6 Appendix

Here we give the FORTRAN program for computing ${\sl \Omega}$ or ${\sl \Upsilon}$ for the transitions considered in the present paper. The program makes use of the data given in Tables 3, 4 and 5. It assumes that the data for the transition in question has been stored (including the heading line of text) in a separate file. The interpolations are performed by the function programs SPLINE and POLY4. The authors are willing to send files of the program and tables by e-mail, on request.

#       PROGRAM LILIKE Computes Omega and Upsilon for LiLike ions *N.B.    IUNIT is the UNIT number for the input data files. *        Ensure that the value is suitable for your computer. Code:        LOGICAL OK        CHARACTER ANS*1,OU*1        DIMENSION SMN(5,5)        IUNIT=1 *Input Smn matrix file     1  CALL SMNINP(IUNIT,OU,ITYPE,C,CZ,NMAX,SMN,OK)        IF (OK.EQV..FALSE.) GO TO 5     2  PRINT*        PRINT*, 'Enter: Nuclear charge Z0, Eij (Ryd or cm-1), Ej(Ryd)'        PRINT*, '(Use a -ve value to exit from a sequence)'        PRINT* *Enter Z0        WRITE(*,100) '     Z0 = '        READ*,Z        IF (Z.LT.0.0) GO TO 5 *Enter Eij        WRITE(*,100) '    Eij = '        READ*,EIJ        IF (EIJ.LT.0.0) GO TO 5        IF (EIJ.GT.9.0*Z*Z) EIJ=EIJ/1.09737E5        Z=Z-3.0        ZR=Z/(Z+CZ)     3  PRINT* *Enter Ej or T        IF (OU.EQ.'O') WRITE(*,100) '     Ej = '        IF (OU.EQ.'U') WRITE(*,100) '      T = '        READ*, X        IF (X.LT.0.0) GO TO 4        IF (OU.EQ.'U') X=6.3336E-6*X        XR=X/(X+C*EIJ) *Interpolate in Z and Ej or T        Y=FINTER(ITYPE,NMAX,SMN,ZR,XR)        EPS=2.6626E-5 *Calculate Omega (see eq. 62)        IF (OU.EQ.'O') THEN         Y=(1.0+EPS*(X+EIJ))*(1.0+EPS*X)*Y/(Z+1.0)**2         WRITE(*,101) '  Omega =',Y        ENDIF *Calculate Upsilon (see eq. 62)        IF (OU.EQ.'U') THEN         Y=(1.0+EPS*(EIJ+X*(2.0+EPS*(EIJ+2.0*X))))*Y/(Z+1.0)**2         WRITE(*,101) 'Upsilon =',Y        ENDIF        GO TO 3     4  GO TO 2     5  WRITE(*,100) 'Another case? (Y/N): '         READ*, ANS        IF ((ANS.NE.'Y').AND.(ANS.NE.'N').AND.(ANS.NE.'y').AND.(ANS.NE.      + 'n')) GO TO 5        IF ((ANS.EQ.'Y').OR.(ANS.EQ.'y')) GO TO 1        STOP   100  FORMAT((A$))   101  FORMAT(A9,1PE11.4)       END ******        SUBROUTINE SMNINP(IUNIT,OU,ITYPE,C,CZ,NMAX,SMN,OK)        CHARACTER ANS*1, FILENM*15, HEAD*80, OU*1        LOGICAL FOUND,AVAIL,OK        DIMENSION SMN(5,5)     1  WRITE(*,100) 'Smn file name = '        READ*, FILENM        INQUIRE (FILE=FILENM, EXIST=FOUND)        IF (.NOT.FOUND) THEN         PRINT*, 'File not found.'         OK=.FALSE.         RETURN        ENDIF        OPEN (UNIT=IUNIT, FILE=FILENM)        REWIND(UNIT=IUNIT)        READ (UNIT=IUNIT,FMT=101,ERR=200) HEAD        READ (UNIT=IUNIT,FMT=*,ERR=200) ITYPE,C,CZ        IF ((ITYPE.NE.12).AND.(ITYPE.NE.212)) GO TO 200        IF ((C.LE.0.0).OR.(CZ.LE.0.0)) GO TO 200        IF (ITYPE.EQ.12) NMAX=5        IF (ITYPE.EQ.212) NMAX=4        READ (UNIT=IUNIT,FMT=*,ERR=200) ((SMN(M,N),N=1,NMAX),M=1,NMAX)        CLOSE(UNIT=IUNIT)        OK=.TRUE.        OU=HEAD(1:1)        PRINT*        WRITE(*,101) 'Contents of Smn file:', HEAD        WRITE(*,102) ITYPE,C,CZ        DO 2 M=1,NMAX         WRITE(*,103) (SMN(M,N),N=1,NMAX)     2  CONTINUE        RETURN   100  FORMAT((A$))   101  FORMAT(A80)   102  FORMAT(I5,2F10.5)   103  FORMAT(5F10.5)   200  PRINT*, 'File unreadable.'        INQUIRE (UNIT=IUNIT, OPENED=AVAIL)        IF (AVAIL) CLOSE(UNIT=IUNIT)        OK=.FALSE.        RETURN       END ******        FUNCTION FINTER(ITYPE,NMAX,SMN,ZR,XR)        DIMENSION SMN(5,5),P(5),Q(5)        DO 2 N=1,NMAX         DO 1 M=1,NMAX           P(M)=SMN(M,N)     1   CONTINUE *Interpolate in Z         IF (ITYPE.EQ.12) THEN          Q(N)=SPLINE(P,ZR)         ELSE          Q(N)=POLY4(P,ZR)         ENDIF     2  CONTINUE *Interpolate in E or T        IF (ITYPE.EQ.12) THEN         FINTER=SPLINE(Q,XR)        ELSE         FINTER=POLY4(Q,XR)        ENDIF        RETURN       END ******        FUNCTION SPLINE(P,X) Calculates  5-point spline interpolation of Y(X), *  for X in the range (0,1). *Input: *  Nodal values P(1)=Y(0),P(2)=Y(1/4),P(3)=Y(1/2),P(4)=Y(3/4),P(5)=Y(1) *  and X. *Output: *  SPLINE=Y(X). Code:        DIMENSION P(5)        S=1.0/30.0        S2=32.0*S*(19.0*P(1)-43.0*P(2)+30.0*P(3)-7.0*P(4)+P(5))        S3=160.0*S*(-P(1)+7.0*P(2)-12.0*P(3)+7.0*P(4)-P(5))        S4=32.0*S*(P(1)-7.0*P(2)+30.0*P(3)-43.0*P(4)+19.0*P(5))        IF(X.GT.0.25) GO TO 1        X0=X-0.125        T3=0.0        T2=0.5*S2        T1=4.0*(P(2)-P(1))        T0=0.5*(P(1)+P(2))-0.015625*T2        GO TO 4     1  IF(X.GT.0.5) GO TO 2        X0=X-0.375        T3=20.0*S*(S3-S2)        T2=0.25*(S2+S3)        T1=4.0*(P(3)-P(2))-0.015625*T3        T0=0.5*(P(2)+P(3))-0.015625*T2        GO TO 4     2  IF(X.GT.0.75) GO TO 3        X0=X-0.625        T3=20.0*S*(S4-S3)        T2=0.25*(S3+S4)        T1=4.0*(P(4)-P(3))-0.015625*T3        T0=0.5*(P(3)+P(4))-0.015625*T2        GO TO 4     3  X0=X-0.875        T3=0.0        T2=0.5*S4        T1=4.0*(P(5)-P(4))        T0=0.5*(P(4)+P(5))-0.015625*T2     4  SPLINE=T0+X0*(T1+X0*(T2+X0*T3))        RETURN       END ******        FUNCTION POLY4(P,X) Calculates 4-point polynomial interpolation of Y(X), *   for X in the range (0,1). *Input: *   Nodal values P(1)=Y(0), P(2)=Y(1/3), P(3)=Y(2/3), P(4)=Y(1) and X. *Output: *   POLY4=Y(X). Code:        DIMENSION P(4)        T=3.0*X        T1=(T-1.0)*(T-2.0)*(1.0-X)        T2=T*(T-2.0)*(T-3.0)        T3=T*(T-1.0)*(3.0-T)        T4=X*(T-1.0)*(T-2.0)        POLY4=0.5*(T1*P(1)+T2*P(2)+T3*P(3)+T4*P(4))        RETURN       END ******