LISTING OF PROGRAM SOLVE2

 1 PROGRAM

 2 PRINT "PART (A): SEARCH FIT ON IP, WEIGHTED LINEAR REGRESSION ON"

 3 PRINT "    EFFECTIVE POLARIZABILITIES (START WITH IP0=1.055*EMAX)."

 4 IPRIME=414922.5

 5 SIGNIFIC 9

 6 FOR I=1,15

 7 IP=IPRIME

 8 EXECUTE BEAR

 9 PRINT IP CHISQR

10 IPRIME=AVERAGE(E+TH+APAR(1)*RY*RM4+APAR(2)*RY*RM6)

11 ENDLOOP I

12 PRINT " "

13 IP=414922.75

14 PRINT "DETAILS OF FINAL FIT"

15 EXECUTE BEAR

16 PRINT ZETA,AM,IP

17 TABULATE N,L,E,TH,RM4,RM6

18 PRINT CHISQR,DF,PROB

19 PRINT APAR

20 SIGNIFIC 5

21 TABULATE Y,SIG,YFIT,X,EFIT,DELTAE

22 PRINT "INTERPOLATION AND EXTRAPOLATION"

23 EXECUTE BEAR

24 PRINT APAR

25 EFIT=IP-TH-APAR(1)*RY*RM4-APAR(2)*RY*RM6

26 DELTAE=EFIT-E

27 TABULATE Y,SIG,YFIT,X,EFIT,DELTAE

28 PRINT "PART (C): CHI-SQUARED PROBABILITY"

29 PRINT PROB

30 END

 

 

LISTING OF PROGRAM BEAR

 1 PROGRAM

 2 GRAPHICS(WIN32)

 3 RY=109737.3155-60.2/AM

 4 ALPHA=1/137.03602

 5 L1=L+.5

 6 L2=L*(L+1)

 7 L4=(L-1)*L2*(L+2)

 8 L5=(L-.5)*L*(L+.5)*(L+1)*(L+1.5)

 9 L9=(L-1.5)*(L-1)*L5*(L+2)*(L+2.5)

10 N2=N**2

11 N3=N**3

12 N4=N**4

13 TH=(1+(N/L1-.75)*(ALPHA*ZETA/N)**2)*RY*(ZETA/N)**2

14 RM4=(ZETA**4)*(3-L2/N**2)/(2*N3 * L5)

15 RM6=(ZETA**6)*(35-30*L2/N2+25/N2+3*L4/N4)/(8*N3*L9)

16 $ PRINT ZETA,AM,IP

17 $ TABULATE N,L,E,TH,RM4,RM6

18 X=RM6/RM4

19 Y=(IP-E-TH)/(RY*RM4)

20 SIG=DE/(RY*RM4)

21 W=1/SIG**2

22 APAR=LSQPOL(X,Y,1,R,W,CHISQR)

23 YFIT=POLYVAL(APAR,X)

24 DF=-1+NOELS(X)-NOELS(APAR)

25 PROB=CHIPROB(CHISQR,DF)

26 $ PRINT CHISQR,PROB

27 $ PRINT APAR

28 EFIT=IP-TH-APAR(1)*RY*RM4-APAR(2)*RY*RM6

29 DEFIT=EFIT-E

30 $ TABULATE Y,SIG,YFIT,X,EFIT,DEFIT

31 END

 

 

EXECUTE SOLVE2

PART (A): SEARCH FIT ON IP, WEIGHTED LINEAR REGRESSION ON

          EFFECTIVE POLARIZABILITIES (START WITH IP0=1.055*EMAX).

IP =  414922.5     CHISQR =  4.15830148

IP =  414922.541   CHISQR =  3.2135416

IP =  414922.581   CHISQR =  2.44751039

IP =  414922.621   CHISQR =  1.84938246

IP =  414922.659   CHISQR =  1.40887127

IP =  414922.697   CHISQR =  1.11620421

IP =  414922.733   CHISQR =  .962098742

IP =  414922.769   CHISQR =  .937739583

IP =  414922.805   CHISQR =  1.03475699

IP =  414922.839   CHISQR =  1.24520598

IP =  414922.873   CHISQR =  1.56154648

IP =  414922.906   CHISQR =  1.97662436

IP =  414922.938   CHISQR =  2.4836534

IP =  414922.969   CHISQR =  3.07619797

IP =  414923       CHISQR =  3.74815655

 

DETAILS OF FINAL FIT

ZETA =  4   AM =  29   IP =  414922.75

 

 N  L      E          TH           RM4            RM6

 *  *  *********  **********  *************  *************

 6  5  366026.17  48771.6111  2.66034834E-4  8.44555028E-6

 7  5  379000.09  35832.2407  1.84627257E-4  7.65542237E-6

 8  5  387423.4   27434.0672  1.31118881E-4  6.18594369E-6

 7  6  379060     35832.1187  7.10104833E-5  1.03053763E-6

 8  6  387465.5   27433.9855  5.2031302E-5   9.82813483E-7

 9  6  393229.2   21676.2414  3.86907261E-5  8.36504857E-7

 9  7  393239.1   21676.1993  1.74685741E-5  1.71103266E-7

 

CHISQR =  .935384545   DF =  4   PROB =  .919430348

  APAR (A 2 Component Array)

  3.70728195  18.0014306

 

    Y      SIG     YFIT       X      EFIT     DELTAE

 ******  *******  ******  ********  ******  *********

 4.2807  .017127  4.2788  .031746   366026   .057461

 4.4629  .024679  4.4537  .041464   379000   .18691

 4.5372  .03475   4.5566  .047178   387423  -.2786

 3.9309  .064165  3.9685  .014512   379060  -.29284

 4.0746  .087571  4.0473  .018889   387466   .15572

 4.0767  .11777   4.0965  .02162    393229  -.08398

 3.8868  .052167  3.8836  .0097949  393239   .0061266

 

 

LISTING OF PROGRAM BEAR2

 1 PROGRAM

 2 GRAPHICS(WIN32)

 3 RY=109737.3155-60.2/AM

 4 ALPHA=1/137.03602

 5 L1=LP+.5

 6 L2=LP*(LP+1)

 7 L4=(LP-1)*L2*(LP+2)

 8 L5=(LP-.5)*LP*(LP+.5)*(LP+1)*(LP+1.5)

 9 L9=(LP-1.5)*(LP-1)*L5*(LP+2)*(LP+2.5)

10 N2=NP**2

11 N3=NP**3

12 N4=NP**4

13 TH=(1+(NP/L1-.75)*(ALPHA*ZETA/NP)**2)*RY*(ZETA/NP)**2

14 RM4=(ZETA**4)*(3-L2/NP**2)/(2*N3 * L5)

15 RM6=(ZETA**6)*(35-30*L2/N2+25/N2+3*L4/N4)/(8*N3*L9)

16 EFIT=IP-TH-APAR(1)*RY*RM4-APAR(2)*RY*RM6

17 TABULATE NP LP EFIT

18 END

 

EXECUTION BEAR2

 

 NP  LP   EFIT

 **  **  ******

 6   5   366026

 7   5   379000

 8   5   387423

 7   6   379060

 8   6   387466

 9   6   393229

 9   7   393239

 8   7   387479

 9   8   393243

 

:_