------USING INTERFACE SUBROUTINE SECTION. 260 CONTINUE !Using the interface subroutine section. WRITE (iw,2600) 2600 FORMAT (/, | ' ',22x,'USING THE INTERFACE SUBROUTINE',/, | ' ',22x,'----- --- --------- ----------',2(/), | ' ','I. Purpose. ',/, | ' ',' The interface subroutine CHECK is des', | 'igned to be an outlet of the program ',/, | ' ',' into which alterations can be easily ', | 'plugged. Programs are normally modified',/, | ' ',' by searching through the program, ide', | 'ntifying the appropriate areas for ',/, | ' ',' alterations, and interspersing new co', | 'mmands while deleting some old ones. ',/, | ' ',' This process can get tricky unless on', | 'e actively documents the alterations: ',/, | ' ',' one might lose track of all of the mo', | 'difications and deletions. Thus, it is ',/, | ' ',' worthwhile to put most if not all of ', | 'the necessary changes into one ',/, | ' ',' subroutine which is to be called from', | ' strategic locations in the main ',/, | ' ',' program. Furthermore, by putting cha', | 'nges into one small subroutine, one need',/, | ' ',' only to compile the subroutine CHECK ', | 'each time instead of the entire nucleo- ',/, | ' ',' synthesis code. ',8(/), | ' ','(Enter 1 to continue, to end): ',$) READ (ir,1001) inum IF (inum.eq.1) THEN WRITE (iw,2602) 2602 FORMAT (/, | ' ','II. Description. ',/, | ' ',' Subroutine CHECK is an empty subrouti', | 'ne with a large COMMON area, giving the ',/, | ' ',' user ready access to all of the impor', | 'tant variables in the computations. The',/, | ' ',' routine is called from various locati', | 'ons in the main program and the location',/, | ' ',' spot in the program is labeled by the' | ,' flag "itime". The set call locations ',/, | ' ',' are given below: ',/, | ' ',' A. itime = 1 (NUC123, very beginning', | ' of program run) ',/, | ' ',' (appropriate for opening files, i', | 'nitializing variables) ',/, | ' ',' B. itime = 2 (NUC123, right before g', | 'oing into the RUN section) ',/, | ' ',' C. itime = 3 (RUN, right before goin', | 'g into DRIVER to do the computations) ',/, | ' ',' D. itime = 4 (DRIVER, in 1st R-K loo', | 'p after computing derivatives in DERIVS)',/, | ' ',' E. itime = 7 (DRIVER, in 2nd R-K loo', | 'p after computing derivatives in DERIVS)',/, | ' ',' F. itime = 8 (RUN, right after comin', | 'g back from DRIVER) ',/, | ' ',' G. itime = 9 (NUC123, right after co', | 'ming back from the RUN section) ',/, | ' ',' H. itime =10 (NUC123, very end of pr', | 'ogram run) ',/, | ' ',' (appropriate for closing files) ',/, | ' ',' The difference between the (2,9) pair', | 'ing and the (3,8) pairing is that for a ',/, | ' ',' multiple run, the (3,8) pairing would', | ' be called before and after every run ',/, | ' ',' but the (2,9) pairing would be called', | ' before and after the entire sequence. ',4(/), | ' ','(Enter 1 to continue, to end): ',$) READ (ir,1001) inum IF (inum.eq.1) THEN WRITE (iw,2604) 2604 FORMAT (/, | ' ','III. Implementation. ',/, | ' ',' The additional program statements ar', | 'e needed in the subroutine CHECK. If a',/, | ' ',' particular command is to be executed', | ' when the computer is at a certain ',/, | ' ',' location in the program -- say label', | 'ed by itime = 8 -- then in CHECK, one ',/, | ' ',' must place the command under the sta', | 'tement, IF (itime.eq.8).... The user ',/, | ' ',' is at leisure to place his own locat', | 'ion indicators (5,6) and CALL CHECK ',/, | ' ',' statements anywhere in the program a', | 's long as there is a COMMON /checkcb/ ',/, | ' ',' statement in the particular subrouti', | 'ne to carry the value of itime along. ',15(/), | ' ','(Enter to go back to help menu): ',$) READ (ir,*) GO TO 300 ELSE GO TO 300 END IF !(inum.eq.1) ELSE GO TO 300 END IF !(inum.eq.1) C27--------EXIT SECTION--------------------------------------------------------- 270 CONTINUE !Exit section. RETURN C30--------GO BACK TO MAIN MENU------------------------------------------------- 300 CONTINUE GO TO 100 END C========================IDENTIFICATION DIVISION================================ SUBROUTINE setcom C----------LINKAGES. C CALLED BY - [program] nuc123 C CALLS - none C----------REMARKS. C Allows resetting of computation parameters. C----------PARAMETERS. PARAMETER (ir=5) !Input unit number (previous value = 1). PARAMETER (iw=6) !Output unit number (previous value = 1). C----------COMMON AREAS. COMMON /compr0/ cy0,ct0,t9i0,t9f0,ytmin0,inc0 !Default comp parameters. COMMON /compr/ cy,ct,t9i,t9f,ytmin,inc !Computation parameters. COMMON /varpr0/ dt0,eta0 !Default variationl params. COMMON /varpr/ dt1,eta1 !Variational parameters. C==========================DECLARATION DIVISION================================= C----------DEFAULT COMPUTATION PARAMETERS. REAL cy0 !Default cy. REAL ct0 !Default ct. REAL t9i0 !Default t9i. REAL t9f0 !Default t9f. REAL ytmin0 !Default ytmin. INTEGER inc0 !Default accumulation increment. C----------COMPUTATION PARAMETERS. REAL cy !Time step limiting constant on abundances. REAL ct !Time step limiting constant on temperature. REAL t9i !Initial temperature (in 10**9 K). REAL t9f !Final temperature (in 10**9 K). REAL ytmin !Smallest abundances allowed. INTEGER inc !Accumulation increment. C----------DEFAULT VARIATIONAL PARAMETERS. REAL dt0 !Default initial dt. C----------VARIATIONAL PARAMETERS. REAL dt1 !Initial time step. C----------LOCAL VARIABLES. INTEGER inum !Selection number. C===========================PROCEDURE DIVISION================================== C10--------PRINT RESET SELECTION AND AWAIT RESPONSE----------------------------- C..........RETURN FROM LOOPING. 100 CONTINUE C..........DISPLAY RESET SELECTIONS. WRITE (iw,1000) cy,ct,dt1,t9i,t9f,ytmin,float(inc) 1000 FORMAT (8(/), | ' ',21x,'SET COMPUTATION PARAMETERS SELECTION',/, | ' ',21x,'--- ----------- ---------- ---------',//, | ' ',10x,' 1. CHANGE TIME-STEP LIMITING CONSTANT 1 FROM ', | f5.3,/, | ' ',10x,' 2. CHANGE TIME-STEP LIMITING CONSTANT 2 FROM ', | f5.3,/, | ' ',10x,' 3. CHANGE INITIAL TIME-STEP FROM ', | 1pe8.2,' SECONDS',/, | ' ',10x,' 4. CHANGE INITIAL TEMPERATURE FROM ', | 1pe8.2,' (10**9 K)',/, | ' ',10x,' 5. CHANGE FINAL TEMPERATURE FROM ', | 1pe8.2,' (10**9 K)',/, | ' ',10x,' 6. CHANGE SMALLEST ABUNDANCES ALLOWED FROM ', | 1pe8.2,/, | ' ',10x,' 7. CHANGE ACCUMULATION INCREMENT FROM ', | 1pe8.2,' ITERATIONS',/, | ' ',10x,' 8. RESET ALL TO DEFAULT VALUES',/, | ' ',10x,' 9. EXIT',5(/), | ' ',10x,'Enter selection (1-9): ',$) C..........READ IN SELECTION NUMBER. READ (ir,1001) inum 1001 FORMAT (i1) C20--------BRANCH TO APPROPRIATE SECTION---------------------------------------- GO TO (210,220,230,240,250,260,270,280,300),inum GO TO 300 !Improper input or . 210 CONTINUE !Change time step limiting const 1 section. WRITE (iw,2100) 2100 FORMAT (' ','Enter value for time step limiting constant 1: ',$) READ (ir,*) cy 2101 FORMAT (f5.3) GO TO 400 220 CONTINUE !Change time step limiting const 2 section. WRITE (iw,2200) 2200 FORMAT (' ','Enter value for time step limiting constant 2: ',$) READ (ir,*) ct GO TO 400 230 CONTINUE !Change initial time step section. WRITE (iw,2300) 2300 FORMAT (' ','Enter value for initial time step: ',$) READ (ir,*) dt1 GO TO 400 240 CONTINUE !Change initial temperature section. WRITE (iw,2400) 2400 FORMAT (' ','Enter value for initial temperature: ',$) READ (ir,*) t9i GO TO 400 250 CONTINUE !Change final temperature section. WRITE (iw,2500) 2500 FORMAT (' ','Enter value for final temperature: ',$) READ (ir,*) t9f GO TO 400 260 CONTINUE !Change smallest abundances allowed section. WRITE (iw,2600) 2600 FORMAT (' ','Enter value for smallest abundances allowed: ',$) READ (ir,*) ytmin GO TO 400 270 CONTINUE !Change accumulation increment section. WRITE (iw,2700) 2700 FORMAT (' ','Enter value for accumulation increment: ',$) READ (ir,*) inc GO TO 400 280 CONTINUE !Reset all to default values section. cy = cy0 !Time step limiting constant on abundances. ct = ct0 !Time step limiting constant on temperature. dt1 = dt0 !Time step. t9i = t9i0 !Initial temperature. t9f = t9f0 !Final temperature. ytmin = ytmin0 !Smallest abundances allowed. inc = inc0 !Accumulation increment. WRITE (iw,2800) 2800 FORMAT (' ','All values reset to default - Press ' | ,'to continue: ',$) READ (ir,*) GO TO 400 300 CONTINUE !Exit section. RETURN C40--------GO BACK TO MENU------------------------------------------------------ 400 CONTINUE GO TO 100 END C========================IDENTIFICATION DIVISION================================ SUBROUTINE setmod C----------LINKAGES. C CALLED BY - [program] nuc123 C CALLS - none C----------REMARKS. C Allows resetting of model parameters. C----------PARAMETERS. PARAMETER (ir=5) !Input unit number (previous value = 1). PARAMETER (iw=6) !Output unit number (previous value = 1). C----------COMMON AREAS. COMMON /modpr0/ c0,cosmo0,xi0 !Default model parameters. COMMON /modpr/ g,tau,xnu,c,cosmo,xi !Model parameters. COMMON /varpr0/ dt0,eta0 !Default variationl params. COMMON /varpr/ dt1,eta1 !Variational parameters. C==========================DECLARATION DIVISION================================= C----------DEFAULT MODEL PARAMETERS. REAL c0(3) !Default c. REAL cosmo0 !Default cosmological constant. REAL xi0(3) !Default neutrino degeneracy parameters. C----------EARLY UNIVERSE MODEL PARAMETERS. REAL c(3) !c(1) is variation of gravitational constant. | !c(2) is neutron lifetime (sec). | !c(3) is number of neutrino species. REAL cosmo !Cosmological constant. REAL xi(3) !Neutrino degeneracy parameters. C----------DEFAULT VARIATIONAL PARAMETERS. REAL eta0 !Default eta. C----------VARIATIONAL PARAMETERS. REAL eta1 !Intial baryon-to-photon ratio. C----------USER RESPONSE VARIABLES. INTEGER inum !Selection number. C===========================PROCEDURE DIVISION================================== C10--------PRINT RESET SELECTION AND AWAIT RESPONSE----------------------------- C..........RETURN FROM LOOPING. 100 CONTINUE C..........DISPLAY RESET SELECTIONS. WRITE (iw,1000) c(1),c(2),c(3),eta1,cosmo,xi(1),xi(2),xi(3) 1000 FORMAT (8(/), | ' ',24x,'SET MODEL PARAMETERS SELECTION',/, | ' ',24x,'--- ----- ---------- ---------',//, | ' ',10x,' 1. CHANGE GRAVITATIONAL CONSTANT FROM ', | 1pe10.3,/, | ' ',10x,' 2. CHANGE NEUTRON LIFETIME FROM ', | 1pe10.3,' SECONDS',/, | ' ',10x,' 3. CHANGE NUMBER OF NEUTRINO SPECIES FROM ', | 1pe10.3,/, | ' ',10x,' 4. CHANGE FINAL BARYON-TO-PHOTON RATIO FROM ', | 1pe10.3,/, | ' ',10x,' 5. CHANGE COSMOLOGICAL CONSTANT FROM ', | 1pe10.3,/, | ' ',10x,' 6. CHANGE XI-ELECTRON FROM ', | 1pe10.3,/, | ' ',10x,' 7. CHANGE XI-MUON FROM ', | 1pe10.3,/, | ' ',10x,' 8. CHANGE XI-TAUON FROM ', | 1pe10.3,/, | ' ',10x,' 9. RESET ALL TO DEFAULT VALUES',/, | ' ',10x,'10. EXIT',4(/), | ' ',10x,' Enter selection (1-10): ',$) C..........READ IN SELECTION NUMBER. READ (ir,1001) inum 1001 FORMAT (i2) C20--------BRANCH TO APPROPRIATE SECTION---------------------------------------- GO TO (210,220,230,240,250,260,270,280,290,300),inum GO TO 300 !Improper input or . 210 CONTINUE !Change gravitational constant section. WRITE (iw,2100) 2100 FORMAT (' ','Enter value for variation of gravitational ', | 'constant: ',$) READ (ir,*) c(1) GO TO 400 220 CONTINUE !Change neutron lifetime section. WRITE (iw,2200) 2200 FORMAT (' ','Enter value for neutron lifetime (sec): ',$) READ (ir,*) c(2) GO TO 400 230 CONTINUE !Change number of neutrino species section. WRITE (iw,2300) 2300 FORMAT (' ','Enter value for number of neutrino species: ',$) READ (ir,*) c(3) GO TO 400 240 CONTINUE !Change baryon-to-photon ratio section. WRITE (iw,2400) 2400 FORMAT (' ','Enter value for baryon-to-photon ratio: ',$) READ (ir,*) eta1 GO TO 400 250 CONTINUE !Change cosmological constant section. WRITE (iw,2500) 2500 FORMAT (' ','Enter value for cosmological constant: ',$) READ (ir,*) cosmo GO TO 400 260 CONTINUE !Change neutrino degeneracy section. WRITE (iw,2600) 2600 FORMAT (' ','Enter value for xi electron: ',$) READ (ir,*) xi(1) GO TO 400 270 CONTINUE !Change neutrino degeneracy section. WRITE (iw,2700) 2700 FORMAT (' ','Enter value for xi muon: ',$) READ (ir,*) xi(2) GO TO 400 280 CONTINUE !Change neutrino degeneracy section. WRITE (iw,2800) 2800 FORMAT (' ','Enter value for xi tauon: ',$) READ (ir,*) xi(3) IF ((xi(3).ne.0.).and.(c(3).lt.3.)) THEN c(3) = 3. WRITE (iw,2802) 2802 FORMAT (' ','Number of neutrinos set to 3') WRITE (iw,2804) 2804 FORMAT (' ','Press to continue: ',$) READ (ir,*) END IF GO TO 400 290 CONTINUE !Reset all to default values section. c(1) = c0(1) c(2) = c0(2) c(3) = c0(3) cosmo = cosmo0 xi(1) = xi0(1) xi(2) = xi0(2) xi(3) = xi0(3) eta1 = eta0 WRITE (iw,2900) 2900 FORMAT (' ','All values reset to default - Press ' | , 'to continue: ',$) READ (ir,*) GO TO 400 300 CONTINUE !Exit section. RETURN C40--------GO BACK TO MENU------------------------------------------------------ 400 CONTINUE GO TO 100 END C========================IDENTIFICATION DIVISION================================ SUBROUTINE run C----------LINKAGES. C CALLED BY - [program] nuc123 C CALLS - [subroutine] driver C----------REMARKS. C Activates computation routine. C----------PARAMETERS. PARAMETER (ir=5) !Input unit number (previous value = 1). PARAMETER (iw=6) !Output unit number (previous value = 1). PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (lrec=64) !Total # of nuclear reactions for irun = 2. PARAMETER (krec=34) !Total # of nuclear reactions for irun = 3. PARAMETER (nnuc=26) !Number of nuclides in calculation. PARAMETER (lnuc=18) !Total # of nuclides for irun = 2. PARAMETER (knuc=9) !Total # of nuclides for irun = 3. C----------COMMON AREAS. COMMON /modpr/ g,tau,xnu,c,cosmo,xi !Model parameters. COMMON /varpr/ dt1,eta1 !Variational parameters. COMMON /checkcb/ itime !Computation location. COMMON /runopt/ irun,isize,jsize !Run options. C==========================DECLARATION DIVISION================================= C----------MODEL PARAMETERS. REAL eta1 !Baryon-to-photon ratio. REAL c(3) !c(1) is variation of gravitational constant. | !c(2) is neutron lifetime (sec). | !c(3) is number of neutrino species. REAL cosmo !Cosmological constant. REAL xi(3) !Neutrino degeneracy parameters. C----------RUN OPTION. INTEGER irun !Run network size. INTEGER isize !Number of nuclides in computation. INTEGER jsize !Number of reactions in computation. C----------USER INTERACTION VARIABLES. REAL rnumb1 !Run parameter for outer loop. REAL rnumb2 !Run parameter for middle loop. REAL rnumb3 !Run parameter for inner loop. REAL rnum1(3) !Run parameter starting value. REAL rnum2(3) !Run parameter end value. REAL rnum3(3) !Run parameter increment. INTEGER inumb !Selection number. INTEGER inum(3) !Selection number. INTEGER jnum !Number of loopings to be done. INTEGER knum !Number of loopings rejected. INTEGER lnumb1 !Run parameter for outer loop. INTEGER lnumb2 !Run parameter for middle loop. INTEGER lnumb3 !Run parameter for inner loop. INTEGER lnum(3) !Run parameter end value. INTEGER lchose !User response (alphanumeric). C----------FLAG AND LABELS. INTEGER itime !Computation location. CHARACTER*22 vtype(8) !Label for quantities being varied. C----------EQUIVALENCE VARIABLE. REAL qvary(7) !Array set equal to c, cosmo, and xi. C----------EQUIVALENCE STATEMENTS. EQUIVALENCE (qvary(1),c(1)), (qvary(4),cosmo), (qvary(5),xi(1)) C==============================DATA DIVISION==================================== C----------LABELS FOR QUANTITIES BEING VARIED. DATA vtype /'baryon/photon ratio ', | 'gravitational constant', | 'neutron lifetime ', | '# of neutrino species ', | 'cosmological constant ', | 'xi-electron ', | 'xi-muon ', | 'xi-tauon '/ C===========================PROCEDURE DIVISION================================== C10--------PRINT RUN SELECTION AND AWAIT RESPONSE------------------------------- C..........RETURN FROM LOOPING. 100 CONTINUE C..........DISPLAY RUN SELECTIONS. WRITE (iw,1000) 1000 FORMAT (8(/), | ' ',32x,'RUN SELECTION',/, | ' ',32x,'--- ---------',//, | ' ',27x,' 1. SET RUN NETWORK',/, | ' ',27x,' 2. GO',/, | ' ',27x,' 3. DO MULTIPLE RUNS',/, | ' ',27x,' 4. EXIT',10(/), | ' ',27x,' Enter selection (1-4): ',$) C..........READ IN SELECTION NUMBER. READ (ir,1001) inumb 1001 FORMAT (i1) C20--------BRANCH TO APPROPRIATE SECTION---------------------------------------- GO TO (210,220,230,240),inumb GO TO 240 !Improper input or . C21--------SET RUN NETWORK SECTION---------------------------------------------- 210 CONTINUE WRITE (iw,2100) 2100 FORMAT (' ','Enter network size (1-26 nuclides (default); ', | '2-18; 3-9): ',$) READ (ir,*) inumb !Read in selection number. IF ((inumb.ne.1).and.(inumb.ne.2).and.(inumb.ne.3)) inumb = 1 !Default. IF (inumb.ne.irun) THEN !Run network changed from previously. irun = inumb !Run network size selection. END IF IF (irun.eq.1) THEN !Maximal network size. isize = nnuc jsize = nrec ELSE IF (irun.eq.2) THEN !Abridged network size. isize = lnuc jsize = lrec ELSE IF (irun.eq.3) THEN !Minimal network size. isize = knuc jsize = krec END IF END IF END IF !(irun.eq.1) WRITE (iw,2104) irun 2104 FORMAT (' ','Run network set to ',i1,' - Press ', | 'to continue: ',$) READ (ir,*) GO TO 300 C22--------GO SECTION----------------------------------------------------------- 220 CONTINUE WRITE (iw,2200) 2200 FORMAT (' ','Begin computation run....') itime = 3 CALL check !Call interface subr before computation. CALL driver !Do nucleosynthesis computation. itime = 8 CALL check !Call interface subr after computation. WRITE (iw,2202) 2202 FORMAT (' ','Computation completed - Press to ' | ,'continue: ',$) READ (ir,*) GO TO 300 C23--------DO MULTIPLE RUNS SECTION--------------------------------------------- C..........GET NUMBER OF LOOPINGS. 230 CONTINUE WRITE (iw,2300) 2300 FORMAT (' ','Enter the number of loopings to be done (1 ', | '(default); 2; 3): ',$) READ (ir,*) jnum !Read in number of loopings to be done. IF ((jnum.ne.1).and.(jnum.ne.2).and.(jnum.ne.3)) THEN jnum = 1 !Default number of loopings. END IF knum = 0. !No loopings rejected for now. DO i = 1,3 IF (i.gt.jnum) THEN rnum1(i) = 0. !Initialize initial parameter. rnum2(i) = 0. !Initialize terminal parameter. rnum3(i) = 1. !Initialize incremental parameter. inum(i) = 0 !Initialize selection number. ELSE C..........OBTAIN QUANTITY TO VARY. WRITE (iw,2302) 2302 FORMAT (8(/), | ' ',30x,'QUANTITY TO VARY',/, | ' ',30x,'-------- -- ----',//, | ' ',25x,' 1. ETA (LOGRITHMIC VARIATION)',/, | ' ',25x,' 2. G (LINEAR VARIATION)',/, | ' ',25x,' 3. TAU (LINEAR VARIATION)',/, | ' ',25x,' 4. # NEUTRINOS (LINEAR VARIATION)',/, | ' ',25x,' 5. LAMBDA (LINEAR VARIATION)',/, | ' ',25x,' 6. XI-ELECTRON (LINEAR VARIATION)',/, | ' ',25x,' 7. XI-MUON (LINEAR VARIATION)',/, | ' ',25x,' 8. XI-TAUON (LINEAR VARIATION)',/, | ' ',25x,' 9. NO SELECTION',5(/), | ' ',25x,' Enter selection (1-9): ',$) READ (ir,1001) inum(i) IF ((inum(i).lt.1).or.(inum(i).gt.8)) THEN !No selection made. WRITE (iw,2304) 2304 FORMAT (' ','No selection made - Reduce number of ', | 'loopings by one',/, | ' ','Press to continue: ',$) READ (ir,*) knum = knum + 1 !Step up number of loopings rejected. rnum1(i) = 0. !Initialize initial parameter. rnum2(i) = 0. !Initialize terminal parameter. rnum3(i) = 1. !Initialize incremental parameter. inum(i) = 0 !Initialize selection number. ELSE !((inum(i).ge.1).and.(inum(i).le.8)) C..........INPUT RUN SPECIFICATIONS. 231 CONTINUE WRITE (iw,2306) 2306 FORMAT (' ','Enter minimum value: ',$) READ (ir,*) rnum1(i) !Read in starting value. WRITE (iw,2308) 2308 FORMAT (' ','Enter maximum value: ',$) READ (ir,*) rnum2(i) !Read in terminating value. 232 CONTINUE WRITE (iw,2310) 2310 FORMAT (' ','Enter increment: ',$) READ (ir,*) rnum3(i) !Read in incremental value. IF (rnum3(i).eq.0.) THEN !Trouble with 0 division later on. WRITE (iw,2312) 2312 FORMAT (' ','Zero increment not allowed: trouble with ', | 'dividing by zero') GO TO 232 END IF WRITE (iw,2314) rnum1(i), rnum2(i), rnum3(i) !Display input info. 2314 FORMAT (' ','Run from ',1pe12.5,' to ',1pe12.5, | ' in increments of ',1pe12.5) WRITE (iw,2316) 2316 FORMAT (' ','Confirm these values (Y or N): ',$) c READ (ir,2301) lchose !Get confirmation. 2301 FORMAT (a1) c IF ((lchose.ne.'Y').and.(lchose.ne.'y')) GO TO 231 END IF !((inum(i).lt.1).or.(inum(i).gt.8)) END IF !(i.gt.jnum) END DO !i = 1,3 jnum = jnum-knum !Number of valid loopings. IF (jnum.ne.0) THEN !Run requested. C..........WRITE OUT QUANTITY TO VARY, RUN SPECIFICATIONS. DO l = 1,jnum+knum !Check all loopings. IF (inum(l).ne.0) THEN !Proper selection was made. WRITE (iw,2318) vtype(inum(l)),rnum1(l), !Display run params. | rnum2(l), rnum3(l) 2318 FORMAT (' ','Run ',a22,/, | ' from ',1pe12.5,' to ',1pe12.5, | ' in increments of ',1pe12.5) C..........GET LOGS OF eta VALUES FOR LOGRITHMIC INCREMENTATION. IF (inum(l).eq.1) THEN !Work with exponents for eta increments. rnum1(l) = log10(rnum1(l)) rnum2(l) = log10(rnum2(l)) END IF END IF END DO C..........COMPUTE NUMBER OF RUNS FOR EACH LOOPING. DO l = 1,3 lnum(l) = nint((rnum2(l)-rnum1(l)+rnum3(l))/rnum3(l)) END DO C..........DO MULTIPLE RUNS. WRITE (iw,2200) !Inform user of beginning of computation. DO lnumb1 = 0,lnum(1)-1 !Outer loop. rnumb1 = rnum1(1)+float(lnumb1)*rnum3(1) !Value of param for run. IF ((inum(1).ge.1).and.(inum(1).le.8)) THEN IF (inum(1).eq.1) THEN eta1 = 10**rnumb1 !Vary baryon-to-photon ratio. ELSE qvary(inum(1)-1) = rnumb1 !Vary other quantities. END IF END IF DO lnumb2 = 0,lnum(2)-1 !Middle loop. rnumb2 = rnum1(2)+float(lnumb2)*rnum3(2) !Value of param for run. IF ((inum(2).ge.1).and.(inum(2).le.8)) THEN IF (inum(2).eq.1) THEN eta1 = 10**rnumb2 !Vary baryon-to-photon ratio. ELSE qvary(inum(2)-1) = rnumb2 !Vary other quantities. END IF END IF DO lnumb3 = 0,lnum(3)-1 !Inner loop. rnumb3 = rnum1(3)+float(lnumb3)*rnum3(3) !Value of parameter. IF ((inum(3).ge.1).and.(inum(3).le.8)) THEN IF (inum(3).eq.1) THEN eta1 = 10**rnumb3 !Vary baryon-to-photon ratio. ELSE qvary(inum(3)-1) = rnumb3 !Vary other quantities. END IF END IF itime = 3 CALL check !Check interface subr before computation. CALL driver !Do nucleosynthesis computation. itime = 8 CALL check !Check interface subroutine after computation END DO !lnumb3 = 0,lnum(3)-1 END DO !lnumb2 = 0,lnum(2)-1 END DO !lnumb1 = 0,lnum(1)-1 WRITE (iw,2202) !Inform user of completion of computation. ELSE !(jnum.eq.0) WRITE (iw,2320) 2320 FORMAT (' ','No selection made - ', | 'Press to continue: ',$) END IF !(jnum.ne.0) READ (ir,*) GO TO 300 C24--------EXIT SECTION--------------------------------------------------------- 240 CONTINUE RETURN C30--------GO BACK TO MENU------------------------------------------------------ 300 CONTINUE GO TO 100 END C========================IDENTIFICATION DIVISION================================ SUBROUTINE output C----------LINKAGES. C CALLED BY - [program] nuc123 C CALLS - none C----------REMARKS. C Outputs computational results either into an output file or onto C the screen C----------PARAMETERS. PARAMETER (ir=5) !Input unit number (previous value = 1). PARAMETER (iw=6) !Output unit number (previous value = 1). PARAMETER (nnuc=26) !Number of nuclides in calculation. PARAMETER (itmax=400) !Maximum # of line to be printed. C----------COMMON AREAS. COMMON /compr/ cy,ct,t9i,t9f,ytmin,inc !Computation parameters. COMMON /modpr/ g,tau,xnu,c,cosmo,xi !Model parameters. COMMON /flags/ ltime,is,ip,it,mbad !Flags, counters. COMMON /outdat/ xout,thmout,t9out,tout,dtout, !Output data. | etaout,hubout COMMON /outopt/ nout,outfile !Output option. C==========================DECLARATION DIVISION================================= C----------COMPUTATION SETTINGS. REAL cy !Time step limiting constant on abundances. REAL ct !Time step limiting constant on temperature. REAL t9i !Initial temperature (in 10**9 K). REAL t9f !Final temperature (in 10**9 K). REAL ytmin !Smallest abundances allowed. C----------EARLY UNIVERSE MODEL PARAMETERS. REAL c(3) !c(1) is variation of gravitational constant. | !c(2) is neutron lifetime (sec). | !c(3) is number of neutrino species. REAL cosmo !Cosmological constant. REAL xi(3) !Neutrino degeneracy parameters. C----------COUNTER. INTEGER it !# times accumulated in output buffer. C----------OUTPUT ARRAYS. REAL xout(itmax,nnuc) !Nuclide mass fractions. REAL thmout(itmax,6) !Thermodynamic variables. REAL t9out(itmax) !Temperature (in units of 10**9 K). REAL tout(itmax) !Time. REAL dtout(itmax) !Time step. REAL etaout(itmax) !Baryon-to-photon ratio. REAL hubout(itmax) !Expansion rate. C----------OUTPUT FILE STATUS. INTEGER nout !Number of output requests. LOGICAL outfile !Indicates if output file used. C----------USER INTERACTION VARIABLES. INTEGER inum !Selection number. C===========================PROCEDURE DIVISION================================== C10--------PRINT OUTPUT SELECTION AND AWAIT RESPONSE---------------------------- C..........RETURN FROM LOOPING. 100 CONTINUE C..........DISPLAY OUTPUT SELECTIONS. WRITE (iw,1000) 1000 FORMAT (8(/), | ' ',30x,'OUTPUT SELECTION',/, | ' ',30x,'------ ---------',//, | ' ',25x,' 1. REQUEST OUTPUT FILE',/, | ' ',25x,' 2. REQUEST OUTPUT ON SCREEN',/, | ' ',25x,' 3. EXIT',11(/), | ' ',25x,' Enter selection (1-3): ',$) C..........READ IN SELECTION NUMBER. READ (ir,1001) inum 1001 FORMAT (i1) C..........BRANCH TO APPROPRIATE SECTION. GO TO (200,300,400),inum GO TO 400 !Improper input or . C20--------REQUEST OUTPUT SECTION----------------------------------------------- 200 CONTINUE c DO j = 1,it !Temperature in MeV. c t9out(j) = t9out(j)*.08617 c END DO c DO j = 1,it !Energy density as fraction of total. c thmout(j,1) = thmout(j,1)/thmout(j,6) !Rhog. c thmout(j,2) = thmout(j,2)/thmout(j,6) !Rhoe. c thmout(j,3) = thmout(j,3)/thmout(j,6) !Rhone. c thmout(j,4) = thmout(j,4)/thmout(j,6) !Rhob. c END DO C..........PRINT CAPTION. nout = nout + 1 !Keep track of number of output requests. IF (nout.eq.1) THEN WRITE (2,2000) 2000 FORMAT (54x,'NUCLIDE ABUNDANCE YIELDS',/, | 54x,'------- --------- ------',//) END IF WRITE (2,2002) cy,ct,t9i,t9f,ytmin 2002 FORMAT (' Computational parameters:',/, | ' cy = ',f5.3,'/ ct = ',f5.3, | '/ initial temp = ',1pe8.2, | '/ final temp = ',1pe8.2, | '/ smallest abundances allowed = ',1pe8.2) WRITE (2,2004) c(1),c(2),c(3),cosmo,xi(1),xi(2),xi(3) 2004 FORMAT (' Model parameters:',/, | ' g = ',f5.2,'/ tau = ',f6.2, | '/ # nu = ',f5.2,'/ lambda = ',1pe10.3, | '/ xi-e = ',e10.3,'/ xi-m = ',e10.3, | '/ xi-t = ',e10.3,/) C..........PRINT HEADINGS, ABUNDANCES FOR NEUTRON TO LI8. WRITE (2,2006) 2006 FORMAT (4x,'Temp',8x,'N/H',10x,'P',10x,'D/H',9x,'T/H',8x, | 'He3/H',8x,'He4',8x,'Li6/H',7x,'Li7/H',7x, | 'Be7/H',6x,'Li8/H&up',/,132('-')) DO j = 1,it WRITE (2,2008) t9out(j),(xout(j,i),i=1,10) 2008 FORMAT (1pe10.3,1p10e12.3) END DO C..........PRINT THERMODYNAMIC QUANTITIES. WRITE (2,2010) 2010 FORMAT (' ',/,4x,'Temp',9x,'T',10x,'rhog',8x,'rhoe',7x, | 'rhone',8x,'rhob',8x,'phie',9x,'dt',9x, | 'eta',10x,'H',/,132('-')) DO j = 1,it WRITE (2,2012) t9out(j),tout(j),(thmout(j,i),i=1,5),dtout(j), | etaout(j),hubout(j) 2012 FORMAT (1pe10.3,9e12.3) END DO WRITE (2,2014) 2014 FORMAT (///) outfile = .true. !Output file requested. WRITE (iw,2016) 2016 FORMAT (' ','Output file requested - Press to ' | ,'continue: ',$) READ (ir,*) GO TO 500 C30--------REQUEST OUTPUT ON SCREEN SECTION------------------------------------- C..........RETURN FROM LOOPING. 300 CONTINUE c DO j = 1,it !Temperature in MeV. c t9out(j) = t9out(j)*.08617 c END DO c DO j = 1,it !Energy density as fraction of total. c thmout(j,1) = thmout(j,1)/thmout(j,6) !Rhog. c thmout(j,2) = thmout(j,2)/thmout(j,6) !Rhoe. c thmout(j,3) = thmout(j,3)/thmout(j,6) !Rhone. c thmout(j,4) = thmout(j,4)/thmout(j,6) !Rhob. c END DO C..........DISPLAY SCREEN OUTPUT SELECTIONS. WRITE (iw,3000) 3000 FORMAT (8(/), | ' ',26x,'SCREEN OUTPUT SELECTION',/, | ' ',26x,'------ ------ ---------',//, | ' ',25x,' 1. DISPLAY D,T,HE3,HE4,LI7',/, | ' ',25x,' 2. DISPLAY N,P,LI6,BE7,LI8&UP',/, | ' ',25x,' 3. DISPLAY RHOG,RHOE,RHONE,RHOB',/, | ' ',25x,' 4. DISPLAY T,DT,PHIE,ETA,H',/, | ' ',25x,' 5. EXIT',9(/), | ' ',25x,' Enter selection (1-5): ',$) C..........READ IN SELECTION NUMBER. READ (ir,1001) inum GO TO (310,320,330,340,350),inum GO TO 350 !Improper input or . 310 CONTINUE !Display d,t,he3,he4,li7. C..........PRINT CAPTION. WRITE (iw,2014) WRITE (iw,3100) cy,ct,t9i,t9f,ytmin 3100 FORMAT (' ','Computational parameters:',/, | ' ',' cy = ',f5.3,'/ ct = ',f5.3, | '/ initial temp = ',1pe8.2, | '/ final temp = ',1pe8.2,/, | ' ',' smallest abundances allowed = ',1pe8.2) WRITE (iw,3102) c(1),c(2),c(3),cosmo,xi(1),xi(2),xi(3) 3102 FORMAT (' ','Model parameters:',/, | ' ',' g = ',f5.2,'/ tau = ',f6.2, | '/ # nu = ',f5.2,'/ lambda = ',1pe10.3,/, | ' ',' xi-e = ',e10.3,'/ xi-m = ',e10.3, | '/ xi-t = ',e10.3,/) C..........PRINT HEADINGS, ABUNDANCES FOR D,T,HE3,HE4,LI7. WRITE (iw,3104) 3104 FORMAT (4x,'Temp',8x,'D/H',9x,'T/H',8x,'He3/H',8x, | 'He4',8x,'Li7/H',/,' ',80('-')) DO j = 1,it WRITE (iw,3106) t9out(j),(xout(j,i),i=3,6),xout(j,8) 3106 FORMAT (1pe10.3,1p5e12.3) END DO WRITE (iw,2014) WRITE (iw,3108) 3108 FORMAT (' ','Press to continue: ',$) READ (ir,*) GO TO 360 320 CONTINUE !Display n,p,li6,be7,li8&up. C..........PRINT CAPTION. WRITE (iw,2014) WRITE (iw,3100) cy,ct,t9i,t9f,ytmin WRITE (iw,3102) c(1),c(2),c(3),cosmo,xi(1),xi(2),xi(3) C..........PRINT HEADINGS, ABUNDANCES FOR N,P,LI6,BE7,LI8&UP. WRITE (iw,3204) 3204 FORMAT (4x,'Temp',8x,'N/H',10x,'P',9x, | 'Li6/H',7x,'Be7/H',6x,'Li8/H&up',/,' ',80('-')) DO j = 1,it WRITE (iw,3106) t9out(j),(xout(j,i),i=1,2),xout(j,7), | (xout(j,i),i=9,10) END DO WRITE (iw,2014) WRITE (iw,3108) READ (ir,*) GO TO 360 330 CONTINUE !Display rhog,rhoe,rhone,rhob. C..........PRINT CAPTION. WRITE (iw,2014) WRITE (iw,3100) cy,ct,t9i,t9f,ytmin WRITE (iw,3102) c(1),c(2),c(3),cosmo,xi(1),xi(2),xi(3) C..........PRINT ENERGY DENSITIES. WRITE (iw,3304) 3304 FORMAT (4x,'Temp',8x,'rhog',8x,'rhoe',7x,'rhone',8x,'rhob', | /,' ',80('-')) DO j = 1,it WRITE (iw,3306) t9out(j),(thmout(j,i),i=1,4) 3306 FORMAT (1pe10.3,4e12.3) END DO WRITE (iw,2014) WRITE (iw,3108) READ (ir,*) GO TO 360 340 CONTINUE !Display t,dt,phie,eta,hubcst. C..........PRINT CAPTION. WRITE (iw,2014) WRITE (iw,3100) cy,ct,t9i,t9f,ytmin WRITE (iw,3102) c(1),c(2),c(3),cosmo,xi(1),xi(2),xi(3) C..........PRINT THERMODYNAMIC QUANTITIES. WRITE (iw,3404) 3404 FORMAT (4x,'Temp',8x,'time',8x,'phie',9x,'dt',9x,'eta',10x, | 'H',/,' ',80('-')) DO j = 1,it WRITE (iw,3406) t9out(j),tout(j),thmout(j,5),dtout(j), | etaout(j),hubout(j) 3406 FORMAT (1pe10.3,5e12.3) END DO WRITE (iw,2014) WRITE (iw,3108) READ (ir,*) GO TO 360 350 CONTINUE !Exit. GO TO 500 360 CONTINUE GO TO 300 C40--------EXIT SECTION--------------------------------------------------------- 400 CONTINUE RETURN C50--------GO BACK TO MENU------------------------------------------------------ 500 CONTINUE GO TO 100 END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C This code now modified to run under Linux C (by Scott Dodelson, Oct'01) C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C Changes (to run inder DEC unix f77): C ----------------------------------- C COMMON /therm/ -> COMMON /thermcb/ C COMMON /bessel/ -> COMMON /besselcb/ C COMMON /check/ -> COMMON /checkcb/ C COMMON /time/ -> COMMON /ttime/ C C Updated Correction to helium-4 abundance (using fitted rates and C smallest step-size) - Sarkar, Rep. Prog Phys. 59, 1493 (1996): C ---------------------------------------------------------------- C Y_p = Y_p - 0.0025 -> Y_p = Y_p - 0.0003 C C output nucint.dat -> newint.dat C C========================IDENTIFICATION DIVISION================================ SUBROUTINE check C----------REMARKS. C This is an interface subroutine, C a flexible module which allows user to manipulate physical quantities C of interest at certain key points during the computer run. C Included within this subroutine is a roster of all global variables C and their respective COMMON areas. C Current instructions accumulate abundances of deuterium, helium-3, C helium-4, and lithium-7 for eventual plotting, taking into account C the contribution of beryllium-7 to lithium-7 and tritium to helium-3. C----------PARAMETERS. PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (nvar=29) !Number of variables to be evolved. PARAMETER (nnuc=26) !Number of nuclides in calculation. PARAMETER (itmax=400) !Maximum # of lines to be printed. C----------COMMON AREAS. COMMON /recpr0/ reacpr !Reaction parameter values. COMMON /recpr/ iform,ii,jj,kk,ll,rev,q9 !Reaction parameter names. COMMON /rates/ f,r !Reaction rates. COMMON /evolp1/ t9,hv,phie,y !Evolution parameters. COMMON /evolp2/ dt9,dhv,dphie,dydt !Evolution parameters. COMMON /evolp3/ t90,hv0,phie0,y0 !Evolution parameters. COMMON /compr0/ cy0,ct0,t9i0,t9f0,ytmin0,inc0 !Default comp parameters. COMMON /compr/ cy,ct,t9i,t9f,ytmin,inc !Computation parameters. COMMON /modpr0/ c0,cosmo0,xi0 !Default model parameters. COMMON /modpr/ g,tau,xnu,c,cosmo,xi !Model parameters. COMMON /varpr0/ dt0,eta0 !Default variationl params. COMMON /varpr/ dt1,eta1 !Variational parameters. COMMON /ttime/ t,dt,dlt9dt !Time variables. COMMON /thermcb/ thm,hubcst !Dynamic variables. COMMON /endens/ rhone0,rhob0,rhob,rnb !Energy densities. COMMON /lncoef/ a,b,yx !Linear eqn coefficients. COMMON /nucdat/ am,zm,dm !Nuclide data. COMMON /besselcb/ bl1,bl2,bl3,bl4,bl5, !Eval function bl(z). | bm1,bm2,bm3,bm4,bm5, !Eval function bm(z). | bn1,bn2,bn3,bn4,bn5 !Eval function bn(z). COMMON /kays/ bk0,bk1,bk2,bk3,bk4 !Coefficients K. COMMON /flags/ ltime,is,ip,it,mbad !Flags,counters. COMMON /checkcb/ itime !Computation location. COMMON /outdat/ xout,thmout,t9out,tout,dtout, !Output data. | etaout,hubout COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Neutrino parameters. COMMON /runopt/ irun,isize,jsize !Run options. COMMON /outopt/ nout,outfile !Output option. C==========================DECLARATION DIVISION================================= C----------REACTION PARAMETER VALUES. REAL reacpr(nrec,8) !Reaction parameters. C----------REACTION PARAMETER NAMES. INTEGER iform(nrec) !Reaction type code (1-11). INTEGER ii(nrec) !Incoming nuclide type (1-26). INTEGER jj(nrec) !Incoming light nuclide type (1-6). INTEGER kk(nrec) !Outgoing light nuclide type (1-6). INTEGER ll(nrec) !Outgoing nuclide type (1-26). REAL rev(nrec) !Reverse reaction coefficient. REAL q9(nrec) !Energy released in reaction (in 10**9 K). C----------REACTION RATES. REAL f(nrec) !Forward reaction rate coefficients. REAL r(nrec) !Reverse reaction rate coefficients. C----------EVOLUTION PARAMETERS. REAL t9 !Temperature of photons (units of 10**9 K). REAL hv !Defined by hv = M(atomic)n(baryon)/t9**3. REAL phie !Chemical potential of electron. REAL y(nnuc) !Relative number abundances. C----------EVOLUTION PARAMETERS (DERIVATIVES). REAL dt9 !Change in temperature. REAL dhv !Change in hv. REAL dphie !Change in chemical potential. REAL dydt(nnuc) !Change in relative number abundances. C----------EVOLUTION PARAMETERS (ORIGINAL VALUES). REAL y0(nnuc) !Rel # abundances at end of 1st R-K loop. C----------DEFAULT COMPUTATION PARAMETERS. REAL cy0 !Default cy. REAL ct0 !Default ct. REAL t9i0 !Default t9i. REAL t9f0 !Default t9f. REAL ytmin0 !Default ytmin. INTEGER inc0 !Default accumulation increment. C----------COMPUTATION PARAMETERS. REAL cy !Time step limiting constant on abundances. REAL ct !Time step limiting constant on temperature. REAL t9i !Initial temperature (in 10**9 K). REAL t9f !Final temperature (in 10**9 K). REAL ytmin !Smallest abundances allowed. INTEGER inc !Accumulation increment. C----------DEFAULT MODEL PARAMETERS. REAL c0(3) !Default c. REAL cosmo0 !Default cosmological constant. REAL xi0(3) !Default neutrino degeneracy parameters. C----------EARLY UNIVERSE MODEL PARAMETERS. REAL g !Gravitational constant. REAL tau !Neutron lifetime (sec). REAL xnu !Number of neutrino species. REAL c(3) !c(1) is variation of gravitational constant. | !c(2) is neutron half-life (min). | !c(3) is number of neutrino species. REAL cosmo !Cosmological constant. REAL xi(3) !Neutrino degeneracy parameters. | !xi(1) is e neutrino degeneracy parameter. | !xi(2) is m neutrino degeneracy parameter. | !xi(3) is t neutrino degeneracy parameter. C----------DEFAULT VARIATIONAL PARAMETERS. REAL dt0 !Default initial time step. REAL eta0 !Default baryon-to-photon ratio. C----------VARIATIONAL PARAMETERS. REAL dt1 !Initial time step. REAL eta1 !Baryon-to-photon ratio. C----------TIME VARIABLES. REAL t !Time. REAL dt !Time step. REAL dlt9dt !(1/t9)*d(t9)/d(t). C----------DYNAMIC VARIABLES. REAL thm(14) !Thermodynamic variables (energy densities). REAL hubcst !Expansion rate of the universe. C----------ENERGY DENSITIES. REAL rhone0 !Initial electron neutrino energy density. REAL rhob0 !Initial baryon energy density. REAL rhob !Baryon energy density. REAL rnb !Baryon energy density (ratio to init value). C----------MATRIX COEFFICIENTS FOR LINEAR EQUATION. DOUBLE PRECISION a(nnuc,nnuc)!Relates y(t+dt) to y(t). REAL b(nnuc) !Contains y0 in inverse order. REAL yx(nnuc) !yy in reverse order. C----------NUCLIDE DATA. REAL am(nnuc) !Atomic number of nuclide. REAL zm(nnuc) !Charge of nuclide. REAL dm(nnuc) !Mass excess of nuclide. C----------EVALUATION OF FUNCTIONS bl,bm,bn. REAL bl1,bl2,bl3,bl4,bl5 !Evaluation of function bl(z). REAL bm1,bm2,bm3,bm4,bm5 !Evaluation of function bm(z). REAL bn1,bn2,bn3,bn4,bn5 !Evaluation of function bn(z). C----------EVALUATION OF MODIFIED BESSEL FUNCTIONS. REAL bk0,bk1,bk2,bk3,bk4 !Values k0(r),k1(r),k2(r),k3(r),k4(r). C----------FLAGS AND COUNTERS. INTEGER ltime !Indicates if output buffer printed. INTEGER is !# total iterations for particular model. INTEGER ip !# iterations after outputing a line. INTEGER it !# times accumulated in output buffer. INTEGER mbad !Indicates if gaussian elimination failed. C----------COMPUTATION LOCATION. INTEGER itime !Time check. C----------OUTPUT ARRAYS. REAL xout(itmax,nnuc) !Nuclide mass fractions. REAL thmout(itmax,6) !Thermodynamic variables. REAL t9out(itmax) !Temperature (in units of 10**9 K). REAL tout(itmax) !Time. REAL dtout(itmax) !Time step. REAL etaout(itmax) !Baryon to photon ratio. REAL hubout(itmax) !Expansion rate. C----------NEUTRINO PARAMETERS. REAL t9mev !Temperature (in units of MeV). REAL tnmev !Neutrino temperature (in units of MeV). REAL tnu !Neutrino temperature. REAL cnorm !Normalizing constant. REAL rhonu !Neutrino energy density. INTEGER nu !Type of neutrino. C----------RUN OPTION. INTEGER irun !Run network size. INTEGER isize !Number of nuclides in computation. INTEGER jsize !Number of reactions in computation. C----------OUTPUT FILE STATUS. INTEGER nout !Number of output requests. LOGICAL outfile !Indicates if output file used. C===========================PROCEDURE DIVISION================================== C10--------OPEN FILE------------------------------------------------------------ IF (itime.eq.1) THEN !Beginning of program. OPEN (unit=3, file='newint.dat', status='unknown') END IF C20--------WRITE INTO FILE------------------------------------------------------ IF (itime.eq.8) THEN !Right after a run. xout(it,8) = xout(it,8) + xout(it,9) !Add beryllium to lithium. xout(it,5) = xout(it,5) + xout(it,4) !Add tritium to helium-3. xout(it,6) = xout(it,6) - 0.0003 ! my correction for fitted rates+coarse steps WRITE (3,200) c(3), c(2), etaout(it),xout(it,3), | xout(it,5),xout(it,6),xout(it,8) | !Output N_nu, tau_n, eta, H2, He3, He4, and Li7. 200 FORMAT (7(e13.5,' ')) END IF C30--------CLOSE FILE----------------------------------------------------------- IF (itime.eq.10) THEN !End of program. CLOSE (unit=3) END IF RETURN C----------REFERENCES----------------------------------------------------------- C 1) D.A. Dicus, E.W. Kolb, A.M. Gleeson, E.C.G. Sudarshan, V.L. Teplitz, C M.S. Turner, Phys. Rev. D26 (1982) 2694. (Rad corr, Coulomb Corr) C 2) D. Seckel, Bartol preprint BA-93-16; G. Guyk and M.S. Turner, C FERMILAB preprint FERMILAB-Pub-93/181-A. (Nucleon mass) C 4) S. Dodelson and M.S. Turner, Phys. Rev. D46 (1992) 3372; B. Fields, C S. Dodelson and M.S. Turner, Phys. Rev. D47 (1993) 4309. (Nu heating) C 5) S. Sarkar, Rep. Prog Phys. 59 (1996) 1493 (review) END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C This code now modified to run under Linux C (by Scott Dodelson, Oct'01) C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Changes (to run inder DEC unix f77): C ----------------------------------- C COMMON /bessel/ -> COMMON /besselcb/ C COMMON /therm/ -> COMMON /thermcb/ C COMMON /time/ -> COMMON /ttime/ C ir=1 -> ir=5 C iw=1 -> iw=6 C All `entry' routines removed C========================IDENTIFICATION DIVISION================================ SUBROUTINE driver C----------LINKAGES. C CALLED BY - [subroutine] run C CALLS - [subroutine] start, derivs, accum C----------REMARKS. C Runge-Kutta computational routine C----------PARAMETERS. PARAMETER (nvar=29) !Number of variables to be evolved. PARAMETER (nnuc=26) !Number of nuclides in calculation. PARAMETER (cl=1.e-16) !Lower limit on size of time step. C----------COMMON AREAS. COMMON /evolp1/ t9,hv,phie,y !Evolution parameters. COMMON /evolp2/ dt9,dhv,dphie,dydt !Evolution parameters. COMMON /evolp3/ t90,hv0,phie0,y0 !Evolution parameters. COMMON /compr/ cy,ct,t9i,t9f,ytmin,inc !Computation parameters. COMMON /ttime/ t,dt,dlt9dt !Time variables. COMMON /flags/ ltime,is,ip,it,mbad !Flags,counters. COMMON /tcheck/ itime !Computation location. COMMON /runopt/ irun,isize,jsize !Run options. C==========================DECLARATION DIVISION================================= C----------EVOLUTION PARAMETERS. REAL t9 !Temperature (in units of 10**9 K). REAL hv !Defined by hv = M(atomic)n(baryon)/t9**3. REAL phie !Chemical potential for electron. REAL y(nnuc) !Relative number abundances. C----------EVOLUTION PARAMETERS (DERIVATIVES). REAL dydt(nnuc) !Change in rel number abundances. C----------EVOLUTION PARAMETERS (ORIGINAL VALUES). REAL y0(nnuc) !Rel # abund at beginning of iteration. C----------COMPUTATION PARAMETERS. REAL cy !Time step limiting constant on abundances. REAL ct !Time step limiting constant on temperature. REAL t9f !Final temperature (in 10**9 K). REAL ytmin !Smallest abundances allowed. INTEGER inc !Accumulation increment. C----------TIME AND TIME STEP VARIABLES. REAL t !Time. REAL dt !Time step. REAL dlt9dt !(1/t9)*d(t9)/d(t). C----------COUNTERS AND FLAGS. INTEGER loop !Counts which Runge-Kutta loop. INTEGER ltime !Indicates termination status. INTEGER is !# total time steps for particular run. INTEGER ip !# time steps after outputting a line. C----------COMPUTATION LOCATION. INTEGER itime !Time check. C----------RUN OPTION. INTEGER isize !Number of nuclides in computation. C----------TIME AND TIME STEP VARIABLES. REAL dtmin !Mininum time step. REAL dtl !Time step from limitation on abund changes. C----------LABELS FOR VARIABLES TO BE TIME EVOLVED. INTEGER mvar !Total number of variables to be evolved. REAL v(nvar) !Variables to be time evolved. REAL dvdt(nvar) !Time derivatives. REAL v0(nvar) !Value of variables at original point. REAL dvdt0(nvar) !Value of derivatives at original point. C----------EQUIVALENCE STATEMENTS. EQUIVALENCE (v(4),y(1)),(dvdt(4),dydt(1)),(v0(4),y0(1)) C===========================PROCEDURE DIVISION================================== C10--------INPUT INITIALIZATION INFORMATION, RELABEL---------------------------- ltime = 0 !Set termination indicator to zero. CALL start !Input initialization information. mvar = isize + 3 !Total number of variables to be evolved. C20--------LOOP ONE------------------------------------------------------------- 200 continue !Begin Runge-Kutta looping. loop = 1 !Loop indicator. C..........COMPUTE DERIVATIVES OF VARIABLES TO BE EVOLVED. CALL derivs(loop) itime = 4 !Time = 1st R-K loop. CALL check !Check interface subroutine. C..........ACCUMULATE. IF ((t9.le.t9f).or. !Low temp. | (dt.lt.abs(cl/dlt9dt)).or. !Small dt. | (ip.eq.inc)) CALL accum !Enough iterations. C..........POSSIBLY TERMINATE COMPUTATION. IF (ltime.eq.1) THEN !Return to run selection. RETURN END IF C..........RESET COUNTERS. IF (ip.eq.inc) THEN !Reset iteration counters. ip = 0 END IF ip = ip + 1 is = is + 1 C..........ADJUST TIME STEP. IF (is.gt.3) THEN !Adjust time step after 3 iterations. dtmin = abs(1./dlt9dt)*ct !Trial value for minimum time step (Ref 1). DO i = 1,isize !Go through all abundance changes. IF ((dydt(i).ne.0.).and.(y(i).gt.ytmin)) THEN dtl = abs(y(i)/dydt(i))*cy | *(1.+(alog10(y(i))/alog10(ytmin))**2) !(Ref 2). IF (dtl.lt.dtmin) dtmin = dtl !Find smallest time step. END IF END DO IF (dtmin.gt.1.5*dt) dtmin = 1.5*dt !Limit change in time step. dt = dtmin !Set new time step. END IF t = t + dt !Increment time. C..........STORE AND INCREMENT VALUES (Ref 3). DO i = 1,mvar v0(i) = v(i) dvdt0(i) = dvdt(i) v(i) = v0(i) + dvdt0(i)*dt IF ((i.ge.4).and.(v(i).lt.ytmin)) v(i) = ytmin !Set at minimum value. END DO C30--------LOOP TWO------------------------------------------------------------- loop = 2 !Step up loop counter. C..........COMPUTE DERIVATIVES OF VARIABLES TO BE EVOLVED. CALL derivs(loop) itime = 7 !Time = 2nd R-K loop. CALL check !Check interface subroutine. C..........INCREMENT VALUES. DO i = 1,mvar v(i) = v0(i) + .5*(dvdt(i)+dvdt0(i))*dt IF ((i.ge.4).and.(v(i).lt.ytmin)) v(i) = ytmin !Set at minimum value. END DO GO TO 200 C----------REFERENCES----------------------------------------------------------- C 1) Constraint on dt from the requirement that C (d(t9)/dt)*(dt/t9) < ct C Wagoner, R.V. 1969, Ap J. Suppl. No. 162, 18, page 293, equation C6. C 2) Constraint on dt from C dtl < y/(dy/dt)*cy*(1+(log(y)/log(ytmin))**2) C Wagoner, R.V. 1969, page 293, equation C7 but with log term squared. C 3) Wagoner, R.V. 1969, page 292, equations C1, C2. END C========================IDENTIFICATION DIVISION================================ SUBROUTINE start C----------LINKAGES. C CALLED BY - [subroutine] driver C CALLS - [subroutine] rate1, bessel, rate0 C - [function] ex C----------REMARKS. C Sets initial conditions. C----------PARAMETERS. PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (nnuc=26) !Number of nuclides in calculation. PARAMETER (const1=0.09615) !Relation between time and temperature. PARAMETER (const2=6.6700e-8) !Gravitational constant. C----------COMMON AREAS. COMMON /rates/ f,r !Reaction rates. COMMON /evolp1/ t9,hv,phie,y !Evolution parameters. COMMON /evolp2/ dt9,dhv,dphie,dydt(nnuc) !Evolution parameters. COMMON /evolp3/ t90,hv0,phie0,y0 !Evolution parameters. COMMON /compr/ cy,ct,t9i,t9f,ytmin,inc !Computation parameters. COMMON /modpr/ g,tau,xnu,c,cosmo,xi !Model parameters. COMMON /varpr/ dt1,eta1 !Variational parameters. COMMON /ttime/ t,dt,dlt9dt !Time variables. COMMON /endens/ rhone0,rhob0,rhob,rnb !Energy densities. COMMON /besselcb/ bl1,bl2,bl3,bl4,bl5, !Eval of function bl(z). | bm1,bm2,bm3,bm4,bm5, !Eval of function bm(z). | bn1,bn2,bn3,bn4,bn5 !Eval of function bn(z). COMMON /flags/ ltime,is,ip,it,mbad !Flags,counters. COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Neutrino parameters. COMMON /runopt/ irun,isize,jsize !Run options. C==========================DECLARATION DIVISION================================= C----------REACTION RATES. REAL f(nrec) !Forward reaction rate coefficients. REAL r(nrec) !Reverse reaction rate coefficients. C----------EVOLUTION PARAMETERS. REAL t9 !Temperature (in units of 10**9 K). REAL hv !Defined by hv = M(atomic)n(baryon)/t9**3. REAL phie !Chemical potential of electron. REAL y(nnuc) !Relative number abundances. C----------EVOLUTION PARAMETERS (ORIGINAL VALUES). REAL y0(nnuc) !Rel # abund at start of iteration. C----------COMPUTATION SETTINGS. REAL t9i !Initial temperature (in 10**9 K). REAL ytmin !Smallest abundances allowed. INTEGER inc !Accumulation increment. C----------EARLY UNIVERSE MODEL PARAMETERS. REAL g !Gravitational constant. REAL tau !Neutron lifetime. REAL xnu !Number of neutrino species. REAL c(3) !c(1) is variation of grav. constant. | !c(2) is neutron lifetime (sec). | !c(3) is number of neutrino species. REAL xi(3) !Neutrino degeneracy parameters. C----------VARIATIONAL PARAMETERS. REAL dt1 !Initial time step. REAL eta1 !Baryon-to-photon ratio. C----------TIME VARIABLES. REAL t !Time. REAL dt !Time step. C----------ENERGY DENSITIES. REAL rhone0 !Initial electron neutrino mass density. REAL rhob0 !Initial baryon mass density. C----------EVALUATION OF FUNCTIONS bl,bm,bn. REAL bl1,bl2,bl3,bl4,bl5 !Evaluation of function bl(z). C----------COUNTERS AND FLAGS. INTEGER ltime !Indicates if output buffer printed. INTEGER is !# total time steps for particular run. INTEGER ip !# time steps after outputting a line. INTEGER it !# times accumulated in output buffer. INTEGER mbad !Indicates if gaussian elimination fails. C----------NEUTRINO PARAMETERS. REAL tnu !Neutrino temperature. REAL cnorm !Normalizing constant. C----------RUN OPTION. INTEGER isize !Number of nuclides in computation. C----------LOCAL VARIABLES. REAL z !Defined by z = m(electron)*c**2/k*t9. C===========================PROCEDURE DIVISION================================== C10--------INITIALIZE FLAGS AND COUNTERS---------------------------------------- ltime = 0 !No output yet. is = 1 !First iteration coming up. ip = inc !Set to maximum allowed # of iteration. it = 0 !No accumulation yet. mbad = 0 !No computational errors. C20--------SETTINGS------------------------------------------------------------- C..........COMPUTATIONAL SETTINGS. t9 = t9i !Initial temperature. tnu = t9 !Initial neutrino temperature. t = 1/(const1*t9)**2 !Initial time (Ref 1). dt = dt1 !Initial time step. C..........MODEL SETTINGS. g = const2*c(1) !Modify gravitational constant. tau = c(2) !Convert n half-life (min) to lifetime (sec). tau = tau/0.98 !Coulomb correction (Ref 2). xnu = c(3) !Number of neutrino species. C30--------COMPUTE INITIAL ABUNDANCES FOR NEUTRON AND PROTON-------------------- IF ((15.011/t9+xi(1)).gt.58.) THEN !Overabundance of antineutrinos. y(1) = 1.e-25 !Very little of neutrons. y(2) = 1. !Essentially all protons. ELSE IF ((15.011/t9+xi(1)).lt.-58.) THEN !Overabundance of neutrinos. y(1) = 1. !Essentially all neutrons. y(2) = 1.e-25 !Very little of protons. ELSE y(1) = 1./(ex(15.011/t9+xi(1))+1.) !Initial n abundance (Ref 3). y(2) = 1./(ex(-15.011/t9-xi(1))+1.) !Initial p abundance (Ref 3). END IF END IF IF (xi(1).ne.0.) THEN !Electron neutrino degeneracy. cnorm = 1. tnu = .00001 !Low temperature. CALL rate1(0.00001) !Find normalization constant at low temp. cnorm = 1/tau/f(1) END IF y0(1) = y(1) y0(2) = y(2) write(6,134) t9i,y0(1),y0(2) 134 format(1x,1p3e14.6) C40--------FIND RATIO OF BARYON DENSITY TO TEMPERATURE CUBED-------------------- z = 5.930/t9 !Inverse of temperature. CALL bessel(z) hv = 3.3683e+4*eta1*2.75 !(Ref 4 but with final eta). phie = hv*(1.784e-5*y(2)) !Chemical potential of electron (Ref 5). | /(.5*z**3*(bl1-2.*bl2+3.*bl3-4.*bl4+5.*bl5)) rhob0 = hv*t9**3 !Baryon density. IF ((xi(1).eq.0.).and.(xi(2).eq.0.).and.(xi(3).eq.0)) THEN !Nondegen. rhone0 = 7.366*t9**4 !Electron neutrino density (Ref 6). END IF C50--------SET ABUNDANCES FOR REST OF NUCLIDES---------------------------------- y(3) = y(1)*y(2)*rhob0*ex(25.82/t9)/(.471e+10*t9**1.5) !(Ref 7). y0(3) = y(3) DO i = 4,isize y(i) = ytmin !Set rest to minimum abundance. y0(i) = y(i) !Init abundances at beginning of iteration. END DO CALL rate0 !Compute weak decay rates. RETURN C----------REFERENCES----------------------------------------------------------- C 1) Wagoner, R.V., Fowler, W.A., and Hoyle, F. 1967, Ap. J. 148, C page 44, equation A15. C 2) Coulomb correction obtained by dividing by correction factor Fp(t9) C Fp(t9) = 1 - 0.5(pi/(137/c)) C Wagoner, R.V. 1973, Ap. J. 179, page 358. C 3) For the nondegenerate case: C Wagoner, R.V., Fowler, W.A., and Hoyle, F. 1967, Ap. J. 148, C page 4, equation 3. C For the case with neutrino degeneracy: C Beaudet,G. and Goret,P., 1976, Astron. & Astrophys., 49, C page 417, equation 9. C 4) Wagoner, R.V. 1969, Ap J. Suppl. No. 162, 18, page 250, equation 4. C 3.3683e+4 = Mu(ng/t9**3) with Mu the atomic mass, ng the C photon density. 2.75 is for the 11/4 factor difference C between the initial and final values of eta. C 5) Kawano, L., 1992, Fermilab preprint FERMILAB-PUB-92/04-A, C Kellogg Radiation Lab preprint OAP-714. C equation D.2. C 6) Wagoner, R.V., Fowler, W.A., and Hoyle, F. 1967, Ap. J. 148, C page 43, equation A4. C 7.366 is used instead of 14.73 as the latter is the sum total C for 2 neutrino species. C 7) Initial deuterium abundance from nuclear statistical equilibrium C Wagoner, R.V., Fowler, W.A., and Hoyle, F. 1967, Ap. J. 148, C page 19, equation 17. END C========================IDENTIFICATION DIVISION================================ SUBROUTINE derivs(loop) C----------LINKAGES. C CALLED BY - [subroutine] driver C CALLS - [subroutine] therm, rate1, rate4, rate3, rate2, sol C----------REMARKS. C Computes derivatives of C - Temperature C - hv C - Chemical potential C - abundances C----------PARAMETERS. PARAMETER (nvar=29) !Number of variables to be evolved. PARAMETER (nnuc=26) !Number of nuclides in calculation. PARAMETER (pi=3.141593) C----------COMMON AREAS. COMMON /evolp1/ t9,hv,phie,y !Evolution parameters. COMMON /evolp2/ dt9,dhv,dphie,dydt !Evolution parameters. COMMON /evolp3/ t90,hv0,phie0,y0 !Evolution parameters. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi(3) !Model parameters. COMMON /ttime/ t,dt,dlt9dt !Time variables. COMMON /thermcb/ thm,hubcst !Dynamic variables. COMMON /endens/ rhone0,rhob0,rhob,rnb !Energy densities. COMMON /nucdat/ am(nnuc),zm,dm !Nuclide data. COMMON /flags/ ltime,is,ip,it,mbad !Flags,counters. COMMON /runopt/ irun,isize,jsize !Run options. C==========================DECLARATION DIVISION================================= C----------EVOLUTION PARAMETERS. REAL t9 !Temperature (in units of 10**9 K). REAL hv !Defined by hv = M(atomic)n(baryon)/t9**3. REAL phie !Chemical potential for electron. REAL y(nnuc) !Relative number abundances. C----------EVOLUTION PARAMETERS (DERIVATIVES). REAL dt9 !Change in temperature. REAL dhv !Change in hv. REAL dphie !Change in chemical potential. REAL dydt(nnuc) !Change in rel number abundances. C----------EVOLUTION PARAMETERS (ORIGINAL VALUES). REAL y0(nnuc) !Rel # abund at beginning of iteration. C----------MODEL PARAMETERS. REAL g !Gravitational constant. REAL cosmo !Cosmological constant. C----------TIME VARIABLES. REAL dlt9dt !(1/t9)*d(t9)/d(t). C----------DYNAMIC VARIABLES. REAL thm(14) !Thermodynamic variables. REAL hubcst !Expansion rate. C----------ENERGY DENSITIES. REAL rhob0 !Initial baryon mass density. REAL rhob !Baryon mass density. REAL rnb !Baryon mass density (ratio to init value). C----------NUCLIDE DATA. REAL zm(nnuc) !Charge of nuclide. REAL dm(nnuc) !Mass excess of nuclide. C----------COUNTERS AND FLAGS. INTEGER mbad !Indicates if gaussian elimination fails. C----------RUN OPTION. INTEGER irun !Run network size. INTEGER isize !Number of nuclides in computation. C----------SUMS. REAL sumy !Sum of abundances. REAL sumzy !Sum of charge*abundances. REAL sumdy !Sum of abundance flows. REAL summdy !Sum of (mass excess)*(abundance flows). REAL sumzdy !Sum of (charge)*(abundance flows). C----------DERIVATIVES. REAL dphdt9 !d(phi e)/d(t9). REAL dphdln !d(phi e)/d(h). REAL dphdzy !d(phi e)/d(sumzy). REAL dlndt9 !(1/h)*d(h)/d(t9). REAL bar !Baryon density and pressure terms. C----------LOCAL VARIABLES. INTEGER loop !Counts which Runge-Kutta loop. C===========================PROCEDURE DIVISION================================== C10--------COMPUTE DERIVATIVES FOR ABUNDANCES----------------------------------- rnb = hv*t9*t9*t9/rhob0 !Baryon mass density (ratio to init value). C..........VARIOUS THERMODYNAMIC QUANTITIES. CALL therm hubcst = sqrt((8./3.)*pi*g*(thm(10))+(cosmo/3.)) !Expansion rate. rhob = thm(9) !Baryon mass density. C..........COMPUTE REACTION RATE COEFFICIENTS. CALL rate1(t9) GO TO (100,110,120), irun !Run network selection. 100 CONTINUE CALL rate4 !Forward rate for all of reactions. 110 CONTINUE CALL rate3 !Forward rate for reactions with A < 19. 120 CONTINUE CALL rate2 !Forward rate for reactions with A < 10. C..........SOLVE COUPLED DIFFERENTIAL EQUATIONS. CALL sol(loop) IF (mbad.gt.0) RETURN !Abort in case matrix not invertible. C20--------COMPUTE DERIVATIVES FOR TEMPERATURE, hv, AND CHEMICAL POTENTIAL------ C..........INITIALIZE SUMS TO ZERO. sumy = 0. sumzy = 0. sumdy = 0. summdy = 0. sumzdy = 0. C..........ACCUMULATE TO GET SUM. DO i = 1,isize sumy = sumy + y(i) !Sum of abundance. sumzy = sumzy + zm(i)*y(i) !Sum of charge*abundance. sumdy = sumdy + dydt(i) !Sum of abundance flow. summdy = summdy + dm(i)*dydt(i) !Sum of (mass excess)*(abundance flow). sumzdy = sumzdy + zm(i)*dydt(i) !Sum of (charge)*(abundance flow). END DO C..........CHANGES IN TEMPERATURE, hv, AND CHEMICAL POTENTIAL. dphdt9 = thm(12)*(-1.070e-4*hv*sumzy/t9 - thm(11)) dphdln = -thm(12)*3.568e-5*hv*sumzy dphdzy = thm(12)*3.568e-5*hv bar = 9.25e-5*t9*sumy + 1.388e-4*t9*sumdy/(3.*hubcst) | + summdy/(3.*hubcst) dlndt9 = -(thm(2) + thm(5) + thm(6)*dphdt9 + thm(9)*1.388e-4* | sumy)/(thm(1) + thm(3) + thm(4) + thm(7) + thm(9)*bar | + thm(6)*(dphdln + dphdzy*sumzdy/(3.*hubcst))) !(Ref 1). dt9 = (3.*hubcst)/dlndt9 dlt9dt = dt9/t9 dhv = -hv*((3.*hubcst) + 3.*dlt9dt) !(Ref 2). dphie = dphdt9*dt9 + dphdln*(3.*hubcst) + dphdzy*sumzdy !(Ref 3). RETURN C----------REFERENCES----------------------------------------------------------- C 1) Kawano, L., 1992, Fermilab preprint FERMILAB-PUB-92/04-A, C Kellogg Radiation Lab preprint OAP-714, C equation D.35. C 2) Kawano, L., 1992, preprint, equation D.19. C 3) Kawano, L., 1992, preprint, equation D.20. END C========================IDENTIFICATION DIVISION================================ SUBROUTINE accum C----------LINKAGES. C CALLED BY - [subroutine] driver C CALLS - none C----------REMARKS. C Output accumulator. C----------PARAMETERS. PARAMETER (nvar=29) !Number of variables to be evolved. PARAMETER (nnuc=26) !Number of nuclides in calculation. PARAMETER (itmax=400) !Maximum # of lines to be printed. C----------COMMON AREAS. COMMON /evolp1/ t9,hv,phie,y !Evolution parameters. COMMON /compr/ cy,ct,t9i,t9f,ytmin,inc !Computation parameters. COMMON /ttime/ t,dt,dlt9dt !Time variables. COMMON /thermcb/ thm,hubcst !Dynamic variables. COMMON /nucdat/ am,zm(nnuc),dm(nnuc) !Nuclide data. COMMON /flags/ ltime,is,ip,it,mbad !Flags,counters. COMMON /outdat/ xout,thmout,t9out,tout,dtout, !Output data. | etaout,hubout COMMON /runopt/ irun,isize,jsize !Run options. C==========================DECLARATION DIVISION================================= C----------EVOLUTION PARAMETERS. REAL t9 !Temperature (in units of 10**9 K). REAL hv !Defined by hv = M(atomic)n(baryon)/t9**3. REAL phie !Chemical potential for electron. REAL y(nnuc) !Relative number abundances. C----------COMPUTATION PARAMETERS. INTEGER inc !Accumulation increment. C----------TIME PARAMETERS. REAL t !Time. REAL dt !Time step. C----------DYNAMIC VARIABLES. REAL thm(14) !Thermodynamic variables. REAL hubcst !Expansion rate. C----------NUCLIDE DATA. REAL am(nnuc) !Atomic number of nuclide. C----------COUNTERS AND FLAGS. INTEGER ltime !Indicates if output buffer printed. INTEGER it !# times accumulated in output buffer. INTEGER ip !# time steps after outputting a line. C----------OUTPUT ARRAYS. REAL xout(itmax,nnuc) !Nuclide mass fractions. REAL thmout(itmax,6) !Thermodynamic variables. REAL t9out(itmax) !Temperature (in units of 10**9 K). REAL tout(itmax) !Time. REAL dtout(itmax) !Time step. REAL etaout(itmax) !Baryon-to-photon ratio. REAL hubout(itmax) !Expansion rate. C----------RUN OPTION. INTEGER isize !Number of nuclides in computation. C===========================PROCEDURE DIVISION================================== it = it + 1 !Set up accumulation counter. C10--------SET UP OUTPUT VARIABLES---------------------------------------------- C..........DIVIDE NUMBER FRACTION BY THAT OF PROTON. DO i = 1,isize xout(it,i) = y(i)/y(2) END DO xout(it,2) = y(2)*am(2) !Exception for proton. xout(it,6) = y(6)*am(6) !Exception for helium. C..........SUM UP ABUNDANCES OF HEAVY NUCLIDES. xout(it,10) = xout(it,10)+xout(it,11)+xout(it,12)+xout(it,13) | +xout(it,14)+xout(it,15)+xout(it,16)+xout(it,17) | +xout(it,18)+xout(it,19)+xout(it,20)+xout(it,21) | +xout(it,22)+xout(it,23)+xout(it,24)+xout(it,25) | +xout(it,26) !Li8 to O16. C..........RELABEL TEMPERATURE, TIME, THERMODYNAMIC VARIABLES, ETC. t9out(it) = t9 !Temperature. tout(it) = t !Time. thmout(it,1) = thm(1) !rho photon. thmout(it,2) = thm(4) !rho electron. thmout(it,3) = thm(8) !rho neutrino. thmout(it,4) = thm(9) !rho baryon. thmout(it,5) = phie !Chemical potential. thmout(it,6) = thm(10) !rho total. dtout(it) = dt !Time step. etaout(it) = hv/(3.3683e+4)!Baryon to photon ratio. hubout(it) = hubcst !Expansion rate. C20--------INDICATE TERMINATION OF ACCUMULATION IF APPROPRIATE------------------ IF ((it.eq.itmax).or.(ip.lt.inc)) ltime = 1 RETURN END C========================IDENTIFICATION DIVISION================================ SUBROUTINE therm C----------LINKAGES. C CALLED BY - [subroutine] derivs C CALLS - [subroutine] bessel, nudens C - [function] ex C----------REMARKS. C Computes various temperature dependent thermodynamic quantities. C----------PARAMETER. PARAMETER (nnuc=26) !Number of nuclides in calculation. PARAMETER (q=2.531) !(mass(neutron)-mass(proton))/m(electron) C----------COMMON AREAS. COMMON /evolp1/ t9,hv,phie,y(nnuc) !Evolution parameters. COMMON /compr/ cy,ct,t9i,t9f,ytmin,inc !Computation parameters. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi !Model parameters. COMMON /thermcb/ thm,hubcst !Dynamic variables. COMMON /endens/ rhone0,rhob0,rhob,rnb !Energy densities. COMMON /besselcb/ bl1,bl2,bl3,bl4,bl5, !Eval of function bl(z). | bm1,bm2,bm3,bm4,bm5, !Eval of function bm(z). | bn1,bn2,bn3,bn4,bn5 !Eval of function bn(z). COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Integration parameters. C==========================DECLARATION DIVISION================================= C----------EVOLUTION PARAMETERS. REAL t9 !Temperature (in units of 10**9 K). REAL phie !Chemical potential for electron. C----------COMPUTATION PARAMETERS. REAL t9i !Initial temperature (in 10**9 K). C----------EARLY UNIVERSE MODEL PARAMETERS. REAL xnu !Number of neutrino species. REAL xi(3) !Neutrino degeneracy parameters. C----------DYNAMIC VARIABLES. REAL thm(14) !Thermodynamic variables. C----------ENERGY DENSITIES. REAL rhone0 !Initial electron neutrino mass density. REAL rhob0 !Initial baryon mass density. REAL rnb !Baryon mass density (ratio to init value). C----------EVALUATION OF FUNCTIONS bl,bm,bn. REAL bl1,bl2,bl3,bl4,bl5 !Evaluation of function bl(z). REAL bm1,bm2,bm3,bm4,bm5 !Evaluation of function bm(z). REAL bn1,bn2,bn3,bn4,bn5 !Evaluation of function bn(z). C----------NEUTRINO PARAMETERS. REAL tnu !Neutrino temperature. REAL rhonu !Neutrino energy density. INTEGER nu !Type of neutrino. C----------LOCAL VARIABLE. REAL z !Defined by z = m(electron)*c**2/k*t9. C===========================PROCEDURE DIVISION================================== C10--------COMPUTE FACTORS------------------------------------------------------ z = 5.930/t9 !z = m(electron)c**2/k(t9). tnu = ((rnb)**(1./3.))*t9i !Neutrino temperature. C..........FACTORS OF z. z1 = z z2 = z*z z3 = z*z*z z4 = z*z*z*z z5 = z*z*z*z*z C..........TRIGNOMETRIC FUNCTION VALUES. IF (phie.le.17.) THEN !No chance of overflow. cosh1 = cosh(phie) cosh2 = cosh(2.*phie) cosh3 = cosh(3.*phie) cosh4 = cosh(4.*phie) cosh5 = cosh(5.*phie) sinh1 = sinh(phie) sinh2 = sinh(2.*phie) sinh3 = sinh(3.*phie) sinh4 = sinh(4.*phie) sinh5 = sinh(5.*phie) ELSE cosh1 = 0. cosh2 = 0. cosh3 = 0. cosh4 = 0. cosh5 = 0. sinh1 = 0. sinh2 = 0. sinh3 = 0. sinh4 = 0. sinh5 = 0. END IF CALL bessel(z) C20--------COMPUTE THERMODYNAMIC VARIABLES-------------------------------------- thm(1) = 8.418*t9*t9*t9*t9 !(Ref 1). thm(2) = 4.*thm(1)/t9 !(Ref 2). thm(3) = thm(1)/3. !(Ref 3). thm(4) = 3206.*(bm1*cosh1 - bm2*cosh2 + bm3*cosh3 !(Ref 4). | - bm4*cosh4 + bm5*cosh5) thm(5) = 3206.*(z/t9)*(bn1*cosh1 - 2.*bn2*cosh2 !(Ref 5). | + 3.*bn3*cosh3 - 4.*bn4*cosh4 + 5.*bn5*cosh5) thm(6) = 3206.*(bm1*sinh1 - 2.*bm2*sinh2 + 3.*bm3*sinh3 !(Ref 6). | - 4.*bm4*sinh4 + 5.*bm5*sinh5) thm(7) = 3206.*(bl1*cosh1/z - bl2*cosh2/(2.*z) !(Ref 7). | + bl3*cosh3/(3.*z) - bl4*cosh4/(4.*z) | + bl5*cosh5/(5.*z)) IF ((xi(1).eq.0.).and.(xi(2).eq.0.).and.(xi(3).eq.0)) THEN !Nondegen. thm(8) = xnu*rhone0*(rnb**(4./3.)) !(Ref 8). ELSE !Include effects of neutrino degeneracy. thm(8) = 0. DO nu = 1,xnu !For every neutrino family. CALL nudens !Compute neutrino energy density. thm(8) = thm(8) + 12.79264*rhonu !Have 12.79264 from units change. END DO END IF thm(9) = rhob0*rnb !(Ref 9). thm(10) = thm(1) + thm(4) + thm(8) + thm(9) !(Ref 10). thm(11) = -(z**3/t9)*(sinh1*(3.*bl1-z*bm1)-sinh2*(3.*bl2 !(Ref 11). | -2.*z*bm2) + sinh3*(3.*bl3-3.*z*bm3) - sinh4 | *(3.*bl4-4.*z*bm4) + sinh5*(3.*bl5-5.*z*bm5)) thm(12) = z**3*(cosh1*bl1- 2.*cosh2*bl2 !(Ref 12). | + 3.*cosh3*bl3 - 4.*cosh4*bl4 + 5.*cosh5*bl5) IF (thm(12).ne.0.) thm(12) = 1./thm(12) thm(13) = 1.000 + 0.565/z1 - 6.382/z2 + 11.108/z3 !(Ref 13). | + 36.492/z4 + 27.512/z5 thm(14) = (5.252/z1 - 16.229/z2 + 18.059/z3 + 34.181/z4 !(Ref 14). | + 27.617/z5)*ex(-q*z) RETURN C----------REFERENCES AND NOTES------------------------------------------------- C 1) thm(1) = rho photon C (Wagoner, R.V., Fowler, W.A., and Hoyle, F. 1967, Ap. J. 148, C page 43, equation A2.) C 2) thm(2) = d(rho photon)/d(t9) C 3) thm(3) = (p photon)/c**2 C (Wagoner, R.V., Fowler, W.A., and Hoyle, F. 1967, C page 43, equation A3.) C 4) thm(4) = rho electron+positron C (Fowler, W.A. and Hoyle, F., 1964, Ap. J. Suppl. No. 91, 9, C page 281, equation B44.) C 5) thm(5) = d(rho electron+positron)/d(t9) C 6) thm(6) = d(rho electron+positron)/d(phi e) C 7) thm(7) = (p electron+positron)/c**2 C (Fowler, W.A. and Hoyle, F., 1964, Ap. J. Suppl. No. 91, 9, C page 279, equation B27.) C 8) thm(8) = rho neutrino C = # neutrino species x rho electron neutrino (nondegenerate) C = rho nu(e) + rho nu(m) + rho nu(t) (degenerate) C 9) thm(9) = rho baryon C 10) thm(10) = rho total C = rho photon + rho electron+positron + rho neutrino C + rho baryon C 11) thm(11) = d /pi**2(hbar*c)**3(ne- - ne+)*z**3\ C d(t9) \ 2 (mc**2)**3 / C 12) thm(12) = d /pi**2(hbar*c)**3(ne- - ne+)*z**3\ C d(phi e) \ 2 (mc**2)**3 / C 13) thm(13) = rate for n->p C 14) thm(14) = rate for p->n END C========================IDENTIFICATION DIVISION================================ SUBROUTINE bessel(z) C----------LINKAGES. C CALLED BY - [subroutine] start, therm C CALLS - [subroutine] knux C----------REMARKS. C Evaluates functions bl(z), bm(z), and bn(z) using solutions to C modified Bessel functions. C----------COMMON AREAS. COMMON /besselcb/ bl1,bl2,bl3,bl4,bl5, !Eval function bl(z). | bm1,bm2,bm3,bm4,bm5, !Eval function bm(z). | bn1,bn2,bn3,bn4,bn5 !Eval function bn(z). COMMON /kays/ bk0,bk1,bk2,bk3,bk4 !Coefficients K. C==========================DECLARATION DIVISION================================= C----------EVALUATION OF FUNCTIONS bl,bm,bn. REAL bl1,bl2,bl3,bl4,bl5 !Single variables equivalenced to array blz. REAL bm1,bm2,bm3,bm4,bm5 !Single variables equivalenced to array bmz. REAL bn1,bn2,bn3,bn4,bn5 !Single variables equivalenced to array bnz. C----------EVALUATIION OF MODIFIED BESSEL FUNCTIONS. REAL bk0,bk1,bk2,bk3,bk4 !Values k0(r),k1(r),k2(r),k3(r),k4(r). C----------LOCAL VARIABLES. REAL blz(5) !Array containing values from function bl. REAL bmz(5) !Array containing values from function bm. REAL bnz(5) !Array containing values from function bn. REAL z !Defined by z = m(electron)*c**2/k*t9. REAL r !Multiples of z. C----------EQUIVALENCE STATEMENTS. EQUIVALENCE (blz(1),bl1),(blz(2),bl2),(blz(3),bl3),(blz(4),bl4), | (blz(5),bl5) EQUIVALENCE (bmz(1),bm1),(bmz(2),bm2),(bmz(3),bm3),(bmz(4),bm4), | (bmz(5),bm5) EQUIVALENCE (bnz(1),bn1),(bnz(2),bn2),(bnz(3),bn3),(bnz(4),bn4), | (bnz(5),bn5) C===========================PROCEDURE DIVISION================================== C10--------LOCALLY DEFINED FUNCTIONS-------------------------------------------- bl(z) = bk2/z !Function bl. bm(z) = 0.25*(3.*bk3+bk1)/z !Function bm. bn(z) = 0.5*(bk4+bk2)/z !Function bn. C20--------CALCULATE FOR 1 THRU 5 Z--------------------------------------------- DO i=1,5 r=i*z !Multiples of z. CALL knux(r) !Get k0(r),k1(r),k2(r),k3(r),k4(r),k(5). blz(i) = bl(r) !Put value from function bl into array. bmz(i) = bm(r) !Put value from function bm into array. bnz(i) = bn(r) !Put value from function bn into array. END DO RETURN END C========================IDENTIFICATION DIVISION================================ SUBROUTINE knux(z) C----------LINKAGES. C CALLED BY - [subroutine] bessel C CALLS - [function] exp C----------REMARKS. C A subroutine for modified bessel functions of the second kind C k-nu(z). C----------COMMON AREAS. COMMON /kays/ bk0,bk1,bk2,bk3,bk4 !Coefficients K. C===========================DECLARATION DIVISION================================ C-----------MODIFIED BESSEL FUNCTION VALUES. REAL bk0,bk1 !Values k0(z),k1(z) REAL bi0,bi1 !Values i0(z),i1(z). REAL bk2,bk3,bk4 !Values k2(z),k3(z),k4(z). C-----------EXPANSION COEFFICIENTS. REAL ci0(7) !Expansion coefficients for i0 (z.le.2). REAL ci1(7) !Expansion coefficients for i1 (z.le.2). REAL ck0(7) !Expansion coefficients for k0 (z.le.2). REAL ck1(7) !Expansion coefficients for k1 (z.le.2). REAL c0(7) !Expansion coefficients for k0 (z.gt.2). REAL c1(7) !Expansion coefficients for k1 (z.gt.2). C-----------VARIABLES TO BE EVALUATED. REAL z !Input variable. REAL y !Expansion variable = z/2. REAL t !Expansion variable = z/3.75. REAL coeff !Logrithmic or exponential coefficient. C==============================DATA DIVISION==================================== C----------EXPANSION COEFFICIENTS. DATA ci0 / 1., | 3.5156229, 3.0899424, 1.2067492, | 0.2659732, 0.0360768, 0.0045813/ DATA ci1 / 0.5, | 0.87890594, 0.51498869, 0.15084934, | 0.02658733, 0.00301532, 0.00032411/ DATA ck0 /-0.57721566, | 0.42278420, 0.23069756, 0.03488590, | 0.00262698, 0.00010750, 0.00000740/ DATA ck1 / 1., | 0.15443144, -0.67278579, -0.18156897, | -0.01919402, -0.00110404, -0.00004686/ DATA c0 / 1.25331414, | -0.07832358, 0.02189568, -0.01062446, | 0.00587872, -0.00251540, 0.00053208/ DATA c1 / 1.25331414, | 0.23498619, -0.03655620, 0.01504268, | -0.00780353, 0.00325614, -0.00068245/ C===========================PROCEDURE DIVISION================================== C10--------COMPUTE K0 AND K1---------------------------------------------------- IF (z.le.2.) THEN !(Ref. 1). C..........COMPUTE FACTORS. t = (z/3.75) y = (z/2) coeff = alog(y) C..........VALUES FOR i0(z) and i1(z). bi0 = ci0(1) bi1 = ci1(1) bk0 = ck0(1) bk1 = ck1(1) DO i = 2,7 bi0 = bi0 + ci0(i)*t**(2*(i-1)) bi1 = bi1 + ci1(i)*t**(2*(i-1)) bk0 = bk0 + ck0(i)*y**(2*(i-1)) bk1 = bk1 + ck1(i)*y**(2*(i-1)) END DO C..........VALUES FOR k0(z) and k1(z). bk0 = -coeff*bi0 + bk0 bk1 = coeff*bi1*z + bk1/z ELSE !(z.le.2.) !(Ref. 2). C..........COMPUTE FACTORS. y = (2.0/z) coeff = (ex(-z)/sqrt(z)) C..........VALUES FOR k0(z) and k1(z). bk0 = c0(1) bk1 = c1(1) DO i = 2,7 bk0 = bk0 + c0(i)*y**(i-1) bk1 = bk1 + c1(i)*y**(i-1) END DO bk0 = coeff*bk0 bk1 = coeff*bk1 END IF !(z.le.2.) C20--------FIND K2, K3, AND K4 BY ITERATION (Ref. 3)---------------------------- bk2 = 2.*(bk1/z) + bk0 !k2(z). bk3 = 4.*(bk2/z) + bk1 !k3(z). bk4 = 6.*(bk3/z) + bk2 !k4(z). RETURN C----------REFERENCES----------------------------------------------------------- C Handbook of Mathematical Functions (Abramowitz and Stegun), C Dover Publications, Inc., New York C 1) Polynomial approximations for z.le.2 C page 378, equations 9.8.1 and 9.8.3. C page 379, equations 9.8.5 and 9.8.7. C 2) Polynomial approximations for z > 2 C page 379, equations 9.8.6 and 9.8.8. C 3) Recursion relation from 1st line of 9.6.26, page 376. END C========================IDENTIFICATION DIVISION================================ SUBROUTINE nudens C----------LINKAGES. C CALLED BY - [subroutine] therm C CALLS - [function] xintd, eval C----------REMARKS. C Computes energy density contribution from neutrinos. C----------PARAMTER. PARAMETER (iter=50) !Number of gaussian quads. C----------COMMON AREAS. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi !Model parameters. COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Integration parameters. C----------EXTERNAL FUNCTIONS. EXTERNAL func5 !Integral for neutrinos. EXTERNAL func6 !Integral for antineutrinos. C==========================DECLARATION DIVISION================================= C----------MODEL PARAMETERS. REAL xi(3) !Neutrino degeneracy parameters. C----------NEUTRINO PARAMETERS. REAL tnu !Neutrino temperature (units of 10**9 K). REAL rhonu !Neutrino energy density. INTEGER nu !Which neutrino type. C----------LOCAL VARIABLES. REAL uplim1 !Upper limit for neutrino energy integral. REAL uplim2 !Upper limit for antineu energy integral. C===========================PROCEDURE DIVISION================================== C10--------COMPUTE NEUTRINO ENERGY DENSITIES------------------------------------ IF (abs(xi(nu)).le.0.03) THEN C..........SMALL xi APPROXIMATION. rhonu = 2.*(3.14159**2/30.)*(tnu)**4 | *(7./8.+(15./(4*3.14159**2))*xi(nu)**2 | +(15./(8.*3.14159**4))*xi(nu)**4) ELSE IF (abs(xi(nu)).ge.30.) THEN C..........LARGE xi APPROXIMATION. rhonu = ((tnu)**4)/(8.*3.14159**2)*xi(nu)**4 | *(1+12.*1.645 /xi(nu)**2) ELSE C..........DO INTEGRATION uplim1 = (88.029+xi(nu))*tnu uplim2 = (88.029-xi(nu))*tnu IF (uplim2.le.0.) THEN rhonu = xintd(0.,uplim1,func5,iter) ELSE rhonu= xintd(0.,uplim1,func5,iter) | + xintd(0.,uplim2,func6,iter) END IF END IF !(abs(xi(nu)).ge.30.) END IF !(abs(xi(nu)).le.0.03) RETURN C----------REFERENCES----------------------------------------------------------- C Forms of the integrals involved can be found in C Beaudet,G. and Goret,P., 1976, Astron. & Astrophys., 49, 415. C Freese, K., Kolb, E.W., Turner, M.S., 1983, Phys. Rev. D, 27, 1689. END C========================IDENTIFICATION DIVISION================================ C===========================PROCEDURE DIVISION================================== C10--------1ST PART OF INTEGRAL FOR n->p RATE----------------------------------- **************************************************************************** real function func1(x) C----------LINKAGES. C CALLED BY - [subroutine] rate1, nudens C CALLS - [function] ex C----------REMARKS. C Contains integrands to be integrated. C----------COMMON AREAS. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi !Model parameters. COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Integration parameters. C==========================DECLARATION DIVISION================================= C----------MODEL PARAMETERS. REAL xi(3) !Neutrino degeneracy parameters. C----------NEUTRINO PARAMETERS. REAL t9mev !Temperature (in units of MeV). REAL tnmev !Neutrino temperature (in units of MeV). REAL tnu !Neutrino temperature (units of 10**9 K). REAL cnorm !Normalizing constant. C----------LOCAL VARIABLES. REAL x !Value at which function is evaluated. REAL part1 !Exponential expression with photon temp. REAL part2 !Exponential expression with neutrino temp. IF (x.le.0.) THEN func1 = 0. ELSE part1 = 1./(1.+ex(-.511*x/t9mev)) part2 = 1./(1.+ex(+(x-2.531)*(.511/tnmev)-xi(1))) func1 = cnorm*x*(x-2.531)**2*(x**2-1)**.5*part1*part2 END IF RETURN end C20--------2ND PART OF INTEGRAL FOR n->p RATE----------------------------------- real function func2(x) C----------LINKAGES. C CALLED BY - [subroutine] rate1, nudens C CALLS - [function] ex C----------REMARKS. C Contains integrands to be integrated. C----------COMMON AREAS. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi !Model parameters. COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Integration parameters. C==========================DECLARATION DIVISION================================= C----------MODEL PARAMETERS. REAL xi(3) !Neutrino degeneracy parameters. C----------NEUTRINO PARAMETERS. REAL t9mev !Temperature (in units of MeV). REAL tnmev !Neutrino temperature (in units of MeV). REAL tnu !Neutrino temperature (units of 10**9 K). REAL cnorm !Normalizing constant. C----------LOCAL VARIABLES. REAL x !Value at which function is evaluated. REAL part1 !Exponential expression with photon temp. REAL part2 !Exponential expression with neutrino temp. IF (x.le.1.) THEN func2 = 0. ELSE part1 = 1./(1.+ex(+.511*x/t9mev)) part2 = 1./(1.+ex(-(x+2.531)*(.511/tnmev)-xi(1))) func2 = cnorm*x*(x+2.531)**2*(x**2-1)**.5*part1*part2 END IF RETURN end C30--------1ST PART OF INTEGRAL FOR p->n RATE----------------------------------- real function func3(x) C----------LINKAGES. C CALLED BY - [subroutine] rate1, nudens C CALLS - [function] ex C----------REMARKS. C Contains integrands to be integrated. C----------COMMON AREAS. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi !Model parameters. COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Integration parameters. C==========================DECLARATION DIVISION================================= C----------MODEL PARAMETERS. REAL xi(3) !Neutrino degeneracy parameters. C----------NEUTRINO PARAMETERS. REAL t9mev !Temperature (in units of MeV). REAL tnmev !Neutrino temperature (in units of MeV). REAL tnu !Neutrino temperature (units of 10**9 K). REAL cnorm !Normalizing constant. C----------LOCAL VARIABLES. REAL x !Value at which function is evaluated. REAL part1 !Exponential expression with photon temp. REAL part2 !Exponential expression with neutrino temp. IF (x.le.1.) THEN func3 = 0. ELSE part1 = 1./(1.+ex(-.511*x/t9mev)) part2 = 1./(1.+ex(+(x+2.531)*(.511/tnmev)+xi(1))) func3 = cnorm*x*(x+2.531)**2*(x**2-1)**.5*part1*part2 END IF RETURN end C40--------2ND PART OF INTEGRAL FOR p->n RATE----------------------------------- real function func4(x) C----------LINKAGES. C CALLED BY - [subroutine] rate1, nudens C CALLS - [function] ex C----------REMARKS. C Contains integrands to be integrated. C----------COMMON AREAS. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi !Model parameters. COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Integration parameters. C==========================DECLARATION DIVISION================================= C----------MODEL PARAMETERS. REAL xi(3) !Neutrino degeneracy parameters. C----------NEUTRINO PARAMETERS. REAL t9mev !Temperature (in units of MeV). REAL tnmev !Neutrino temperature (in units of MeV). REAL tnu !Neutrino temperature (units of 10**9 K). REAL cnorm !Normalizing constant. C----------LOCAL VARIABLES. REAL x !Value at which function is evaluated. REAL part1 !Exponential expression with photon temp. REAL part2 !Exponential expression with neutrino temp. IF (x.le.1.) THEN func4 = 0. ELSE part1 = 1./(1.+ex(+.511*x/t9mev)) part2 = 1./(1.+ex(-(x-2.531)*(.511/tnmev)+xi(1))) func4 = cnorm*x*(x-2.531)**2*(x**2-1)**.5*part1*part2 END IF RETURN end C50--------INTEGRAL FOR ENERGY DENSITY OF NEUTRINO------------------------------ real function func5(x) C----------LINKAGES. C CALLED BY - [subroutine] rate1, nudens C CALLS - [function] ex C----------REMARKS. C Contains integrands to be integrated. C----------COMMON AREAS. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi !Model parameters. COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Integration parameters. C==========================DECLARATION DIVISION================================= C----------MODEL PARAMETERS. REAL xi(3) !Neutrino degeneracy parameters. C----------NEUTRINO PARAMETERS. REAL t9mev !Temperature (in units of MeV). REAL tnmev !Neutrino temperature (in units of MeV). REAL tnu !Neutrino temperature (units of 10**9 K). REAL cnorm !Normalizing constant. C----------LOCAL VARIABLES. REAL x !Value at which function is evaluated. REAL part1 !Exponential expression with photon temp. REAL part2 !Exponential expression with neutrino temp. func5 = 1./(2*3.14159**2)*x**3/(1.+exp(x/tnu-xi(nu))) RETURN end C60--------INTEGRAL FOR ENERGY DENSITY OF ANTINEUTRINO-------------------------- real function func6(x) C----------LINKAGES. C CALLED BY - [subroutine] rate1, nudens C CALLS - [function] ex C----------REMARKS. C Contains integrands to be integrated. C----------COMMON AREAS. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi !Model parameters. COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Integration parameters. C==========================DECLARATION DIVISION================================= C----------MODEL PARAMETERS. REAL xi(3) !Neutrino degeneracy parameters. C----------NEUTRINO PARAMETERS. REAL t9mev !Temperature (in units of MeV). REAL tnmev !Neutrino temperature (in units of MeV). REAL tnu !Neutrino temperature (units of 10**9 K). REAL cnorm !Normalizing constant. C----------LOCAL VARIABLES. REAL x !Value at which function is evaluated. REAL part1 !Exponential expression with photon temp. REAL part2 !Exponential expression with neutrino temp. func6 = 1./(2*3.14159**2)*x**3/(1.+exp(x/tnu+xi(nu))) RETURN end C----------REFERENCES----------------------------------------------------------- C Forms of the integrals involved can be found in C Scherrer,R.J., 1983, Mon.Not.R.astr.Soc., 205, 683. C Beaudet,G. and Goret,P., 1976, Astron. & Astrophys., 49, 415. C========================IDENTIFICATION DIVISION================================ FUNCTION xintd (xlow,xhi,func,nq) C----------LINKAGES. C CALLED BY - [subroutine] rate1, nudens C CALLS - none C----------REMARKS. C Computes the integral of the function "func". C==========================DECLARATION DIVISION================================= C----------INPUT VARIABLES. REAL xlow !Array of low limits. REAL xhi !Array of high limits. INTEGER nq !Number of six point gaussian quads. C----------COMPUTATION VARIABLES. REAL dist !Size of quad interval. REAL cent !Center of quad interval. REAL x !Variables of integration. REAL sum !Summation of terms. C----------COUNTERS. INTEGER nint !Interval number. INTEGER npnt !Point number. INTEGER np !Total number of points in interval. C----------ABSCISSAS AND WEIGHT FACTORS. REAL u(6) !Abscissas. REAL w(6) !Weight factor. C==============================DATA DIVISION==================================== C----------ABSCISSAS AND WEIGHT FACTORS. DATA u/-.93246951420315,-.66120938646627,-.23861918608320, | .23861918608320, .66120938646627, .93246951420315/ DATA w/.17132449237917,.36076157304814,.46791393457269, | .46791393457269,.36076157304814,.17132449237917/ DATA np/6/ !6 point Gaussian integration. C===========================PROCEDURE DIVISION================================== C10--------DO INTEGRATION------------------------------------------------------- sum = 0. dist = (xhi-xlow)/float(nq) !Size of quad interval. DO nint = 1,nq cent = xlow+(float(nint)-0.5)*dist !Center of interval. DO npnt = 1,np x = cent+0.5*dist*u(npnt) !Integration point. f = func(x) !Evaluate function x(1). sum = sum+f*w(npnt) !Add up sum. END DO END DO C20--------GET INTEGRAL VALUE--------------------------------------------------- xintd = sum*dist*0.5 !Do integral. RETURN END C========================IDENTIFICATION DIVISION================================ FUNCTION ex(x) C----------LINKAGES. C CALLED BY - [subroutine] start, rate2, rate3, rate4, sol C - [function] eval C CALLS - none C----------REMARKS. C Exponential function with underflow precaution. C===========================PROCEDURE DIVISION================================== IF (x.gt.88.029) THEN !In danger of overflow. ex = exp(88.029) ELSE IF (x.lt.-88.722) THEN !In danger of underflow. ex = 0. ELSE !Value of x in allowable range. ex = exp(x) END IF END IF RETURN C----------NOTE----------------------------------------------------------------- C The overflow limit for the VAX/VMS system is exp(88.029). C The underflow limit for the VAX/VMS system is exp(-88.722). END C========================IDENTIFICATION DIVISION================================ SUBROUTINE sol(loop) C----------LINKAGES. C CALLED BY - [subroutine] derivs C CALLS - [subroutine] eqslin C - [function] ex C----------REMARKS. C Computes reverse strong and electromagnetic reaction rates. C Fills and solves matrix equation for dydt(i). C----------PARAMETERS. PARAMETER (ir=5) !Input unit number. PARAMETER (iw=6) !Output unit number. PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (nnuc=26) !Number of nuclides in calculation. C-----------COMMON AREAS. COMMON /recpr/ iform,ii,jj,kk,ll,rev,q9 !Reaction parameters names. COMMON /rates/ f,r !Reaction rates. COMMON /evolp1/ t9,hv,phie,y !Evolution parameters. COMMON /evolp2/ dt9,dhv,dphie,dydt !Evolution parameters. COMMON /evolp3/ t90,hv0,phie0,y0 !Evolution parameters. COMMON /ttime/ t,dt,dlt9dt !Time varying parameters. COMMON /thermcb/ thm(14),hubcst !Dynamic variables. COMMON /endens/ rhone0,rhob0,rhob,rnb !Energy densities. COMMON /lncoef/ a,b,yx !Linear eqn coefficients. COMMON /flags/ ltime,is,ip,it,mbad !Flags,counters. COMMON /runopt/ irun,isize,jsize !Run option. C==========================DECLARATION DIVISION================================= C----------REACTION PARAMETERS. INTEGER iform(nrec) !Reaction code number (1-88). INTEGER ii(nrec) !Incoming nuclide type (1-26). INTEGER jj(nrec) !Incoming light nuclide type (1-6). INTEGER kk(nrec) !Outgoing light nuclide type (1-6). INTEGER ll(nrec) !Outgoing nuclide type (1-26). REAL rev(nrec) !Reverse reaction coefficient. REAL q9(nrec) !Energy released in reaction. C----------REACTION RATES. REAL f(nrec) !Forward reaction rate coefficients. REAL r(nrec) !Reverse reaction rate coefficients. C----------EVOLUTION PARAMETERS. REAL t9 !Temperature (in units of 10**9 K). REAL y(nnuc) !Relative number abundances. C----------EVOLUTION PARAMETERS (DERIVATIVES). REAL dydt(nnuc) !Change in rel number abundances. C----------EVOLUTION PARAMETERS (ORIGINAL VALUES). REAL y0(nnuc) !Rel # abund at start of iteration. C----------TIME VARIABLES. REAL dt !Time step. C----------DYNAMIC VARIABLES. REAL hubcst !Expansion rate. C----------ENERGY DENSITIES. REAL rhob !Baryon mass density. C----------COMPONENTS OF MATRIX EQUATION. DOUBLE PRECISION a(nnuc,nnuc)!Relates y(t-dt) to y(t). REAL b(nnuc) !Contains y0 in inverse order. REAL yx(nnuc) !yy in reverse order. C----------COUNTERS AND FLAGS. INTEGER loop !Counts which Runge-Kutta loop. INTEGER ip !# time steps after outputting a line. INTEGER mbad !Indicates if gaussian elimination fails. C----------RUN OPTIONS. INTEGER isize !Number of nuclides in computation. INTEGER isize1 !Equals isize + 1. INTEGER jsize !Number of reactions in computation. C----------EVOLUTION EQUATION COEFFICIENTS. INTEGER i,j,k,l !Equate to ii,jj,kk,ll. REAL ri,rj,rk,rl !Equate to si,sj,sk,sl. REAL ci,cj,ck,cl !Coefficients of rate equation. C----------LOCAL VARIABLES. REAL yy(nnuc) !Abundances at end of iteration. REAL si(11),sj(11),sk(11),sl(11) !# of nuclide i,j,k,l REAL bdln !(10**(-5))*volume expansion rate. INTEGER ind !Equate to iform. INTEGER ierror !Element which does not converge. C==============================DATA DIVISION==================================== C----------NUMBER OF NUCLIDES IN REACTION TYPES 1-11. DATA si /1.,1.,1.,1.,1.,2.,3.,2.,1.,1.,2./ DATA sj /0.,1.,1.,0.,1.,0.,0.,1.,1.,1.,0./ DATA sk /0.,0.,1.,0.,0.,1.,0.,0.,1.,0.,2./ DATA sl /1.,1.,1.,2.,2.,1.,1.,1.,2.,3.,1./ C===========================PROCEDURE DIVISION================================== C10--------TEMPERATURE FACTORS AND INITIAL VALUES------------------------------- C..........TEMPERATURE FACTORS. t932 = t9**1.5 !t9**(3/2). t9m32 = 1./t932 !t9**(-3/2). C..........MATRIX SIZE. isize1 = isize + 1 C..........INITIALIZE A-MATRIX. DO i = 1,isize DO j = 1,isize a(j,i) = 0.d0 !Set a-matrix to zero. END DO END DO C20--------COMPUTE FACTORS FOR THE A-MATRIX------------------------------------- DO n = 1,jsize C..........EQUATE VARIABLES TO ARRAYS. ind = iform(n) !Type of reaction. i = ii(n) !ID # of incoming nuclide i. j = jj(n) !ID # of incoming nuclide j. k = kk(n) !ID # of outgoing nuclide k. l = ll(n) !ID # of outgoing nuclide l. IF ((ind.ne.0).and.(i.le.isize).and.(l.le.isize)) THEN !Reaction okay. ri = si(ind) !# of incoming nuclide i. rj = sj(ind) !# of incoming nuclide j. rk = sk(ind) !# of outgoing nuclide k. rl = sl(ind) !# of outgoing nuclide l. C..........COMPUTE DIFFERENT REACTION RATES. GO TO (201,202,203,204,205,206,207,208,209,210,211),ind 201 CONTINUE !1-0-0-1 configuration. ci = f(n) !(Ref 1). cj = 0. ck = 0. cl = r(n) GO TO 212 202 CONTINUE !1-1-0-1 configuration. r(n) = rev(n)*1.e+10*t932*ex(-q9(n)/t9)*f(n) !(Ref 2). f(n) = rhob*f(n) ci = y(j)*f(n)/2. cj = y(i)*f(n)/2. ck = 0. cl = r(n) GO TO 212 203 CONTINUE !1-1-1-1 configuration. f(n) = rhob*f(n) r(n) = rev(n)*ex(-q9(n)/t9)*f(n) !(Ref 3). ci = y(j)*f(n)/2. cj = y(i)*f(n)/2. ck = y(l)*r(n)/2. cl = y(k)*r(n)/2. GO TO 212 204 CONTINUE !1-0-0-2 configuration. ci = f(n) cj = 0. ck = 0. cl = y(l)*r(n)/2. GO TO 212 205 CONTINUE !1-1-0-2 configuration. f(n) = rhob*f(n) r(n) = rev(n)*ex(-q9(n)/t9)*f(n) !(Ref 3). ci = y(j)*f(n)/2. cj = y(i)*f(n)/2. ck = 0. cl = y(l)*r(n)/2. GO TO 212 206 CONTINUE !2-0-1-1 configuration. f(n) = rhob*f(n) r(n) = rev(n)*ex(-q9(n)/t9)*f(n) !(Ref 3). ci = y(i)*f(n)/2. cj = 0. ck = y(l)*r(n)/2. cl = y(k)*r(n)/2. GO TO 212 207 CONTINUE !3-0-0-1 configuration. r(n) = rev(n)*1.e+20*t932*t932*ex(-q9(n)/t9)*f(n) !(Ref 4). f(n) = rhob*rhob*f(n) ci = y(i)*y(i)*f(n)/6. cj = 0. ck = 0. cl = r(n) GO TO 212 208 CONTINUE !2-1-0-1 configuration. r(n) = rev(n)*1.e+20*t932*t932*ex(-q9(n)/t9)*f(n) !(Ref 4). f(n) = rhob*rhob*f(n) ci = y(j)*y(i)*f(n)/3. cj = y(i)*y(i)*f(n)/6. ck = 0. cl = r(n) GO TO 212 209 CONTINUE !1-1-1-2 configuration. f(n) = rhob*f(n) r(n) = rev(n)*1.e-10*t9m32*rhob*ex(-q9(n)/t9)*f(n) !(Ref 5). ci = y(j)*f(n)/2. cj = y(i)*f(n)/2. ck = y(l)*y(l)*r(n)/6. cl = y(k)*y(l)*r(n)/3. GO TO 212 210 CONTINUE !1-1-0-3 configuration. f(n) = rhob*f(n) r(n) = rev(n)*1.e-10*t9m32*rhob*ex(-q9(n)/t9)*f(n) !(Ref 5). ci = y(j)*f(n)/2. cj = y(i)*f(n)/2. ck = 0. cl = y(l)*y(l)*r(n)/6. GO TO 212 211 CONTINUE !2-0-2-1 configuration. f(n) = rhob*f(n) r(n) = rev(n)*1.e-10*t9m32*rhob*ex(-q9(n)/t9)*f(n) !(Ref 5). ci = y(i)*f(n)/2. cj = 0. ck = y(l)*y(k)*r(n)/3. cl = y(k)*y(k)*r(n)/6. 212 CONTINUE C30--------CONSTRUCT THE A-MATRIX----------------------------------------------- i = isize1 - i !Invert i index. j = isize1 - j !Invert j index. k = isize1 - k !Invert k index. l = isize1 - l !Invert l index. C..........FILL I NUCLIDE COLUMN. IF (j.le.isize) a(j,i) = a(j,i) + rj*ci IF (k.le.isize) a(k,i) = a(k,i) - rk*ci a(i,i) = a(i,i) + ri*ci a(l,i) = a(l,i) - rl*ci C..........FILL J NUCLIDE COLUMN. IF (j.le.isize) THEN a(j,j) = a(j,j) + rj*cj IF (k.le.isize) a(k,j) = a(k,j) - rk*cj a(i,j) = a(i,j) + ri*cj a(l,j) = a(l,j) - rl*cj END IF C..........FILL K NUCLIDE COLUMN. IF (k.le.isize) THEN IF (j.le.isize) a(j,k) = a(j,k) - rj*ck a(k,k) = a(k,k) + rk*ck a(i,k) = a(i,k) - ri*ck a(l,k) = a(l,k) + rl*ck END IF C..........FILL L NUCLIDE COLUMN. IF (j.le.isize) a(j,l) = a(j,l) - rj*cl IF (k.le.isize) a(k,l) = a(k,l) + rk*cl a(i,l) = a(i,l) - ri*cl a(l,l) = a(l,l) + rl*cl END IF !((ind.ne.0).and.(i.le.isize).and.(l.le.isize)) END DO !n = 1,jsize C40--------PUT A-MATRIX AND B-VECTOR IN FINAL FORM OF MATRIX EQUATION----------- bdln = 1.e-5*(3.*hubcst) !(10**(-5))*(Expansion rate). DO i = 1,isize i1 = isize1 - i !Invert the rows. DO j = 1,isize j1 = isize1 - j !Invert the columns. IF (dabs(a(j,i)).lt.bdln*y0(j1)/y0(i1)) THEN a(j,i) = 0.d0 !Set 0 if tiny. ELSE a(j,i) = a(j,i)*dt !Bring dt over to other side. END IF END DO a(i,i) = 1.d0 + a(i,i) !Add identity matrix to a-matrix. b(i1) = y0(i) !Initial abundances. END DO C50--------SOLVE EQUATIONS TO GET DERIVATIVE------------------------------------ C..........SET MONITOR FLAG AND SOLVE BY GAUSSIAN ELIMINATION. IF (loop.eq.1) THEN CALL eqslin(ip,ierror) ELSE CALL eqslin(0,ierror) END IF C..........OBTAIN DERIVATIVE. DO i = 1,isize yy(i) = yx(isize1-i) !Abundance at t+dt. dydt(i) = (yy(i) - y0(i))/dt !Take derivative. END DO C60--------POSSIBLE ERROR MESSAGES AND EXIT------------------------------------- IF (mbad.ne.0) THEN !Problem in gaussian elimination. IF (mbad.eq.-1) WRITE (iw,6000) ierror !Error message. IF (mbad.ge. 1) WRITE (iw,6002) mbad !Error message. 6000 FORMAT (' ','** y(', i2, ') fails to converge **') 6002 FORMAT (' ','** ', i2, ' th diagonal term equals zero **') END IF RETURN C----------REFERENCES----------------------------------------------------------- C 1) The coefficients are given in general as: C ci = ri*(y(j)**rj)*(y(i)**(ri-1)*f(n)/ C ((ri+rj)*fac(ri)*fac(rj)) C cj = rj*(y(i)**ri)*(y(j)**(rj-1)*f(n)/ C ((ri+rj)*fac(ri)*fac(rj)) C ck = rk*(y(l)**rl)*(y(k)**(rk-1)*f(n)/ C ((rk+rl)*fac(rk)*fac(rl)) C cl = rl*(y(k)**rk)*(y(l)**(rl-1)*f(n)/ C ((rk+rl)*fac(rk)*fac(rl)) C in which fac(x) is the factorial of x. C 2) Form of reverse rate given in C Wagoner, R.V.,1969, Ap. J. Suppl. No. 162, 18, 247, C tables 1B, 4B, 7B. C 3) Form of reverse rate given in C Wagoner, R.V.,1969, Ap. J. Suppl. No. 162, 18, 247, C tables 2B, 3B, 5B, 6B, 8B, 9B, 10B. C 4) Form of reverse rate given in C Wagoner, R.V.,1969, Ap. J. Suppl. No. 162, 18, 247, C table 11B. C 5) Form of reverse rate given in C Wagoner, R.V.,1969, Ap. J. Suppl. No. 162, 18, 247, C tables 12B, 13B. END C========================IDENTIFICATION DIVISION================================ SUBROUTINE eqslin(icnvm,ierror) C----------LINKAGES. C CALLED BY - [subroutine] sol C CALLS - none C----------REMARKS. C Solves for new abundances using gaussian elimination C with back substitution, no pivoting. C----------PARAMETERS. PARAMETER (nnuc=26) !Rank of matrix. PARAMETER (mord=1) !Higher order in correction. PARAMETER (eps=2.e-4) !Tolerance for convergence (.ge. 1.e-7). C----------COMMON AREAS. COMMON /compr/ cy,ct,t9i,t9f,ytmin,inc !Computation parameters. COMMON /lncoef/ a,b,y !Lin eqn coefficients. COMMON /flags/ ltime,is,ip,it,mbad !Flags, counters. COMMON /runopt/ irun,isize,jsize !Run options. C==========================DECLARATION DIVISION================================= C----------COMPUTATION PARAMETER. INTEGER inc !Accumulation increment. C----------MATRIX COEFFICIENTS FOR LINEAR EQUATION. DOUBLE PRECISION a(nnuc,nnuc)!Coefficient array. REAL b(nnuc) !Right-hand vector w/o manipulation. REAL y(nnuc) !Solution vector. C----------COUNTERS AND FLAGS. INTEGER mbad !Indicates type of error. C----------RUN OPTION. INTEGER isize !Number of nuclides in computation. C----------LOCAL MATRICES AND VECTORS. DOUBLE PRECISION a0(nnuc,nnuc)!Coefficient array w/o manipulation. DOUBLE PRECISION x(nnuc) !Right-hand vector. C----------LOCAL COMPUTATION VARIABLES. DOUBLE PRECISION cx !Scaling factor in triangularization. DOUBLE PRECISION sum !Sum for backsubstitution. REAL xdy !Relative error. C----------LOCAL COUNTERS. INTEGER nord !Order of correction. INTEGER icnvm !Convergence monitor. INTEGER ierror !ith nuclide fails to converge. C===========================PROCEDURE DIVISION================================== C10--------INITIALIZE VECTOR---------------------------------------------------- C..........SET COUNTERS TO ZERO. nord = 0 !No corrections yet. mbad = 0 !No errors yet. C..........SET RIGHT-HAND AND SOLUTION VECTORS TO INITIAL VALUES. DO i = 1,isize x(i) = b(i) !Right-hand vector. y(i) = 0. !Solution vector. END DO C..........SAVE MATRIX. IF (icnvm.eq.inc) THEN !Monitor convergence. DO i = 1,isize DO j = 1,isize a0(j,i) = a(j,i) !Initial value of coefficient array. END DO END DO END IF C20--------TRIANGULARIZE MATRIX AND SAVE OPERATOR------------------------------- C..........CHECK TO SEE THAT THERE ARE NO ZEROES AT PIVOT POINTS. DO i = 1,isize-1 IF (a(i,i).eq.0.d0) THEN !Don't want to divide by zero. mbad = i !Position of zero coefficient. RETURN !Terminate matrix evaluation. END IF C..........TRIANGULARIZE MATRIX. DO j = i+1,isize IF (a(j,i).ne.0.d0) THEN !Progress diagonally down the column. cx = a(j,i)/a(i,i) !Scaling factor down the column. DO k = i+1,isize !Progress diagonally along row. a(j,k) = a(j,k) - cx*a(i,k) !Subtract scaled coeff along row. END DO a(j,i) = cx !Scaled coefficient. C..........OPERATE ON RIGHT-HAND VECTOR. x(j) = x(j) - cx*x(i) !Subtract off scaled coefficient. END IF END DO END DO C30--------DO BACK SUBSTITUTION------------------------------------------------- 300 CONTINUE x(isize) = x(isize)/a(isize,isize) !Solution for ultimate position. y(isize) = y(isize) + x(isize) DO i = isize-1,1,-1 !From i = penultimate to i = 1. sum = 0.d0 DO j = i+1,isize sum = sum + a(i,j)*x(j) !Sum up all previous terms. END DO x(i) = (x(i) - sum)/a(i,i) y(i) = y(i) + x(i) !Add difference to initial value. END DO C40--------TESTS AND EXITS------------------------------------------------------ IF (icnvm.eq.inc) THEN DO i = 1,isize IF (y(i).ne.0.) THEN xdy = dabs(x(i)/y(i)) !Relative error. IF (xdy.gt.eps) THEN IF (nord.lt.mord) THEN !Continue to higher orders. nord = nord + 1 C..........FIND ERROR IN RIGHT-HAND VECTOR. DO j = 1,isize r = 0.d0 !Initialize r. DO k = 1,isize r = r + a0(j,k)*y(k) !Left side with approximate solution. END DO x(j) = b(j) - r !Subtract difference from right side. END DO C..........OPERATE ON RIGHT-HAND VECTOR. DO j = 1,isize-1 DO k = j+1,isize x(k) = x(k) - a(k,j)*x(j) !Subtract off scaled coefficient. END DO END DO GO TO 300 !Go for another iteratiion. ELSE C..........NOT ENOUGH CONVERGENCE. mbad = -1 !Signal error problem. ierror = i !ith nuclide for which x/y checked. RETURN END IF !(nord.lt.mord) END IF !(xdy.gt.eps) END IF !(y(i).ne.0) END DO !i = 1,isize END IF !(icnvm.eq.inc) RETURN !No more iterations & relative error small. END CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C This code now modified to run under Linux C (by Scott Dodelson, Oct'01) C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C Changes (to run inder DEC unix f77): C ----------------------------------- C COMMON /therm/ -> COMMON /thermcb/ C COMMON /rates/ f,r(nrec) -> COMMON /rates/ f,r C C Default neutron lifetime 888.54 -> 885.7 SUBROUTINE rate0 C----------LINKAGES. C CALLED BY - [subroutine] start C CALLS - none C----------REMARKS. C Generates weak decay rates. C----------PARAMETER. PARAMETER (nrec=88) !Number of nuclear reactions. C----------COMMON AREA. COMMON /rates/ f,r !Reaction rates. C==========================DECLARATION DIVISION================================= C----------REACTION RATE COEFFICIENTS. REAL f(nrec) !Forward reaction rate coefficients. REAL r(nrec) C===========================PROCEDURE DIVISION================================== C10--------SET DECAY RATE COEFFICIENTS------------------------------------------ C.......H3 -> e- + v + He3.........(Tilly-Weller-Hasan 1987) f(2) = 1.79e-9 C.......Li8 -> e- + v + 2He4.......(Ajzenberg-Selove 1988) f(3) = 8.27e-1 C.......B12 -> e- + B + C12........(Ajzenberg-Selove 1990) f(4) = 3.43e+1 C.......C14 -> e- + v + N14........(Ajzenberg-Selove 1986) f(5) = 3.834e-12 C.......B8 -> e+ + v + 2He4........(Ajzenberg-Selove 1988) f(6) = 9.00e-1 C.......C11 -> e+ + v + B11........(Ajzenberg-Selove 1990) f(7) = 5.668e-4 C.......N12 -> e+ + v + C12........(Ajzenberg-Selove 1990) f(8) = 6.301e+1 C.......N13 -> e+ + v + C13........(Ajzenberg-Selove 1986) f(9) = 1.159e-3 C.......O14 -> e+ + v + N14........(Ajzenberg-Selove 1986) f(10) = 9.8171e-3 C.......O15 -> e+ + v + N15........(Ajzenberg-Selove 1986) f(11) = 5.6704e-3 RETURN C----------REFERENCES----------------------------------------------------------- C Ajzenberg-Selove, F., 1990, Nucl. Phys. A506, 1. C Ajzenberg-Selove, F., 1988, Nucl. Phys. A490, 1. C Ajzenberg-Selove, F., 1986, Nucl. Phys. A449, 1. C Tilley, D.R., Weller, H.R., and Hasan, H.H., 1987, Nucl. Phys. A474, 1. END C========================IDENTIFICATION DIVISION================================ SUBROUTINE rate1(tph) C----------LINKAGES. C CALLED BY - [subroutine] start, derivs C CALLS - [function] xintd, eval C----------REMARKS. C Generates rate coefficients for weak n->p and p->n reactions. C----------PARAMETERS. PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (iter=50) !Number of gaussian quads. C----------COMMON AREAS. COMMON /rates/ f,r !Reaction rates. COMMON /modpr/ g,tau,xnu,c(3),cosmo,xi !Model parameters. COMMON /thermcb/ thm,hubcst !Dynamic variables. COMMON /nupar/ t9mev,tnmev,tnu,cnorm,nu,rhonu !Integration parameters. C----------EXTERNAL FUNCTIONS. EXTERNAL func1 !Part 1 of n->p rate. EXTERNAL func2 !Part 2 of n->p rate. EXTERNAL func3 !Part 1 of p->n rate. EXTERNAL func4 !Part 2 of p->n rate. C==========================DECLARATION DIVISION================================= C----------REACTION RATES. REAL f(nrec) !Forward reaction rate coefficients. REAL r(nrec) !Reverse reaction rate coefficients. C----------EARLY UNIVERSE MODEL PARAMETERS. REAL tau !Neutron lifetime. REAL xi(3) !Neutrino degeneracy parameters. | !xi(1) is e neutrino degeneracy parameter. | !xi(2) is m neutrino degeneracy parameter. | !xi(3) is t neutrino degeneracy parameter. C----------DYNAMIC VARIABLES. REAL thm(14) !Thermodynamic variables (energy densities). C----------NEUTRINO PARAMETERS. REAL t9mev !Temperature (in units of MeV). REAL tnmev !Neutrino temperature (in units of MeV). C----------LOCAL VARIABLES. REAL tph !Photon temperature. REAL w(2),x(2), !Upper limits for exponentials, forward rate. | y(2),z(2) !Upper limits for exponentials, reverse rate. REAL uplim1,uplim2, !Upper limits for integrals for forward rate. | uplim3,uplim4 !Upper limits for integrals for reverse rate. REAL part1,part2, !Parts of integrals for forward rate. | part3,part4 !Parts of integrals for reverse rate. C===========================PROCEDURE DIVISION================================== C10--------COMPUTE WEAK REACTION RATES (NONDEGENERATE)-------------------------- IF (xi(1).eq.0.) THEN f(1) = thm(13)/tau !Forward rate for weak np reaction. r(1) = thm(14)/tau !Reverse rate for weak np reaction. ELSE C20--------COMPUTE WEAK REACTION RATES (DEGENERATE)----------------------------- t9mev = tph*.086171 !Convert photon temp to units of MeV. tnmev = tnu*.086171 !Convert neutrino temp to units of MeV. C..........COMPUTE OVERFLOW LIMITS FOR LIMITS OF INTEGRATION (Ref 1 & 2). w(1) = (-(t9mev/.511)*(-88.722)) w(2) = ((tnmev/.511)*(88.029+xi(1))+2.531) x(1) = ((t9mev/.511)*(88.029)) x(2) = (-(tnmev/.511)*(-88.722+xi(1))-2.531) y(1) = (-(t9mev/.511)*(-88.722)) y(2) = ((tnmev/.511)*(88.029-xi(1))-2.531) z(1) = ((t9mev/.511)*(88.029)) z(2) = (-(tnmev/.511)*(-88.722-xi(1))+2.531) C..........COMPARE LIMITS AND TAKE LARGER OF THE TWO. uplim1 = abs(w(1)) uplim2 = abs(x(1)) uplim3 = abs(y(1)) uplim4 = abs(z(1)) IF (uplim1.lt.abs(w(2))) uplim1 = w(2) IF (uplim2.lt.abs(x(2))) uplim2 = x(2) IF (uplim3.lt.abs(y(2))) uplim3 = y(2) IF (uplim4.lt.abs(z(2))) uplim4 = z(2) C..........EVALUATE THE INTEGRALS NUMERICALLY. part1 = xintd(1.,uplim1,func1,iter) part2 = xintd(1.,uplim2,func2,iter) part3 = xintd(1.,uplim3,func3,iter) part4 = xintd(1.,uplim4,func4,iter) f(1) = part1 + part2 !Add 2 integrals to get forward rate. r(1) = part3 + part4 !Add 2 integrals to get reverse rate. END IF !(xi(1).eq.0.) RETURN C----------REFERENCES----------------------------------------------------------- C 1) Forms of the integrals involved can be found in C Scherrer,R.J., 1983, Mon.Not.R.astr.Soc., 205, 683. C Beaudet,G. and Goret,P., 1976, Astron. & Astrophys., 49, 415. C C 2) The overflow limit for the VAX/VMS system is exp(88.029). C The underflow limit for the VAX/VMS system is exp(-88.722). END C========================IDENTIFICATION DIVISION================================ SUBROUTINE rate2 C----------LINKAGES. C CALLED BY - [subroutine] derivs C CALLS - [function] ex C----------REMARKS. C Generates rate coefficients for reactions involving nuclides C up to A = 9. C----------PARAMETER. PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (nnuc=26) !Number of nuclides in calculation. C----------COMMON AREAS. COMMON /rates/ f,r !Reaction rates. COMMON /evolp1/ t9,hv,phie,y(nnuc) !Evolution parameters. C==========================DECLARATION DIVISION================================= C----------REACTION RATES. REAL f(nrec) !Forward reaction rate coefficients. real r(nrec) C----------EVOLUTION PARAMETER. REAL t9 !Temperature of photons (units of 10**9 K). C===========================PROCEDURE DIVISION================================== C10--------TEMPERATURE FACTORS-------------------------------------------------- t913 = t9**(.33333333) !t9**(1/3) t923 = t913*t913 !t9**(2/3) t943 = t923*t923 !t9**(4/3) t953 = t9*t923 !t9**(5/3) t912 = sqrt(t9) !t9**(1/2) t932 = t9*t912 !t9**(3/2) t9m1 = 1/t9 !t9**(-1) t9m23 = 1.0/t923 !t9**(-2/3) t9m32 = 1.0/t932 !t9**(-3/2) t9a = t9/(1.0+13.076*t9) !For reaction 17. t9a32 = t9a**(1.5) !t9a**(3/2) t9b = t9/(1.+49.18*t9) !For reaction 18. t9b32 = t9b**(1.5) !t9b**(3/2) IF (t9.gt.10.) THEN !For reaction 22. t9c = 1. ELSE t9c = t9/(1.-9.69e-2*t9+2.84e-2*t953/(1.-9.69e-2*t9)**(2./3.)) END IF t9c13 = t9c**(.3333333) !t9c**(1/3) t9c56 = t9c**(.8333333) !t9c**(5/6) t9d = t9/(1.+0.759*t9) !For reaction 24. t9d13 = t9d**(.3333333) !t9d**(1/3) t9d56 = t9d**(.8333333) !t9d**(5/6) t9e = t9/(1.+0.1378*t9) !For reaction 26. t9e13 = t9e**(.3333333) !t9e**(1/3) t9e56 = t9e**(.8333333) !t9e**(5/6) t9f = t9/(1.+0.1071*t9) !For reaction 27. t9f13 = t9f**(.3333333) !t9f**(1/3) t9f56 = t9f**(.8333333) !t9f**(5/6) C20--------NEUTRON, PHOTON REACTIONS-------------------------------------------- C.......H(n,g)H2...................(Smith-Kawano-Malaney 1992) f(12) = 4.742e+4*(1.-.8504*t912+.4895*t9-.09623*t932 | +8.471e-3*t9*t9-2.80e-4*t9*t932) C.......H2(n,g)H3..................(Wagoner 1969) f(13) = 6.62e+1*(1.+18.9*t9) C.......He3(n,g)He4................(Wagoner 1969) f(14) = 6.62e+0*(1.+905.*t9) C.......Li6(n,g)Li7................(Malaney-Fowler 1989) f(15) = 5.10e+3 C30--------NEUTRON, PROTON REACTIONS-------------------------------------------- C.......He3(n,p)H3.................(Smith-Kawano-Malaney 1992) f(16) = 7.21e+8*(1.-.508*t912+.228*t9) C.......Be7(n,p)Li7................(Smith-Kawano-Malaney 1992) f(17) = 2.675e+9*(1.-.560*t912+.179*t9-.0283*t932 | + 2.214e-3*t9*t9-6.851e-5*t9*t932) | + 9.391e+8*t9a32*t9m32 | + 4.467e+7*t9m32*ex(-0.07486/t9) C40--------NEUTRON, ALPHA REACTIONS--------------------------------------------- C.......Li6(n,a)H3.................(Caughlan-Fowler 1988) f(18) = 2.54e+9*t9m32*ex(-2.39/t9) | + 1.68e+8*(1.-.261*t9b32/t932) C.......Be7(n,a)He4................(Wagoner 1969) f(19) = 2.05e+4*(1.+3760.*t9) C50--------PROTON, PHOTON REACTIONS--------------------------------------------- C.......H2(p,g)He3.................(Smith-Kawano-Malaney 1992) f(20) = 2.65e+3*t9m23*ex(-3.720/t913) | *(1.+.112*t913+1.99*t923+1.56*t9+.162*t943+.324*t953) C.......H3(p,g)He4.................(Caughlan-Fowler 1988) f(21) = 2.20e+4*t9m23*ex(-3.869/t913) | *(1.+.108*t913+1.68*t923+1.26*t9+.551*t943+1.06*t953) C.......Li6(p,g)Be7................(Caughlan-Fowler 1988) f(22) = 6.69e+5*t9c56*t9m32*ex(-8.413/t9c13) C60--------PROTON, ALPHA REACTIONS---------------------------------------------- C.......Li6(p,a)He3................(Caughlan-Fowler 1988) f(23) = 3.73e+10*t9m23*ex(-8.413/t913-(t9/5.50)**2) | *(1.+.050*t913-.061*t923-.021*t9+.006*t943+.005*t953) | + 1.33e+10*t9m32*ex(-17.763/t9) | + 1.29e+09*t9m1*ex(-21.820/t9) C.......Li7(p,a)He4................(Smith-Kawano-Malaney 1992) f(24) = 1.096e+9*t9m23*ex(-8.472/t913) | - 4.830e+8*t9d56*t9m32*ex(-8.472/t9d13) | + 1.06e+10*t9m32*ex(-30.442/t9) | + 1.56e+5*t9m23*ex((-8.472/t913)-(t9/1.696)**2) | *(1.+.049*t913-2.498*t923+.860*t9+3.518*t943+3.08*t953) | + 1.55e+6*t9m32*ex(-4.478/t9) C70--------ALPHA, PHOTON REACTIONS---------------------------------------------- C.......H2(a,g)Li6.................(Caughlan-Fowler 1988) f(25) = 3.01e+01*t9m23*ex(-7.423/t913) | *(1.+.056*t913-4.85*t923+8.85*t9-.585*t943-.584*t953) | + 8.55e+1*t9m32*ex(-8.228/t9) C.......H3(a,g)Li7.................(Smith-Kawano-Malaney 1992) f(26) = 3.032e+5*t9m23*ex(-8.090/t913) | *(1.+.0516*t913+.0229*t923+8.28e-3*t9 | -3.28e-4*t943-3.01e-4*t953) | + 5.109e+5*t9e56*t9m32*ex(-8.068/t9e13) C.......He3(a,g)Be7................(Smith-Kawano-Malaney 1992) f(27) = 4.817e+6*t9m23*ex(-14.964/t913) | *(1.+.0325*t913-1.04e-3*t923-2.37e-4*t9 | -8.11e-5*t943-4.69e-5*t953) | + 5.938e+6*t9f56*t9m32*ex(-12.859/t9f13) C80--------DEUTERIUM, NEUTRON AND DEUTERIUM, PROTON REACTIONS------------------- C.......H2(d,n)He3.................(Smith-Kawano-Malaney 1992) f(28) = 3.95e+8*t9m23*ex(-4.259/t913) | *(1.+.098*t913+.765*t923+.525*t9+9.61e-3*t943+.0167*t953) C.......H2(d,p)H3..................(Smith-Kawano-Malaney 1992) f(29) = 4.17e+8*t9m23*ex(-4.258/t913) | *(1.+.098*t913+.518*t923+.355*t9-.010*t943-.018*t953) C.......H3(d,n)He4.................(Smith-Kawano-Malaney 1992) f(30) = 1.063e+11*t9m23*ex(-4.559/t913-(t9/.0754)**2) | *(1.+.092*t913-.375*t923-.242*t9+33.82*t943+55.42*t953) | + 8.047e+8*t9m23*ex(-0.4857/t9) C.......He3(d,p)He4................(Smith-Kawano-Malaney 1992) f(31) = 5.021e+10*t9m23*ex(-7.144/t913-(t9/.270)**2) | *(1.+.058*t913+.603*t923+.245*t9+6.97*t943+7.19*t953) | + 5.212e+8/t912*ex(-1.762/t9) C90--------THREE PARTICLE REACTIONS--------------------------------------------- C.......He3(He3,2p)He4.............(Caughlan-Fowler 1988) f(32) = 6.04e+10*t9m23*ex(-12.276/t913) | *(1.+.034*t913-.522*t923-.124*t9+.353*t943+.213*t953) C.......Li7(d,na)He4...............(Caughlan-Fowler 1988) f(33) = 2.92e+11*t9m23*ex(-10.259/t913) C.......Be7(d,pa)He4...............(Caughlan-Fowler 1988) f(34) = 1.07e+12*t9m23*ex(-12.428/t913) RETURN C----------REFERENCES----------------------------------------------------------- C Smith, M., Kawano, L.H., and Malaney, R.A., 1992, submitted to Ap. J. C Malaney, R.A., and Fowler, W.A., 1989, Astrophys. J., 345, L5. C Caughlan, G.R., and Fowler, W.A., 1988, Atomic Data and Nuclear Data C Tables, 40, 283. C Wagoner, R.V.,1969, Ap. J. Suppl. No. 162, 18, 247. END C========================IDENTIFICATION DIVISION================================ SUBROUTINE rate3 C----------LINKAGES. C CALLED BY - [subroutine] derivs C CALLS - [function] ex C----------REMARKS. C Generates rate coefficients for reactions involving nuclides C up to A = 18. C----------PARAMETER. PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (nnuc=26) !Number of nuclides in calculation. C----------COMMON AREAS. COMMON /rates/ f,r !Reaction rates. COMMON /evolp1/ t9,hv,phie,y(nnuc) !Evolution parameters. C==========================DECLARATION DIVISION================================= C----------REACTION RATES. REAL f(nrec) !Forward reaction rate coefficients. real r(nrec) C----------EVOLUTION PARAMETER. REAL t9 !Temperature of photons (units of 10**9 K). C===========================PROCEDURE DIVISION================================== C10--------TEMPERATURE FACTORS-------------------------------------------------- t913 = t9**(.33333333) !t9**(1/3) t923 = t913*t913 !t9**(2/3) t943 = t923*t923 !t9**(4/3) t953 = t9*t923 !t9**(5/3) t912 = sqrt(t9) !t9**(1/2) t932 = t9*t912 !t9**(3/2) t915 = t9**(.2) !t9**(1/5) t954 = t9**(1.25) !t9**(5/4) t9m1 = 1.0/t9 !t9**(-1) t9m23 = 1.0/t923 !t9**(-2/3) t9m32 = 1.0/t932 !t9**(-3/2) t9m34 = sqrt(t9m32) !t9**(-3/4) t9m15 = 1.0/t915 !t9**(-1/5) t9m54 = 1.0/t954 !t9**(-5/4) t9a = t9/(1.+t9/15.1) !For reaction 53. t9a13 = t9a**(.3333333) !t9a**(1/3) t9a56 = t9a**(.8333333) !t9a**(5/6) C20--------NEUTRON, PHOTON REACTIONS-------------------------------------------- C.......Li7(n,g)Li8................(Wagoner 1969) f(35) = 4.90e+3 + 9.96e+3*t9m32*ex(-2.62/t9) C.......B10(n,g)B11................(Wagoner 1969) f(36) = 6.62e+4 C.......B11(n,g)B12................(Malaney-Fowler 1989) f(37) = 7.29e+2 + 2.40e+3*t9m32*ex(-0.223/t9) C30--------NEUTRON, PROTON REACTIONS-------------------------------------------- C.......C11(n,p)B11................(Caughlan-Fowler 1988) f(38) = 1.69e+8*(1.-.048*t912+.010*t9) C40--------NEUTRON, ALPHA REACTIONS--------------------------------------------- C.......B10(n,a)Li7................(Caughlan-Fowler 1988) f(39) = 5.07e+8 C50--------PROTON, PHOTON REACTIONS--------------------------------------------- C.......Be7(p,g)B8.................(Caughlan-Fowler 1988) f(40) = 3.11e+5*t9m23*ex(-10.262/t913) | + 2.53e+3*t9m32*ex(-7.306/t9) C.......Be9(p,g)B10................(Caughlan-Fowler 1988) f(41) = 1.33e+7*t9m23*ex(-10.359/t913-(t9/.846)**2) | *(1.+.040*t913+1.52*t923+.428*t9+2.15*t943+1.54*t953) | + 9.64e+4*t9m32*ex(-3.445/t9) | + 2.72e+6*t9m32*ex(-10.620/t9) C.......B10(p,g)C11................(Caughlan-Fowler 1988) f(42) = 4.61e+5*t9m23*ex(-12.062/t913-(t9/4.402)**2) | *(1.+.035*t913+.426*t923+.103*t9+.281*t943+.173*t953) | + 1.93e+5*t9m32*ex(-12.041/t9) | + 1.14e+4*t9m32*ex(-16.164/t9) C.......B11(p,g)C12................(Caughlan-Fowler 1988) f(43) = 4.62e+7*t9m23*ex(-12.095/t913-(t9/.239)**2) | *(1.+.035*t913+3.00*t923+.723*t9+9.91*t943+6.07*t953) | + 7.89e+3*t9m32*ex(-1.733/t9) | + 9.68e+4*t9m15*ex(-5.617/t9) C.......C11(p,g)N12................(Caughlan-Fowler 1988) f(44) = 4.24e+4*t9m23*ex(-13.658/t913-(t9/1.627)**2) | *(1.+.031*t913+3.11*t923+.665*t9+4.61*t943+2.50*t953) | + 8.84e+3*t9m32*ex(-7.021/t9) C60--------PROTON, NEUTRON REACTIONS-------------------------------------------- C.......B12(p,n)C12................(Wagoner 1969) f(45) = 4.02e+11*t9m23*ex(-12.12/t913) C70--------PROTON, ALPHA REACTIONS---------------------------------------------- C.......Be9(p,a)Li6................(Caughlan-Fowler 1988) f(46) = 2.11e+11*t9m23*ex(-10.359/t913-(t9/.520)**2) | *(1.+.040*t913+1.09*t923+.307*t9+3.21*t943+2.30*t953) | + 4.51e+8*t9m1*ex(-3.046/t9) | + 6.70e+8*t9m34*ex(-5.160/t9) C.......B10(p,a)Be7................(Caughlan-Fowler 1988) f(47) = 1.26e+11*t9m23*ex(-12.062/t913-(t9/4.402)**2) | *(1.+.035*t913-.498*t923-.121*t9+.300*t943+.184*t953) | + 2.59e+9*t9m1*ex(-12.260/t9) C.......B12(p,a)Be9................(Wagoner 1969) f(48) = 2.01e+11*t9m23*ex(-12.12/t913) C80--------ALPHA, PHOTON REACTIONS---------------------------------------------- C.......Li6(a,g)B10................(Caughlan-Fowler 1988) f(49) = 4.06e+6*t9m23*ex(-18.790/t913-(t9/1.326)**2) | *(1.+.022*t913+1.54*t923+.239*t9+2.20*t943+.869*t953) | + 1.91e+3*t9m32*ex(-3.484/t9) | + 1.01e+4*t9m1*ex(-7.269/t9) C.......Li7(a,g)B11................(Caughlan-Fowler 1988) f(50) = 3.55e+7*t9m23*ex(-19.161/t913-(t9/4.195)**2) | *(1.+.022*t913+.775*t923+.118*t9+.884*t943+.342*t953) | + 3.33e+2*t9m32*ex(-2.977/t9) | + 4.10e+4*t9m1*ex(-6.227/t9) C.......Be7(a,g)C11................(Caughlan-Fowler 1988) f(51) = 8.45e+7*t9m23*ex(-23.212/t913-(t9/4.769)**2) | *(1.+.018*t913+.488*t923+.061*t9+.296*t943+.095*t953) | + 1.25e+4*t9m32*ex(-6.510/t9) | + 1.29e+5*t9m54*ex(-10.039/t9) C90--------ALPHA, PROTON REACTIONS---------------------------------------------- C.......B8(a,p)C11.................(Wagoner 1969) f(52) = 1.08e+15*t9m23*ex(-27.36/t913) C100-------ALPHA, NEUTRON REACTIONS--------------------------------------------- C.......Li8(a,n)B11................(Malaney-Fowler 1989) f(53) = 8.62e+13*t9a56*t9m32*ex(-19.461/t9a13) C.......Be9(a,n)C12................(Caughlan-Fowler 1988) f(54) = 4.62e+13*t9m23*ex(-23.870/t913-(t9/.049)**2) | *(1.+.017*t913+8.57*t923+1.05*t9+74.51*t943+23.15*t953) | + 7.34e-5*t9m32*ex(-1.184/t9) | + 2.27e-1*t9m32*ex(-1.834/t9) | + 1.26e+5*t9m32*ex(-4.179/t9) | + 2.40e+8*ex(-12.732/t9) C110-------DEUTERIUM, NEUTRON AND DEUTERIUM, PROTON REACTIONS------------------- C.......Be9(d,n)B10................(original Wagoner code) f(55) = 7.16e+8*t9m23*ex(6.44-12.6/t913) C.......B10(d,p)B11................(original Wagoner code) f(56) = 9.53e+8*t9m23*ex(7.30-14.8/t913) C.......B11(d,n)C12................(original Wagoner code) f(57) = 1.41e+9*t9m23*ex(7.40-14.8/t913) C120-------THREE PARTICLE REACTIONS--------------------------------------------- C.......He4(an,g)Be9...............(Caughlan-Fowler 1988) f(58) = (2.59e-6/((1.+.344*t9)*t9**2))*ex(-1.062/t9) C.......He4(2a,g)C12...............(Caughlan-Fowler 1988) f(59) = 2.79e-8*t9m32*t9m32*ex(-4.4027/t9) | + 1.35e-8*t9m32*ex(-24.811/t9) C.......Li8(p,na)He4...............(original Wagoner code) f(60) = 8.65e+9*t9m23*ex(-8.52/t913-(t9/2.53)**2) | + 2.31e+9*t9m32*ex(-4.64/t9) C.......B8(n,pa)He4................(original Wagoner code) f(61) = 4.02e+8 C.......Be9(p,da)He4...............(Caughlan-Fowler 1988) f(62) = 2.11e+11*t9m23*ex(-10.359/t913-(t9/.520)**2) | *(1.+.040*t913+1.09*t923+.307*t9+3.21*t943+2.30*t953) | + 5.79e+8*t9m1*ex(-3.046/t9) | + 8.50e+8*t9m34*ex(-5.800/t9) C.......B11(p,2a)He4...............(Caughlan-Fowler 1988) f(63) = 2.20e+12*t9m23*ex(-12.095/t913-(t9/1.644)**2) | *(1.+.034*t913+.140*t923+.034*t9+.190*t943+.116*t953) | + 4.03e+6*t9m32*ex(-1.734/t9) | + 6.73e+9*t9m32*ex(-6.262/t9) | + 3.88e+9*t9m1*ex(-14.154/t9) C.......C11(n,2a)He4...............(Wagoner 1969) f(64) = 1.58e+8 RETURN C----------REFERENCES----------------------------------------------------------- C Malaney, R.A., and Fowler, W.A., 1989, Astrophys. J., 345, L5. C Caughlan, G.R., and Fowler, W.A., 1988, Atomic Data and Nuclear Data C Tables, 40, 283. C Wagoner, R.V.,1969, Ap. J. Suppl. No. 162, 18, 247. END C========================IDENTIFICATION DIVISION================================ SUBROUTINE rate4 C----------LINKAGES. C CALLED BY - [subroutine] derivs C CALLS - [function] ex C----------REMARKS. C Generates rate coefficients for rest of reactions. C----------PARAMETER. PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (nnuc=26) !Number of nuclides in calculation. C----------COMMON AREAS. COMMON /rates/ f,r !Reaction rates. COMMON /evolp1/ t9,hv,phie,y(nnuc) !Evolution parameters. C==========================DECLARATION DIVISION================================= C----------REACTION RATES. REAL f(nrec) !Forward reaction rate coefficients. real r(nrec) C----------EVOLUTION PARAMETER. REAL t9 !Temperature of photons (units of 10**9 K). C===========================PROCEDURE DIVISION================================== C10--------TEMPERATURE FACTORS-------------------------------------------------- t913 = t9**(.33333333) !t9**(1/3) t923 = t913*t913 !t9**(2/3) t943 = t923*t923 !t9**(4/3) t953 = t9*t923 !t9**(5/3) t912 = sqrt(t9) !t9**(1/2) t932 = t9*t912 !t9**(3/2) t935 = t9**(.6) !t9**(3/5) t965 = t9**(1.2) !t9**(6/5) t938 = t9**(.375) !t9**(3/8) t9m13 = 1.0/t913 !t9**(1/3) t9m23 = 1.0/t923 !t9**(-2/3) t9m32 = 1.0/t932 !t9**(-3/2) t9m65 = 1.0/t965 !t9**(-6/5) t9a = t9 !For reaction 82. | /(1.+4.78e-2*t9+7.56e-3*t953/(1.+4.78e-2*t9)**(2./3.)) t9a13 = t9a**(.33333333) !t9a**(1/3) t9a56 = t9a**(.83333333) !t9a**(5/6) t9b = t9 !For reaction 84. | /(1.+7.76e-2*t9+2.64e-2*t953/(1.+7.76e-2*t9)**(2./3.)) t9b13 = t9b**(.33333333) !t9b**(1/3) t9b56 = t9b**(.83333333) !t9b**(5/6) C20--------NEUTRON, PHOTON REACTIONS-------------------------------------------- C.......C12(n,g)C13................(Wagoner 1969) f(65) = 4.50e+2 C.......C13(n,g)C14................(Wagoner 1969) f(66) = 1.19e+2 + 2.38e+5*t9m32*ex(-1.67/t9) C.......N14(n,g)N15................(Wagoner 1969) f(67) = 9.94e+3 C30--------NEUTRON, PROTON REACTIONS-------------------------------------------- C.......N13(n,p)C13................(Caughlan-Fowler 1988) f(68) = 1.88e+8*(1.-.167*t912+.037*t9) C.......N14(n,p)C14................(Caughlan-Fowler 1988) f(69) = 2.39e+5*(1.+.361*t912+.502*t9) | + 1.112e+8/t912*ex(-4.983/t9) C.......O15(n,p)N15................(Caughlan-Fowler 1988) f(70) = 3.50e+8*(1.+.452*t912-.191*t9) C40--------NEUTRON, ALPHA REACTIONS--------------------------------------------- C.......O15(n,a)C12................(Caughlan-Fowler 1988) f(71) = 3.50e+7*(1.+.188*t912+.015*t9) C50--------PROTON, PHOTON REACTIONS--------------------------------------------- C.......C12(p,g)N13................(Caughlan-Fowler 1988) f(72) = 2.04e+7*t9m23*ex(-13.690/t913-(t9/1.500)**2) | *(1.+.030*t913+1.19*t923+.254*t9+2.06*t943+1.12*t953) | + 1.08e+5*t9m32*ex(-4.925/t9) | + 2.15e+5*t9m32*ex(-18.179/t9) C.......C13(p,g)N14................(Caughlan-Fowler 1988) f(73) = 8.01e+7*t9m23*ex(-13.717/t913-(t9/2.000)**2) | *(1.+.030*t913+.958*t923+.204*t9+1.39*t943+.753*t953) | + 1.21e+6*t9m65*ex(-5.701/t9) C.......C14(p,g)N15................(Caughlan-Fowler 1988) f(74) = 6.80e+6*t9m23*ex(-13.741/t913-(t9/5.721)**2) | *(1.+.030*t913+.503*t923+.107*t9+.213*t943+.115*t953) | + 5.36e+3*t9m32*ex(-3.811/t9) | + 9.82e+4*t9m13*ex(-4.739/t9) C.......N13(p,g)O14................(Caughlan-Fowler 1988) f(75) = 4.04e+7*t9m23*ex(-15.202/t913-(t9/1.191)**2) | *(1.+.027*t913-.803*t923-.154*t9+5.00*t943+2.44*t953) | + 2.43e+5*t9m32*ex(-6.348/t9) C.......N14(p,g)O15................(Caughlan-Fowler 1988) f(76) = 4.90e+7*t9m23*ex(-15.228/t913-(t9/3.294)**2) | *(1.+.027*t913-.778*t923-.149*t9+.261*t943+.127*t953) | + 2.37e+3*t9m32*ex(-3.011/t9) | + 2.19e+4*ex(-12.530/t9) C.......N15(p,g)O16................(Caughlan-Fowler 1988) f(77) = 9.78e+8*t9m23*ex(-15.251/t913-(t9/.450)**2) | *(1.+.027*t913+.219*t923+.042*t9+6.83*t943+3.32*t953) | + 1.11e+4*t9m32*ex(-3.328/t9) | + 1.49e+4*t9m32*ex(-4.665/t9) | + 3.80e+6*t9m32*ex(-11.048/t9) C60--------PROTON, ALPHA REACTIONS---------------------------------------------- C.......N15(p,a)C12................(Caughlan-Fowler 1988) f(78) = 1.08e+12*t9m23*ex(-15.251/t913-(t9/.522)**2) | *(1.+.027*t913+2.62*t923+.501*t9+5.36*t943+2.60*t953) | + 1.19e+8*t9m32*ex(-3.676/t9) | + 5.41e+8/t912*ex(-8.926/t9) | + 4.72e+7*t9m32*ex(-7.721/t9) | + 2.20e+8*t9m32*ex(-11.418/t9) C70--------ALPHA, PHOTON REACTIONS---------------------------------------------- C.......C12(a,g)O16................(Caughlan-Fowler 1988) f(79) = 1.04e+8/t9**2*ex(-32.120/t913-(t9/3.496)**2) | /(1.+.0489*t9m23)**2 | + 1.76e+8/(t9)**2/(1.+.2654*t9m23)**2*ex(-32.120/t913) | + 1.25e+3*t9m32*ex(-27.499/t9) | + 1.43e-2*(t9)**5*ex(-15.541/t9) C80--------ALPHA, PROTON REACTIONS---------------------------------------------- C.......B10(a,p)C13................(Wagoner 1969) f(80) = 9.60e+14*t9m23*ex(-27.99/t913) C.......B11(a,p)C14................(Caughlan-Fowler 1988) f(81) = 5.37e+11*t9m23*ex(-28.234/t913-(t9/0.347)**2) | *(1.+.015*t913+5.575*t923+.576*t9+15.888*t943+4.174*t953) | + 5.44e-3*t9m32*ex(-2.827/t9) | + 3.36e+2*t9m32*ex(-5.178/t9) | + 5.32e+6/t938*ex(-11.617/t9) C.......C11(a,p)N14................(Caughlan-Fowler 1988) f(82) = 7.15e+15*t9a56*t9m32*ex(-31.883/t9a13) C.......N12(a,p)O15................(Caughlan-Fowler 1988) f(83) = 5.59e+16*t9m23*ex(-35.60/t913) C.......N13(a,p)O16................(Caughlan-Fowler 1988) f(84) = 3.23e+17*t9b56*t9m32*ex(-35.829/t9b13) C90--------ALPHA, NEUTRON REACTIONS--------------------------------------------- C.......B10(a,n)N13................(Caughlan-Fowler 1988) f(85) = 1.20e+13*t9m23*ex(-27.989/t913-(t9/9.589)**2) C.......B11(a,n)N14................(Caughlan-Fowler 1988) f(86) = 6.97e+12*t9m23*ex(-28.234/t913-(t9/0.140)**2) | *(1.+.015*t913+8.115*t923+.838*t9+39.804*t943 | +10.456*t953) | + 1.79e+0*t9m32*ex(-2.827/t9) | + 1.71e+3*t9m32*ex(-5.178/t9) | + 4.49e+6*t935*ex(-8.596/t9) C.......B12(a,n)N15................(Wagoner 1969) f(87) = 3.04e+15*t9m23*ex(-28.45/t913) C.......C13(a,n)O16................(Caughlan-Fowler 1988) f(88) = 6.77e+15*t9m23*ex(-32.329/t913-(t9/1.284)**2) | *(1.+.013*t913+2.04*t923+.184*t9) | + 3.82e+5*t9m32*ex(-9.373/t9) | + 1.41e+6*t9m32*ex(-11.873/t9) | + 2.00e+9*t9m32*ex(-20.409/t9) | + 2.92e+9*t9m32*ex(-29.283/t9) RETURN C----------REFERENCES----------------------------------------------------------- C Caughlan, G.R., and Fowler, W.A., 1988, Atomic Data and Nuclear Data C Tables, 40, 283. C Wagoner, R.V.,1969, Ap. J. Suppl. No. 162, 18, 247. END C========================IDENTIFICATION DIVISION================================ BLOCK DATA C----------PARAMETERS. PARAMETER (nrec=88) !Number of nuclear reactions. PARAMETER (nnuc=26) !Number of nuclides in calculation. C----------COMMON AREAS. COMMON /recpr0/ reacpr !Reaction parameter values. COMMON /compr0/ cy0,ct0,t9i0,t9f0,ytmin0,inc0 !Default comp parameters. COMMON /modpr0/ c0,cosmo0,xi0 !Default model parameters. COMMON /varpr0/ dt0,eta0 !Default variationl params. COMMON /nucdat/ am,zm,dm !Nuclide data. C==========================DECLARATION DIVISION================================= C----------REACTION PARAMETERS VALUES. REAL reacpr(nrec,8) !Reaction parameters. C----------DEFAULT COMPUTATION PARAMETERS. REAL cy0 !Default time step limiting constant. REAL ct0 !Default time step limiting constant. REAL t9i0 !Default initial temperature (in 10**9 K). REAL t9f0 !Default final temperature (in 10**9 K). REAL ytmin0 !Default smallest abundances allowed. INTEGER inc0 !Default accumulation increment. C----------DEFAULT MODEL PARAMETERS. REAL c0(3) !c0(1) is default variation of grav constant. | !c0(2) is default neutron half-life. | !c0(3) is default number of neutrinos. REAL cosmo0 !Default cosmological constant. REAL xi0(3) !Default neutrino degeneracy parameters. C----------DEFAULT VARIATIONAL PARAMETERS. REAL dt0 !Default initial time step. REAL eta0 !Default baryon-to-photon ratio. C----------NUCLIDE DATA. REAL am(nnuc) !Atomic number of nuclide. REAL zm(nnuc) !Charge of nuclide. REAL dm(nnuc) !Mass excess of nuclide. C==============================DATA DIVISION==================================== C Nuclide and corresponding number C -------------------------------- C 1) N 7) Li6 13) B10 19) C13 25) O15 C 2) P 8) Li7 14) B11 20) N13 26) O16 C 3) H2 9) Be7 15) C11 21) C14 C 4) H3 10) Li8 16) B12 22) N14 C 5) He3 11) B8 17) C12 23) O14 C 6) He4 12) Be9 18) N12 24) N15 C-----------NUCLIDE DATA. DATA am /1.,1.,2.,3.,3.,4.,6.,7.,7.,8.,8.,9.,10.,11.,11.,12., | 12.,12.,13.,13.,14.,14.,14.,15.,15.,16./ DATA zm /0.,1.,1.,1.,2.,2.,3.,3.,4.,3.,5.,4.,5.,5.,6.,5., | 6.,7.,6.,7.,6.,7.,8.,7.,8.,8./ DATA dm /.008665,.007825,.014102,.016050,.016030,.002603,.015125, | .016004,.016929,.022487,.024609,.012186,.012939,.009305, | .011432,.014354,.000000,.018641,.003354,.005738,.003242, | .003074,.008597,.000108,.003070,-.005085/ C----------REACTION RATE COEFFICIENTS (Ref 1). DATA ((reacpr(i,j),j=1,8),i=1,11) / C reac# type n1 n2 n3 n4 rev-coeff q-value C ---- ---- -- -- -- -- --------- ------- | 1.,1., 1.,0.,0., 2., 0.0 , 0.0 , !N->P | 2.,1., 4.,0.,0., 5., 0.0 , 0.0 , !H3->He3 | 3.,4.,10.,0.,0., 6., 0.0 , 0.0 , !Li8->2He4 | 4.,1.,16.,0.,0.,17., 0.0 , 0.0 , !B12->C12 | 5.,1.,21.,0.,0.,22., 0.0 , 0.0 , !C14->N14 | 6.,4.,11.,0.,0., 6., 0.0 , 0.0 , !B8->2He4 | 7.,1.,15.,0.,0.,14., 0.0 , 0.0 , !C11->B11 | 8.,1.,18.,0.,0.,17., 0.0 , 0.0 , !N12->C12 | 9.,1.,20.,0.,0.,19., 0.0 , 0.0 , !N13->C13 | 10.,1.,23.,0.,0.,22., 0.0 , 0.0 , !O14->N14 | 11.,1.,25.,0.,0.,24., 0.0 , 0.0 / !O15->N15 DATA ((reacpr(i,j),j=1,8),i=12,22) / C reac# type n1 n2 n3 n4 rev-coeff q-value C ---- ---- -- -- -- -- --------- ------- | 12.,2., 2.,1.,0., 3., 0.471, 25.82, !H(n,g)H2 | 13.,2., 3.,1.,0., 4., 1.63 , 72.62, !H2(n,g)H3 | 14.,2., 5.,1.,0., 6., 2.61 , 238.81, !He3(n,g)He4 | 15.,2., 7.,1.,0., 8., 1.19 , 84.17, !Li6(n,g)Li7 | 16.,3., 5.,1.,2., 4., 1.002, 8.863, !He3(n,p)H3 | 17.,3., 9.,1.,2., 8., 0.998, 19.081, !Be7(n,p)Li7 | 18.,3., 7.,1.,4., 6., 1.070, 55.494, !Li6(n,a)H3 | 19.,5., 9.,1.,0., 6., 4.70 , 220.39, !Be7(n,a)He4 | 20.,2., 3.,2.,0., 5., 1.63 , 63.750, !H2(p,g)He3 | 21.,2., 4.,2.,0., 6., 2.61 , 229.932, !H3(p,g)He4 | 22.,2., 7.,2.,0., 9., 1.19 , 65.054/ !Li6(p,g)Be7 DATA ((reacpr(i,j),j=1,8),i=23,33) / C reac# type n1 n2 n3 n4 rev-coeff q-value C ---- ---- -- -- -- -- --------- ------- | 23.,3., 7.,2.,5., 6., 1.07 , 46.631, !Li6(p,a)He3 | 24.,5., 8.,2.,0., 6., 4.69 , 201.291, !Li7(p,a)He4 | 25.,2., 6.,3.,0., 7., 1.53 , 17.118, !H2(a,p)Li6 | 26.,2., 6.,4.,0., 8., 1.11 , 28.640, !H3(a,p)Li7 | 27.,2., 6.,5.,0., 9., 1.11 , 18.423, !He3(a,p)Be7 | 28.,6., 3.,0.,1., 5., 1.73 , 37.935, !H2(d,p)He3 | 29.,6., 3.,0.,2., 4., 1.73 , 46.798, !H2(d,n)H3 | 30.,3., 4.,3.,1., 6., 5.54 , 204.117, !H3(d,n)He4 | 31.,3., 5.,3.,2., 6., 5.55 , 212.980, !He3(d,p)He4 | 32.,11.,5.,0.,2., 6., 3.39 , 149.230, !He3(He3,2p)He4 | 33.,9., 8.,3.,1., 6., 9.95 , 175.476/ !Li7(d,na)He4 DATA ((reacpr(i,j),j=1,8),i=34,44) / C reac# type n1 n2 n3 n4 rev-coeff q-value C ---- ---- -- -- -- -- --------- ------- | 34.,9., 9.,3.,2., 6., 9.97 , 194.557, !Be7(d,pa)He4 | 35.,2., 8.,1.,0.,10., 1.31 , 23.59, !Li7(n,g)Li8 | 36.,2.,13.,1.,0.,14., 3.04 , 132.95, !B10(n,g)B11 | 37.,2.,14.,1.,0.,16., 2.34 , 39.10, !B11(n,g)B12 | 38.,3.,15.,1.,2.,14., 1.002, 32.080, !C11(n,p)B11 | 39.,3.,13.,1.,6., 8., 0.758, 32.382, !B10(n,a)Li7 | 40.,2., 9.,2.,0.,11., 1.30 , 1.595, !Be7(p,g)B8 | 41.,2.,12.,2.,0.,13., 0.973, 76.427, !Be9(p,g)B10 | 42.,2.,13.,2.,0.,15., 3.03 , 100.840, !B10(p,g)C11 | 43.,2.,14.,2.,0.,17., 7.01 , 185.173, !B11(p,g)C12 | 44.,2.,15.,2.,0.,18., 2.33 , 6.975/ !C11(p,g)N12 DATA ((reacpr(i,j),j=1,8),i=45,55) / C reac# type n1 n2 n3 n4 rev-coeff q-value C ---- ---- -- -- -- -- --------- ------- | 45.,3.,16.,2.,1.,17., 3.00 , 146.08, !B12(p,n)C12 | 46.,3.,12.,2.,6., 7., 0.618, 24.674, !Be9(p,a)Li6 | 47.,3.,13.,2.,6., 9., 0.754, 13.301, !B10(p,a)Be7 | 48.,3.,16.,2.,6.,12., 0.292, 79.89, !B12(p,a)Be9 | 49.,2., 7.,6.,0.,13., 1.58 , 51.753, !Li6(a,g)B10 | 50.,2., 8.,6.,0.,14., 4.02 , 100.538, !Li7(a,g)B11 | 51.,2., 9.,6.,0.,15., 4.02 , 87.539, !Be7(a,g)C11 | 52.,3.,11.,6.,2.,15., 3.08 , 86.00, !B8(a,p)C11 | 53.,3.,10.,6.,1.,14., 3.07 , 76.96, !Li8(a,n)B11 | 54.,3.,12.,6.,1.,17.,10.3 , 66.160, !Be9(a,n)C12 | 55.,3.,12.,3.,1.,13., 2.07 , 50.63/ !Be9(d,n)B10 DATA ((reacpr(i,j),j=1,8),i=56,66) / C reac# type n1 n2 n3 n4 rev-coeff q-value C ---- ---- -- -- -- -- --------- ------- | 56.,3.,13.,3.,2.,14., 6.44 , 107.13, !B10(d,p)B11 | 57.,3.,14.,3.,1.,17.,14.9 , 159.36, !B11(d,n)C12 | 58.,8., 6.,1.,0.,12., 0.584, 18.260, !He4(an,g)Be9 | 59.,7., 6.,0.,0.,17., 2.00 , 84.420, !He4(2a,g)C12 | 60.,9.,10.,2.,1., 6., 3.58 , 177.73, !Li8(p,na)He4 | 61.,9.,11.,1.,2., 6., 3.58 , 218.82, !B8(n,pa)He4 | 62.,9.,12.,2.,3., 6., 0.807, 7.555, !Be9(p,da)He4 | 63.,10.,14.,2.,0.,6., 3.50 , 100.753, !B11(p,2a)Be4 | 64.,10.,15.,1.,0.,6., 3.49 , 132.83, !C11(n,2a)He4 | 65.,2.,17.,1.,0.,19., 0.886, 57.41, !C12(n,g)C13 | 66.,2.,19.,1.,0.,21., 3.58 , 94.88/ !C13(n,g)C14 DATA ((reacpr(i,j),j=1,8),i=67,77) / C reac# type n1 n2 n3 n4 rev-coeff q-value C ---- ---- -- -- -- -- --------- ------- | 67.,2.,22.,1.,0.,24., 2.71 , 125.74, !N14(n,g)N15 | 68.,3.,20.,1.,2.,19., 1.002, 34.846, !N13(n,p)C13 | 69.,3.,22.,1.,2.,21., 3.003, 7.263, !N14(n,p)C14 | 70.,3.,25.,1.,2.,24., 1.002, 41.037, !O15(n,p)N15 | 71.,3.,25.,1.,6.,17., 0.709, 98.661, !O15(n,a)C12 | 72.,2.,17.,2.,0.,20., 0.884, 22.553, !C12(p,g)N13 | 73.,2.,19.,2.,0.,22., 1.19 , 87.621, !C13(p,g)N14 | 74.,2.,21.,2.,0.,24., 0.900, 118.452, !C14(p,g)N15 | 75.,2.,20.,2.,0.,23., 3.57 , 53.706, !N13(p,g)O14 | 76.,2.,22.,2.,0.,25., 2.70 , 84.678, !N14(p,g)O15 | 77.,2.,24.,2.,0.,26., 3.62 , 140.734/ !N15(p,g)O16 DATA ((reacpr(i,j),j=1,8),i=78,88) / C reac# type n1 n2 n3 n4 rev-coeff q-value C ---- ---- -- -- -- -- --------- ------- | 78.,3.,24.,2.,6.,17., 0.706, 57.623, !N15(p,a)C12 | 79.,2.,17.,6.,0.,26., 5.13 , 83.111, !C12(a,g)O16 | 80.,3.,13.,6.,2.,19., 9.36 , 47.16, !B10(a,p)C13 | 81.,3.,14.,6.,2.,21.,11.0 , 9.098, !B11(a,p)C14 | 82.,3.,15.,6.,2.,22., 3.68 , 33.915, !C11(a,p)N14 | 83.,3.,18.,6.,2.,25., 4.26 , 111.87, !N12(a,p)O15 | 84.,3.,20.,6.,2.,26., 5.81 , 60.557, !N13(a,p)O16 | 85.,3.,13.,6.,1.,20., 9.34 , 12.287, !B10(a,n)N13 | 86.,3.,14.,6.,1.,22., 3.67 , 1.835, !B11(a,n)N14 | 87.,3.,16.,6.,1.,24., 4.25 , 88.47, !B12(a,n)N15 | 88.,3.,19.,6.,1.,26., 5.79 , 25.711/ !C13(a,n)O16 C----------DEFAULT COMPUTATION PARAMETERS. DATA cy0 /.300/ !Default time step limiting constant. DATA ct0 /.030/ !Default time step limiting constant. DATA t9i0 /1.00e+02/ !Default initial temperature. DATA t9f0 /1.00e-02/ !Default final temperature. DATA ytmin0 /1.00e-25/ !Default smallest abundances allowed. DATA inc0 /30/ !Default accumulation increment. C-----------DEFAULT MODEL PARAMETERS. DATA c0 /1.00,885.7,3.0/ !Default variation of 3 parameters. DATA cosmo0 /0.00/ !Default cosmological constant. DATA xi0 /0.00,0.00,0.00/ !Default neutrino degeneracy parameter. C-----------DEFAULT VARIATIONAL PARAMETERS. DATA dt0 /1.00e-04/ !Default initial time step. DATA eta0 /3.162e-10/ !Default baryon-to-photon ratio. END