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
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