1 . 1i|||||| ‘‘‘‘
\ 2.1:...- 3.5..." ...... .1 ... .......§......._2111112.......... ‘43... . ..v........a. .. ...:...1........._..........._,. r

Ew.§.~1..1.........¥1.11...
:

 

    

   

 

 

.1
.... ..... . J.....__ ......H...z. ..
y ....2.rv...... é . ... ...
_:...-1.. ...... 52.291233.
...:1. ...... ... ...-...... .
2...... .....

 

1.....- . ...:

a... ...... . . ...: ......r... ..pripW...rw1p....
... .. . .... .. r ...

w .....J.......,«.. .1...

                

               

 

 

4—4“... .... .
... . ....1... 133......

                   

3.1.3:...1q
....
..

 

......e
...... 1...».
1.1.....‘..A.?..:. 3;...
11.......;..... ..¢......:_.
...1.....\........... 1.........¢........

... ... . 1......1173 ......

   

 

...A.h..1..:.

   

 

           

r..

  

...
4.».

...; ..1...1

 

11......I.
. 7......31
......I

I? .

:...._....

A .2... ....

is... .....1. ... .

...-......E..-.:.._..» ...“:-

.........1..; . ...:

t......E

.. VI...
:1... 2.! . ..

      

  

 

...... 5... ...“...
...: '35....

           

                 

 

\«I.~‘..‘~.fi.a«> ~

                     
  

 

 

..... 021......Z;
.1...4\_.~.»—

  
   

     

....... .
....x...._....1.....

    

       

 

....1.3.\n .21. .. ..1 1......
.......m.511.1x.1........x...1._....._. #1.??? ..11. ..
\.1(..T;.1:...?.....\...11..

 

......J..1,
...:1... .1.: . 1
.....1.... ......Z... .-.. ....1... . . .1.
2.13.1.1..-......n.-........?-
..........A...._.1..._.:1.....Z._.........:.....

          

 

 

 

 

 

...._
....,......_
. a...

 

 

      

 

.

1-2:...1.

1.........1.....
......

. ......

      

n. 51::.. ..

      

.1...._..T...f...
«1.1.11.3:
......1...._1v.

        

....1
............1......

      

 

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IC:RGIAI

  

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RESO

1'

 

 

 

 

H:

 

 
 

 
 
 

 
 
 
 
 
 
 
 
 
 

 

 

 
 
 

 

 
   
 
 

     

  
   
  

     

 

 

 

 

. . . . . . . . ... . . .. .. . .l
. . ._. .. . . .. . . . . . 1 . 1. 1 .1 1 1 .

. 1 . . . . . .. . T .
. ........_ . .. ~ .. . . . .1 . . ... .. . . 1 .

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. 1 . . , . .m...11 15.11.1173??? 43/? 4:111:11:

 
 

 

......1.....;..:.
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15318

 
  
    

 
  

LIB If {RY
MlChlz 1 State
University

 

This is to certifg that the

thesis entitled

HIGH RESOLUTION ABSORPTION, ZEEMAN
AND MAGNETIC ROTATION SPECTRA OF ‘
THE FUNDAMENTAL AND SATELLITE
BANDS OF NITRIC OXIDE IN

THE NEAR INFRARED
presented by

Donald B. Keck

has been accepted towards fulfillment
of the requirements for

Ph. D

° degree mm

. 7 /"

Major professor

DaeNovember 17, 1967

 

0-169

 

 

 

 

 

 

ABSTRACT
HIGH RESOLUTION ABSORPTION, ZEEMAN AND MAGNETIC ROTATION

SPECTRA OF THE FUNDAMENTAL AND SATELLITE BANDS
OF NITRIC OXIDE IN THE NEAR INFRARED

by Donald B° Keck

The absorption, Zeeman and magnetic rotation spectra
of the 1—0 vibration—rotation bands of nitric oxide have been
obtained using the Michigan State University high resolution
(mo.07 cm"1 at NZOOO cm'l) near infrared spectrometer. This
included the weak satellite transitions, Zflfi + 2H3 and 2H3 +
znio Improved values of the molecular constants have been
obtained by a simultaneous least squares analysis of combi-
nation differences and frequencies° The spin-orbit constant
was determined directly by means of the satellite band fre-
quencies which were includedo

Theoretical calculations of the Zeeman patterns and
intensities have been giveno The observed spectra match
these predictions very closelyo

A phenomenological,theory of magnetic rotation spectra
is outlined° Predictions made on the basis of this theory
eXplain the major features of the observed magnetic rotation
Signals starting from rather basic principles. These features
include the doublet structure of lines at high pressure and

the intensity contour of the 2—subband.

 

 

 

 

ABSTRACT
HIGH RESOLUTION ABSORPTION, ZEEMAN AND MAGNETIC ROTATION

SPECTRA OF THE FUNDAMENTAL AND SATELLITE BANDS
OF NITRIC OXIDE IN THE NEAR INFRARED

by Donald B. Keck

The absorption, Zeeman and magnetic rotation spectra
of the 1—0 vibration-rotation bands of nitric oxide have been
obtained using the Michigan State University high resolution
(~0.o7 cm'1 at ~2000 cm‘l) near infrared spectrometer. This
included the weak satellite transitions, 2H5 + 2H3 and 2H3 +
2H§. Improved values of the molecular constants have been
obtained by a simultaneous least squares analysis of combi—
nation differences and frequencies° The spin-orbit constant
was determined directly by means of the satellite band fre—
quencies which were includedo

Theoretical calculations of the Zeeman patterns and
intensities have been giveno The observed spectra match
these predictions very closelyo

A phenomenological,theory of magnetic rotation spectra
is outlined. Predictions made on the basis of this theory
explain the major features of the observed magnetic rotation
Signals starting from rather basic principles» These features
include the doublet structure of lines at high pressure and

theintensity contour of the 2-subband°

 

 

 

 

Donald B. Keck

Modifications made in the above mentioned instrument
are discussed. These include a rod source, a vacuum polarizer
assembly, new monochromator mirrors, a new grating drive as-
sembly, and new detectors° All air paths in the entire opti-

cal train have been eliminated.

 

4 44m.--m-__¥P .l_

 

 

HIGH RESOLUTION ABSORPTION, ZEEMAN AND MAGNETIC ROTATION
SPECTRA OF THE FUNDAMENTAL AND SATELLITE BANDS

OF NITRIC OXIDE IN THE NEAR INFRARED

BY

Donald B. Keck

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Physics

1967

 

 

(HSLM‘B
3—3-4s

ACKNOWLEDGEMENTS

I am very grateful to Professor C. D. Hause for his help
and guidance throughout my work. I have considered it a
privilege to work and learn under him. It was he who sug—
gested this problem and encouraged me throughout the research.
I owe a special thanks to Professor T. H. Edwards. He too

has given much helpful advice and assistance during all phases

of this worko I wish to thank Professors P. M. Parker, R. D.
l Spence and J. A. Cowen. All presented excellent courses and
{ have been helpful with many questions.

I wish to thank former graduate students, Drs. Joseph
Aubel and Melvin Olman for their friendship and assistance.
Dr. Aubel was an excellent teacher concerning the spectro—
meter and the magnetic rotation work. Dr. Olman was very
helpful with the modifications of the instrument, the com-
pUter work and the analysis.

I am also indebted to former graduate students, Drso
Jerry Johnston, Kent Moncur, Tom Barnett and Lew Snyder for
their friendship and many discussions.

The friendship of my fellow graduate students Lamar
"Dutch" Bullock, Pete Willson, Dick Blank and Dick Peterson

is greatly appreciated. A special thanks is extended to

much Bullock for his collaboration on several projects.

ii

 

 

 

I wish to thank the National Science Foundation for
their generous support of this work through various grants
and fellowships. The M. S. U. Computer Center has also been
very helpful in this work.

I want to take this opportunity to thank my father,

Dr. W. G. Keck, for all the valuable guidance and training
he has given me which stood me in good stead for this work.
Finally, but by no means least, I want to thank my

wife Ruth for her encouragement throughout this work and

the many hours she spent in the preparation of this thesis.

 

 

 

 

TABLE OF CONTENTS

Page
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . ii
LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . V
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . Vi
LIST OF APPENDICES. . . . . . . . . . . . . . . . . . . Viii
INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . 1
Chapter

1 ROTATION—VIBRATION ENERGY FOR AN
INTERMEDIATE 211 STATE. ., . . . . . . . . . . . . 4

2 WAVEFUNCTIONS AND INTENSITIES. l3

0
o
o
o
a
o
o
o
0

3 ZEEMAN ENERGIES. . . o o . . . . . . . . . . . . 26
4 MAGNETIC ROTATION THEORY . . . . o o . . . . . . 29
5 ABSORPTION ANALYSIS. . . . . . . o . . o . . . . 36
6 ZEEMAN ANALYSIS. . . . . o . . . o a o o o o o o 53

7 MAGNETIC ROTATION ANALYSIS 57

a
o
O
0
o
o
o
D
a
o
o

8 SPECTROMETER DESCRIPTION . . . . . . . . . . . . 81
SUMMARY 0 0 O 0 0 0 O 0 B O 9 o B O O O O 0 0 B 0 0 O Q 104
REFERENCESO O o 6 D o O O O D 0 O 0 D O D 0 0 0 6 0 O 0 105

APPENDICESO o o o a o o o o o o o o o o o a o o o o o o 1-10

iv

 

 

 

 

LIST OF TABLES

Matrix of H; in Pure Case (a) Basis. .

Matrix of H£ + A(fn§) in Symmetrized
Case (a) Basis . . . . . . . . . . . .

_ —> —>

Matrix of H} + A(L°S). . . . . . . . .
Direction Cosine Matrix Elements . . .
Experimental Conditions for Absorption

Effective Constants for NO . . . . . .

Spectra

a o o 0

Comparison of Effective Constants for NO . . .

Rotational Constants for NO. . . . . .
Spin—Orbit Constants for NO. . . . . .

Isotopic Calculations for 15N160 . . .

o a o a

o a o o

Zeeman Splittings for the (l— O), P2(5/2)
and R2(3/2) Lines of 1 N16 O and 15N160 as a

Function of Field. . . . . . . . . . .

Spectrometer Optics. . . . . . . . . .

n

Page

18
37
44
46
47
48

48

56

87

 

 

LIST OF FIGURES

Figure

5.1 High resolution spectra of the Q- -branch region
of the 1- 0 HES band of 15N16 o . . . . . . .

5.2 High resolution spectra of the Q- -branch region
of the 1- o LES band of 15 5N1 6o . . . . . . .

6.1 a) Observed Zeeman s ectra for the 1—0 band,
P2(5/2) line of 1“‘N1 O as a function of field
b) Predicted Zeeman spectra for the same
conditions as in a) . . . . . . . . . . . . . .

7.1 Magnetic rotation spectra of the 1-0 band,
P-branch of 11+N160 as a function of pressure. .

7.2 Magnetic rotation spectra of the l— 0 band
of 1L+N160 as a function of pathlength . . . . .

7.3 Magnetic rotation spectra of the l— 0 band,
P- branch of 1“N160 as a function of field . . .

7.4 Magnetic rotation spectra of the 1—0 band
of 1“N160 as a function of polarizer angle. . .

7.5 Magnetic rotation spectra of the R- branch
region of the 1- 0 HES band of 1L+N160 as a
function of field and pressure. . . . . . . . .

7.6 Predicted Zeeman patterns and relative
intensities for the 1-0 band, P—branch of
1"‘Nleo for a magnetic field strength
of 6000 gauss . . . . . . . . . . . . . . . . .

7.7 Typical anomalous dispersion curves for a
simple Zeeman doublet . . . . . . . . . . . . .

7.8 Predictions of the terms making up the magnetic
rotation signal of the l- 0 band, P1 (15/2)
line of 1”N6 . . . . . . . . . . . . . . . .

7.9a Predictions of the magnetic rotation signal for

the 1-0 band, P1(15/2) line at pressures
of 1.0 and 10.3 torr. . . . . . . . . . . . . .

vi

 

Page

38

39

54

58

59

60

61

62

65

66

68

72

 

 

 

Figure

 

Predictions of the magnetic rotation signal for

the 1-0 band, P2(15/2) line at pressures
of 1.0 and 10.3 torr. . . . . . . . . . . . .

Predictions of the magnetic rotation signal for

the l- 0 band, P2 subband of 1”N160 at
pressures of 1.0 and 10. 3 torr. . . . . . .

Predicted Zeeman patterns and relative
intensities for the 1-0 HES band, R-branch of
1“N160 for a field strength of 6000 gauss . .

Rod source. . . . . . . . . . . . . . . . .

Rod source power supply . . . . . . . . . . .

o

Foreoptics, polarizer assembly and solenoid
Polarizer assembly. . . . . . . . . . . . . .
Monochromator and exit optics . . . . . . . .
Grating drive train . . . . . . . . . . . . .

Calibration system. . . . . . . . . . . . . .

 

Page

73

75

78
83
84
86
90
91
96

98

 

‘m. 3—.--

 

 

Appendix
I A.
B0
II A.
B0
III A.
B.

IV
V A.
B.

VI
A0
B6
C0

VII
A.
B0
C0
D.
E.
F.
G.
H.
VIII A.
B0
IX A.
B.
X A0
B.

LIST OF APPENDI

Matrix elements of Hr 9
Matrix elements of A(L S

Intermediate wave functions for the

v = 0 and v = 1 states 0

Intermediate wave functions for the

v = 0 and v = 1 states 0

Calculated line strengths for 1“N160.
Calculated line strengths for 15N160.

Calculated values for the integrated
for 1”N160.

absorption coefficients

g— —factors for 1L’N160. .
g- factors for 15N160.

Expressions used in the
Combination differences
Frequencies . . . .
A- doublet splittings. .

Computer programs

SHAFT . . . . . . .
DIFF. . . . . . . . . .
ROTCONS
ALLFIT. . . . . . . . .
LAMCON. . . . . . . . .
STEPFIT . . . . . . . .
ZEEPUN. . . . . . . . .
PLOTPUN . . . . . . . .

o
r.
o
o
o
o
0
0

CBS

0 o o

) o a o

o

f 1L+N1600

f15N10.

o o o o

n o o o

o a o o

a

o

a

o o 0

programs

0

a

o

a

o

e

GSCD and frequency fit (inputing constants
1L*N 6o .

from the GSCD fit) for

o

o

o o o

GSCD and frequency fit (inputing constants
15N50...

from the GSCD fit) for

Frequency fit for 11+N160.
Frequency fit for 15N160.

A-doublet splitting fit for l“N160.
A-doublet splitting fit for 15N160.

viii

o

Page

110
111

112
116

120
123

126

131
133

135
135
137

139
164
176
176
176
176
196
203

220

228

235
240

245
248

 

 

 

 

INTRODUCTION

Nitric oxide, being the only stable diatomic molecule
possessing an odd number of electrons and an electronic
angular momentum, has been the subject of many investiga—
tions (1-16). The result is a 2H ground state whose com-
ponents are separated by N120 cm"1 by a spin—orbit inter—
action. The coupling is intermediate between Hund's cases
(a) and (b). In addition the intermediate coupling makes
both H states magnetically sensitive.

Improvements in infrared detectors since Shaw's (6)
work on NO in 1956 has led to an increased interest in the
vibration—rotation spectra of the fundamental region
(~19oo cm“1).

This work has been concerned with obtaining and ana-
lyzing high resolution absorption, Zeeman and magnetic
rotation spectra of both 1L*Nleo and 15N160 for this region,
including the weak satellite transitions, 2H1 + 2H3 and
2H3 + 2H1”

The system used in obtaining the spectra is described
in Chapter 8. This includes an account of the modifications
Which were necessary to extend the range of the instrument

to enable these spectra to be recorded.

 

 

Analysis of the absorption spectra was carried out
using the existing theory (9, l7, l8, 19, 20) which is
outlined in Chapter 1. A simultaneous analysis of all
observed transitions for each isotope is carried out in
Chapter 5 and leads to improved values of existing molec-
ular constants through the use of least squares fits to
both combination differences and frequencies. Inclusion
of the satellite data provides a direct determination of
of the spin—orbit coupling constant and helps resolve
previous differences regarding this quantity.

Zeeman components were resolved for two low J-value
lines for both isotopes. The theory necessary to explain
their positions and a brief analysis of them is given in
Chapters 3 and 6 respectively.

In Chapter 2 the quantum mechanical theory for the
intensities of the transitions is given. These calcula—
tions are necessary for the magnetic rotation analysis.

Buckingham and Stephens (21) have given a review of
the theory for magnetic rotation spectra from a phenomenol-
Ogical viewpoint. A brief account of their approach and
the deviations from it as proposed by Aubel (22) are given
in Chapter 4. Aubel“s approach coupled with the results
Of Chapter 2 enable theoretical predictions of the magnetic
rotation signal to be made starting from rather basic prin—
Ciples. With the help of the computer these predictions
have been made for several representative transitions and

are given together with the observations in Chapter 7.

 

 

It is found that the major features of the observed signal
can be explained by this theory on a semi-quantitative

level.

 

 

 

CHAPTER 1

ROTATION-VIBRATION»ENERGY FOR AN
INTERMEDIATE AH STATE

The molecular Hamiltonian of a diatomic molecule, for
the region of spectrum being considered here, can be written
(23) as a sum of an electronic, a vibrational, and a rota-

tional term, viz.
H = H + H + H . (1.1)
e v r

Vibrational Term

 

Assuming an anharmonic oscillator as a model, the
form for the Vibrational energy has long been known. Herz-

berg (24) gives the term value as:
_ _ ‘-2 - j 3
G(V) — we(v+£) wexe(v+§) + weye(v+§) + ... . (1.2)

where G(V) is in ch], v is the vibrational quantum number

and w >>w x >>w y are vibrational constants.
e e e e e

Rotational Term

Here the pure end over end rotation of the molecule
is considered. If J is the total angular momentum quantum
number in units of h, and assuming the possibility of
orbital, L, and spin, S, electronic angular momenta, the

end over end rotational angular momentum of the molecule is:

 

+ + + +
P=J-L-S. (1.3)

For the case of the diatomic molecule, taking the body
fixed z-direction along the internuclear axis, P2 = 0 so
that:

l— 2_ - - 2 - _ 2
Hr — BP — B[(JX Lx sx) + (JY Ly SY) ]

= B[J2 -_A2 + 82 - 23-§ + L2 - A2]

+ 2B[(LXSX + LySy)

- (JXLX + JYLY)] , (1.4)
where B is the rotational constant.

The matrix elements for the Hamiltonian in equation
(1.4) have been given by Van Vleck (18) and later by Dous-
manis, Sanders and Townes (20) for a pure Hund's case (a)
coupling scheme. These are listed in Appendix I-A with
their phase conventions. In this representation both L
and S are quantized along the internuclear axis with the

eigenvalues A and 2 respectively. Herzberg (25) discusses

this and other coupling schemes in detail. The total

 

angular momentum along the axis is designated by 9 = [A + X
For the case of NO or any other molecule with an un-
paired p-electron, L = 1, its projection A = 0,il, S = §

1%. With these quantum numbers six
28+1|A|

and its projection 2

case (a) states can be formed with the designation A+2

viz.

Zni, 2H_%, 2H3, 2H_3, 22%, 22_£ .

 

'U+
II
C—N'
I
L'Nv
I
UN

(1.3)

For the case of the diatomic molecule, taking the body
fixed z-direction along the internuclear axis, P2 = 0 so

that:

l_ 2_ _ _ 2 _ _ 2
Hr - BP — BHJX LX Sx) + (J Ly Sy) ]

Y

+

= B[J2 —_A2 + 32 - 2J°S + L2 - A2]

+ 2B[(LXSX + LySy) - (JXLx + JyLy)] , (1.4)

where B is the rotational constant.

The matrix elements for the Hamiltonian in equation
(1.4) have been given by Van Vleck (l8) and later by Dous—
manis, Sanders and Townes (20) for a pure Hund's case (a)
coupling scheme. These are listed in Appendix I-A with
their phase conventions. In this representation both L
and S are quantized along the internuclear axis with the
eigenvalues A and 2 respectively. Herzberg (25) discusses

this and other coupling schemes in detail. The total

 

angular momentum along the axis is designated by Q = [A + X

For the case of NO or any other molecule with an un-
paired p-electron, L = 1, its projection A = O,il, S = i

eand its projection Z = 3%. With these quantum numbers six

case (a) states can be formed with the designation P‘s-HIM!”Z

ViJL

2n£, 2n_£, 2H3, 2n_3, 22$, 22_£ .

 

The interactions of these six states form a 6X6 matrix,
as given in Table 1.1. This matrix can be factored by
choosing as a ba51s, symmetric and antisymmetric combina—
tions first prOposed by Kronig (26), of the six pure case

(a) wave functions. v12.

w(A,z,mS a = /-%-'[tp(A,Z,Q) . w(-A,-Z,-§2)] (1.5)

.‘7

This factorization breaks the Hamiltonian matrix into
two 3X3 blocks of Opposite parity, similar to that shown in
Table 1.2. The eigenvalues of the symmetric (antisymmetric)
block corresponds to the C(d) level (A-doublet levels) of
Mulliken (27). The only difference between the two blocks
is in the 2-2 and the ani terms. These matrix elements
stem from the last line of equation (1.4) which is off
diagonal in A. The degeneracy in A is lifted by the inter-
action of the H with the nearby 2 state. Similar terms

will enter when the sp1n=orbit interaction is considered.

Electronic Term

 

For this work only the ground electronic state need
be considered. Its energy may be taken as some constant,
Te° An additional energy will arise when the electronic
(orbital and spin angular momentum interaction is included.

fPhe total electronic energy can therefore be written:

He 2 Te + A(L»S) (1.6)

 

Table 1.1 Matrix of H; in Pure Case (a) Basis.

 

 

 

21 111 H 7 -. H H
g 2 3 «1 -1 -i
I J E}; x, O K; O
;'<
H* 6* Y1 O O O
H' =
6* * 0 OL 61 n
'k
C* O 61 Bi 8
k 0 0 O n* 8* Y1 )

 

 

Table 1.2 Matrix of H} + A(LoS) in
Symmetrized Case (a) Basis.

 

 

 

 

s .s s a a a
L n, n z n n
i 2 3 i i 3
s s
K h n
(US)* 8 e O
-> —>- 71* 6* Y
H' + A(L S) = a a
r K p n
O (u )* B e
I
nit ~* I J

 

4 +-->
Table 1.3 Matrix of H} + A(LmS).

 

 

H'I H
2 E
j j 8+02(B12+€2) €[l+02(81+Y1)]
H' + A LvS' = ~ .
r ( ) . 6*[l+oé(81+v1)] Y+02(Y12+€2)

where p 3 Dn/B".

 

 

 

 

2 2 2

l O. 6“ n O
. ’k

61 B} E: f

n* 6* Y1

a =

6* 0 0 e?

\ 0 0 O n*

H_£ H_3
Z; O
O 0
0 0
01 n
81 E
6* Y1

 

Table 1.2 Matrix of H

—> —> ,
' + A(Las) 1n

Symmetrized Case (a) Basis.

 

_s s s
L’ H- H
i i 3
s s
l K 11 7‘1
(us)* 6 E
a + ’ n* 5* Y
H' + A(LOS) =
O
I
l

o
a a
K p n
a
(u )* B e
n* 6* N

 

Table 193, Matrix of

H; + A(fmS).

 

H1
2

8+02(B12+62)

H' + A Lo§ = »
r ( ) e*[l+p4(sl+yl)]

where p E DW/B".

“a

e[l+pz(81+Y1)]
Y+92(Y12+52)

 

 

 

 

 

Matrix elements of the spinmorbit Hamiltonian are given in
Appendix I—B in the pure case (a) basis. In the symmetrized
basis discussed above the matrix of H; + A(L-S) is given in

Table 1.2.

Diagonalization of He and Er
At this point the two 3X3 subblocks of Table 1.2, ob—

tained by adding He + H”, may be diagonalized to obtain

r

rotational and electronic eigenvalues. Dousmanis, Sanders
and Townes (20) have shown that by diagonalizing to succes—

sively higher orders in (E )71 the problem reduces to

elec

diagonalizing the 2x2 submatrix:

B . (1.7)
E:

-<(“)

f

t A
This is acceptable for the case of NO since it is

known that the ground state is the 2H and Ew—n is N120 cm'1

and EZ—n is m32,000 cm‘l. Terms in 1/EZ_=Tr will therefore

be small. It is seen that to this order the eigenvalues

for the symmetric and antisymmetric blocks are equal.

These eigenvalues are:
E1 2 = )(B + y) . )[(B — y)2 + 4[.|2]é
)7
= i<e + y) = 1B"x (1.8)
where

x = [4(J+§)Z + 1(1-4)]5 ; 1 = A/BTT

 

marml’l We",

 

Here the upper (lower) sign is used with E1 (E2) where this
energy corresponds to an intermediate Zfli (2H3) state. These
energies were first given by Hill and Van Vleck (17) starting
from pure case (b) wave functions. Van Vleck (18) later ob-
tained the same answer starting from pure case (a) wave

functions as was outlined here.

CentrifugalyDistortion

 

Thus far our model for rotation has been that of a
rigid rotator. To account for nonsrigidity a term must be
added to H; which varies as P“. A term of this form was
added by Almy and Horsfall (19). Their Hamiltonian including

the spin=orbit term is:
Hr = BP2 - DP“ + A(Eog) , (1.9)

where D is the centrifugal distortion constant. Finally,
considering matrix elements in the symmetrized basis which
only involve the H states, as was done in Eq. (1.7), this
Hamiltonian matrix is as given in Table 1.3. This matrix

can be diagonalized with the result that:
E1 2 = B“[(J+§)2 — A2] + B"[L(L+1) - 12]
i
. [AA(A - 4B”)A2 + B"2(J+))2]i

- D”[J2(J+1)2 - )J(J+1) + 13/16] . (1.10)

In this expression terms of order DW/B1T have been omitted.

The term L2 - A2 was also omitted in the PL+ term.

 

 

10

Vibration-Rotation Interactions

To this point the vibration and rotation of the molecule
have been considered as independent motions. It is reason-
able to assume that the rotational constants considered so
far are really time averages over the period of vibration.
It is also reasonable that, because of the anharmonicity, the
average separation will increase with increasing vibrational
quantum numbers. The rotational constant, B, which varies
as r"2 will be a decreasing function of v. From rather in—
volved calculations (for a simple example, see Pauling and

Wilson (28)) the rotational constants are given by:

l _ 1
13V — Be ae(v+2) (1.11)

D = De + 6e(v+)) , (1.12)

where me and Be are the vibration—rotation interaction con-
stants. Here Be(cm‘1) = fi/4wcuré, where re is the equi-
librium separation of the atoms and u is the reduced mass.
The spin-orbit coupling constant has also been found
to have a vibrational dependence by many researchers (11,

13, l4, 16). It is written as:

Av = Ae - xe(v+)) . (1.13)

When this is done, only a single G(V) need be used to ac—
count for the vibrational energy of both components of the

2H ground state.

 

 

 

ll

Lambda Doubling

It has already been pointed out that the eigenvalues
of the symmetric and antisymmetric blocks in Table 1.2 are
slightly different, each one giving the energy of one of
the A-doublet levels. Herzberg (29) discusses this un-
coupling phenomena in some detail. The splitting of the
levels is symmetric and the energies, in this intermediate

VJA°(JI7V) T'(JIV) " EA=(JIV) 0 (1°11)

Neglecting the term in (E )_1, the effects of which

Z-H

are too small to be observed in this work, E£(v) is:

l4q, 2p

E9(V) = 2pA(J+§) + i A + ——w~£—
A -2 (A -2)
v v

 

2][(J+i)3 — (J+))] (1.15)

I

4q 2p l
A_ A+ A

111,11 [(J+§)3 e (J+))] . (1.16)
1 e2 (1 =2)2
V V

 

 

Here pA and qA are the A-doubling constants.

Total Energy Expression

 

Finally to the order of approximation considered so
far, the total energy of a diatomic molecule with a 2H
ground state and with a coupling scheme intermediate between

Hund“s cases (a) and (b) can be written:

 

12

w’i\(J,v) = Te + G(V) + BV[(J+§)2-A2] + BV[L(L+1)-A2]
+ (-1)i[E,Av(AV — 4BV)A2 + Bv2(J+))2]§
-Dv[(J+))” - (J+§)2 + 1]
E£(J,V) (1.17)

where i = 1(2) corresponds to the intermediate Zflfi (2H3)

state respectively.

 

 

 

1..__ 1”,! 11...-.. ”1,171 $.11..__1_r

 

 

CHAPTER 2

WAVEFUNCTIONS AND INTENSITIES

The allowed transitions and intensities will now
be considered. The expressions for the linear combina—
tions of pure case (a) wave functions chosen as a basis

for the energy calculations must be found.

Intermediate Wavefunctions

 

The linear combinations of symmetrized wavefunc—
tions which diagonalize the 2X2 matrix of Eq. (1.7) are
a good approximation for the system. For the inter—

mediate wavefunctions one can write the matrix equation:

Izms”a = c |2n>sia , (2.1)

where the wavefunctions (Zn) and [2H> are in the inter-
mediate and the symmetrized case (a) basis respectively.
The s (a) denotes the symmetric (antisymmetric) linear
combinations. The matrix C, is evaluated from H" = CHC+
and the normalization condition; CC+ = l. The result is:

1’ ”b \

c=[]:1 a , (2.2)

 

4

where,
, F 5
a _'xw2+)2 b _x+2-1
Jv‘i'zx ‘ ' Jv‘ 2X °

13

 

14

Therefore the intermediate wave functions to this order are:

2 S a _ 2 51a _ . 2 s a
I Hi) ’ — aJvl H§> val H3> ’ (2.3a)
|2H3)S’a = aJVIZH3>S’a + va|2n£>s’a (2.3b)

The symmetries of the wave function have been carried merely
as a formality since to the order considered here, the ener-
gies and therefore the wave functions are identical for both
the symmetric and antisymmetric blocks of Table 1.2.

A complete tabulation of these wave functions for the
states v = 0 and v = 1 and for J up to 49/2 is given in
Appendix II, for 1L‘NI‘S’O and 15N160. It is seen that the

wave functions are very nearly pure case (a).

Intensities

To obtain the selection rules and for later calcula—
tions, the integrated absorption coefficient (30, 31) (often
called the absolute or integrated line intensity) S (cm-2)
will be needed. For a transition from the state m to m” it
is:

em, -= (Nm - Nm,) hvmm,Bmm, , (2.4)

where Nm is the number of absorbing molecules in the mEfl

State, vmm' is the frequency (cm‘l) of the transition, Bmm'

is the Einstein coefficient of induced absorption, and h is

Planck”s constant. For this work, N is negligible, and

m7
Bmm' can be obtained from time—dependent perturbation theory

(32). From this treatment it is seen that three cases must

 

14

Therefore the intermediate wave functions to this order are:

s,a

IZH£)S’a = (2.3a)

S a
aJvl2H12> I - va_l2Hg>

s,a >s,a

._ 2 2 s,a
‘ aJvl “3 + val H5)

IZHE) (2.3b)

The symmetries of the wave function have been carried merely
as a formality since to the order considered here, the ener-
gies and therefore the wave functions are identical for both
the symmetric and antisymmetric blocks of Table 1.2.

A complete tabulation of these wave functions for the
states v = 0 and v = 1 and for J up to 49/2 is given in
Appendix II, for 1“N160 and 15N160. It is seen that the

wave functions are very nearly pure case (a).

Intensities

To obtain the selection rules and for later calcula—
tions, the integrated absorption coefficient (30, 31) (often
called the absolute or integrated line intensity) S (cm—2)
will be needed. For a transition from the state m to m‘I it
is:

smm” = (Nm _ Nm') hvmm'Bmm' ’ (2°4)

where Nm is the number of absorbing molecules in the mEB

state, vmm' is the frequency (cm'l) of the transition, Bmm'

is the Einstein coefficient of induced absorption, and h is

Planck"s constant. For this work, N is negligible, and

mi
Bmm" can be obtained from time-dependent perturbation theory

(32). From this treatment it is seen that three cases must

 

 

 

15

be considered. These are; a) no magnetic field, non—
polarized radiation, b) longitudinal magnetic field, non—
polarized radiation, and c) longitudinal magnetic field,
radiation linearly polarized in the X—direction. (The
values of Bmm“ for these three cases are identical as they
must be, but for completeness all are given here.) A
coordinate system having the space fixed Z—axis parallel
to an applied magnetic field and along the direction of
propagation is chosen. (From this it is apparent that in
later references to Zeeman patterns, it is a longitudinal
effect that is being considered.)

In the following expressions [(uAH2 is the square of
the absolute value of the space fixed electric dipole moment
matrix element in the intermediate basis of the absorbing

molecule, with A = X, Y, Z.

(a) No magnetic field, non—polarized radiation.

2n
3mm. = 3:2— {|(ux)l2 + my)!2 + [(uz>|2} <2o5a)

This is effectively the case of isotropic radiation since
the molecular dipole moments are randomly oriented. Since
any direction is equivalent to any other, the three terms
in the above sum may be replaced by 3 times any one of

them.

(b) Longitudinal magnetic field, non-polarized radiation.

Bmm' = 2n
2,132

 

{l(uX)l2 + |(uY)|2} (2.5b)

 

16

In writing this it has been assumed that the magnitude of

the electric fields in the X“ and Y-directions are equal.

(0) Longitudinal magnetic field, radiation linearly

polarized in the X-direction.

B .
mm

2

= —1 |(uX)|2 (2.5c)
{'12

| The electric dipole matrix elements must now be

i evaluated. For a diatomic molecule the body fixed dipole

moment is along the internuclear or z—axis. The value of

the A—component in the space fixed system is then:

uA = g )Aaua (2.6)

where AAa is the direction cosine transformation coef-
ficient relating the A— (space fixed) and a—axis components
of a vector, where A = X, Y, Z and a = x, y, z.

The quantum numbers v, J, 0, M will describe the
system completely for what is now needed. With primes de-
noting the final state the square of the absolute value of
the matrix element of “A in the intermediate basis can be

written (assuming no vibration—rotation interaction):

(V.IJIPQ'IM3IHAIVIJIQIMJ)l2 =

((v'luzlvH2 I<J'.n',M3IAAzlJ,n.MJ)l2 . (2.7)

The term, I(v'|uz[v)|2 is a vibration transition probability
and will be designated IRVIZ. The non—zero elements for

this quantity, assuming anharmonic oscillator wavefunctions,

L11

 

 

17

will occur (33) for v' = vtl,12,’-'3Mo . Cross, Hainer and
King (34) have shown that the second matrix element of

Eq. (2.7) can be written:

(J',9',M'lx

J IJIQIMJ) =

A2

¢ (J';J)©

Az (J'r9'7J,9)¢AZ(J',M';J,M) . (2.8)

A2

Table 2.1 lists the values for these terms as they
apply to the pure case (a) representation. It is noted
that only the term ¢AZ(J',Q';J,Q) will be affected by the
intermediate wavefunctions° It is also true that I(ux)l2 =
[(uYH2 so that the only element which need be calculated
is [(uX)I2.

The pure case (a) angular momentum selection rules
for this coordinate system may be seen directly from these
matrix elements. They are AJ = -l,0,+l corresponding to
the P, Q, and R branches respectively, A9 = O which implies
A2 = 0 (since we are considering transitions within the 2H
state AA = O) and AM = i1.

Since only the ¢ components will need to be con-

Az
sidered, the subscript will be dropped. The absolute square

of the non—zero terms in Eqo (208) are as follows:

(i) |q>(J-1;J)|2 [16J2(2J+1)(2J-1)]"l (2.9a)

|q>(J;J)|2 [16J2(J+1)2]‘1 (2.9b)

I¢(J+1;J)I2 [l6(J+l)2(2J+l)(2J+3)]-1 (2.9c)

 

18

 

WHAHIEHWVAEHHVHH mmAH+2ubVAZHWVH WHAN+ZHHVAH+SHhVHH

NHNEINHL NI 2N

H WHAH+SIhVAH+E+bVHm

U
A2.nlafizr.bv xeflfi n

5
Az.hlafiz..nv we

5
Azrnlz:.nv Ne

 

WHAHIGHHVACHUVHH WHAH+GHUVAGHWVH mmfim+awaAH+Gubvaw

mmmcumbimu cm wmxa+cnhvna+c+bVHm

HIHMHAHIbNVAH+bNVHvH HIHAH+bevH Hlfimmxm+bmvAH+bNVHAH+vaV

Ae.buaflar.nvx¢eflw n

m
Aarhlafla..hv as

N
Aarhlar.nv as

Anu.bv e

 

th. N .b h. H ..n. HIT” H .h.

 

 

 

,;Avmv mpcmsmam xflnpmz manmoo coapomuflo axm.manme.

i r( v'l.|‘l\

 

l9

 

(ii) Here the notation 91,92 for Q = §,3 respectively is
used°
(a) A9 = 0
¢ J-l Q ;J 9 2 = 4 a a Jz-QZ £
I ( ' 112 I 112)l { J—l,v' JIV[ 1'2]
2_ 2 i 2
+ bJ_ l v' bJ V[J Q 2'1] } (2.10a)

2
4{aJ,v'aJ,v91,2 + bJ,V'bJ,v92,1} (2°10b)

¢ J+1 9 ;J a ) 2 = 4{a J+1 2 - 92 5
I ( ' 1:2 ' 1,2 I J+1 V' V[( ) 1,2 1

2 _ 2 i 2
+ bJ+1 V, bJ v[(J+l) 92f:] } (2.10c)

'(b) M2 = :1

 

¢ J-l Q ;J 0 2 = 4 a b Jz-QZ £
l ( I 2&1 ’ 1:2)l { J’livu JIV[ 2'1]
_. 2_2 £2
bJ-l,v”aJ,v[J QIyZ] } (2.11a)
|<I>(Jsz :J,9 )l2 =
I 1:2
- 2
4{aJ'V,bJfl/,S22’1 bJ,v"aJ,v91,2} (2.11b)
¢ J+1 Q ;J 9 2 = 4 J+1 2 - 92 £
I ( I 2'1 I 1a2)l {aJ+lI Va bJI V[( ) 2’1]
_ 2_ 2 £2
bJ+l,v'aJ,v[(J+l) 91,2] } (2.llc)

It is to be noted that in the intermediate basis the
values A9 = i1 are allowed, for here the quantum number 9

merely denotes the limiting pure case (a) value. The

 

20

following terms give the relative intensities of the Zeeman

components for each branch:

(iii) |<1>(J+1,M:1;J,M)|2 = (JiM)(J¢M—l) (2.12a)
|¢(J,M:1;J,M)l2 = (J$M)(J1M+1) (2.12b)
|¢(J+1,Mi1;J,M)[2 = (JiM+l)(JiM+2) a (2.12c)

The line strength for a particular branch is obtained
from the product of the appropriate AJ terms from Eqso (2.9)
and (2.10) or (2.11) multiplied by the sum over all possible

M and AM values of the corresponding term from Eq. (2012):

These sums are:

Z[(J—M)(J—M—l) + (J+M)(J+M—l)] =
M

§J<2J+1)(2J—1) (2.13a)

X[(J+M)(J+M+1) + (J+M)(J-M+l)] =
M
§J(J+1)(2J+l) (2.13b)
Z[(J+M+1)(J+M+2) + (J-M+l)(J-M+2)] =
M
§(J+1)(2J+1)(2J+3) . (2.13c)

Then defining s(J',Q';J,Q) as the line strength, one can

write:
s(J-l,Q';J,Q) = I%5|¢(J-1,9';J,m|2 (2.14a)
s(J,9'7J,Q) = I%%%§%%yl¢(J,Q";J,9)IZ (2.14b)

s(J+l,Q“;J,Q) = I2.7%:34<1>(J+1,s2';J,:2)|2 . (2°14c)

 

 

21

The calculated values for these line strengths are given in
Appendix III for the four possible bands (ioec, A9 transi-
tions) up to J = 49/2 for 1“N160 and 15N160o The values
of the line strength for the A9 = 11 transitions are seen
to be considerably less than those for A9 = 0.

The effect of the symmetry of the wave functions has
been neglected hereo It has been shown that for each value
of J there are two levels (A-doublet levels) of opposite

parityo The general symmetry selection rule is (35):

+<—->-

I+7L"+I'7L'*'o (2-15)

Each line of a branch will consist of two transitions of
equal intensity, and the line strengths given above must be
divided by 2 to prOperly account for this A-doubling.

The Einstein coefficient of induced absorption may

now be giveno For the field free case it is:
B(V”,J”,Q';V,J,Q) = allR [2s(J',a';J,9) a (2:16)
452"

In the presence of a magnetic field, the values given
in the preceding equation must be multiplied by a field
factor corresponding to the particular branch needed: This

gives:

B(v5,Jxl,Q”,Mfil;v,J,Q,M) =

B(v",J~l,9';v,J,9) %~E%§¥%§%§%§%g (2.17a)

22

B(v',J,Q',Mil;V,J,Q,M) =

(J:M)(JiM+l)
J(J+l)(2J11)

 

.] (2.17b)

an»

B(V',J,Q';V,J,Q) [

B(V',J+1,Q',M11;V,J,Q,M) =

. ,. 3 (JiM+l)(JiM+2)
B(v ,J+l,9 ,v,J,Q) [I (J+1)(2J+1)(2J+3)]°(2°l7c)

Here again the symmetry of the levels has been neglected.
Finally an expression for the number of absorbing molec-

ules in the initial state is needed. This can be obtained

from Boltzmann statistics. If N is the total number of ab-

sorbers taking part in the absorption process/unit volume,

then the number of absorbers in the state characterized by

the numbers i, v, J, M (i denoting the electronic state) will

be given to a very good approximation by:

N = N exp(-ei/kT)exp(-wev/kT) x

ivJM

exp[-BVJ(J+1)/kT]exp(-A/kT)/ZiZVZJZM (2.18)

where BV is the rotational constant, A is the Zeeman energy
of the state M, and Zi’ Zv’ ZJ and ZM are partition functions
for the electronic, vibrational, rotational and magnetic

states. Since the magnetic energies are small compared with

.kT the magnetic term becomes:

exp(-A/kT)= l (2.19)

ZM (2J+])

frhe evaluation of the vibrational and rotational terms is

giwnnlin many places (see e.g. Townes and Schawlow (36)).

 

 

 

 

 

23

They can be written:

exp(-wev/kT)

exp(—wev/kT)[l-exp(-we/kT)] (2.20)

Z
V

and

exp[—BVJ(J+l)/kT]

(2J;%)Bv exp[-BVJ(J+l)/kT] . (2.21)

ZJ

For the case of nitric oxide only the 2H electronic
states need be considered in evaluating the electronic term.
This becomes:

— kT
exp( E:112/ )

_ l
Zi _ l+eXp(:Ae/kT)

(2.22)

 

where A5 = E2 - E1 = A (the spin—orbit constant). It must
be remembered that the -(+) sign above is used for the tran-
sition a = 5, A9 = 0,+1 (a = 3, A0 = 0,—1).

The complete expression for the integrated absorption
coefficient in the absence of a magnetic field is then ob-
tained from the product of Eqs. (2.16), (2.19), (2.20),

(2.21), and (2.22) as:
S(v',J',0';V,J,Q) =

thZBV P exp(-wev/kT)[l — exp(—we/kT)]

 

X

(M?)2 [1 + eXp(¢A€/kT)]
eXP['BvJ(J+l)/kT]B(V',J',Q';V,J,9)v(v',J',Q';v,J,Q) (2.23)

where P is the partial pressure of the absorbing gas (the

ideifl.gas law has been used) and all other quantities are

 

 

as previously defined.

The integrated absorption coefficient is usually writ-

ten in the form:
5 = SOP (2.24)

where So is given in cm‘Z/atm.

By making use of James" (12) experimental determina-
tion of IRVI2 = (8.14 x 10‘2 Debye)2 the values of So can
be calculated. This was done for 1”N160 for the Vibra-
tional transition v=0 + v=l for values of J up to 49/2 for
all possible values of A9 and AJ. These are tabulated in
Appendix IV. Shaw and Abels (38) have also carried out

portions of this calculation though by a different method.

Transitions

The pure case (a) selection rules, the intermediate
wavefunctions, the intensities and the energies having
already been given, the spectrum can be predicted. The
main points should be summarized. It will consist of two
subbands, Znfi + 2H£ and 2H3 + 2H3 and two satellite bands,
Zflfi + 2H3 and 2H; + 2H2 for the particular vibration being
considered. To facilitate later notation these transi-
tions will be designated 1, 2, H, and L respectively. The
two satellite transitions may also be called HES and LES
(high and low energy satellite) respectively. Each of
these transitions will have a P, Q and R branch corres—

ponding to AJ = —l,0,+l respectively. In addition each

 

 

 

line of these branches will be a doublet, since for each

value of J, there are two levels of opposite parity. A
typical spectral line within a vibration—rotation band might
be labeled PH(7/2)+, which indicates a transition from

J = 7/2, 0 = i to J'= 5/2, Q = 3. The plus sign is merely

a designation to indicate the higher frequency component of

the A-doublet.

 

 

CHAPTER 3
ZEEMAN ENERGIES

The intensities and selection rules for the Zeeman
transitions were given in the preceding chapter. Here our
concern will be the energy levels of the system in the
presence of a magnetic field. The effect of the inter-
mediate wavefunctions will be quite apparent, for contrary
to the pure case (a) coupling scheme where the 2H2 state
would have a magnetic moment of zero, a non—zero value is
now obtained. Dousmanis, Sanders and Townes (20) have given
a treatment of the Zeeman energies in the intermediate case.

The magnetic Hamiltonian is:

—> —>
Hm — - (10H . (3.1)

In the body fixed system the magnetic moment operator is:
K = —u0(f+2's’) (3.2)

where “0 is the Bohr magneton.

Since this work is concerned with only the 2H states,
only the z-component of L will have non—zero matrix elements.
To transform the magnetic moment operator to the space fixed

system the direction cosines, A must again be used.

AOL’
Since the magnetic field is taken along the space fixed Z-axis,

only this component of the magnetic moment is needed, viz.

26

 

 

 

 

 

 

27

“Z = -u0[21ZXSX + ZAZySy + AZZ(A+ZSZ)] o (3.3)

From Appendix I and Table 2.1 the matrix elements of “Z can

be calculated by a simple direct product of A and 8“.

Ad

In the.pure case (a) basis the matrix elements needed are:

-u09M
<J,Q,MIuZIJ,Q,M> = ——n—mm(A+22) (3.4a)
J(J+1)

+uo[(J;9)(JiQ+l)]£M
<J,911,MIuZIJ,9,M> = ,

 

X

J(J+1)
[S(S+l) - 2(211)]i . (3.4b)

Inserting the appropriate values for the quantum numbers

yields:
<2H£|uZ|2H£> = 0 (3.5a)
'3U0M
<2H31UZIZH3> = _____l (3.5b)
J(J+1)

+1.1 0M E
_~_mmy[(J-£)(J+3)] . (3.5c)
1

<2H In lzn > = <2n In |2n > =
£22 32) J...

From this the expectation values for “z in the intermediate

basis can be calculated, viz.

wow) 3 [2(J-fi) (J+3) + 3 - 3x1
(HZ) = __“_fi_ {2 1 } (3.6)
J(J+1) X

 

where the upper (lower) sign corresponds to the intermediate

Zflfi (2H3) state.

 

28
The Zeeman energies can be written:

where gJ is the molecular g-factor given by dividing Eq.
(3.6) by -u0M. Calculated values for gJ are given in
Appendix V for the vibrational states v = 0 and v = l and
for J—values through 49/2 for both 1”N160 and 15N160.

Eq. (3.6) agrees with that given by DST (20) al-
though the method by which it was obtained follows that of
Lin (39).

The strengths obtained for the Zeeman components in
Chap. 2 did not include the perturbing effect of the magnetic
field. They are certainly good to a first approximation
and will be used throughout.

If one were to consider Hm = -E~fi, as a perturbation,
the perturbed intermediate rotational wave functions, from

first order perturbation theory (40), can be written:

(J+1,Q,M(uZ|J,Q,M)H

 

 

|J,9,M)' = IJ,Q,M) + IJ+l,Q,M)
AE
R
(J-l,Q,M|pZIJ,Q,M)H
‘ AE - (J-I,Q,M) , (3.8)
P
where AER,P = EJ+l-EJ and EJ-EJ_l respectively. This ap-

proach was carried out for a pure case (a) basis and the
results indicated that the intensities would change by

less than 1%. The exact perturbation calculation is not
conceptually difficult; however, the algebra involved, because

of two magnetically sensitive levels, will be extremely tedious.

 

CHAPTER 4

MAGNETIC ROTATION THEORY

As early as 1846 Faraday (41) showed that optical
activity (rotation of the plane of polarization) can be
induced in matter by a magnetic field. This furnished
one of the first connections between optics and magnetism
and provided an impressively strong hint as to the elec-
tromagnetic character of light.

A medium exhibits magnetic circular birefringence
(MCB)(or Faraday rotation) when, as the name implies, a
longitudinal magnetic field causes the refractive indices
for right and left circularly polarized light to be un-
equal, thereby rotating the plane of polarization. In
addition the field causes different absorption coefficients
for the two polarizations, giving rise to magnetic circular
dichroism (MCD). These two effects are interrelated. Mag-
netic rotation spectra (MRS) in which the total intensity
transmitted through crossed polarizers is measured, stems
from these two effects.

Buckingham and Stephens(B&S) (21) have recently given an
extensive review of magnetic optical activity from a pheno-
menological standpoint. Their starting point is essentially

that of Rosenfeld (42), Kramers (43) and Serber (44) with

29

 

30

the extensions of Carroll (45). It should be mentioned that
Hameka (46, 47, 48) has treated magneto-optic phenomena by
resonance fluorescence techniques. While this is probably

a more rigorous approach, it loses sight of the relevant
phenomenological parameters and consequently will not be
considered here.

The phenomenological calculation considered by 8&8
is carried out in three steps: the observable is related to
the difference in the complex refractive indices of right
and left circularly polarized light; Maxwell's equations
are used to express the complex indices in terms of the
moments induced by the radiation; finally, these moments
are calculated quantum mechanically.

This approach is general enough to be applicable to
all material phases; however, things can be simplified,
both conceptually and practically, for the gaseous phase
which is our immediate concern.

The approach which will be used is an extension of
that of Aubel (22), and parallels quite closely that of
B&S. The first step of both approaches is the same.

In complex notation the electric vector describing
a circularly polarized wave prOpagating in the +Z-direction

is (21):

i

E = ExiiiE 3 = Eoexp[i(wt-kiZ)](iii3) (4.1)

Y

where E+ (E_) represents the electric field for a right

(left) circular polarization in the conventional right hand

 

 

31

sense (i.e., for radiation traveling in the +Z-direction,

right circularly polarized will mean a rotation of the

electric vector in the counter-clockwise sense viewed into

the beam), k+ (k‘) is the corresponding propagation con-

stant, and w is the angular frequency of the radiation.
Then a wave linearly polarized in the X- and Y-

directions can be written in terms of E+ and E":

_ l —
EX — —2-(E+ + E) (4.2a)
E = L<E+ — E') (4 2b)
y 21 ° °

For an optically active media there will be two different

indices of refraction:
n = —' o (403)

If a wave initially linearly polarized in the X-direction
traverses an absorbing media of length L, then upon emerging

there will be a Y-component given by:

+
EY = g-g—b/T=F exp[i(wt+P - EE$£)]

—/T= exp[i(wt-P - 2%2£)]} . (4.4)

T+

and T' are the transmission fractions for the right and
left circularly polarized components respectively. The
ratio of the intensity transmitted by an analyzer whose
axis is parallel to the Y—direction relative to that of one

at an angle P relative to the X-direction and in the absence

of the media is:

 

32

IE I2
T 3 _X~2 = 1 T+ + T' - /T*T“ exp{i[2P+2£(n--n+)]}
IE0) I C

-VT¥T' exp{-i[2P+3%(n‘-n+)]}

%{T+ + T” - 2VT'T' cos2(P+e)} , (4.5)

where e = nvL(n’-n+) and v is the frequency in cm‘l.
Assuming a normal exponential law of absorption, the trans-

mission fraction is given:

1

T = exp(-aiL) , (4.6)

where a+ (a‘) is the absorption coefficient for right (left)

circularly polarized lignt. One usually defines a quantity:
+> . (4.7)

With this, Eq. (4.5) can be written:

 

 

. “r _ /*=

T“ = {(’/T 2 T )2 + /T*T'sin2(P+e)} (4.8a)
_ + -

= exp[mLa-;a )L]{sin2(P+e) + sinh2¢} . (4.8b)

It should be understood that ni, a- and therefore 6, ¢ and
T' are functions of frequency. The form of Eq. (4.8a) makes

it easy to separate it into a circular dichroism term:

 

 

CD = 1r-“ 4 = (4.9a)

and a circular birefringence term:

+ ...
CB = VTTT‘sin2(P+e) = exp[«i34:1—LL]sin2(P+6)

2 . (4.9b)

This completes step one.

 

 

33

At step two B&S obtain the complex indices in terms
of the magnetic and electric polarizabilities. Following
Aubel it is simpler to express them in terms of the absorp-
tion coefficients for right and left circularly polarized
light. From Penner (49) one finds that the absorption coef-
ficient can be written in the following forms for various
conditions of pressure.

At very low pressure, Doppler broadening is the major

contribution to line width. The absorption coefficient is:

-§_1_n_2) 222- 2
aD(vi) YD( ) eXpl YD (v vi) ] (4.10)

H

where S is the integrated absorption coefficient, is the

YD
Doppler halfwidth, and vi is the frequency of the iEQ absorp—
tion line. In speaking of halfwidths, it will always be
assumed to mean one half the total width at one half the
maximum height (HWHM) unless otherwise designated. The
Doppler halfwidth is given by:

= :3 2kT 1n21§
7M

YD C (4.11)

where k is the Boltzmann constant, M the mass of the molecule
and T the absolute temperature.

At the other extreme, that of high pressure, the line
shape should be Lorentzian and the absorption coefficient

will be:

s YL 1
W

 

0L (v.) =
L l (v—Vi)2 + YLZ (4.12)

where YL is the Lorentz halfwidth and S is as before.

 

 

F_______________________________________________:IIIIIIIIIIIllllllllllfifiiiiiiiiiiii

\_

34
YL is pressure dependent and can be written (50):

O

YL = YL P I (4.13)

. 0 -
where P 15 the pressure. Values for YL (cm 1/torr) must
be found experimentally.
Most of our work falls in an intermediate pressure

range where the absorption coefficient is:
SYL 1n, 1 expl-(ln2/YD2)n2]dn
YD

 

G(Vi) = . (4.14)

 

3

w YLZ + (V-vi-n)2

-€D

If there is an applied longitudinal magnetic field
there will be an absorption coefficient for each Zeeman
component. When the absorption coefficient for each vi
has been found, the total absorption coefficient is found
for right or left circular polarizations by a single sum-
mation:

at(v) = Zat(vi) . (4.15)
l

The integrated absorption coefficient determines
whether Vi absorbs the right or left component as will be
shown shortly.

Finally the Kramers-Kronig relations (51) are used
to obtain the indices of refraction, viz.

co

9(V) = l [3121211221 (4.16a)
" (v'Z—VZ)

(v')dv'

¢(v) = ~3 J9 (4.16b)
V 0(vl2_V2)

 

35

The quantum mechanical calculation of the integrated
absorption coefficient which was treated in Chapter 2, com—
pletes the third step. From time dependent perturbation
theory it is known (52) that AM = +1 (-1) absorbs right
(left) circularly polarized radiation.

This completes the phenomenological calculation and
one must now combine Eqs. (4.6), (4.7), (4.8a), (4.14),
(4.15) and (4.16a) to obtain, in principle, the magnetic
rotation intensity T'(v) as would be observed by a spectro-
meter having infinite resolving power.

In practice the spectrometer halfwidth is much greater
than the line widths being considered. Therefore to predict
the MRS signal which would be observed, an integration over
the spectrometer slit—function must be performed. The nor-
malized MRS signal will then be given by:

IT' (v)o(\))d\)

T(v) = . (4.17)
Io(v)dv

 

Here 0(v) is the spectrometer slit-function which can be
obtained by recording the profile of a very narrow emission
line.

It should be mentioned that the integrations involved
in Eqs. (4.14), (4.16) and (4.17) can not be done in closed

form and numerical integration techniques must be used.

 

CHAPTER 5
ABSORPTION ANALYSIS

Spectra of the l- and 2-subbands, the HES and LES for
the V = 0 + V = 1 transition for both 1”N160 and 15N150
were obtained using the high resolution infrared spectrometer.
Details of the instrument will be treated in Chapter 8. Ex—
perimental details for obtaining the absorption spectra of
the four bands of both 11+N160 and 15N160 are given in Table
5.1. Figures 5.1 and 5.2 show typical absorption records
for portions of the HES and LES spectra for 15N160. 15N160
and 1”N150 were obtained from the Isomet Corporation and the
Matheson Company respectively. 15N160 had sufficient
purity as obtained; however, the 1“N160 contained nitrogen
compound impurities which were frozen out for the LES region.

Calibration was accomplished using Edser-Butler bands
as recently reviewed (53). Bands of CO, HCl, and HCN meas-
ured by Rank et. a1. (53) were used as standards. Standard
deviations of the calibration fits ranged from 0.001 cm"1
to 0.003 cm_1. All frequencies used in the analysis were
measured on at least two different records.

The absorption charts were photographed, the raw data
then digitized using the Hydel system (54) and finally reduced

to absorption frequencies by the computer program SHAFT, which

36

 

37

Table 5.1 Experimental Conditions for Absorption Spectra.

)

 

 

 

 

 

 

 

 

1”N160 Calibration
Chart Band Region Pressure Fringe Eff. Standard Order Pressure S.D.
(cm-1) (Torr) Order 51. Width (Torr) -
(cm-1)
5/26 HES 1945-2070 100-200 9 .062 HCl (2-0) 3 10-20 0.0014
co (1-0) 1 1
5/27 HES 1990-2020 200 9 .062 C0 (1-0 1 80-3 0.0015
5/31—1 HES 1990-2020 200 9 .062 C0 1-0 1 80-3 0.0012
5/31-2 HES 1990-2020 200 9 .062 CO (1-0) 1 80-3 0.0010
5/31-3 HES 1990-2020 100 9 .062 CO (1-0) 1 80-3 0.0015
6/1-1 HES 1990-2020 100 9 .062 co (1-0) 1 77-9 0.0017
6/1-2 HES 1995-2080 100-200 9 .062 C0 (1-0) 1 80-1 0.0021
6/2-1 HES 1995-2080 100—200 9 .062 C0 (1-0) 1 80-1 0.0023
6/2-2 HES 1950-1990 100-200 9 .062 HCl (2-0) 3 6-10 0.0015
CO (1-0) 1 50-10
6/3 HES 1950-1990 100—200 9 .062 HCl (2-0) 3 6-14 0.0012
CO (1-0) 1 50-10
6/7 FUND 1905-1990 1-260 9 .062 HCl (2-0) 3 4 0.0013
CO (1-0) 1 50-10
6/10 FUND 1905-1990 1-260 9 .062 HCl (2-0) 3 4 0.0016
CO (1-0) 1 50-8
6/13 FUND 1800-1930 .5-2 9 .061 HCN (101) 3 5 0.0020
Hc1 (2-0) 3 6-9
6/14 FUND 1800-1910 .5-2 9 .061 HCN (101) 3 5 0.0022
HCl (2-0) 3 6-10 3
6/22 FUND 1705-1800 230—2 11 059 HCN (001) 2 4-10 0.0022
HCN (101) 3 5
6/23 FUND 1705-1800 200-2 10 059 HCN (001) 2 5-10 0.0013
HCN (101) 3 5
6/24 LES 1670-1830 250—100 10 062 HCN (001) 2 1 0.0019
HCl (2-0) 3 10-6
7/5 LES 1670—1840 200-100 11 .062 HCN (001) 2 1-2 0.0019
HCl (2-0) 3 9-6
11/1 LES 1690-1795 100 (0 .016 HCN (001) 2 2 0.0030
HCN (101) 3 5-3
11/2 LES 1690-1795 100 11 .036 HCN (001) 2 2 0.0038
HCN (101) 3 3
lsulto Calibration
7/11 HES 1930-2020 76 9 .060 HCl (2-0) 3 4-3 0.0016
co (1-0) 1 3-1
7/13 HES 1920-2015 75 9 060 HCl (2-0) 3 4-3 0.0018
CO (1-0) 1 3-2
7/15 LES 1690-1780 71 10 .062 HCN (001) 2 1-2 0.0020
HCN (101) 3 4
7/18-1 LES 1660-1690 70 10 055 HCN (001) 2 1 0.0021
‘ HCN (101) 3 5
7/18-2 LES 1645-1690 70 11 .055 HCN (001) 2 1 0.0021
HCN (101) 3 4
7/19 LES 1700-1780 68 11 .062 HCN (001) 2 1 0.0026
HCN (101) 3 4
7/20 FUND 1705-1790 66-2 10 .065 HCN (001) 2 4 0.0031
HCN (101) 3 3
7/21-1 FUND 1710-1790 66-2 11 065 HCN (001) 2 3 0.0025
HCN (101) 3 3
7/21-2 FUND 1770-1890 .5—2 9 .057 HCN (101) 3 3 0.0027
HCl (2-0) 3 3
7/22 FUND 1790-1890 5-2 9 .057 HCN (101) 3 2 0.0027
_ HCl (2-0) 3 3
7/25 FUND 1890-1970 1-64 9 .058 HCl (2-0) 3 3 0.0026
CO (1-0) 1 80-60
7/26 FUND 1890-1970 1—64 9 .058 HCl (2-0) 3 4 0.0018
co (1-0) 1 80-60

 

 

All of the above spectra were recorded with the following conditions:

Pathlength, 945 cm;
grating, 300 lines/mm; detector, Kodak PbSe E-2; grating rotations, 0.02 and 0.05 degs./min.

 

 

38

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40

is described in Appendix VII-A. Identification of the trans-
itions presented no difficulty.

The "effective" rotational, vibrational and spin—orbit
constants may be obtained from the method of combination
differences (55) and/or from frequencies.. Both of these
approaches were used. In each case the appropriate formula
was fit to the observed data by the method of least squares
using the M. S. U. CDC 3600 computer. Data from all bands
for a given isotopic species were fit simultaneously. The
least squares subroutine used in-all fitting programs gives
estimators for the constants and their standard errors.
From this the simultaneous confidence intervals (SCI) (56)
can be calculated for each constant. On all fits a level
of significance of 0.05 was chosen (i.e., a 95% SCI was
used).

Combination differences were calculated from the ob-
served frequencies using program DIFF. This program,
given in Appendix VII-B, calculates all possible A1F and
A2F's and forms a weighted average of the appropriate
components to determine the final values for both the
ground and upper state. Because of the statistical nature
of the problem, one may use both A1F and A2F's in deter--
Inining the constants. Frequencies used in forming the
cxxnbination differences are the average of the A—doublet

frequencies .

 

41

Effective Energy Expressions
For the 2H state of NO, L = 1, A = $1, and 1V = Av/Bv
=73. The radical in Eq. (1.17) may therefore be expanded

in powers of (J+§)2. Keeping terms through (J+fi)6 yields:

TQ(J,v) = Te + G(v) - 0V + (-1>iC1V/2

2 _ L1 6
+ Bvi(J+§) Dvi(J+§) + Hvi(J+§)

i E£(J,v) , (5.1a)
where
Clv = AV - 23V - 2BV2/AV + ... , (5.1b)
Bvi = BV + DV + (-1)ti[1V + 21V2 + ...] , (5.1c)
Dvi = DV + (-l)iBV[Av3 + 61V“ + ...] , (5.1d)
Hvi = (-l)iBV[2)V5 + 201V6 + ...] . (5.1e)
B

vi’ Dvi and HVi are "effective" rotational constants. The

energies in Eq. (5.1a) are essentially those of two simple

diatomic molecules with an electronic energy separation of

C) .

v
From Eqs. (5.1c), (5.1d) and (5.1e) the "true" rota-

tional constants are:

B = Vl -—VZ - D (5.2a)

 

 

 

H
fl“... _ _, -1 4

 

 

 

_ v1 v2
DV _ 2 (502b)
H + H
_ v1 v2 :
Hv _ - 2- _ O . (5.2c)

The "effective" rotational and spin-orbit constants were

assumed to be linear functions of v, viz.

BVi = Boi - div , (5.3a)
DVi = Doi + Biv , (5.3b)
Hvi = Hoi - yiv , (5.3c)
AV = A0 - xv . (5.3d)

The expressions for the combination differences and fre-
quencies, including the above assumptions, which were fit
are found in Appendix VI-A and VI—B. They are listed there
in a form readily adaptable for computer use.

Two methods were used in obtaining the molecular con-
stants. In the first method the ground state combination
difference data were first fit, using program ROTCONS given
in Appendix VII-C, to determine the “effective" ground state
rotational constants. 80 and 76 non-zero weighted GSCD with
J-values up to 71/2 for 1”N150 and 15N160 respectively were
fit. These ground state constants were then fixed in the
frequency fit (using program ALLFIT given in Appendix VII-D)
‘thereafter determining only the "effective" upper state con-
stants. The fits indicated that the upper state "effective"

(nanstants were determined less accurately in a fit of the

 

 

 

 

43

upper state combination differences than in the fit of fre-
quencies in which the ground state "effective" constants were
fixed. For this reason all upper state constants quoted were
determined from a fit of frequencies. From preliminary fits

it was found that Hv and Hv2 were equal and opposite to the

1
accuracy of our measurements; consequently they were replaced

by a single constant, HV' = Hv2 = —H The final least

v1°
squares output from these two fits, for both molecules, is
given in Appendix VIII, which includes the observed, predicted
and observed minus predicted values for all data points.

In the second method, a frequency fit was made in which
all constants, both upper and ground "effective" rotational,
spin-orbit and vibrational, were determined simultaneously.

The final least squares output from this fit for both molec-

ules is given in Appendix IX.

Effective Rotational Constants

 

The values of the "effective" rotational constants with
their 95% SCI from these two methods are listed in Table 5.2
under Case I and Case II respectively. While the constants
overlap in almost all cases, within their 95% SCI, it is
still disconcerting that the overall standard deviations of
the frequency fits, also listed there, should differ by such
an amount. Attempts were made to remove this discrepancy.
One of these was the inclusion of an AJ dependence suggested

by James (13). While the AJ term was on the verge of signifi-

cance, it did not improve this situation.

 

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45

Our values of the "effective" rotational constants
from Case I are listed in Table 5.3 along with those of
other researchers. Small differences between our constants
and others could arise from the fact that an Hv dependence
has been included. In fitting the data this will of neces-

sity affect the values of the other constants.

Rotational Constants

The rotational constants for both molecules were cal-
culated from Eqs. (5.2a) and (5.2b) and are given in Table
5.4. In this Eqs. (1.11) and (1.12) have been used. These
rotational constants, determined from Case I and Case II

"effective" constants, agree to well within their 95% SCI.

Spin-Orbit Constants

The constants(jw and X were determined directly from
the frequency fit since satellite data is included. From
the values ofC10 and B0, A0 can be obtained by solution of
the simple quadratic (obtained by neglecting terms of order
zBV3/AV2 = 0.0006 cm'“1 and higher) of Eq. (5.1b). Table 5.5
lists the values of A0, A1, Ae and Xe obtained. It is seen
from this that the spin-orbit constants from Case I are the
same, within their 95% SCI, for both isotopes, as are those
from Case II. Our values for A0 and A1 should be compared
with those of James (13) for 1L‘N16O (A0 = 123.1610.02 cm—1

and A1 = 122.91:o.02 cm-l).

 

46

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48

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ONOOO0.0HmvwwHooo mNOOOOOOHmNmoHooo «Hoooooon¢mmHooo PHOOOOOOHvamHooo a
m
vmooooooMmmvwvmoa hmooooocnmvvvvwoa mmoooooOHmmwvvmoH *thOO0.0HHmvwvmoH m
- HH wmmo . -H WWMUTs, .--- , HH mwmu .- . - H mmmu pneumoou
, ADHHUV oowmhwsi-, 1 1 - Amoov,ommzma-.
.AHIEUV Oolzmb now msoHDMHDUHmo UHQODOmH w.m UHQMB
mHm>HmusH UUGUUHHQOU mDOUQMDHDEHm wmm a
m
mmooooHNNvmoo mhoooonmvmoo mmoooonHvNoo HmOOOOmemNoo x
m
mhooooHNmomomma mmoooohvmmmomma 0000.0nmwom.MNH HHooo a hmmomma fl
NmoooonmvmoNNH vaOOOHH¢mmomma hmoooOH©w¢moNNH mvooooHHNmmoNNH H<
Nmoo.o«Hme.mmH mvooooHomomomma bmooooHHmmHomma *mvoooOHmwONommH ed
.; HH mmmu H mmmo 1 HH mmmo , , H mmmo puebmsoo
oefizma omfizaa

 

 

.Arusoc oz 000 mucmquoo hangoucaem m.m magma

 

49

Lambda Doubling Constants

A least squares fit to determine the A-doubling con-
stants was also performed for each molecule. The expres-
sions which were fit (using program LAMCON given in Appendix
VII-E) are given in Appendix VI-C. Doublet separations from
both the HES and LES were used. The least squares output
for both isotopes is given in Appendix X. Values for these

constants (cm‘l) are:

 

 

This Work Microwave (5)
15N160 14N160 15N160 luNleo
pA x 103 5.67210.058* 5.82810.063 5.686 5.876
qA x 105 3.911.1 4.6¢l.l 2.4 3.84
No. pts. fit 29 41
Std. dev. 0.0028 0.0043

 

* 95% Simultaneous Confidence Intervals

The values for pA agree very well with those obtained from
microwave measurements. While the values for qA do not over-
lap theirs, it should be pointed out that much higher J-values
are being fit (e.g., up to J = 47/2 for 1“N160 and J = 41/2

for 15N160).

Vibrational Constants
Since only one vibrational transition was observed,
only one vibrational constant, AG(1), can be determined.

The difference in vibrational term values is:

AG(v) s G(v) - G(O) = (we-wexe) v - wexe v2 + .. . (5.4)

 

50

The values for AG(1) from the two cases, given here for com-

pleteness, are:

14N160
Case I Case II
AG(1) 1875.9872 5 0.0038 1875.9904 1 0.0026
15N160
Case I Case II
AG(1) 1842.9366 5 0.0030 1842.9378 1 0.0023

The Case I and Case II values do overlap within their 95%

SCI.

Isotopic Calculations

 

The theoretical relations for rotational and vibra-
tional constants between isotOpically related molecules in

terms of the reduced mass are:
Bel = pZBe, (one)1 = page, Del = que, wel = owe, (5.5)

where i refers to the substituted species and 02 = u/ui,

u being the reduced mass of the normal species. Assuming
1”N160 to be the normal species, Table 5.6 lists observed
and calculated values for the isotope 15N160. A value of

p = 0.98211970 was obtained from the AIP Handbook (57).

It is seen that these calculated values agree very well with

the observed values.

 

 

51

Discussion

The measurement of the line frequencies used in the
analysis is believed to be accurate to 0.003-0.004 cm'l.

The "effective" ground state rotational constants de-
termined from the ground state combination difference data
are probably the more meaningful of the two sets. It is
generally accepted (58) that fitting combination differences
leads to a more accurate determination of these constants
than a polynomial fit of the frequencies. In addition, the
constants determined in this way will not be affected by
perturbations of the upper states, and the ground state is
less likely to be affected by perturbations.

The difference between the standard deviation of the
frequency fit of Case I and Case II could arise due to the
fact that in Case I, the fit is being forced to accept
values for several of the constants. The curve obtained by
varying the remaining constants may not be able to match
the experimental curve as well as when all the constants are
varied. It is still possible however, that the accuracy of
the present data is sufficient for this difference to be
pointing to an inadequacy of the present theory. The diffi-
culty does appear to come in large part from trying to fit
the satellite and fundamental data simultaneously. James (13)
reported difficulty in using constants determined from the
fundamental band to accurately predict the observed HES fre-
QUencies. The double set of constants is carried throughout

to klighlight this difficulty.

 

52

It is comforting that the "true" rotational constants
(Table 5.4) from the two cases are in good agreement. The
values for re, which are the same, as expected, for both
isotopes, are good to the accuracy stated.

It should be stressed that the spin-orbit constants
for the two isotopes are in very good agreement for both
Case I and Case II. This indicates that both isotopes have
identical electronic structure to the accuracy of the data.

The Q—branches of the fundamental subbands overlap
considerably, leaving very few unblended lines. This is due
in part to the A-doubling in the Q1 lines which is quite
large at high J (e.g., 60.24 cm"1 at J = 21/2). For this
reason these Q-branches were not included in any of the
fits.

It should be emphasized that the data input to all the
fits included the lines from both fundamental subbands to-
gether with lines from the HES and LES. For reference, the
95% SCI quoted throughout, are ~4 times the commonly used

standard errors of the coefficients.

CHAPTER 6
ZEEMAN ANALYSIS

In general, Zeeman spectra have not been recorded in
the infrared because the resolution was not sufficient to
show the individual AM transitions. It happens that the
splittings for the 2-subband of both 1“N160 and 15N160
are sufficiently large and the experimental conditions
such that for small J—values the extreme components of the
transitions could be resolved and their splittings measured.
Fig. 7.6 shows Zeeman patterns for the P—branches of the l-
and 2—subbands for low J-values. In Fig. 6.1a the observed
Zeeman spectra for the P2(5/2) line of the (1-0) band of
1“'Nl‘SO at five different magnetic fields are shown. The
patterns for 15N160 are not significantly different and
hence are not reproduced.

The magnetic fields producing these patterns were ob-
tained from an air-core, water cooled solenoid built by the
Magnion Corporation. This solenoid is capable of producing
fields up to 6800 gauss. It has a central core diameter of
seven inches and is forty-eight inches long. Over the region
containing the absorption cell, the field is homogeneous to

within i2%.

53

54

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.3180 emo.o .zmzm aoflpoeswuuaHh uso mam .rumemaruam

"Huou v .muommwum .onHH Ho coHuUcom m we 022:H H0 UGHH
Amxmcam .eemn oua 0:0 now 6006066 gramme em>nmmno A6 .H.e .mam

 

 

 

Seenw.z ooooo.r

to to- to to-

//.E .

@0000 . I 00000.: o .I

55

From the work of Chapters 2 and 3 the theoretical
Zeeman-patternS»can be predicted. Figure 6.1b shows the
predicted Zeeman pattern for the P2(5/2) transition for:
the same fields as above. (These were obtained from program
PLOTPUN given in Appendix VII—H.) The central components
of these transitions overlap considerably; however, the
two outermost components appear as single lines.

Measurements of the splittings of the components of the
P2(5/2) and R2(3/2) lines from the zero field position were
made for both 1”N160 and 15N160. Table 6.1 lists the observed
and predicted values (predicted from program ZEEPUN, Appendix
VII-G) of these splittings for the various field-conditions.
The uncertainty in measurement is probably no greater than
0.004 cm‘l; however, the field and therefore the splitting
uncertainty ranges between 0.9 and 1.5%. The observed and
predicted values agree reasonably well. Microwave measure-
ments of these splittings (58, 59, 60) are more accurate,
but the above agreement is good enough so that the inter-

pretation of the observed pattern is certainly correct.

 

 

 

56

Table 6.1 Zeeman Splittings for the (l—O)
P2(5/2) and R2(3/2) Lines of 1”N160 and 15NléO
as a Function of Field.

 

 

 

 

 

 

 

 

 

Splittingsa
p2(5/2) R2(3/2)
FIELD Obs. Calc. Obs. Calc.
(Gauss)
4000 0.3807 0.3764 -- -—
5000 0.4785 0.4704 0.4784 0.4702
14N16O
6000 0.5718 0.5644 0.5648 0.5642
6700 0.6398 0.6304 0.6328 0.6300
4000 0.3862 0.3760 -- --
5000 0.4732 0.4702 0.4806 0.4708
15N16O
6000 0.5686 0.5642 0.5693 0.5650
6700 0.6248 0.6300 0.6350 0.6308
a) Separation between the most extreme Zeeman

components in cm'l.

 

 

CHAPTER 7

MAGNETIC ROTATION ANALYSIS

From October 7—27, 1966, quite an extensive series
of magnetic rotation spectra were run on the l-O band of
both 1”N160 and 15N160 as a function of pressure, path length,
field and polarizer angle. This included a look at the HES
of 1"‘N160. Figures 7.1, 7.2, 7.3, 7.4 and 7.5 summarize the
main features of these spectra. The experimental arrange—
ment used in obtaining them is described in Chapter 80

Most features in Figs. 7.1 = 7.4 have been given a
qualitative explanation. The opposite rotations of the l—
and 2-subbands of Fig. 7.4 has been observed and accounted
for by Mann and Hause (62) and by Aubel and Hause (63). A
general explanation for the intensity minimum of the P2 and
R2 lines near J = 9/2, visible in Figs. 7.1 - 7.4, was also
given by the latter. The doublet structure seen in the lines
in Figs. 7.1 and 7.2 has also been observed by Robinson (64)
who simply attributed the occurrence to absorption from a
background of non-uniform intensity.

A semi-quantitative description of the above features
has been attempted. Using the M. S. U. CDC 3600 computer
the numerical integrations of Eqs. (4.14), (4.16a) and (4.17)

WeIe carried out to predict the magnetic rotation signal.

57

 

 

58

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mums wmonfi .wHSmmmum mo coauocsm m mm Om 2.: mo gunman
um Joann ona 93 mo muuommm counumuou oufiwc m: .HK .mflm

... w ... ... m m. 4mm
3.. ______i____________

am N N N N _N N_ N m
3.. _l__4__4__4__w__fl__._.__._.___

 

 
 

3x0... NAN - wmsmwmza

 

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59

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60

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ll .1 Br r I; _ L»?

 

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61

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one .HIEU H.o mo zmzm COHHUCDMIuHHw m paw EU mam wo Qumcma
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——————i
63

These predictions also give a clearer picture of the whole
magnetic rotation effect. In all calculations it is assumed
that the adjacent lines do not add appreciably to the circu-
lar birefringence or dichroism. The effect of overlap is
considered later. Program PLOTPUN, listed in Appendix VII-H,
carried out the necessary computations and plotted the output.
Pertinent magnetic rotation parameters which are input are
the Doppler HWHM, Lorentz HWHM, spectrometer HWHM, pressure,
pathlength, integrated absorption coefficient, polarizer
angle, the Zeeman splittings including the A—doubling and the
relative intensities. The Doppler HWHM for NO at room tem—
perature, calculated from Eq. (4.11) is w0.002 cm-l. The
Lorentz HWHM must be found experimentally. Shaw and Abels
(38) have done so for NO and found YL = 8><10_5 cm'l/torr.

It is slightly dependent on the transition. This value has
been found to be too low, by at least a factor of 2, to give
reasonable matches to the observed magnetic rotation signal.
Buckingham and Segal (65) found that a value 4 times larger
than this was needed in their predictions for the 3—0 band
of NO. The difficulty must be studied in more detail; however,
for the time a value increased by 2X will be used. For pres—

sures : l torr, = 10y and one would expect a Do 1er line-
L PP

YD
shape; however, for pressures of m20 torr, YD = YL° Therefore
the intermediate lineshape of Eq. (4.14) was used, which should
handle both conditions. A spectrometer HWHM of 0.05 cm"1 was

used. For general reference this is N3 times smaller than

that used by Aubel and Hause (63) for the 2-0 band. This was

64

possible due to greater dispersion in the region of the l-O
band coupled with a larger percent magnetic rotation. In
the calculations so far, a Gaussian form has been assumed
for the spectrometer slit-function. In actual fact, for
the mechanical slit—widths used, the slit-function should
be more nearly trapezoidal. Eventually careful plots of a
narrow emission line should be run for the region of in-
terest and the exact slit-function input to the program.
The integrated absorption coefficient was input as calcula—
ted from Eq. (2.23). Zeeman splittings were calculated
from Eq. (3.7) using program ZEEPUN, and input.

The Zeeman splitting is symmetric to the order of ap-
proximation considered here. Fig. 7.6 shows some of the pat-
terns and relative intensities, including the A—doubling, for
both the l- and 2-subbands. Each transition is a collection
of (2J+l) symmetric doublets, the components of which are
characterized by AM = +1 and —l, and which absorb, in equal
amounts, right and left circularly polarized light respectively.

The magnetic rotation signal, as will be seen later, is
predominantly due to circular birefringence. Typical
anomalous dispersion curves for a simple doublet along with
the rotation angle 9, are shown in Fig. 7.7. e is directly
prOportional to the integrated absorption coefficient, and
the calculations show it can attain magnitudes of N70 radians
for the 1-0 band. In the central region of the doublet, e
is changing rapidly. One therefore expects sinze to oscillate

rapidly between 0 and l. The frequency of this oscillation

l-QEBAND

 

«Inc I I I

I mun

J J 1"”-

-Jl A 3'“

 

Fi . 7.6. Predicted Zeeman patterns
for the l-0 band, P-branchuof ll“N160

strength of 6000 gauss. Lines drawn

65

Z-SUBBAND

 

 

 

 

 

 

o'sm
J-M
_° Liza .4 IIIIIIIII 5 .L - The
J-Il/Z
-o‘B ' L 'IIIIIIIL A ohm
. L 1 IIIlln .4 9.9/2 4
0.51: IIII II obi:
I l 1 m
l; v' I I 1 1 5 k 4*”
-osoo I I I I o
I I a 52
mg L 4 T J 1

 

pond to AM = +1 (-1) transitions.

and relative intensities
for a magnetic field
upward (downward) corres—

66

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.hao>fluoommou coauofloou ponwnoaom haumasouflo umoa mam ucmwu

How cofiuomumou mo movatcw osu ouo I: can +c .uoansom cmEooN
oHQEMm o How mobuso :onHonHC msonEoco Hmofimee .e.h . am

 

 

 

 

67

will decrease as one proceeds toward the wing of the tran-
sition since there 6 changes less rapidly. Finally, as 9
becomes less than n/Z, the circular birefringence will de-
crease to zero. In the extreme wings of the line, the Kramers-
Kronig relations (i.e. Eq. (4.16a)) predict 6 a 1/v° The
frequency range for n>e>o is consequently larger and this
last oscillation in the sinze term is broad compared to
those closer to the line center. Absorption is also taking
place throughout this region. The absorption coefficients,
for right and left circular polarizations, calculated from
Eq. (4.14) and the path lengths used are such that the
transmission fractions for even the weakest Zeeman components
are zero near the center of the line. However, the absorp-
tion coefficient decreases to zero, and the transmission
fraction therefore goes to unity, more rapidly than does 6
as can be seen from Eq. (4.14). Fig. 7.8 shows the contri-
butions of these various terms for the P1(15/2) line for one
set of conditions. This line, like other lwsubband lines,
displays nearly a simple doublet Zeeman pattern. The trans-
mission fractions for right and left circular polarizations
are shown in Fig. 7.8a. The circular birefringence term
(Eq. (4.9b)) will appear, as in Fig 7.8b with nearly zero
intensity near the zero field position due to the /T$T:
coefficient, oscillate to a peak in the wings due to the
sinze term and finally decrease to zero as 6 + 0. One

notes that there can be no circular birefringence con—

tribution to the magnetic rotation intensity in the absence

68

 

 

C)

 

 

Fig. 7.8. Predictions of the terms making up the magnetic
rotation signal of the 1—0 band, plus/2) line of ”N16

a) Transmission fractions, T+ and T“. b) Circular bire-
fringence. c) Circular dichroism. d) Integration of the
sum of (b) and (c) over the spectrometer slit—function.
Field strength, 6000 gauss; pathlength, 315 cm;

pressure, 1 torr; slit—function FWHM, 0.1 cm‘l.

 

 

69

of either component of circular polarization.

The circular dichroism pattern, shown in Fig. 7.8c,
is obtained directly from Eq. (4.9a). It is seen that
this term is non-zero over a comparatively small frequency
range and cannot attain a value greater than 0.25. When
an integration over the slit—function is performed, it is
found that the contribution due to this term is almost
negligible.

Finally, Fig. 7.8d shows the MR signal after integra-
tion over the spectrometer slit-function. The intensity at
line center is m0.25. Not enough checks of the observed
intensity transmitted through parallel polarizer—analyzer
were taken. Ultra-violet radiation progressively fogged
the first plate of the AgCl polarizer thereby vitiating
quantitative intensity measurements; however, earlier
measurements indicate that the actual MR signal is m0.30.
The calculated versus observed agreement is reasonable.

As Aubel (63) points out, the magnetic rotation
signal for the l—subband should follow the normal band
intensity contour since 6 is proportional to the integrated
absorption coefficient and all the Zeeman patterns are
very nearly the same. Also, as he points out, the angle 6
is calculated to be positive in the wings of these lines,
thereby giving rise to an enhancement of the magnetic rota-
tion signal for positive polarizer setting.

The 2-subband Zeeman patterns, Fig. 7.6, are quite

different from the single doublet character of the l-subband.

 

70

However, after calculating the anomalous dispersion and trans-
mission fraction for each line and performing the appropriate
summations, one still ends up with a doublet character as
regards right and left circularly polarized lignt. One
expects the 2-subband to have slightly weaker magnetic rota-
tion signals due to both a smaller integrated absorption
coefficient and the greater amount of overlap of AM = +1
and -1 transitions. A series of plots similar to the ones
ianig. 7.8 have been made for the 2-subband but essentially
the same type patterns are obtained. Consequently they
have not been included.

Having discussed the makeup of the magnetic rotation
signal, let's examine some specific features of Figs. 7.1—

7.4.

Doublet Character 2£_M§ Lines

 

As was stated earlier, Robinson (64) qualitatively
attributed the effect to simple-absorption from a non-
uniform background. This is certainly correct; however,
going back to Fig 7.8a one can see exactly how it enters. The
transmission fraction is zero near the zero field position.
If, as was the case in Fig. 7.8, the spectrometer slit-
function is much wider than this region of zero transmission,
the magnetic rotation signal will appear as a single line.
If the absorption coefficient or the pathlength is increased,
the region of zero transmission will broaden and may eventu-

ally become comparable to the slit-function. At the same

 

71

time the angle 9 extends its region of non-zero values so
that it is always broader than the /T*T= term. Upon inte—
gration over the slit—function a decrease in magnetic rota-
tion signal will be observed. Figs. 7.9a and 7.9b show pre-
dictions for the P1 and P2 (15/2) lines at two different
pressures which demonstrate this effect. Both the integrated
and unintegrated patterns are shown. It should be remarked
that the absorption coefficient is increased by an increase
in pressure (see Eq. 2.23 and 4.12). This will have a bigger
effect than increasing the pathlength since by changing the
pressure the lineshape is also altered. An increase in pres-
sure makes the 1ine more nearly Lorentzian, its tail in-

creasing and thereby adding to the doubling effect.

2-Subband Intensity Contour

 

It was stated earlier that the 2—subband should be slightly
weaker than the l-subband due to a smaller absorption coefficient
and greater overlap of right and left circular polarization
regions. It is this latter point which is giving rise to
the intensity minimums near J = 9/2. Consider the 2-subband
patterns in Fig. 7.6. If one calculates the ratio of the
intensity of the strongest component and the nearest com-
ponent of opposite polarization one finds a minimum for J =
9/2. That is, one can expect a smaller value in the calcula-
tion of ¢ in Eq. (4.7) from these components.

This can be extended over all (2J+l) components to

predict a smaller magnetic rotation signal from this trans-

«It

72

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now Hmcwfim coanouou oeuonmoe onv mo mCOHuoHUoum .Mm.e .mHm

 

 

 

 

 

 

 

   

 

 

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73

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new ouflcwm on» own unmflu onm umoa onu no mo>nso one .Huou

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_ I b . .OI Sud. _ _ b (Ed:
. 4 a I J q J n . 4 _

 

mmoe.mnmnm

 

 

74

ition. This is certainly not the entire story however. It
is noted that the largest components of the P2 (9/2) line

do not lie directly on top of a component of the opposite
polarization. In order to get a large cancellation effect
these components must overlap within their individual line
widths. They are separated by 0.0064 cm'l, thus the absorp-
tion coefficient must have a HWHM approaching this to get
the maximum cancellation. On the other hand, the J = ll/2
components are separated by only 0.0003 cm—l. One might
therefore expect the minimum in the magnetic rotation signal
to move toward higher J-values for lower pressures, and
therefore smaller absorption coefficients. This is borne
out by experiment (see Fig. 7.1). By the same line of
reasoning, at lower field strengths, where the Zeeman com—
ponents are closer together, the minimum should move toward
lower J—value (see Fig. 7.3). Predictions of the magnetic
rotation signal agree very well with experiment as regards
this minimum. Fig. 7.10 shows predictions for the P2 sub-
band for J = 5/2 to 15/2 for two different pressures. It

is seen that at the higher pressure the minimum is shifted

by one to J = 9/2 in agreement with Fig. 7.1.

Directions of Rotation

 

The subject of the opposing rotations of the 1-
relative to the 2—subband has been well explained (63).
Let it suffice to say that the predictions made from the

theory of Chapter 4 are in complete agreement with the

x“

75

P-I.O TORR P-IOS TORR

 

 

 

 

 

 

J-IIQ
A _ , M ...,

 

 

 

 

 

 

 

 

 

Fi . 7.10. Predictions of the magnetic rotation signal for
the 1-0 band, P2 subband of 1”N160 at pressures of 1.0 and
10.3 torr. Field strength, 6000 gauss; pathlength, 315 cm;
slit-function FWHM, 0.1 cm‘l.

76

observation that the rotation is positive (negative) for

the l- (2-)subband.‘ While there are no complete cancella-
tions in the l-O band similar to those observed (63) in the
2-0 band, there are nevertheless partial cancellations which
become obvious as the absorption is increased. In Fig 7.1
in the region from J = 7/2 to 19/2 for a pressure of 21.2
torr, it is noted that the inner components of the doublets
are weaker than the outer. While some of this can be at-
tributed to instrumental factors it is too regular to be
explained solely on this basis. It is reasonable to assume
that the Lorentz tail on the absorption coefficients for the
l- and 2-subband lines is producing enough overlap to result

in partial cancellation of rotations.

Magnetic Rotation Spectra of the HES

 

Fig 7.5 shows the meager traces of magnetic rotation
spectra which were obtained from the 1”N160 HES. A wide
range of conditions of pressure, field and pathlength were
tried with no better success than this. The transmission
for these lines is between 10-15%. There appears to be no
one condition of field or pressure which will simultaneously
maximize all lines.

The weakness of the observed signals can be attributed
to instrumental sensitivity. The failure to observe more
lines must be attributed to the combination of line-width
(yL = 0.1 cm-l), A—doubling, and Zeeman splittings

being right to produce cancellation. This could

77

explain the non-existence of the Q-branch in Fig. 7.5 as
there the overlap of components is great. (For the actual
positions of the Q-branch lines see Fig. 5.1.) Fig. 7.11
shows predicted Zeeman patterns, including A-doublet split-
tings, for the HES R-branch lines for J up to 11/2. It is
seen that for J = 11/2, and therefore for all higher J-values,
the most intense Zeeman components for both A-doublet com-
ponents, are well within the Lorentz halfwidth of the lines.
This will result in cancellation which will be less severe
at higher values of the field. Also as the pressure, and
therefore YL’ is increased there will be more overlap of the
AM = +1 and -1 components resulting in smaller signals at

higher J-values. This is observed in Fig. 7.5.

Discussion

 

The calculations, incorporating intensities determined
quantum mechanically, inserted into an expression derived
using classical dispersion theory and including the effects
of a finite resolution spectrometer, have successfully pre-
dicted the major features of the magnetic rotation Spectrum
of the fundamental band of 1L‘Nl‘SO. The agreement is not
perfect. This is perhaps due partly to the rather crude
numerical integrating techniques in which basically the areas
of rectangles with equal bases were added for all regions.
It is quite conceivable that this led to a distortion of the
form of the lineshape and of the rotation angle 6. Never-

theless it would appear that the overall approach is correct.

78

-O m I——-¢-—-+—<VAIH p O b ——~——-—§——o III—"m
J'Il/Z

 

Ohm

J-VZ

 

...—n+— IIIIWM‘H . . -0.“

J- 7/2

 

‘ ‘ ‘ ‘ 4 » : fin ,
.O_'..m I . I II 0 um

Fi . 7.11. Predicted Zeeman patterns and relative intensities
for the I-0 HES band, R-branch of 1“N150 for a field strength
of 6000 gauss. Lines drawnlupward (downward) correspond to
AM = +1 (-1) transitions.

79

From the plots obtained it appears that the line shape
and the exact position of the Zeeman components are the most
criticaljparameters. A change in the integrated absorption
coefficient produces a comparatively small change in the
magnetic rotation signal.

It would appear that, as regards the determination of
any molecular parameters, the magnetic rotation as measured
here is of limited usefulness due to the number of super—
imposed quantities. It has been pointed out (63) however,
that the integrated effect as seen here can be used to show
the presence of magnetic splittings even when these Splittings
are more than a factor of 10 below the resolution capabilities
of the instrument.

Buckingham and Stephens (21) have mentioned the pos-
sibility of reducing the complexity by separating the MCB
and MCD terms through application of a "small" alternating
magnetic field and using a phase sensitive detector. It is
not clear that the magnetic rotation effect would be meas-
urable for "small" fields, however, this possibility should
be explored. Eberhardt (66) has also managed to experimen—
tally isolate the quantities 0 and o. He accomplished this
by chopping the beams with a plane polarizer to isolate the
angle of rotation e, and by chOpping with quarter-wave plates
to isolate o. These measurements should provide direct deter-
mination of molecular transition probabilities. One may have

trouble making quarter~wave plates for the near infrared;

80

however, this approach also has good possibilities. Addi-
tional work should be done in obtaining better agreement
between theory and experiment for the work presented here.
It is still possible that, if the effect can be predicted
accurately enough, information on molecular parameters can

be extracted.

CHAPTER 8
SPECTROMETER DESCRIPTION

The high resolution infrared instrument used in this
work is the result of an evolutionary process beginning with
R. H. Noble (67) and including, among others, Brown (68) and
Aubel (22). Aubel has given a detailed description of the
instrument in its next to present form including alignment
procedures.

The modifications which put the instrument in its
present form were made during the period from September 1964
to May 1965. An account of these follows. Since the basic
alignment procedure has not been altered it has not been in—

cluded.

Carbon Egg Source

The previously used 300 watt Zr arcs were plagued with
a number of difficulties such as; l) instability in a magnetic
field, 2) an envelope which failed to transmit sufficiently
well beyond 2.7u, 3) short and unpredictable outputs and
lifetime.

A rod source was developed patterned after the work of
Rank (69) and Rao, Spanbauer and Fraley (70) to overcome some
of the above difficulties. It is in a water-cooled housing

which mounts directly to the tank wall, thereby eliminating

81

 

82

a previous air path. A 2" x 3/16" CaF2 window presently
provides isolation between the rod enclosure and the main
vacuum chamber; however, almost any window of similar di-
mensions could be used. The CaF2 transmits in excess of
95% out to 7u. The back end of the enclosure is removable
and, as seen in Fig. 8.1, serves as a base for two 1" water-
cooled brass posts which deliver current to the rod.

The rod itself is 0.25" X 2" and has an ~l3° V 0.125"
deep cut longitudinally in it to make it more nearly a
black body radiator. National SPK graphite was found to be
the most suitable rod material. Electrical contact is made
to the rod by means of 2 two-turn coils of #18 copper wire
which are pushed over the ends. This is then pushed into
two coaxial holes in the 1" posts.

Figure 8.2 is a schematic of the rod power supply.
Basically it is a "variac" driven welding transformer Oper-
ating step—down off the 220 VAC line. Pressure, water and
rod breakage cutouts are provided in the system. Typical
operating conditions are 410 amps at 7.5 VAC which heats the
rod to ~2700°C. The supply will furnish 500 amps; however,
rod lifetime is cut by about a factor of 3 and output is
increased by only m15%. At the normal operating current,
the average lifetime is about 20 hrs during which the output
is constant. The output is not affected by a magnetic field.

A one atmosphere environment of ultra pure argon is

provided during operation which retards evaporation of the rod.

 

Rod Source.

8.1.

84

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85

Pressures as high as three atmospheres have been tried with
no significant increase in rod life.

It has been found that the rod output at 4400 cm"1 is
about 30% better than the previously used Zr arcs and very

stable throughout its lifetime.

ForeOptics

 

The basic Optical path in the foreoptics has been
modified little from the work of Aubel (22), however, a
vacuum polarizer assembly has been added to eliminate the
last air path in the entire optical train. A false 1"
aluminum baseplate has been added, and Can "windows" are
used throughout to allow increased range. The baseplate
provides a stable platform for mounting the mirrors and
eliminates mirror displacement during tank evacuation.

Fig. 8.3 shows the present mirror configuration. Table 8.1
lists the specifications on the various mirrors. The only
significant change in foreoptics mirrors was to make M2 on

a quartz blank. This was done because of its close proximity
to the rod source and the small thermal expansion coefficient
of quartz. The foreoptics mirrors are versatile enough to
permit the use of a shorter 36.7 cm cell; however, the homo-
geneity of the field of the present Magion solenoid is suf-
ficient to obviate its use.

The alignment procedure has been previously given (22).
This has been facilitated by an assembly which positions a

25 watt Zr arc at the same point as the "carbon" rod.

86

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87

 

 

 

 

 

Table 8.1 Spectrometer Optics
Element Type Comments
Foreoptics
Ml* ellipse 4" dia; foci 44:176 cm
M2* flat 3%" square; hole 2 cm dia.
(fused silica blank)
M3,4* flat 3%" square
M5,6,7* sphere 6" dia., cut to make M5,6,7;
R = 78.7 cm
M8,9* flat 3%" square
M10* ellipse 4" dia.; foci 128:64 cm
Mll* flat 4" square with beveled edge
M12* ellipse 6" dia.; foci 114:57 cm
M26 flat 2" dia.
Wl,2,3,4 window CaF2, 2", l", l", and 2" dia.
Monochromator
Ml3* parabola 10" dia.; focus 106 cm
M14 flat 10" dia.; rectangular hole 2.5 x 6 cm
(cut off 10 cm from and parallel to
hole)
M15 flat 10" dia.
G grating see text
M16 flat 4 x 3.4 cm, rear mount
Exit Optics
Ml7* ellipse 4" dia.; foci 40:112 cm
M18* flat 4" dia.; hole 1.6 cm dia.
Ml9,20* flat 2)" square
L1 plano-convex 2" dia.; foci -28:10; CaF2

lens

 

Table

88

(cont.)

 

Element Type

Comment

 

Calibration Optics

 

W5,6 window
L2,3,4,5 convex lens
M21,22,23 flat
M24,25 flat

P prism

2" diameter

f = 25 cm; achromatic
2" x 2%"; 2 — g" x .3.“
2" x 2%"

height 2", long side 9.55 cm
angles 50°, 60° and 70°

 

* Protected with 8102 coating

All mirrors are front surface type

 

89

The vacuum polarizer assembly is pictured in Fig. 8.4.
It has provision for simultaneously removing both polarizer
and analyzer from the beam to allow normal absorption or
longitudinal Zeeman spectra to be recorded. In addition the
polarizer and analyzer may be independently rotated and their
angles readout to 0.1 degrees. This rotation is consistent
with the conventions chosen in the MRS work. Two sets of
polarizers will soon be available. The presently available
set which operates between 2.5 and 12u consists of 6 AgCl
plates at Brewster”s angle. The plates are mounted in pre-
cisely machined grooves in a tubelike structure made.from
"phenolboard." Equal numbers of plates are inclined in
Opposite directions to eliminate beam displacement upon ro-
tation of the polarizer. This arrangement gives ~95 percent
polarization. An Irtran II window is mounted in front of
the first polarizer to eliminate the large amount of ultra-
violet radiation which fogs the AgCl plates. The new set
will use Polaroid HR plates as the polarizing elements and
will be useful between 0.7 and 2.3u.

F in Fig. 8.3 represents a filter holder by means of
which one can insert any one of three IR filters for elimi-
nating unwanted wavelengths from the beam. These filters

out off radiation below 1.06u, 1.8u and 3.0u respectively.

Monochromator

 

Fig. 8.5 shows the present configuration of the mono-

chromator. Modifications made here include: new entrance

 

 

Fig

8.4.

 

Polarizer Assembly.

 

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92

slit jaws; insertion of two new 25 cm flats; a new pickoff
mirror assembly; a new grating drive; and relocation of the
gratings. As one might expect the entire monochromator had
to be realigned and with insignificant exceptions the pro-
cedure given in (22) was followed.

The entrance slit is presently being formed by two
razor blades manufactured by Edward Weck & Company. Almost
every brand of razor blade currently manufactured was checked
with a 30X microscope against the surface of a Johansen block.
All blades with the exception of the Weck were found to have
curvature and/or nicks in excess of lOu. The Week blades
appear straight to within 1 or 2 microns over a length in
excess of 2 cm and are free from nicks. These blades are
mounted to the former slit jaws which have now been provided
with an adjustable stOp to prevent damaging the blades upon
closing.

The greatest problem with this arrangement is in getting
the two blades mounted in the same plane. The procedure used
to accomplish this was to illuminate the slits from behind.
The blades were then shimmed until no parallax existed as
ones head was moved symmetrically from side to side. This
procedure had to be carried out simultaneously with checking
the blades for parallelism with the 30X microscope.

The flats M14 and M15, were identical 25 cm diameter
mirrors and replace the former 20 cm diameter flats. This
change allows the grating to be covered completely over a

larger angular region and improves resolution at lower

   

93

angles. M14 has a rectangular hole 25 x 60 mm in its center
and has been cut off along a line 10 cm from the center and
parallel to the long axis of this hole. This allows a) the
beam to enter the monochromator almost along the axis of the
paraboloid and b) the exit slit to be placed as close to
the pickoff mirror, M16, as possible. This latter feature
allows the pickoff mirror to be as small as possible thus
minimizing the amount of the beam obstructed. M15 is used
for double passing the grating. To accomplish this M15 is
rotated about a line perpendicular to the base plate and
parallel to its face, to the best compromise position for
covering the grating at working angles. It is then tipped
until the double pass image at the exit slit is just below
the single pass image. The pickoff mirror is tipped until
the D.P. beam emerges from the exit slit parallel to the
baseplate. The exit optics usually have to be realigned.
The Foucault test must be repeated on the double pass image.
Finally a mask should be placed at the exit slit to block
out the single pass energy. Originally both modes of oper-
ation were to be simultaneously possible; however, the present
hole in M18 is not sufficiently large to transmit both beams.
The grating equation for double pass is obtained as

follows. The general grating equation is (71):

d(sin i + sin 0) = ml , (8.1)

where d is the grating space, i is the angle of incidence,

e is the angle of diffraction, m is the order, and A is the

 

 

94

wavelength. 0 is considered positive (negative) if it lies
on the same (opposite) side of the normal as i. If ¢ is the
angle between M14 and M15 measured from the axis of rotation
of the grating, then for double pass, 0 = i — ¢7 from which

the equation can be written:
d[sin i (l + cos 2f) - sin 2f cos i] = mA (8.2)

where f = ¢/2 is the angle of the double pass central image.

The new pickoff mirror assembly is merely a small stage
which protrudes from the hole in M14 and provides a means of
focusing, tipping and turning M16. This stage is fastened
to the back of the mount for M14. This assembly eliminates
all previous mounting arms which removed portions of the
beam.

G is a mount which holds two Bausch & Lomb gratings
mounted back to back. It has been repositioned so as to
eliminate the so-called "single—double pass" radiation.

This is radiation diffracted by the grating along the normal
to the flat, so as to hit the flat, and then be reflected
back to the grating to be dispersed again. There are three
gratings available; a) 600 lines/mm with a ruled area of
212 x 158 mm2 blazed at 28.8° or 1.6u in first order,

b) 400 lines/mm with a ruled area of 206 x 128 mm2 blazed

at 37.9° or 3p in first order, and c) 300 lines/mm with a
ruled area of 254 x 128 mm2 and blazed at 48.6° or 5p in
first order. Presently the 300 and 600 lines/mm gratings

are mounted and the 300 lines/mm grating was used in this work.

 

 

95

Frequencies are measured on this instrument by a
linear interpolation between calibrated interference fringes
(53). Any variations in a uniform rotation of the grating
will introduce uncertainties in the frequency of a line, a
measure of which is the standard deviation of the calibra-
tion fit. A new grating drive train shown in Fig. 8.6, was
installed to minimize and/or eliminate the variations which
existed in the former selsyn drive system. Three things
were done in this new system; a) the 14" bronze and com-
panion screw gear of the 360:1 reducer were lapped against
one another with fine grinding compound to make as smooth
a contact as possible at this very critical point, b) all
gears at the next critical point in the train were replaced
by precision 3 gears, (PIC Design Corporation) having a
maximum tooth to tooth uncertainty of 0.0001", C) the drive
was made direct by means of an SR-37 Consolidated Vacuum
Corporation double O-ring seal. These changes and other
minor ones now enable the reproduction of the standard fre-
quencies (53) with an average standard deviation of
m0.002 cm‘l. The 10 speed variable reductor (Insco Corpora—
tion) in the drive train gives shaft speeds of 0.01, 0.02,
0.05, 0.1, 0.2, 0.5, l, 2, 5 and 10 RPM at the output of the
90:1 reducer. This in turn drives the grating the same number
of degrees/minute. Spectra are normally recorded at 0.02,

0.05, or 0.1 degrees/minute.

 

 

96

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97

Fringe System

The present Edser-Butler calibration train is shown
in Fig° 807° The major alteration here is the use of a
constant deviation Wadsworth (72) assembly for order sorting
which replaces the interference filters formerly usedo This
system was designed primarily by Dre Mo Do Olmano

The source for the calibration system is a 100 watt
Zr arco The chopper is driven by an 1800 RPM synchronous
motor and interrupts the beam 450 times/seco L2 and L3
deliver an f/S beam to the monochromator by means of two
front surface mirrors, M21 and M22o The fringe beam enters
and leaves the monochromator symmetrically 201 cm above and
below the axis of the paraboloid and traces basically the
same path as the infrared beamc M23 directs the beam to a
collimating lens, L4. The beam then passes through a Fabry-
Perot etalon which has a spacing of 301102 i 000003 mmo

The normal ring system is formed for each wavelength
present in the beamo The condition for a maximum in trans-

mission at the wavelength A is (73):
2t cos¢ = n1 (8°3)

where ¢ is the angle between the axis and the nEE bright
ring and t is the etalon spacingo If n is changed by unity

this corresponds to a change:

(8.4)

Av(cm'1) = 5%:—

 

 

 

98

 

SOURCE
D3 we CHOPPERx/
— x
‘ ‘~.W5
- P
M24 1
“I, —L ‘12
M25 ’ I
ETALON 5
L4 -
» M2!
\ M22
E T. IT
M2 I N SL
[EXIT SLIT
Monochromator same
as in Fig. 8.5
Fig. 8.7. Calibration System.

 

 

99

at the angle ¢ = 0. From the grating equation, the angle
by which the grating must rotate to produce a change in n

of one at the center of the pattern is found:

A9 = (2d sinetane) (EVER) (8.5)

where d is the grating space, 6 the grating angle and m
the order of interference in the light coming from the
grating. From this the relation between the change in

v in the orders m and m" is:
(8.6)

M24 directs the beam to a prism in a Wadsworth mount which
acts as an order sorter. The order sorter must be placed

in the exit optics system so that the same light distribu—
tion is maintained in the monochromator at all times. The
prism is mounted at minimum deviation and the combination

of the prism and M25 form a constant deviation device. L5
brings the various orders to focus in the plane D3. A

lP21 photomultiplier with a slit taped on its face is placed
on the axis of L5. By adjustment of a feed screw the Wads-
worth assembly brings one of the orders into coincidence

with this slit.

Fringe System Alignment

 

Since the fringe system uses the monochromator, it is

assumed that part of the alignment is already done.

99

at the angle ¢ = 0. From the grating equation, the angle
by which the grating must rotate to produce a change in n

of one at the center of the pattern is found:

. , 1
A6 — (2d Sinetane) \m) (8.5)

where d is the grating space, 6 the grating angle and m
the order of interference in the light coming from the
grating. From this the relation between the change in
v in the orders m and m0 is:

" l

'2'? n (806)

l>
C
n
BIB
I>
C
u
318

M24 directs the beam to a prism in a Wadsworth mount which
acts as an order sorter. The order sorter must be placed

in the exit optics system so that the same light distribu-
tion is maintained in the monochromator at all times. The
prism is mounted at minimum deviation and the combination

of the prism and M25 form a constant deviation device. L5
brings the various orders to focus in the plane D3. A

1P21 photomultiplier with a slit taped on its face is placed
on the axis of L5. By adjustment of a feed screw the Wads—
worth assembly brings one of the orders into coincidence

with this slit.

Fringe System Alignment
Since the fringe system uses the monochromator, it is

assumed that part of the alignment is already done.

 

 

100

Position source and chopper on the axis of L2 and L3°
Position L2 so that the "bead" of the source is at its
focal point. This may be done by observing the beam
after L2 with a collimated teleSCOpe and adjusting L2

for the best image.

L3, M21, and M22 must be simultaneously adjusted to

give a sharp image of the source on the entrance slit
17.2 cm above the baseplate and to cover the paraboloid
symmetrically. With this done the beam will automatically
leave the monochromator 0.9 cm below the IR beam. M23

is now tipped and/or turned to give uniform coverage on
L4. L4 should be adjusted so that the beam travels along
its axis,

With a collimated telesc0pe, observe the beam leaving

L4 and adjust L4 for the best image of the exit slit.

A collimated beam is now leaving L4.

Insert M24 so that it intercepts the total beam and
directs it to cover the face of the prism uniformly.
Remove M25 and adjust the prism for minimum deviation
with the feed screw.

Insert M25 and adjust it until the beam travels along

the axis of and uniformly covers L5. Lock down M25o
Connect the external drive and counter to the feed screw.
Insert the photomultiplier so that its slit is on the
axis of L5 and the image of the exit slit is in focus

on it.

101

10. Insert the etalon. Place a sodium lamp in the vicinity
of L4 and observe output from the etalon with a telescope
through W6 by removing M24. A ring pattern and image of
the exit slit should be simultaneously visible. Adjust
the etalon horizontally and vertically until the slit
image is exactly centered in the ring pattern. The exit
slit image is considerably smaller than the central spot
in the ring pattern in order than good modulation is
obtained. In this step it is assumed that the etalon
plates are perfectly parallel by a previous adjustment.

11. Repeat Step 5 by using central image for sufficient in—

tensity.

This completes alignment and the entire train must now
be carefully shielded to prevent stray light from reaching

the photomultiplier.

Detectors

A number of new detectors have been obtained. These
include Kodak types N—2, o-2, p-2 and E—2. The N—2, 0’2 and
P-2 are PbS cells while the E-2 is a PbSe cell. All are:

Coolable°

The PbSe E~2 detector has a sensitive areal of 01,2

a for
4 nmland is most useful from ~4.25u - 6.5u. It.‘flas use:
009!
this work. It has a room temperature resistance of ~23
E3e’
a 77°K resistance of WBMQ, and needs a 9V bias loatteryo
gths

C3ause of its sensitivity at comparatively long wavelen

 

102

the use of a cooled light shield which allows only radiation
from the monochromator to strike it is absolutely essential.
Without this shield it was found that the detectivity can be-
reduced by as much as a factor of 10. The linearity of the
PbSe E-2 detector has not been checked. This must be done
before quantitative intensity measurements are made.

These detectors are, or soon will be, mounted on a
brass base by means of Dow Corning "Silastic". The brass
base is recommended by Kodak to match the thermal expansion

coefficient of the detector.

Electronics

 

With the exception of the infrared preamplifier the
electronics is as described by Aubel (22). The preamp pres-
ently in use is a battery operated solid state FET device
obtained from Denro Labs. It has a frequency response flat
within 2 db from 8 to 105 cps, a continuously variable volt-
age gain of from 10-100 times that input, and an input impe-
dance in excess of 140 M0. It has been found that the noise
equivalent signal (i.e., that signal necessary to produce
an SNR of unity) of this solid state device is essentially
the same as the formerly used Tektronix Model 122 preamp,

and requires three fewer power supplies.

Recommendations

 

During the course of work on this instrument, it was
noted that a number of other changes could be made which

would potentially improve its Operation.

103

New entrance and exit slit mounts and drives should
be constructed. Presently these mechanisms do not even have
the same pitch drive screw. Provision for more accurate
setting and readout of the slit Opening should be made.

A new detector housing should be constructed. It
should have provision for mounting several detectors with
a means of quickly changing them without first warming them.
An adjustable and coolable light shield should be provided.
The detectors are presently the limiting noise factor. Some
evidence exists for obtaining improved detectivity by ad-
justing the detector temperature for a given wavelength. It
appears that with the use of a small heater coil, the temper-
ature of a detector could be adjusted to and held at any tem-
perature from 77°K to room temperature. Further tests should
be run on this with the detectors and incorporated in any new
housing if the improvement warrants it. Some improvement
might also be obtained by selecting the Optimum chopping fre-

quency, this however requires major modifications.

S UMMARY

An analysis of the vibration—rotation transitions for
the 1-0 band including lines from the HES and LES for both
14N160 and 15N160 has been performed. Least squares fits
of both combination differences and frequencies has led to
improved values of the rotational, vibrational and spin-
orbit constants. Values for the A-doubling constants have
also been obtained. Isotopic substitution calculations were
carried out and agree well with observation.

Zeeman patterns were resolved for the lowest J-values
of the fundamental band and the splittings agree reasonably
well with theory.

The magnetic rotation spectra of the fundamental band
for the above two isotopes was recorded. Quantum mechanical
calculation of Zeeman intensities, inserted into a classi-
cally derived expression, and inclusion of the effects of a
finite resolution spectrometer has led to predictions for
the magnetic rotation spectra which agree with the major
features of the observed spectra. These predictions have led
to greater understanding of the magnetic rotation effect.

Modifications were made on the high resolution infrared
spectrometer which have increased its range, and improved its
accuracy and ease of operation. These included addition of a
rod source, a vacuum polarizer assembly and a new grating drive

assembly.
104

 

REFERENCES

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(1939).

2. C. A. Burrus and W. Gordy, Phys. Rev. 22, 1437 (1953).

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4. N. L. Nichols, C. D. Hause and R. H. Noble, J. Chem. Phys.
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5. J. J. Gallagher and C. M. Johnson, Phys. Rev. 103, 1727
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6. J. H. Shaw, J. Chem. Phys. 24, 399 (1956).

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10. Ph. Arcas, C. Haeusler, C. Joffrin, C. Meyer, Nguyen Van
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11. M. D. Olman, M. D. McNelis and C. D. Hause, J. Mol.
Spectry. 14, 62 (1964).

12. T. C. James, J. Chem. Phys. 40, 762 (1964).

13. T. C. James and R. J. Thibault, J. Chem. Phys. 31,
2806 (1964).

14. C. Meyer, C. Haeusler, and P. Barchewitz, J. de Physique,
26, 799 (1965).

15. J. F. Watkins and J. H. Shaw, paper C3, Ohio State Uni-
versity Symposium on Molecular Structure and Spectros—
copy, (1966).

16. J. L. Griggs, K. N. Rao, L. H. Jones and R. M. Potter,
J. Mol. Spectry. 22, 383 (1967).

105

17.
18.

19.

20.

21.

22.

23.

24.
25.
26.
27°

28.

29.

30.

31.

32.
33.

34.

35.

36.

106

E. Hill and J. H. Van Vleck, Phys. Rev. 32, 250 (1928).
J. H. Van Vleck, Phys. Rev. 33, 467 (1929).

G. M. Almy and R. B. Horsfall, Jr., Phys. Rev. 51, 441
(1937). ——

G. C. Dousmanis, T. M. Sanders, and C. H. Townes, Phys.
Rev. 100, 1735 (1955).

A. D. Buckingham and P. J. Stephens, "Magnetic Optical
Activity", Annual Review of Physical Chemistry, Vol. 17.
(Annual Reviews, Inc., PaTO Alto, California, 19667. _—
pp. 399-432.'

 

J. L. Aubel, Thesis, Michigan State University (1964).

 

G. Herzberg, Spectra pf Diatomic Molecules, p. 149,
2nd Ed., D. Van Nostrand, New York (1950).

Ibid., p. 92.

Ibid., pp. 218-226.

R. de L. Kronig, Z. Physik, fig, 814; 22, 347 (1928).
R. S. Mulliken, Rev. Mod° Phys. 3, 89 (1931).

L. Pauling and E. Bright Wilson, Introduction §Q_Quantum
Mgghgnigs, pp. 271-274, McGraw-Hill, New York (1935).

Herzberg, pp. cit. pp. 226-229, 268-271.
W. Gordy, W. V. Smith and R. F. Trambarulo, Microwave

S ectrosco , pp. 185-188, John Wiley and Sons, New
York (1953;.

C. H. Townes and A. L. Schawlow, Microwave Spectroscopy,
pp. 343-344, McGraw-Hill, New York (1955).

 

 

Pauling and Wilson, pp. cit., pp. 302—306.
Herzberg, pp. cit., p. 94.

P. C. Cross, R. M. Hainer, and G. W. King, J. Chem. Phys.
13, 210 (1944).

Herzberg, pp. cit., p. 241.

Townes and Schawlow, pp. cit., pp. 19-200

 

37.

38.
39.

40.

41.

42.

43.

44.
45.
46.
47.

48.

49.

50.

51.

52.

53.

54.

107

J. R. Izatt, Self and Foreigp Gas Broadening in the Pure
Rotation Spectrum of Water Vapor, p. 34, ProgFES§~Report,
The JOhn Hopkins Ufiiversity Laboratory of Astrophysics
and Physical Meterology, Baltimore 18, Maryland. (1960).

 

 

 

 

L. L. Abels and J. H. Shaw, J. Mol. Spectry. 20, 11 (1966).
C. C. Lin, Thesis, Harvard University (1955).

L. I. Schiff, Quantum Mechanics, pp. 150-152, lst Ed.,
McGraw-Hill, New York. (1949).

 

M. Faraday, Phil. Mag., 28, 294 (1846); Phil. Trans.
Roy. Soc. London (1846)

L. Rosenfeld, Z. Physik, El, 835 (1929).

H. A. Kramers, Proc. Acad. Sci., Amsterdam, 33, 959
(1930)° "—

R. Serber, Phys. Rev., 41, 489 (1932).
T. Carroll, Phys. Rev. 52, 822 (1937).
H. F. Hameka, J. Chem. Phys. pp, 2540 (1962).
H. F. Hameka, J. Chem. Phys. 31, 2209 (1962).

D. F. Hutchenson and H. F. Hameka, J. Mol. Spectry. 18,
141 (1965). “—

S. S. Penner, Quantitative Molecular Spectroscopy and
Gas Emissivities, Chaps. 3 and“4, Addison Wesley,
Reading, Mass. (1959).

 

 

Izatt, pp. cit., p. 37.

C. Kittel, Elementary Statistical Physics, pp. 206-210,
John Wiley, New York. (1958) '

 

E. U. Condon and G. H. Shortley, The Theory pf Atomic
Spectra, p. 379, MacMillan, Cambridge, England (1935).

 

K. N. Rao, C. J. Humphreys and D. H. Rank, Wavelength
Standards i2 the Infrared, pp. 160-162, 171, Academic
Press, New York. (1966).

 

 

 

This system, originally used to digitize cloud chamber
data, was recognized to be applicable to the reduction
of spectroscopic data by Prof. T. H. Edwards. Line

position measurements can be reproduced to better than

108

0.03 mm on the original charts and the X-Y coordinates
punched out on computer cards. The system is described
briefly by T. L. Barnett, Thesis, Michigan State Univ-
ersity (1967) and T. H. Edwards, J. Opt. Soc. Am. 52,‘
1311 (1962). “

55. Herzberg, pp. cit., pp. 175—185.

56. J. W. Boyd, Thesis, Michigan State University (1963).
H. Scheffe, The Anal sis of Variance, Chap. 3, Wiley,
New York (1959). T e SCI"fieans that, for a level of
significance a, there is a probability of (l-a) that
all estimators for the constants will simultaneously be
within their SCI of the "true" value of the constants.

57. American Institute pf Ppysics Handbook, pp. 8-6, McGraw-
Hill, New York, (1967). "W

 

 

58. Herzberg, pp. cit., p. 175.

59. R. Beringer, E. B. Rawson, and A. F. Henry, Phys. Rev.
94, 343 (1954).

60. M. Mizushima, J. T. Cox and W. Gordy, Phys. Rev. 2g,
1034 (1955).

61. R. L. Brown and H. E. Radford, Phys. Rev. £41, 6 (1966).

62. G. A. Mann and C. D. Hause, J. Chem. Phys. 33, 1117 (1960).
63. J. L. Aubel and C. D. Hause, J. Chem. Phys. 44, 2659 (1966).
64. D. Wo Robinson, J. Chem. Phys. pp, 4525 (1967).

65. . D. Buckingham and G. A. Segal, Private communication.

A
66. A. F. Stalder and W. H. Eberhardt, Private communication.

67.

'JU
m

Noble, J. Opt. Soc. Am. 42, 330 (1953).
68. R. G. Brown, Theses, Michigan State University (1957, 1959).
69. D. H. Rank, Private communication.

70. R. Spanbauer, P. E. Fraley and K. N. Rao, Appl. Opt. 2,
1340 (1963).

71. F. A. Jenkins and H. E. White, Fundamentals of Optics,
p. 333, 3rd Ed., McGraw-Hill, New York (19577?

 

72. F. O. L. Wadsworth, Astrophys. 1, 232 (1895); 2, 264 (1895).

73. Jenkins and White, pp. cit., p. 2750

109

74. M. D. Olman, Thesis, Michigan State University (1967).

75. M. A. Efroymson, Mathematical Methods for Di ital
Computers, Chap. 17, John Wiley, New York. (1960).

 

APPENDIX I
Assume the following phase convention:

<n|J l921> = i<0IJ Intl> = F(J)
y X
_<z|s |zt1> = i<z|s |z¢1> = F(S)
y X
-<AIL |A11> = i<A|L lAtl>
y X

wvliere F(X) = £[X(X+l) - XZ(XZ*1)]£

2%) Matrix Elements of Hé.

<z£|H£|z£> = <z_£lH£|2_£> = B°[J(J+1)+1] + E s a

<H£|H£IH£> = <H_£|H£IH_£> = B"{[J(J+1)+}‘]

+ [L(L+l)-A2]} a 81

<H3|H£|H3> = <H_3'HI':_|H_3> = BTr{[J(J+l)-Z]

+ [L(L+1)-A2]} a y,
<Z£|H£|Z-§> = BC<J+£) s 6
1
<H3|H£1H§> = <H_3|H£|H_£> = B"[(J-£)(J+3)]2 E e
<H£IH£|2_£> = <H_£|H£IZE> = —2<HIBLyIZ> (J+5) s ;

<H3|H£IZ£> = <H_3lH£|2_i> = -2<H|BLyIZ> x

[<J—1) (J+3)1% n

<H£IH£|Z£> = <H_£IH£IZ_£> = _2<HIBLylZ> 5 61

110

APPENDIX I

Assume the following phase convention:

<Q|J |0i1> = i<QlJ I0i1> F(J)
y x

-<ZISyIZi1> = i<ZIleZi1> F(S)
-<A|L lAi1> = i<A|L [Ail>
y X

Vvhere F(X) = £[X(X+l) - XZ(Xzil)]i

2%) Matrix Elements of Hé.

<Z£|H£IZ£> = <Z_£'H£|2_£> = BG[J(J+1)+&] + E E a
<H£|H£|H£> = <H_§|H£lfl_£> = B“{[J(J+1)+£]

+ [L(L+l)-A2]} s 81
<H3IH£IH3> = <H_3|H;IH 3> = B"{[J(J+l)-Z]

+ [L(L+1)-A2]} 2 Y1
<Z£|H£|2_£> = BO(J+§) s a

1

<H3|H£IH§> = <H_%IH;IH_£> = B"[(J—§)(J+3)]2 s s
<H£|H£l2-£> = <H_%IH£IZ£> = -2<HlBLy|X> (J+fi) E
<H3|H£|X£> = <H_3lH£|Z_£> = -2<HlBLy|Z> X

1
[(J-§)(J+3)]2 s n

<H£IH£IZ£> = <H_£IH'I2_£> = -2<H|BLyI£> s 61

111

Note: The phase conventions chosen are not those of VanVleck
(15) or Dousmanis, Sanders and Townes (20). They are chosen
in such a way as to agree with those of King, Hainer and Cross
(34) used in calculating the direction cosine matrix elements
and yet yield the energies as derived by VanVleck. The con-

stant term LZ-A2 has been included.

B) Matrix Elements of A(foS).
<H_3|A(f°§)lfl_g> :: <H3|A(f°§)lng> = iA = Y2
<H_£|A(E°§)|H_£> = <H§|A(f°§)|fli> = -£A = 82

A fo§ z = II A f.§ = L =
<H£I ( )l £> < _%l ( )|z_%> <HIA y|2> 62
To simplify notation the following definitions are made:

8 5 81 + 82

.<
H

_<

b—‘
+

Y2

APPEN

INTERMEDIATE NAV

DIX II-A

E FUNCTIONS FOR THE

2 PI 1’2; V=U STATE OF 14N160 AS A FUNCTION OF J
[SngM) 3 A [JIMaS> ' B [JOMOS>
[1/7! 1/2;M) =1.000( 1/2IWt1/2> '0o000[ 1’20M13/2>
[1/2: 3’2,M) =10000[ 5/2IW11/2> -00024[ 3/2;M,3/2>
[1/93 S/QIM) =0.9°9[ 5/2:W;l/2> ‘0.U40[ 5’20M03/2>
[1/2: 7’2:M) =00999[ 7/21501/2> ‘0.U54[ 7/23M33/2>
[1/2: 9/2.M) =O.998[ 9/20W11/2> '0.069[ 9/29M,3/2>
[1/2l11/20M) 30.997111/2fiWI1/2> "0.083[11/2:Mo3/2>
[1/?)13/2:M) 30-995113/21W31/2> ‘0.096[13/21Mp3/2>
[1/2,15/2,M) =0n994[15/2DWal/2> '00110t15/20M13/2>
[1/2117/33M) =0.992(17/2IW11/2> '00123I17/21H33/2>
[1/2'19/2;M) =0c991119/20W91/2> '0.137[19/2)M33/2>
[1/2171/2;M) =0.9fl9[21/20W:1/2> FO.149[21/2:Mn3/2>

[1/9193/2gM)
[1/2175/21M)
[1/?:?7/2:M)
[1/2199/2nM)
[1/2131/21M)

=0.985[25/

=0.980I29/

[1/2.35/2.M) =0.973t35/
[1/2137/2,M) =o.970[37/

[1/2:39/2,M)
[1/2o41/2.M)
[1/2:43/2.M3
[1/2:45/2;M)
[1/2:47/2.M)
[1/2:49/2.M)

=0.964[41/

=09956t47/
=0.953[49/

=0.982(27/2:W:1/2>

=0.978(31/2:\4a1/2>

:0.967[30/2:%a1/2>

=0v962143/2IW01/2>
=09959C48/21‘411/2>

30.987f23/ZIWp1/2> -0.162(23/2:M.3/2>

2!*nl/2> '0.175(25/29Mn3/2>

'0.187(27/23M.3/2>
2vWI1/2> -09199I29/20M03/2>

”0.210(31/2pM13/2>
2:4:1/2> "0.222(33/23M93/2>
2’W01/2> -0.233[35/2aM.3/2>
23Wp1/2> ’0.244[37/29N33/2>

'0.254[39/2:Mo3/2>
-0.264(41/23M.3/2>
'0.274(43/2aMp3/2>
~0.284[45/2oMo3/2>
“0.293(47/21Mu3/2>
“0.302(49/2ofin3/2>

2:”:1/2)

2!”;1/2’
2'431/2>

112

 

113

INTERMEDIATE WAVE FUNCTIONS FOR THE

2 P1 312,
[S:J;M)

(3/2:

[3/2:
[3/2:

1/2pM)
3/2gM)
S/ZnM)
[3/2: 7/25M)
[3/2: 9/23M)
[3/?ITl/23M)
[3/2113/2;M)
(3/?;15/2oM)
[3/?;17/2,M)
[3/2n19/2aM)
[3/2.91/2.M1
[3/2a73/21M)
[3/?n95/2;M)
[3/2ag7/2oM)
[3/9179/2.M)
[3/2331/2nM)
[5/2133/2,M)
[3/2135/23M)
[3/7157/2,M)
[3/2939/2.M)
[3/2a41/2:M)
[3/7943/2,M)
[3/?:45/2oM)
[3/2;47/2.M)
[3/2p49/2.M)

A tJ-M.S>

1/21M13/2>

3/2OW13/2>
5/2'W15/2)
=0.999[ 7/2.4.3/2>
=0.998t 9/2:w.3/2>
=0.9o7t11/2.w.3/2>
=0.995[13/2:w.3/2>
=0.994[16/2aw.3/2>
=0.992[17/2aw.6/2>
=0.9°1t19/2-W.S/2>
=0.9A9[21/2:W:S/2>
=0.9a7[23/2aw.3/2>
=0.985t25/2.w.3/2>
=0.9R2[27/2:w.3/2>
=0.980120/2.w.3/2>
80.978t31/2;w.5/2>
=0.975(33/2oq.3/2>
=0.973(36/2.w.5/2>
=0097UT37/2lfll3/2>
=0.967[39/2.%.3/2>
=0.964[41/2»w.5/2>
=0.962t41/2:w.3/2>
=0.959[45/2:M.3/2>
=0.956147/2.w.3/2>
=0.963{4o/2:w,3/2>

=1.000(

=1.000T
=0.999[

v=0 STATE OF 14N160 AS A FUNCTION OF J

B [JJMDS>

+0.000T

‘0.024[
*0.040[

1/2pMa1/2>

3/23M91/2>
5/29M11/2>
+0.054! 7/23M31/2>
*0.069l 9/23M11/2>
*0.083[11/2:M;1/2>
*0.096[13/2:Mp1/2>
+0.110I15/2oMp1/2>
*0.123[17/2:M:1/2>
+0.137ll9/2nf‘1all2)
+0.149T21/2nMn1/2>
+0.16?[23/2aHn1/2>
+0.175l25/20Mo1/2>
*0.187[27/2:Ma1/2>
*0.199[29/2uM.1/2>
*00210131/21Mp1/2>
+0.222l33/2.M.1l2>
+0.233T35/2oMal/2>
+0.244T37/23M31/2>
*0.254[39/2aM.1/2>
+0.264T41/2:M.1/2>
*0.274[43/2pMa1/2>
+0.284l45/2nM.1/2>
+0.293I47/20M01/2>
*0.302T49/2oflo1/2>

 

 

114

INTERMEDIATE WAVE FUNCTIONS FOR THE
9 PI 1/2, V=1 STATE OF 14N160 AS A FUNCTION OF J

[Sp.I;M) : A IJ!M;S> ‘ B [JIMJS>

[1/9: 1/2.M) =1.000[ fl/2:w.1/2> ‘0.000I 1/2.M.3/2>
[1/2: 3/2.M) =1.000[ 3/2aw.1/2> -n.024[ 3/2:M.3/2>
[1/2: 5/2.M) =0.9°9t S/2t*:1/?> ~n.04ot 5/2.M.3/2>
[1/9n 7/2,M) =0.999[ 7/2:W:1/2> -U.054I 7/2.M.3/2>
[1/9. 9/2.M) =0.998[ 0/2:%.1/2> ~0.068I 9/2.M.3/2>
[1/9,11/2.M) =o,997(11/2.q.1/2> '0.082I11/2:M.3/2>
[1/2o13/2.M) :0.995113/2nw.1l2> -n.096[13/2.M.3/2>
[1/2;15/2,M) =o.994[15/2.w,1/2> -0.109[15/2.M.3/2>
[1/2a17/2.M) =0.902[17/2:W-1/2> -0.123£17I2.M.3/2>
[1/9p19/2,M3 =0.991[1¢/2:W:1/2> -0.136[19/2.M.3l2>
[1/2.?1/2.m> =0.9R9(21/2;%;1/2> -o.149[21/2.M.3/2>
I1/2173/2.M) =0.9R7[23/2:w.1/?> -0.161[23/2:M.3/2>
[1/?;?5/2.M) =0.985[25/2:W.1/2> ~0.174I25/2.M.3/2>
(112.?7/2.M5 =0.983[27/2:Wa1/2> -0.186l27/2.M.5/2>
I1/2:Q9/2,M) =o.9aor2o/2:W:1/2> -n.19e[29/2.M.3/2>
[1/9:31/2.M3 =0.978[61/2:%a1/2> -0.209[31/2.M.3/2>
I1/9133/2.M) =0.975I53/21W11/2> "0.221I33/20Mo3/2>
[1/2:35/2.M> =0.973[68/2-W.1/2> '0.232I35l2.M.3/2>
[1/2p37/2,M) =0.970[37/2:W.1/2> -n.242[37/2.M.3/2>
I1/?.39/2.M3 =0.968t3o/2:w:1/2> 90.253I39/2.M.3l2>
I1/2:41/2,M) =o.965[41/2.w.1/2> -o.263[41/2.M,3/2>
[1/2.43/2.M) =0.962[43/2:w.1/2> -o.275[43/2.M.3/2>
I1/2;45/2.M) =0.959[45/2a%:1/2> -0.263I45/2,M.3/2>
[1/2»47/2.M) =0.966[47/2:w.1/2> -0.292I47/2aM.3/2>
[1/2,49/2.M3 =o.954[4o/2.w.1/2> -o.301t49/2.M.3/2>

115

INTERMEDIATE WAVE FUNCTIONS FOR THE

2 PI 3/2. v=1 STATE OF

[39J1h) 3 A IJDMDS)
[3/2: 1/2.M) =1.000I 1/2:%o3/2>
[1/2. 3/2.M> =1.000t 3/2:w.3/2>
[3/2. 5/2.M3 =0.999[ 5/2:%.3/2>
[3/2. 7/2.M) =0.999( 7/2:%.3/2>
[3/2. 9/2.M) =o,998[ 9/2oW93/2>

I3/2;11/21M)
I3/?;IS/Z;M)
I3/2115/2,M)
I3/2117/2,M)
I3/9319/?,M)
I3/2t71/2,M3
[5’9’93/21MI
[3/2’95/23M)
[3/?1?7/23M)
I3/2199/23M)
l3/?.x1/2.M1
I3/2:33/2,M)
I3/?.35/2,M)
[3/2957/29M)
I3/?:59/2.M)
[3/?.41/2,M)
[3/2o43/2,M)
I3/2,45/2,M)
[3/2.47/2,M)
I3/2o49/2gM)

=0o997I11/2aM33/2>
=0o9°5I13/2IW:3/2>
30.994I15/2:W33l2>
a09992I17/2fi‘4:3/2>
30:991I19/2:W:3/2>
=0»9R9I21/2:%93/2>
=0o9R7I23/234o3/2>
30.985I25/2:193/2>
30.933I27/21603/2>
=00930I29/2IW33/2>
30.973T31/21193/2>
30.975I33/23W;3/2>
30.973I35/2:4:3/2>
z0.970I37/2I4a3/2>
=0.968I39/2:fln3/2>
309965I41/QIM;3/2>
=09962I45/2:H:5/2>
30.959I45/2i*:3/2>
309956I47/2:W:3/2>
=UQ9S4I49/20W03/2>

+

14N160 AS A FUNCTION OF J

B IJ9M03>

+0.000l

+0.024I
+0.040I

1’28N31/2>

3/23M:1/2>
5’23M31/2>
+0.054I 7/2aM.1/2>
+0.068I 9’2:M31/2>
*0.082I11/2aMo1/2>
*0.096I13/2:M91/2>
*0.109I15l2nM:1/2>
*0.123I17/2aM:1/2>
*Uo136I19/2anol/2>
*0.149I21/2:Mo1/2>
*0.161I23/21M:1/2>
*0.174I25/2aM.1/2>
*0.186I27/2oH91/2>
*0o198I29/29N31/2>
*0o209I31/21Ma1/2>
*0.221I33/2:Mo1/2>
+0.232l35/2.M.1/2>
*0o242I37/21M01/2>
*0.253I39/2oM,1/2>
*0.263I41/2aM:1/2>
+0.273I43/29M:1/2>
*0.283I45/2:H.1/2>
*0.292I47/2:Mn1/2>
*Oo301I49/21Mo1/2>

 

 

2 PI

I9:

[1/2:
I1/?;
II/Z:
I1/2)
[1/2.

1/2.

ling)
3/21M)
5/2.M)
7/2,M)
9’21M)
I1/2911/2,M)
IT/2913/2gM)
IT/2115/21M)
I1/2117/2,M)
II/2)39/2pMI
I1/2:?3/2pM)
I1/2:?5/21M)
(1/?:?7/2aM)
I1/2:?9/2,M)
IT/2p31/23M)
I1/2’33/29M)
I1/2a35/23M)
Il/Qa37/2aM)
I1/2939/2nM)
I1/2t41/23M)
I1/2:43/2oM)
I1/2145/2gM)
I1/?:47/2:M)
[T/Zt49/29M)
[1/2981/2gM)

APPFNDIX

INTERMFDIATE

s-I I F. ) = A

v=0 STATE

=1.000[
=1o000I
=0.999I
30.999!
:0.998[
=0o997I11/23Mal/2>
=0.996(13/2:Ha1/2>
:09994I15/Zafltl/2>
=0.993(17/2:*:1/2>
=0.991[19/2.w.1/2>
30.989fi21/2:W.1/2>
30.988I23/2:M:1/2>
309936I25/21M11/2>
=0.983[27/2.M,1/2>
30.931I29/2tfl:1/2>
=0.979(31/2HM'1/2)
309977I33/28W11/2>
=09974I35/23M11/2>
=0.972[37/23W:1/2>
=0.969(39/2n1nl/2)
30.966I41/20Ho1/2>
30.964I43/2ofial/2>
309961I45/2oW:1/2>
309958I47/29Ma1/2>
30-956I49/2:M:1/2>
30.953I51/2afi;1/2>

II-B

WAVE FUNCTIONS FOR THE

OF

(JIMoS>

1/2:W:1/2>
3/21W31/2>
5/23W11/2>
7/2:W:1/2>
Q/Z:Wt1/2>

15N160 AS

A FUNCTION OF J
B IJ:MJS>

’00000[
“00024!
900039:

1’23M13/2>
3/2:M93/2>
5/2:M.3/2>
90.053I 7/2:M:3/2>
“0.066I 9’29M:3/2>
'0.080I11/2;M:3/2>
“0.093(13/2:M.3l2>
“0.106I15/2:M.3/2>
90.119I17/29Ma3/2>
”0.132(19/2:M.3/2>
"0.145I21/2pM93/2>
"0.157I23/20Ma3/2>
’00169I25/2’M33/2>
10.181I27/23Ma3/2>
'0.193I29/2oM.3/2>
”0.204(31/21M93/2>
90.21SI33/23M,3/2>
“0.226I35/29MJS/2>
*0.237I37/2:M:3/2>
”0.247I39/23M13/2>
90.257I41/2:Ms3/2>
P0.267I43/2oM.3/2>
”0.276I45/20H33/2>
20.286I47/2:M:3/2>
V09295I49/23H13/2>
‘0o303I51/20M:3/2>

 

11/

INTEQMFDIATE WAVE FUNCTIONS FOR THE

2 PI 3/2.

[5:

h" M)

I3/7p

I3/2:
Iz/Q:

1/2,M)

3/21M)
5/2gM)
IS/Q: 7/2,M)
[3/2. 9/2,M)
I3/2:11/2oM)
I3/2313/2aM)
I3/2315/29M)
I3/?:17/2,M)
[3/9119/2,M)
l3/2.91/g,M3
[3/?:73/23M)
I1/7375/23M)
[3/?:97/2,M)
[3/?,79/2,M1
[3/?131/2,M)
[3/7.33/2,M)
I3/7:15/2:M)
I5/2237/2,M)
I3/?:39/2;M)
I3/2141/2,M)
[3/2143/23M)
I3/?:45/23M)
[3,2,47/2'M,
I3/?:49/2.M)
[3/2151/Z,MI

A [J:M,S>

1/21W33/2>

3/2:W93/2>
5/2:”93/2>
=00999I 7/29‘493/2>
=Oo998I Q/Z:M:3/2>
30.997I11/23M33/2>
30.996[13/2:M:3/2>
30.994IIO/Ztfit3/Z>
309993I17/ZOW03/2>
2“3.991(10/2:‘4»3/2)
“0.989I21/21W93/2>
30.938I23/ZoNoS/2>
30.996I25/2’Wt3/2>
30.983IZ7/2:M03/2>
=01981I2Q/21M33/2>
300979I31/2aW33/2>
300977I33/21933/2>
30.974I35/2IW03/2>
aI0g972I37/2:VHS/2)
=00969I39/29Mp3/2>
=Oo966I41/2’W:3/2>
=00964I43/20%33/2>
a0.961I45/29M93/2>
30.958I47/21Mp3/2>
=0.956[49/29H:3/2>
30.953I51/20%33l2>

=1.000T

=10000I
=Oo999I

4.

v=0 STATE OF 15N160 AS A FUNCTION OF J

B [JOM)S>

+0.000I

+0.024t
+0.039l

1’21Mol/2)

3/29M91/2>
5’21M91/2>
+0.053[ 7/2aM.1/2>
*0.066I 9/21M91/2>
*0o080I11/21M31/2>
*Oo093I13/20M91/2>
*0.106I15/2:M:1/2>
*0.119I17/2oMo1/2>
+0.132I19/2.M.1/2>
*0.145I21/29Mo1/2>
+0.157I23/2oMo1/2>
+0.169I25/23N31/2>
*0.181I27/2oM31/2>
*0.193I29/2:M:1/2>
*0o204I31/21N:1/2>
*0o215I33/21M91/2>
*0.226I35/29M:1/2>
+0.237I37/2oMgl/2>
+0.247I39/2;M.1/2>
*0.257I41/20Mo1/2>
*09267I43/20Mgl/2>
*0.276I45/2pMo1/2>
*0.286I47/2:Mn1/2>
‘09295I49/21M31/2>
*Oc303l51/2oM.1/2>

 

 

 

 

115

INTERMEDIATE WAVE FUNCTIONS FOR THE
2 pl 1/2. V=1 STATE OF 15N160 AS A FUNCTION OF J

[SIJIM)

I1/2; 1/2.M)
I1/?o 3/2,M)
[1/2n 5/2;M)
Ill?) 7/2pM)
I1/?n 9/RaM)
I1/?:11/2oM)
[1/2th/20M)
[1/2115/2,M)
[1/?317/21M)
[1/9u19/21N)
[1/2171/2aM)
I1/?:?3/2aM)
Il/?:?5/21M)
[1/?197/21M)
[1/7n?9/2.M)
[1/9131/2,M)
IT/p033/21M)
[1/2135/29M)
I1/?o37/2pM)
[1/2:39/2.M)
[1/?:41/2.M)
[1/7943/2,M)
[1/?I45/21M)
[1/2I47/23M)
I1/2p49/2pM)
I1/2151/2aM)

= A IJDMOS>

=10000I 1/21W31/2>
=1.000I 3/21W31/2>
=0.999[ 5/2:W.1/2>
=0.999I 7/2-W11/2>
=0.998I Q/Zafln1/2>
=0o997I11/211p1/2>
=0.996[13/2:W:1/2>
=0.994[15/2:W.1/2>
=0.993I17/2:W-1/2>
=0.991(10/20491/2>
=0.9°0[21/2:Mp1/2>
=0.988I23/20W:1/2>
=O.986I25/21W,1l2>
=0.9“4[27/21W-1/2>
=0o982I20/2’Wp1/2>
=0.979[31/2:%:1/2>
=0.977[63/2-W:1/2>
30.974t35/20W11/2>
=0.972[37/2:W:1/2>
=0.969t39/2.M.1/2>
=0.9A7[41/2:M:1/2>
=0c964I43/2-Wo1/2>
=Oo962I45/Zlflnl/2>
=0.959[47/2n%:1/2>
=0.956I4°/2!Wpl/2>
=0.953I51/2»W:1/2>

' B IJaMpS>

“0.000I 1/2oM.3/2>
’0.023I 3/2cM.3/2>
'0.038I 5/2:Mp3/2>
“0.052I 7/20M’3/2>
'0.066I 9/2oM.$/2>
‘0.079I11/2nM;3/2>
‘0.093I13/2:M.3/2>
'0.106I15/29M:3/2>
-n.118[17/2:M.3/2>
'00131I19/25M13/2>
'0.144I21/2pM.3/2>
'0.156I23/2:Mp3/2>
'00168I25/2,M13/2>
'0.180I27/2.M.3/2>
~0.191I29/2:M.3/2>
‘0o203I31/20Ma3/2>
'0.214I33/2:Mn3/2>
~0.224I35/29M13/2>
'0.235I37/2:M;3/2>
'0.245I39/2:Ma5/2>
-0.255I41/2:M:3/2>
“0.265I43/2oM.3/2>
'0.275I45/2;M.3/2>
'0.284[47/2:Ma3/2>
‘0.293I49/2aM,3/2>
’Oo302I51/2JM13/2>

 

119

 

INTERMEDIATE WAVE FUNCTIONS FOR THE

2 PI 3/2. v=1 STATE nF

[S.J,M) A TJ,M,S>
(3/2. 1/2,M) =1.000[ 1/2aw.3/2>
I3/9; 3/2,M) =1.000I 5/23WI5/2>
[3/2. 5/2,M) =0.999t 6/2:W:3/2>
[3/2. 7/2.M) =o.999[ 7/2:«.3/2>
[3/2, 9/2.M) =0.908[ n/2nw.3/2>

I3/7111/2;M)
[3/2113/2,M)
I3/2115/21M)
[3/2117/23M)
[3/7319/21M)
I3/?:?1/2,MI
I3/7I73/2aM)
[3/2I95/21M)
I3/?,?7/23M)
[3/7579/23M)
[3/9131/2,M)
[3/7133/2,M)
[3/7035/21M)
I3/?:57/23M)
I3/2;39/2,M)
[3/7:41/2,M)
I3/?:43/2aM)
I3/2145/2,M)
[3/?v47/25M)
I3/2949/21M)
I3/9:51/2,M)

=0.997[11/2:%,$/2>
=0.9°6[13/2oW.5/2>
=o.9o4r15/2:w.3/2>
=o.993r17/2.w.5/2>
=0.901[10/2»w.3/2>
=0.990t21/2aw.3/2>
=009R8I23/20q03/2>
=0.986[25/2vw.3/9>
=0.984[27/2.w.6/2>
=0.9R2[20/2:w.5/2>
=0.979(31/2:%:3/2>
=0.977t33/2:w.3/2>
=0.974[35/2:%,3/2>
=0.972[57/2aW.5/2>
=0.969I30/29W95/2>
=0.967t41/2.w.3/2>
=0.964[4x/2:w,5/2>
=0.962[48/2:w,3/2>
=o,9s9r47/2.w.3/2>
=0.956!49/2-w.6/2>
=0.953[51/2:w.3/2>

15N160 AS A FUNCTION OF J

B [JnMnS>

40,000:

+0.023I
+0.038I

1’20Mp1/2>

3’21M31/2>
5’21M:1/2>
‘0.052[ 7/2pMpl/2>
+0.066I 9/2:M.1/2>
+OcU79I11/29M11/2)
+0.093IlS/2:Ma1/2>
*U.106I15/20M21/2>
+0.118I17/2nf‘4al/2)
*0.131I19/2pM11/2>
+0.144I21/29Mp1/2>
*Oo156I23/2:M11/2>
+0.168I25/2pMn1/2>
*0.180I27/29Mp1/2>
+n.191[29/2pM.1/2>
*0-203I31/2)M11/2>
*0.214I33/2:Mp1/2>
*0.224I35/2nM11/2>
+0.235I37/2;M.1/2>
+0.245I39/23Mn1/2>
*O.255I41/21M31/2>
*0.265I43/2:M:1/2>
*0o275I45/21M01/2>
+0.284I47/2pMp1/2>
*0.293I49/2oMp1/2>
*Oo302I51/29M:1/2>

 

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2

3/2
5/2
7/2
9/2
11/2
13/2

APPENDIX III-A

P1

0,0000
1.3325
2,3905
3.4264
4.4417
5.4512
6.4576
7.4621
8,4655
9.4681
10.4701
11.4717
12,4730
13,4741
14,4750
15.4758
16.4764
17,4770
18.4775
19,4779
20.4783
21,4707
22,4790
23,4793
24,4795
25,4790

P2

0.0000
1.6003
2.8576
4.0007
540918
6.1549

120

CALCULATED LINE-STRENGTHS FOR 14N160

BRANCH
01

0,6666
0,2673
0.1725
0.1285
0.1029
0,0862
0,0745
0.0658
0.0592
0.0540
0,0497
0.0463
0,0434
0.0410
0,0389
0,0371
0,0355
0,0342
0.0330
0.0319
0.0310
0.0301
0,0294
0,0281
0.0280
0.0275

02

2.3980
1.5395
1,1303
0.9033
0.7483
0,6381

 

R1

1.3325
2.3985
3,4264
4,4416
5,4511
6,4575
7,4621
8.4654
9.4680

10.4700

11.4716

12.4728

13,4739

14.4748

15.4755

16.4761

17.4767

16.4771

19,4775

20.4779

21.4763

22,4786

26,4708

24,4791

22.4793

26,4796

R2

1.6003
2,8576
4,0006
5.0917
6.1548
7.2012

 

15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
2112
23/2
25/2
2772
29/2
31/2
3372
35/2
37/2
39/2
41/2
43/2
45/2
4772
49/2
51/2

3/2
5/2
7/2

792012

8,2367

9,2648
10.2875
11.3064
12.3222
13.3357
14,3474
15,3576
16,3666
17,3746
18,3817
19,3881
20.3939
21,3992
22.4040
23.4084
24.4125
25,4162

PH

0.000+000
0.000+000
2.402'003
7.776*003
1.680'002
3.003’002
4.784'002
7.048'002
9.805'002
1.305'001
1.677'001
2.095'001
2.555-001
3.053'001
3.585-001
4.146'001
4.733'001
5.340'001
5.963'001
6.596'001
7.237'001
7.880.001
8.522'001
9.159'001
9.789-001
1.041*000

PL
8.009'004

9.518'004
1.119*003

121

0,5555
0.4916
0.4399
0.3977
0.3625
0,3326
0.3069
0,2846
0.2651
0.2477
0,2323
0.2105
0.2061
0.1948
0.1845
0.1751
0.1666
0.1567
0.1514

0H

000000000
6,3906004
1.0913003
1,507=006
1,904a006
2.2886003
2,657P005
6.0166006
3,6546006
6.6819006
3.992=006
4,2873006
4,5663006
4,8283006
5,074=006
5,6029006
5.5142006
5,7105006
5,8906006
6.0542006
6,2043006
6,338=006
6.4599006
6,5679006
6.6628006
6,7453006

0L
6,442a004

1,100=003
1‘5193006

602666

902647
10.2874
11.6062
12,3220
16,3355
14,3472
15,6573
16,3666
17.6743
18.3814
19,3878
20,6936
21,6988
22,4066
26,4080
24,4120
25,4158
2604192

RH

8.041’004
9.634.004
1.141'003
1'521'006
14497-003
14665-003
14825-003
1.973'003
24110-003
26254-003
2.345.003
2:443'003
24527'003
20598'003
2.657-003
2.703'003
24737-003
24760-003
20772'003
24776-003
26770-003
2.756'003
2.735-003
2,708-003
2.675'003
2.638‘003

RL
10612'004

3.433?004
5.2909004

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2

1.284-003
1.444'003
1.593'003
1.857~003
1.9709003
2.069-003
2.155'003
2.227'003
2.285.003
2.331*003
2.364-003
2.386'003
2.3974003
2.3989003
2.3909003
2.373-003
2.350'003
2.320'003
2.284'003
2.24$”003
2.198-003

122

 

1.9203005
2,306=005
2.6783003
3.037=005
3.3813006
3.7109005
4.0239003
4.3209003
4.6019003
4.8650006
5,111=005
5.3419006
5.555-003
5.7516003
5.932-006
6.0979006
6.247.003
6.382.003
6.5033003
6.6113005
6.7063006
6.789-005

70123'004
8.902'004
10°60'003
1.221'003
1.372-003
19511-003
10667-003
1.752'003
11854‘003
10943'003
2.020'003
2.085.003
2.158-003
2.180-003
2.212-003
2'254'003
20247'003
20252'003
29250'003
2.240'093
2.225-003
2.205-003

 

 

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2

3/2
5/2
7/2
9/2
11/2
13/2

APPENDIX III-8

Pl

0,0000
1.3325
2,3986
3,4265
4.4418
5.4513
6,4577
7.4623
8.4656
9.4682
10.4702
11.4718
12,4730
13.4740
14.4749
15.4756
16.4762
17.4767
18,4771
19,4775
20,4778
21.4781
22.4784
23.4786
24.4789
25,4791

92

010000
116002
2.8575
4.0005
5,0916
6.1546

123

CALCULATED LINEnSTRENGTHS FOR 15N160

BRANCH
01

0.6666
0,2672
0.1724
0.1284
0.1028
0.0361
0.0743
0.0656
0.0589
0.0557
0.0494
0,0459
0,0430
0.0406
0.0385
0.0567
0.0351
0.0337
0.0325
0.0314
0.0305
0.0296
0.0288
0.0251
0,0275
0.0269

02

2.3981
1.5396
1.1386
0.9038
0,7488
0.6387

RI

1,3326
2,3986
6,4266
4.4419
5.4515
604580
7.4626
8.4660
9,4687
10.4708
11.4724
12.4738
13.4749
14,4759
15.4767
16.4774
17,4779
18.4785
19.4789
20.4793
21.4797
22.4801
23.4804
24.4807
25.4809
26.4812

R2

1,6002
2,8576
4.0006
5.0917
6,1549
7,2012

 

 

 

15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
2572
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2

3/2
5/2
7/2

7,2009

8,2363

9,2643
10,2870
11.3057
12.3215
13,3349
14,3465
15,3566
16.3656
17,3735
18.3805
19,3868
20.3926
21.3978
22.4025
23.4069
24.4109
25,4146

PH

0.000‘000
0.000‘000
2.236'003
7.2517003
1.570'002
2.811-002
4.489'002
6.629-002
9.244-002
1.234-001
1.590‘001
1.990'001
2.4347001
2.916-001
3.434-001
3.984-001
4.561'001
5.160'001
5.778-001
6.410'001
7.053‘001
7.701'001
8.351'001
9.001'001
9.646'001
1.028+000

PL
7.432'004

9.022'004
1.083'003

124

0,5563
0,4921
0.4407
0.3986
0.3655
0,3337
0.3080
0.2858
0,2662
0,2489
0,2336
0.2198
0.2076
0.1961
0.1858
0.1764
0.1673
0.1599
0,1527

0H

0,0004000
5,992=004
1,414-003
1.785=003
2,149=003
2,4985003
2,835=003
3,159a003
3,470=003
3.767=003
4,050=003
4,318;006
4,57js003
4,809=003
5,032c006
5,240=003
5.434s003
5.612.003
5,776=003
5,927=003
6,063:006
6,187-003
6,299-003
6.3983003
6,4862003

0L
5,794=004

9,896=004
1,368=003

8.2367

9.2648
10.2876
11.3064
12.3223
13,3358
14,3475
15,3577
16,3667
17,3747
18.3819
19.3883
20,3941
21.3994
22.4042
23,4086
24.4127
25,4164
26,4199

RH

7.308-004
8.578-004
9.958'004
11129-003
10254-003
1.368'003
1,469-003
1.5570003
18652'003
1.694-003
10746'003
1.780-003
1,806-003
1.820-003
1.824-003
1.819.003
1.805-003
1,783-003
10755'003
1.722-003
1.683-003
11640-003
1.593-003
14544-003
1,493-003
1.440'003

RL
10376'004

2.870'004
4.332-004

 

 

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2

1.271'003
1.459'003
1.645'003
1.827’003
2.003‘003
2.172'003
2.332'003
2.482‘003
2.621'003
2.750'003
2.867'003
2.972'003
3.066.003
3.147'003
3.218'003
3.277-003
3.325-003
3.363-003
3.392'003
3.411'003
3.422*003
3.424-003

125

1,729a006
2.0799003
2,416;003
2,7439006
3.057a006
3.359a003
3,647v003
3,922w006
4.183=003
4,429=006
4.6629003
4.8799005
5,083°003
5.272.003
5.447.003
5.608a006
5,7562003
5.8913006
6.0133003
6.1239006
6,2229003
6.3109006

50716-004
6'998'004
81168-004
9.218.004
10014-003
1.095'003
1.163'003
1.219'003
11263-003
10297-003
1.321'003
1.335'003
1.341'003
1.336-003
10329-003
1.314-003
1.296-003
19268-003
10238'003
10206.003
1.170'003
1.136-003

 

PHHHHHF‘HHHHHHHHHHHHHHPHHHHPPHHHFH
DC)00009090000OGODDDDOCDDCOOOOOODD

1i‘311‘14lleI‘lI‘l'Il’II’lflii‘li11lfilfl'0‘l

APPENDIX IV

IDENTIFICATION
N40 372
N40 572
N40 772
N40 972
N40 1172
N40 1372
N40 1572
N40 1772
N40 1972
N40 2172
N40 2372
N40 2572
N40 2772
N40 2972
N40 3172
N40 3372
N40 3572
N40 3772
N40 3972
N40 4172
N40 4372
N40 4572
N40 4772
N40 4972
N40 5172
N40 172
N40 372
N40 572
N40 772
N40 972
N40 1172
N40 1372
N40 1572

FREQUENCY

1871,0000
1867,6000
1864,2000
1860,7000
1857,2000
1853,7000
1850,1000
1846,5000
1842,9000
1839,2000
1835,5000
1831,8000
1828,0000
1824,2000
1820,4000
1816,5000
1812,6000
1808,6000
1804,7000
1800,7000
1796,6000
1792,6000
1788,4000
1784,3000
1780,1000
1881,0000
1884,3000
1887,5000
1890,7000
1893,8000
1896,9000
1900,0000
1903,1000

 

CALCULATED VALUES FOR YHE INTtGRATEU
ABSORPTION COEFFICIENT FOR 14N160

50

0,79
1,37
1,84
2,22
2,48
2,64
2,69
2,66
2,54
2,36
2,14
1,90
1,64
1,39
1,15
0,94
0,75
0,58
0,45
0,34
0,25
0,18
0,13
0,09
0.82
1,44
1.97
2,42
2,77
3,00
3,13
3,14

Hr‘HbéHF4H69H+4H64HruHh¢HraHraHrAHrJHrAHrAHrAprApkaH69H+AH+AH8AH+4H64HréHriwraer
I am I! 11 11 I! 13 an I! ll 10 I! a 80.11 II a: 11 13 11 an mm mm 09 I! I: an IN
ODOOOCODOOOCODDOQODODOODOCDC)ODDDDDOOODODODOOODOODOOOC’OO

N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40

17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2

1906,1000
1909,1000
1912,0000
1914,9000
1917,8000
1920,7000
1923,5000
1926,2000
1929,0000
1931,7000
1934,3000
1937,0000
1939,6000
1942,1000
1944,6000
1947,1000
1949,6000
1952,0000
1867,2000
1863,6000
1860,1000
1856,5000
1852,8000
1849,2000
1845,5000
1841,7000
1838,0000
1834,2000
1830,3000
1826,4000
1822,5000
1818,6000
1814,6000
1810,6000
1806,6000
1802,5000
1798,4000
1794,3000
1790,2000
1786,0000
1781,7000
1777,5000
1887,6000
1890,9000
1894,1000
1897,3000
1900,5000
1903,6000
1906,7000
1909,7000
1912,7000
1915,7000
1918,7000
1921,5000

 

3,07
2.91
2,69
2,43
2,15
1,85
1,57
1,30
1,06
0,84
0,66
0,50
0,38
0,28
0,20
0,14
0,10
0,07
0,61
1,03
1,34
1,55
1,69
1,74
1,73
1,67
1,56
1942
1,26
1,09
0.92
0,77
0,62
0,50
0,39
0.30
0,22
0,17
0,12
0,09
0.06
0.04
1,10
1,46
1,73
1.92
2,02
2,05
2,01
1.92
1.78
1.61
1,43
1,23

 

'IlIl-‘IIJI‘I‘I‘JZI‘I‘ll‘l‘llllll'lli‘l-IJ

OODOCDODDOOODOD000C300000000009000OOOODODODODOCOOODODOC3

I‘l-‘IJ

HP‘P‘Hrdk‘HIJF‘Hrdk‘HO‘P*Hr‘F‘HIJFAF‘HPJP‘Ht‘r‘Ht‘h‘H!‘P‘Hi‘b¢h¥HFJF‘HFJF‘HFJF‘Hl‘k‘Hr‘P‘H

lliii'i-lelllflililllfifllflI

N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40

29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
5/2
7/2
13/2
19/2-
19/2+
21/2
23/2.
23/2+
27/2-
27/2+
29/29
29/26
31/2-
31/29
3/2
5/2
7/2
9/2
11/2
13/2
15/2-
15/2
15l2+
17/2'
17/26
19/2-
19/2+
21/2—
21/2+
23/2-
23/26
25/2-
25l2+
27/2.
27/26
29/2-
29/2+
31/2-
31l2+
33/Za
33/2+
35/2.

1924,4000
1927,2000
1930,0000
1932,7000
1935,4000
1938,1000
1940,7000
1943,3000
1945,9000
1948,4000
1950,8000
1953,2000
1987,3000
1984,1000
1974,9000
1966,1000
1966,2000
1963,3000
1960,5000
1960,7000
1955,2000
1955,3000
1952,5000
1952,7000
1950,0000
1950,1000
1995,7000
1995,8000
1996,0000
1996,3000
1996,6000
1997,0000
1997,4000
1997,4000
1997,5000
1997,9000
1998,0000
1998,4000
1998,5000
1999,0000
1999,1000
1999,6000
1999,8000
2000,3000
2000,4000
2001,0000
2001,2000
2001,8000
2002,0000
2002,6000
2002,8000
2003,4000
2003,6000
2004,3000

 

1,04
0.87
0,70
0,56
0,44
0,34
0,25
0,19
0,14
0,10
0,07
0,05
1.46-003
4,45-003
2.08-002
1.879002
1187'002
4004-002
2109‘002
2.09—002
1.999002
1.99—002
1.84-002
1.84-002
1.66P002
1066-002
4.05-004
6065-004
8,67-004
1.02'003
1,12-003
1.179003
5,87-004
1,17-003
5,87-004
5,70-004
5.70-004
5.36'004
5,36-004
4.909004
4.90‘004
4,36-004
4.374004
3,79-004
3.79-004
3.22-004
3.229004
2968'004
21689004
2.17’004
2.17'004
1.739004
1.739004
1,359004

 

1-0
180
190
1'0
120
180
180
190
190
190
120
190
1:0
190
190
190

H
3
o

3

F3H+JF*HfJH‘HEJF*HPJ
-81 :1 1:88 31 a
caocacaocncpocacyo

‘I
‘0

N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40
N40

QH
0H
0H
0H
OH
OH
OH
OH
0H
OH
OH
0H
0H
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
PL
PL
pL
PL

PL

35/2+
37/2.
37/2+
39/29
39/2+
41/29
41/2+
43/2-
43l2+
45/2—
45/2+
47/29
47/2+
1/2
3/2
5/2
7/2
9/2
11/2
13/2
15/29
15/2+
17/22
17/2+
19/Zr
19/2+
21/29
21/2+
23/Ze
23/2+
25/2-
25/2+
27/29
27/2+
29/2-
29/2+
31/2-
31/2+
33/26
33/2+
35/29
35/2+
37/25
37/29
39/2.
39/26
41/29
41126
7/2
9/2
11/2-
11/2
13/2-
13/2

129

2004,5000
2005,2000
2005,4000
2006,1000
2006,3000
2007,1000
2007,3000
2008,0000
2008,3000
2009,0000
2009,3000
2010,0000
2010,3000
2000,7000
2004,2000
2007,7000
2011,3000
2015.0000
2018,7000
2022,5000
2026,3000
2026,4000
2030,2000
2030,3000
2034,1000
2034,2000
2038,1000
2038,2000
2042,1000
2042,2000
2046,2000
2046,3000
2050,3000
2050,4000
2054,4000
2054,6000
2058,6000
2058,7000
2062,8000
2063,0000
2067,0000
2067,2000
2071,3000
2071,5000
2075,6000
2075,8000
2079,9000
2080,1000
1743,7000
1739,8000
1735,8000
1735,8000
1731,6000
1731,7000

1135'004
1.035004
1.03fi004
7.71-005
7371-005
5.669005
5.669005
4.089005
4,08-005
2.88‘005
2.889005
2.009005
2.003005
5.242004
6.149004
7.006004
7.666004
8.089004
8.249004
8|14‘004
3.909004
3.909004
3.649004
3.649004
3.31’004
3.319004
2.939004
2.935004
2.54-004
2.549004
2.159004
2’15'004
1'78’004
11783004
1.449004
1.448004
1.149004
1,14-004
8.849005
8.849005
6.722005
6'729005
5.014005
5.019005
3.66-005
3.66’005
2.62-005
2.629005
3.779004
4.023004
2.062004
4112-004
20049004
4,084004

 

114211’0100-4iilrliQI‘Iiid-Iflfiicl‘lfl

rdthPAPaprPtprawsH+APsHPAPIH+4P4H1486H64P6H+APsprfiksprahtprahsp+éPsH+APhHIa
DOOOOGDOOOOOOOODDODC3000ODDOOOOODOQDDDDDOOODOOC)

11112011]IJ-‘ilal-I‘I‘lil

130

N40 PL 1572+ 1727,3000 1.969004
N40 PL 15/2 1727,4000 3.929004
N40 PL 15/2+ 1727,4000 1.96-004
N40 PL 1772+ 1723,0000 1.82-004
N40 PL 1772+ 1723,0000 1.826004
N40 PL 19/2- 1718,4000 1.659004
N40 PL 19/2+ 1718,5000 10653004
N40 PL 2172. 1713,8000 1.469004
N40 PL 21/29 1713,9000 1.46-004
N40 PL 23/2- 1709,0000 1.26-004
N40 PL 2372+ 1709,1000 1.266004
N40 PL 25/2» 1704,1000 1106-004
N40 PL 25/2+ 1704,3000 1.069004
N40 PL 2972. 1694,1000 6.989005
N40 PL 2972+ 1694,2000 6,98-005
N40 pL 31/2- 1688,9000 5.492005
N40 PL 3172+ 1689,0000 5,49+005
N40 PL 33/2- 1683,5000 4.22-005
N40 PL 33/2+ 1683,7000 4.226005
N40 PL 3572- 1678,1000 3,18-005
N40 PL 35/2+ 1678,3000 3.188005
N40 0L 372 1756,1000 2.419004
N40 0L 7/2 1755,3000 5.169004
N40 0L 9/2 1754,7000 6.06-004
N40 0L 1172+ 1754,0000 3.33-004
N40 QL 1372» 1753,1000 3,47,004
N40 0L 13/2 1753,2000 6.952004
N40 0L 1372+ 1753,2000 6.479004
N40 0L 1572 1752,2000 6.97-004
N40 0L 17/2 1751,1000 6.758004
N40 0L 19/2: 1749,8000 3.179004
N40 0L 21/2- 1748,5000 23909004
N40 0L 21/2+ 1748,6000 2.90-004
N40 UL 2372- 1747,0000 2.589004
N40 0L 2372+ 1747,2000 2.582004
N40 RL 7/29 1770,2000 90069005
N40 RL 7/2+ 1770,2000 9.06-005
N40 RL 1172! 1775,5000 1.30-004
N40 RL 17/2- 1782,5000 10399004
N40 RL 17/2+ 1782,6000 1.39-004
N40 RL 21/2~ 1786,6000 1.202004
N40 RL 21/29 1786,7000 1.209004
N40 RL 2772— 1791,8000 7.79-005‘
N40 RL 27/24 1791,9000 7.792005
N40 RL 29/2- 1793,3000 6.40-005

N40 RL 2972+ 1793,5000 6.404005

SUBSTATE

......

fUflJMFOfiJNFOfiJNf‘F‘HP‘r‘H4‘P‘HW‘P‘HP‘F‘PF‘F‘HF‘b‘Ht‘H‘HP;

APPENDIX VwA

G'FACTORS FOR 14N160

J

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
3572
37/2
39/2
41/2
4372
45/2
47/2
49/2
51/2

3/2

5/2

7/2

9/2
11/2
1312
15/2
17/2
19/2

131

V=0

0.0000
0.0230
0.0263
0.0273
0.0277
0.0279
0.0279
0,0278
0,0277
0.0276
0.0274
0,0272
0,0270
0.0267
0.0265
0,0262
0,0259
0,0256
0.0253
0.0250
0,0247
0,0244
0.0241
0.0233

0.0232
0.7770
0.3166
0.1632
0.0935
0.0561
0,0337
0.0192
0.0095
0.0025

VALUES

V=1

0,0000

0.0228
0.0260
0.0270
0.0274
0.0276
0.0276
0.0275
0.0274
0.0273
0.0271
0.0209
0.0267
0.0265
0.0262
0.0260
0.0257
0.0254
0.0251
0.0208
0.0245
0.0242
0.0239
0.0236
0.0233
0.0230
0.7772
0.3168
0.1635
0.0938
0.0564
0.0340
0.0195
0.0097
0.0028

21/2

2372
2572
2772
2972
3172
3372
3572
3772
3972
4172
4372
4572
4772
4972
5172

132

v0.0025

90.0063
00,0092

"000119

90,0131
o0,0145
+0.01ss
°0.0164
90,0170
°000175
'000179

~I0,0102
190,0134
~90.0186‘

90,0187
90,0187

-0.0023

e0.0060
”0,0089
90.0111
90.0129
”0.0142
90.0153
90.01614
90.0168
90.0173
”0.0177
90.0180
30.0183
90.0184
”0.0185
”0.0186

 

SUBSTATE

...;

APPENDIX VaB

GPFACTORS FOR 15N160

J

172

372

572

772

972
1172
1372
1572
1772
1972
2172
2372
2572
2772
2972
3172
3372
3572
3772
3972
4172
4372
4572
4772
4972
5172

372

572

772

972
1172
1372
1572
1772
1972

133

0:0

0.0000

0.0221
0.0252
0.0262
0.0266
0,0268
0.0263
0.0267
0.0266
0.0265
0.0204
0.0202
0.0200
0.0258
0.0255
0.0253
0.0251
0.0240
0.0245
0.0243
0.0240
0.0237
0.0230

0.0231

0.0220
0.0226
0,7779
0.3176
0.1643
0.0946
0.0572
0.0343
0.0203
0.0105
0.0030

VALUES

V=1

0.0000

0.0228
0.0260
0.0270
0.0274
0.0275
0.0276
0.0275
0.0274
0.0272
0.0271
0.0269
0.0267
0.0264
0.0262
0.0259
0.0257
0.0254
0.0251
0.0248
0.0245
0.0242
0.0239
0.0236
0.0233
0.0230
0.7772
0.3169
0.1635
0.0933
0.0564
0.0340
0.0196
0.0093
0.0028

fURJNFUhJNHUDJNFURJNFURJN’N

2172
2372
2572
2772
2972
3172
3372
3572
3772
3972
4172
4372
4572
4772
4972
5172

134

90,0015
90,0053
90,0082
90.0104
“0.0122
90,0136
90,0147
90,0155
-D,0162
90,0168
=0.0172
90,0175
90,0177
=0.0179
90,0180
90,0181

-0.0022
90.0060
90.0089
90.0111
90,0128
'000142
'030153
’000161
-0,0168
”0.0173
90,0177
'0.0180
9000182
-000184
-0,0185
-0.0186

APPENDIX VI

The expressions used in the combination difference,

frequency and A—splitting fits are as follows:

A) Combination differences
AnFi(J,V) = [U(J+n)-U(J)] x Boi
- [U(J+n)2-U(J)2] x Doi
+ (-l)i[U(J+n)3-U(J)3] x Hb
- [U(J+n)-U(J)]V x ai
- [U(J+n)2-U(J)2] v x Bi
- (-l)i[U(J+n)3-U(J)3]V x y' ,

where i = l, 2 refers the the 20% and 203 states respectively,
n = l, 2 corresponding to a difference of l, 2 in J respec-

tively and U(J) = (J+§)2°

B) Frequencies
v(J,n,v,s) = 1.0 x AG(1)
+ (6H,s _ 6L,s) x C10
+ (61,5 - 62,5 - 6H,s + 6L,s)v/2 X X
+ {[U(J+n)-U(J)]61’S - U(J)6H'S + U(J+n)5L’S} x 301
+ {[U(J+n)-U(J)]c32’S + U(J+I‘1)6H’S - U(J)6L,S} X B02

135

 

 

136

(cont.)

-'{[U(J+n)2-U(J)2]<sl’S — U(J)26H’S + U(J+n)26L’S} x
- {[U(J+n)2-U(J)2]6298 + U(J+n)26H’S — U(J)26L’S} x
- {[U(J+n)3-U(J)3]61’S - U(J)36H’S + U(J+n)36L’S} x
+ {[U(J+n)3-U(J)3]62’S + U(J+n)36H’S - U(J)36L’s} x
- {[U(J+n)+§](6lls+6L'S) - £(62’S + 6H’8)}v x
- {[U(J+n)-§](62,S+6H’S) + §(5l’s + aL'S)}v x
- {[U(J+n)2+£](61,s+6L’s) + £(02'S + 5H,s)}V x
- {[U(J+n)2+§](52's+6H’S) + §(5l's + 6L,s)}v x

+ [U(J+n)3] v (51,5 + 6L,s) x

- [U(J+n)3] v (52,5 + 0H S) x

U(J) is the same as for the combination differences except
that n = -l,0,+l corresponding to the P, Q, and R branches

6 and 6 are Kronecker

l,s’ 62,s’ H,s’ L,s

deltas having the value 1 or 0 depending upon whether 5 is

respectively, and 6

equal or unequal to the other subscript. The l, 2, H, and
L refer to the 20%, 203 subbands, the HES and LES respec-

tively°

0‘1

0‘2

81

32

 

 

 

137

C) A-splitting expressions

a
31
n

(J2-1>(J+3)

w
.5
n

(J+§)

 

l-subband

Av(J-l;J) = 2{1+U(J—1)[111-2]‘2 + U(J)[101-2]'2}pA

+ 4{U(J-1)[111-2]'1 + U(J)[101-2]"1}qA

-AV(J;J) = -2{2F(J) - U(J)[111-2]'2 - U(JHAm-Zl-ZmA

+ 4 U(J){[A.1-2]'1 + [101-21‘1}qA

-Av(J+l ;J) = -2{l-U(J+l)[>.11-2]"2 + U(J)[Aol-2]'2}PA

+ 4{U(J+1)[111-2]'1 — U(J)[101-2]'1}qA

2-subband

 

Av(J—l;J) = 2{U(J)[102-2]'2 — U(J-1)[112—2]'2}pA

+ 4{U(J)[102-2]-1 - U(J-l)[112-2]-1}qA

“AV(J7J) = '2 U(J) {[102-2]-2 + [112-21-2}pA

-4 U(J){[102-2]-1 + [112-21'1}qA

-Av(J+l;J) = 2{U(J)[102-2]-2 - U(J+1)[A.2-2]'2}pA

+ 4{U(J)[102-2]'1 - U(J+1)[112-21-1}qA

 

 

 

138

HES

Av(J-l;J) = 2{F(J) - 0(J-1)[1.2-21"2 - U(J)[Ko1-2]-2}pA

- 4{U(J)[AOl-2]‘1 + U(J-1)[112-2]'1}qA

-Av(J;J) = -2{F(J) + U(J)[112-2]’2 = U(J)[101—2]"2}pA

4 U(J){[112-2]-2 - [101-21‘1}q

A

Av(J+l;J) = 2{F(J) U(J+1)[112--2]'2 - U(J)[Ao1-2]-2}p

A

-4{U(J+1)[x12-2]‘1 + U(J)[10,-21‘1}qA

Egg
-Av(J-l;J) = -2{F(J) - U(J-1)[111-2]"2 - U(J)[Aoz-2]'2}pA
+ 4{U(J-1)[111—2]-1 + U(J)[102-2]‘1}qA
-Av(J;J) = —2{F(J) + 0(J)[102-2]‘2 - U(J)[All-2]_2}pA
+ 4 u(J){[All-2]‘1 - [102-21”}qA
-Av(J+l;J) = -2{F(J) - U(J+1)[A11-2]'2 = U(J)[A02-2]'2}pA

+ 4{U(J+1)[111-2]‘1 + U(J)[Aoz-2]_1}qA

 

 

 

 

APPENDIX VII
COMPUTER PROGRAMS

Many computer programs were written during the course
of this worko The major ones are described below with op-

erating instructions.

A. SHAFT

This intricate and very useful program written by
Lo E. Bullock is designed to reduce the raw data, including
code weights from up to eight separate Hydel measurements of
a band to a tabulated output of the average fringe number,
weighted average frequency, weighted standard deviation,
individual measurements and weights of each line measured
in the band° It will also identify these lineso SCAN and
CALFIT (written by Mo D. Olman (74)) are used as subroutines.
SCAN determines the fringe numbers of the individual lines
including calibration lineso Standard calibration frequency
decks are input and matched with the observed calibration
lines° CALFIT performs a least squares fit of the calibra-
tion lines to determine the fringe constants which are then
used to obtain frequencies for the observed lines. The
frequencies are ordered and a weighted average of identical

transitions is performed. All this information is tabulated

139

 

 

 

 

 

 

140

in a convenient output which includes identification of the
transitions, if this is known. This prOgram can also be
used like a normal SCAN program with the Option of getting
punched output of the frequencies, which can later be used
in place of the raw Hydel data to obtain the tabulated out-
put. The user provides the program with identification decks
and a series of tolerances which indicate his maximum uncer—
tainty in the frequency (in cm‘l) of any line so that the
program is able to recognize separate measurements of the
same line. All tolerances and other quantities necessary
for operation are preset to typical values which will be

used in the event they are omitted on input.

STRUCTURE OF DATA DECK

I. thion card

 

 

Col. Variable Field Function
1 NGPS I Indicates number of groups :8

to be averaged.

2 IOP(l)

H

#0 indicates SCAN desired (see
SCAN description for input).

3 IOP(2) I #0 indicates average desired.
=2 indicates punch of identifi-
cation, average frequency and
weight in the identification deck
format is desired.

4 IOP(3)

H

#0 indicates punch frequencies
and weights (8/card) is desired
from SCAN.

5 IDNT I #0 identification deck(s) is used.
=2 identification deck(s) is input.

 

 

Col. Variable

6 ICAL

7 IDON
ll-20 TOLl
21-30 TOL2
31-40 TOL3

Field

I

II. IDENTIFY data deck

 

141

Function

#0 calibration deck(s) is used.
=2 calibration deck(s) is input.
=3 causes fringe constants just
determined to be used to obtain
line frequencies (see below).

:1 provides printout of single
frequencies in the "group" tab-
ulation. =2 omits punching
weights as provided in IOP(2)=2.

Frequencies within a group which
differ by less than TOLl are con-
sidered to be separate measurements
of one line, and their non-weighted
average is formed. TOLl is preset
to 0.05.

Frequencies in the various groups
which differ by less than TOL2 are
considered to be measurements of the
same line. TOL2 is preset to TOLl.

Frequencies which differ by less than
TOL3 from input identification fre-
quencies are assigned the correspon-
ding identification. If two identi-
fications within TOL3 are found, an
asterisk field is printed. If TOL3
is greater than 100 the asterisk
field is suppressed and the same
identification may be punched and/or
printed for all lines.

This section handles both identification and calibration

decks and appears if and only if IDNT or ICAL are equal to 2.

1. Order card:

 

This card is used to convert input frequencies

from.their value in the order in which they were recorded to

their value in the order of the IR. It can be inserted any—

where in the identification deck.

 

 

142

 

 

Col. Variable Field Function
8 IR I Order in which the IR radiation

was recorded.

16 IICAL I Order in which the identification
or calibration line would have
been or was recorded.

75-80 ORDER A "ORDER" specifies an ORDER card.

(Note: if the ORDER card does not appear IR and IICAL are
assumed to be one.)

2. Ident deck cards:
l-8 NAMEl A These two fields contain the
9-16 NAMEZ A identification title that is de-
sired to be printed and/or punched
beside the corresponding frequency.

20-33 XNU F Frequency of identification or
calibration line.

These cards are read until a value of XNU=O is encountered.

III. SCAN data deck

 

This section appears if and only if IOP(l) #0. A descrip-
tion of the SCAN deck is given elsewhere. (The basic structure
is: NEW SCAN card, Operator name card, heading cards, calibra-
tion constants card (OptionL Hydel cards, and 8- or 9-parameter
card.) A non-zero punch in cols. 23—27 of a l-parameter card
acts as a switch to either begin or end punch/averaging depen-
ding upon whether the switch was on or off before. If punch
frequencies are obtained, the fringe constants used are also
punched, whenever they are set, and included with the fre-
quencies. This is done in a format recognized in the averaging
section. The first NGPS groups must end with an 8-parameter

card. The last group ends with a 9-parameter card. The

 

 

143

punch/averaging switch is off at the start of each group.

IV. AVFRQ (averaging) data deck

 

1. Heading cards: Cols. 1-72 of these cards will be listed
on the output. This will continue until END HEAD is found
in cols° 73-80. Cols. l-72 of the last card will also ap-
pear as a heading for the output of each page of this set

of data. If IDNT #0 and the word "IDN HEAD" appears in
cols. 73-80, the first 32 cols. of this card are used as

a two line column heading over the identification titles.

If this card does not appear, the word IDENTIFICATION is

used. (Read by 10A8)

2. Group identification and data (appears NGPS times):

 

Cards a,c must appear once and only once for each group.

Cards b, d, e, and f may appear as many times as needed.

Up to (lOOOO/NGPS+1) data points may appear in each group.
a) Column heading £3391 Contains column headings for
the tabulated output of individual measurements. Place
the first line of heading in cols. 1-8, the second line
in cols. 9-16. If non-zero numbers are found in cols.
21-35 and 36-50 they are treated as updated values of
the fringe constants A and B respectively. These num-
bers are used to convert all succeeding frequencies in
this group, and a new set of punch frequencies is given.

b) Punched frequency cards: Frequencies and weights

 

punched from SCAN or a previous run may be entered here.

The format is 8(4PF8,Rl,X). Frequencies and weights

   

 

144

are read from left to right across the card until the

first three fields are zero.

C)

i) If the first field is zero, the card is treated
as a fringe constants card. The last value read is
used in fringe number calculations. Values may be
input; A in cols. 16—19 and 21-25, and B in cols.
35—39 and 40-44. No decimal point is used!!

ii) If the first two fields are zero, the card is
treated as a code+weight specification card. If
this card does appear the codes weights are read;
4, cols. 21-28; 3, cols. 31-38; 2, cols. 41-48;

1, cols. 51-58; blank, cols. 61-68. If this card
does not appear the code weights are assigned:
4:1.0, 3:0.25, 2:0.62; l=0.l6; 0:10-20; blank=l.0.
The last code weight card is used to assign all code
weights for that particular group.

Blank card: Card with first 20 columns blank to

 

indicate the end of the punched data.

d)

Delete cards: DELETE in cols° ll-l6 with frequency

 

to be deleted in cols. 2l-35.

e)

Change cards: CHANGE in cols. ll-l6 with frequency

 

to be changed in cols. 21-35, new/old value of frequency

in cols. 36-50 and weight code in col. 52.

f)

Punch card: PUNCH in cols. 12-16 causes average

 

frequencies of this particular group, including changes

and excluding deletes to be punched out in the normal

format of b) above.

 

145

3. Calibration constants card: Fringe constant A in
cols. 21-35, B in cols. 36-50. If this card is blank the

last values of fringe constants will be used.

V. SEARCH data deck

 

This section appears if ICAL#0 and must be used in con—
junction with the averaging section. Its purpose is to match
SCAN fringe numbers with the corresponding calibration fre-
quencies and finally do a least squares fit to determine the
fringe constants. A punch deck of the assigned fringe numbers,
frequencies and weights is punched out in the standard CALFIT
format.

1. Number gf lines card: This card specifies the number

 

of calibration line fringe numbers input from SCAN; cols.
l—lO. The search is carried out twice unless the number

of lines identified equals or exceeds the number of lines
on this card on the first pass.

2. Initial identification cards: At least two initial
identifications of calibration lines must be made and input.
This input consists of the identification title exactly as
it was read in for the calibration deck, and the approximate
fringe number (within one) of the calibration line. The
identification is put in cols. 1-16 (A-format) and the
fringe number is in cols. 30-39.

3) 21225.2232i A blank card signals the end of initial

identification cards.

146

4. Heading cards: These are heading cards for the CALFIT
subroutine. Cols. 1-72 of the cards are read and printed

until a card with END HEAD in cols. 73—80 is encountered.

The last card is repeated at the tOp Of all succeeding

pages.

VI. New case

 

NEW CASE in cols° 73—80 indicates that a new case be-
ginning with the Option card follows. Note that if the fringe
constants just determined in section V are to be used for new

SCAN data, a new case is called for with ICAL=3.

VII. Stop card

 

STOP in cols. 77-80 ends execution of the program.

A listing of the program follows.

 

 

147

FILEo69
MAIN.5
FILE END
FTN.L,X

PROGRAM SHAFT

C SCAN HYDEL AVERAGE FRFUUENCIES TARULATE

6100

6200

1

O

100
160

FILE.

C0040N71710P(3).ILS(5).TOL1.TOL2.TDL3.A,B.LP.IUNT.ICALalDON.JUMP
COMMON/27 N
COMMON/3/NAME1(2000).NAME2(2000),NU(20007.NMAX
commoN/a/ICHLAD(9).IHEAD(9.2).IDN(4)
COMMON/5/AVGFREQ(200).AWGT(200).NUM

COMMON/97 CCWT(8.5)

DIMENSION FRQ(1.10000).w75(1.10000)

TYPE INTEGER WTT,wT,wTs

READ 100.NGPS,IOP.IDNT,ICAL.IDON.TOL1.TOL2:TOL6.IFDONE

Ircxrnnwe .20. SH STOP) STOP
IDK(1):8H 0 IDN(2)=8H $ 10~<s)=80
100(4)=aH

JUNPzU

IDEM:10000./NGPS
IF(IDNT.ED.2.0P.ICAL.E0,2) CALL OVERLAY(1..1..)
IF(IDNT) 8200,8100

LP=1

NAMEl(1)=NAMt2(1)=Oh

CONTINUE

(0:1

00 10 1:1,NGPS

ILF(I):1

IF(TOL1.E0.0.) TOL1=.050

IFfTOLP .E0. 0,) TOL2=TOL1

IF(TOL3 .NE. 0.) GO TO 13

1F(ICAL) TUL3=.03

TOL3=.04-TOL3

IFr10P(1>) CALL OVERLAY(2,,2,J,FRO,WTS,NUPS.IDEM)
IF(10P(2)) CALL OVERLAY(3..3.J.FRQ,HTS.NGPS.IUEM)
IF(ICAL) 16.200

CALL UVERLA)(4. .4..)

JUNP:1

ICAL=U

IDNT=1

GO TO 14

READ 160. IFHONE

IF!!FDONE.EO.8H ) so To 200
IF(JFDONE.EQ.8HEND HEAD) Go T0 200
IF<IFDONE.EU.8HNEH CASE) Go T0 1

[F(IFDONE .EU, 8H STOP) STOP
FORMAT(711.3X.3F10.8.32X.A8)

FORMAT (72X.A8)

END

69

OVERLAY.1.1

FILE

END

 

148

FTN,L,X

PROGRAM IDENTIFY
COM%ON/1/IUP(3),ILS(8):TUL1;T0L2'TOL3pA:5:LP.IDNT,lCAL,IDON,JUMP
C0M40N/3/NAME1I2000).NAMt2c2000).Nu<2ooo).NMAx

TYDE REAL mu

Type INTEGER 0RDFR

N=1

NT=1

IR=IICAL=1

READ 1,1NAME1,INAMEZ.XNU.0RDER

iFIJRUFR.EQ.5H JRDER)10,15

IR=INAME1=dH 0

IICAL=INAME2-8H 0

GO TO 20

IFtXNU) 16.25

XNU=XNH*IR/IICAL

IF(N.E0.1) GU TO 6

5 IFIVU(NT-1).LE.XNU) GO TO 6
MU(VT)=NU(NT-1) $ NAME1(NT)=NAME1(NT-1) t NAME2<NTI=MAME2(NT-1)
NT:NT'1
IF‘NT'l) 61615

5 NUIVT)=XNU $ NAME1(NT):INAME1 $ NAME2(NT)=INAME2
N=N+1 x NT=N $ GO TO 20

25 NMAer-l
IFITOL3.GT.100.) GO TO 26
NA4EJ(NMAX+1)zNAME2(NMAX+1)=NAME1(NMAX*2)=8H
NAME2(NMAX+2)= 8H **t
NU<NMAX+1)=U.U
RETJRN

26 NAME1(NMAX+2)=MAME1(1)

NAME?(NMAX+2)=NAME2(1)
PETQRN

1 FonwAT (?A8.3X.F13.4,40X;A8)

END
FILE.69
OVERLAY.2.2
FILE END
FTN.L.X

A

\l

11

PROGRAM ALL SCANIFRQ.wTs,NGPs,IDEM)
COMMON/l/IOPI3),ILS<5),T0L1.T0L2.T0L3.A.6.LPaIDNT:ICAL:IDONvJU“P
COMMON/Z/ NAVF

DIMENSION IFSTIlU).XMt6).YMIé).FRNGX<100I.PSEP<100),FGSEP<100)'

111(2).12(2);IHEAD(9);NAME(2) :NHEAD(1O).UELX(6)aIPFR(3).IPEN(2)o
2WT(6)oWTT(8)

DIMENSION FRQINGPS.IDEM>.HTSINGPS.IDEM)
DATA<IPEN=8H6FIRST ,8H68ECOND >

TYPE INTEGER NTT.WT.WTS

PRINT 9701

READ 7, NAME.IFDONE

FOPMAT (2A8,Sex,A8)

IFIIFDONheaHNEw SCAN)11.13
IFIIFDONEaBHOLD SCAN)8.9

¥

9800
9900

411
410

PRINT 10
IORMAT (81
GO II) 13
TNEN=0

GU TD 1
INFN:1

149

Xt~N0 NAME CARD-ASSUMING MEN SCAN*)

READ 5, IHEAD,IFDONE

)FQTIVT' :3: I

TFCIFDONEa

IH=NIP:1
IFIIOP(3))
PUMCH 3.: I
CIVITIIVUE
fiFQflzNCAL=
IH=1LT=IL=
WD=1
XFREP=FSEP
ASSIGN 360

HEAD
BHEND HEAD) 1p2

9600,9900
HEAD

IP=IFARDS:IFRQQ:IPUNCH:0
ILS(NAVF)=1

:0.0
0 To N60

IF(ICAL) 364.635

IF(ICAL .E

0. 5) GO To 4001

A:0.0 $ 8:1.0 $ NCAL=1
1F(.NUT.IOP(6)) GU T0 335 .
IA=A $ IXA:(A-1A)*l,t5 5 18=B*1.E5 $ XB=d*1.t5 $

PUNCH 70:1
CQMTINUE
READ lUU;(

A.IXA,IB:1XB

XM<I5;YM(I).WT(I),I:1,6):ICOUEoIFN

IF(ICUDE-6) 20?.200:203
IF(ICODE-8) 7000.500118001

IFI4-ICODE
IFIICODE-Z
IFI-ICODE)
PRINT 106,
RC 10 101
PRINT 9701
IFIICAL .E
RETURN
NCOUPD=6
IF(XM(6))
DO 105 1:1
“CHURuzNFU

)5Dln,40001204
) 205.2000.200
1000,10b.105
(XM(I).YM(I).I=1;6>

Q. 3) ICAL=D

104:107
,5
URU31

IF(XM(NCUORU)) GO TO 104

GO F0 101
D0 201 I=1

,NCOORD

XM(1)=0MT2*XM(I)-THETA*YM(I)
IF(1CODE-5) $UOO,SOOU,6000

XFRM:XM
XFWNuszM

FRNG=XFHNG-1.0

IPD: XM(2)
IF(IPUNCH)
IPHNCH:XM(
GO TO 410
IFIXM(3))
CONTINUE

GO TO 411
3)

IPUNCH=U

IXB=(XB'IB)*1.E5

150

GO TO 101
2000 SUMX=SUMY=SUMYY=SUMYX:D,0

GO TO N60

32 CONTINUE
NOFR=O
ASSIGN 6205 T0 NIR
DO 201: 1:6
SUAY = SUMY + YMII)
SUMX = SUMX + XMII)

SUMYY = SUMYY + YM<I)¢YM<I)
20 SUMYX : SUMYX + YM(I)*XM(I)
THFTA : (SUMYX - SUMYASUMX/é.)/(SUMYY - SUMY*SUMY/6,)

THFTAZ=U.5*IHETA*THETA
0MT2=1.0-THETA2
IBAD = 0
DO 50 I 3 106
PEIX<I> = (SUMY-THETAASUMY)/6. + THETAtYM(l) - XMII)
IF(A88F(DELX(I)) .GT. 10.0) IBAD = 1
30 CONTIADfiE
00 T0 (101.31),IH
33 IF (.NDT. INFN) ENCODE(4.11,IFR) XFRM
PRINT 9201,1HEAD,IFH.NAME
IFTTHETA? .UT, 0.0000125) PRINT 6210
IPTIBAD) PRINT 6209
00 T0 101
3000 DDKOO7J=2,MCUOHD.2
[P = IP + 1
XFQEP=XFSEP+1,0
PSEPtIP):XM<J)-XM<J-1)
FSEP:PSEP(IP)+FSEP
3007 CONTINUE
GO TO 101
3600 NFPM=NFRM+1
IPFRINFRM):IFR
IF<.NUT.INEWI ENCODE(4.11.IPFRINFRM))XFRM
11 FORMAT (F4)
00 T0 ( 39.600?),NFRM
3602 VSFPzFSEP/XFSEP
leNFRM-l
PPINT601.IPEN(N1).IPFPINl).NAME .THETA.DELX.(PSEP(1).I=NIP.IP)
601 FDPMAT(A8«PEN SEPARATION FRAME IS N0.*A4/ * MEASURED BY *2A8/
1* POTATION ANGLE IStF10,6* RADIANS*/* ROTATION FITS TO~6<F3*,.). M
21CHOMS*/* OBSERVED PEN SEPARATIONS*(20F5))
3608 NIP=IP+1
IFcTHETAZ .GT. 0.0000125) PRINT 6210
IFIIBAD) PRINT 6209
PRINT 3609.FSEP
3609 FOPMAT (. AVERAGE PEN SEPARATION FOR THIS FRAME 18*F6,1« MICRONS*)
IF<NFRM.E0.2) GO T0 32
IH=2
ASSIGN 32 T0 NGO
PSFPSUM = 0
00 6701 J=1pIP

 

 

151

3701 PSFPSUM=PSEPSUM+PSEP(J)
PENSEP = PSEPSUM/ IP
PRINT9300.PENSEP
GO TO 32
4000 CONTINUE
A = YMIl) + XM(2)*0.00001
§=XW(3)+YM(S)*0.00001
IFIYM(2) .LT. 0.0) B=-B
8:VW(2)*B‘0.00001
4001 PRINT 9400. A. B
NCAL=1
IF(.NOT.IOP(5)) GO TO 101
IA=A 1 IXA=(A-IA)*1,Eb $ IR:B*1.E5 s xa=a*1.t5 $ IXB=(XB-IB)*1.E5
IFCIL.F0.1) 71.8000
71 PUNCH 70.1A.IXA.IB.IXB
70 POPAAT<1SX,14,Y.15.8x,16.x;15)
GO TO 101
5000 00 6001 J : 1.NCOORD
NON = NOF‘R + 1
FRNGXINOFR) = XM(J)
FGSEP<NDFR)=FRNGX(NOFRI-FRNGX(NOFR-l)
5001 CONTINUE
00 T0 101
5010 IFINOFR) GO TO 200
IF(.NOT.INEN) DO TO 200
XFRNszM
FRNO=XFRNG-l.0
HQ 501] 1:1,5
XMII)=¥M(I+13
5011 YMII)=YM(1+1)
XHI6)=YM(6)=U.0
GO TO 200
6000 00 TO NIH
6205 PRINT 9500,XFRNG,THETA,DELX.(FGSEPII),I=Z,NOIR)
ASSIGN 6904 TO NIH
AVFSEP:0.1*(FH NGX(NOFP)-FPNGX(1))/(NOFR'1o)
IEAD = U
00 6206 1:3;00FP
6206 IFIAPSF(IGSEP(I)-FGSEP(I'1)) .GT, AVESEP) IbAU = 1
IFIIBAD) PRINT 6208
Nan
IFINCAL) PRINT 9ébUaA.B
PRINT 9655
IF(IOP(5) .AND, IPUNCH) PRINT 303
303 FORMAT (1H+:40X*THESE FREQUENCIES ARE BEING PUNCHEDA)
6204 DO 6001 J=1TNC00RD
NEXT=8H
x16 = PENSEP + XM(J)
~ DO 6003 1:1,NOFR
6003 IFIXIR.LE,FRNGX(I)) 00 TO 6004
L:N=NOFRr1
NE¥T=8HEX RIGHT
GO TO 6011
6004 Lzl-l

 

6012

6011

300

U}

1009

10
12

8001
8000

333

331

330

9000
6001

7000
3
100
106
301
6208
6209
6210
9201

9300

152

GO TO (601216011),I

NEXT=8HEX LEFT

L=1
FRN01=FRNG+L+IKIR-FRNGX(L))/FGSEP(L+1)
IF(.NOT.NCAL) GO TO 9000
FRCDI=A+BfiFRN01

PRINT 9651, NEXT,FRN01,WT(J),FRE01
IFT.NOT, IPUNCH) GO TO 6001

IFINEXT .NE. 80 ) GO TO 6001
CONTINUE

IF(.NOT. IOP(2)) GO TO
IF (ILT.E0. 1) 00 TO 1009

IF (PROINAVF.ILT —1) .LE. FRE01
FPIINAVF.ILT)=FRO(NAVF.ILT-1)
NTQ<NAVF.ILT):NTS(NAVF,ILT=1)
ILT : ILT - 1
IF (ILT.EQ. 1)
00 TD 5
FPOINAVF.ILT)=PRE01
NT§(NAVF,ILT)=NT(J)
60 TO 10
FROINAVF,ILT)=FRE01
INTI7§(I‘-5A\,/F,1LT)=NT(J)
IL = IL + 1

ILT :: IL

00 TO 5001
ITI.N0T.IDP<5))
”leL'l

PUNCH 301,(FPNINAVF.JJ).NTSINAVF.JJ).JJ:MD.MM)
MD=IL
IFTICODE.GT.4)
ICAHH8:(IL+6)/R
ILL=IL-1

PRINT 331.1LL.ICARDS I PUNCH 331.1LL.ICAHDS

FUPWAT (IbrFREOUENCIES HAVE BEEN PUNCHED 001MB"r CARDS FOR THIS CAS

6001

) GO TO 6

GO TO 6

GO TO 330

333.71

15*)

CDNTINDE

ILRINAVF):ILT

IAVF=NAVF+1

00 T0 (4,102),ICUDE-7

PRINT 9651. NEYTIFRN01:WT(J)

CONTINUE

GO TO 101

READK,NHEAD$PRINT3pNHEAD$GOT0101
FHRMAT‘(1UA8)

FORM/1T (6(2F51F31)1111A4)

FORMAT (AUTHIS CARD HAS A BLANK 0R ZERO CODE*
FORMAT (8(4PF8.R1.X))

FOPMAT (*+r80X*FPINGE SPACING VARIATION .GT,
FORMAT ( 81X*ROTATION FIT .GT. 10 MICRONSt)
FURNAT (*+t80X*THETA 18 .GT. 0.005 RADIANS*)
FORMAT(*5*/*1*9A8/* LINE POSITIONS FOR FRAME*

5X6I2F5.X) /)

10%*)

A4,4X*MEASURED BY

1 t?A8)

FORMAT (*6PEN SEPARATION ON THE FILM =th.1* MICRUNS*)

 

153

9400 FOPWAT(*6THE FOLLOWING CALIBRATION CONSTANTS HAVE BEEN INPUT A
1 =1F11.5« R =*F15.10)

9500 FODMAT <* FIRST FRINGE IS No,.r5,8x *ROTATIUN ANGLE IS*F10.6* RAD!
1ANQt/t ROTATION FITS TO*6(F3*,*)* MICRONSi/‘OFRINGE SEPARATIONS IN
1 MICPONSt/(5X10F5))

9650 FOPMLT(*CALIBRATION CONSTANTS USED ARE*5X*A =tF11.3.5X*B =*F13.IU)

9651 FORWAT (*9wA9,F10,4,X,R1,F13,4)

9655 FOPNAT (/1OX*FRINGE NUMBER FREQUENCY*)

9701 FORWAT (tbr/tligAa)

302 FORWATI/2A8.18*CARDS*)
END

FILE.69
OVERLAY,S,3
FILE END
FTN.L.X
PROGRAM AVFHQ<FRO.NT5.NGPS.IDEMI
COMWON/l/IUPISI,ILSIBI.T0L1nTOL2.T0L3.A,B.LP.IDNT.ICALIIDON,J009
COVNON/3/NAME1IQUDU).NAME2(2000):NU(2000I,NMAx
CONNON/fi/AVGFREO(200),ANGT(200I.NUM
COMWON/7/ LL
C0ANON/8/ICHEAD(9).IHEA0(9.2).IDN(4)
COMMON/9/ CCATI8.5)
HINENSIUN FRQ<NGPS.IUEMI.NTS(NGPS.IDEN)
HIMENSION FRUTIIO).1(a).SIG(8).SNT(8),NIT(8)thV(d),NTT<8).F(1U)
EQUIVAIENCE (F,FHOT)
TYPI: INTEGER WTTANTSAWGTpWIT
TDL=0.1*TOL1
IFITOL.LT.0.0002) TOL:0,0002
MPHQCHzl
LL:1
AZFRU=A
13000533
AVLAST20.
NO§=0
N=NGPS+1
IFIJUMDI Go T0 2013
PRINT 260
PODIAT<1H9/1H1I
IFIIDNT) so To 1307
1 HEAD 160.13HEAO,IFDUNE
160 FQQNAT(10A8)
IFIIFDONF .EO. SHIDN HEAD) GO TO 1107
PRINT 160.ICHEAD
IFIIFDONE .NE. BHEND HEAD) GO TO 1
N = 1
NUH=0
1001 READ 161:(IHEAD(NaJ)oJ=1J2);A,B,INT
IFIN .E0. 1) 00 T0 1002
IFIIHEAD(N.2> .Eo. 8H DELETE) GO TO 50
IFIIHEAD(N.2) .EQ. 8H CHANGE) GO TO 55
IFIIHEAD(N.2),FQ.8H PUNCH) 107,108
107 ILTM=ILS(NM1)

I\)
O‘-

 

1107
1207

1307
103

100?

71

70
7?

77

78

154

PUNCH 106, (FRQ(NM1,J).NTS(NM1.J).le,ILTM)

60 TO 1001

U0 1207 J21:4
IDP(J)=ICHEAD(J)
GO TO 1

100(3):8H IDFNTIF $IDN(4)=8HICATIOV S GO TO 1

CUMTINUE
IF (N .GT. NGPS) GO TO 15
C()ALTI NIJE

CCDT(N,1)=.016 $ CCWT(N,2 :.062 $ CCWT<N:$)=,25 A CCWTIN14)=1,0

CCHTIN,5)=1,0

IPVINT:55

IF'A) 71:72

IAzA I 1XA:(A~IA)*1,E5 0 IR=B*1.ES S x0=u*1.E5 $
PUNCH 70, IA.IXA.IB.IXB
FOL’I'TAT(15X.I4,Y,IbagX;IS:X.15)
Il.:'ILT:ILS(N)

SIG(N):0,

DEV(N)=0.0

SNT(N)=0.

IF(ICAL .NE. 0) 00 TO 2

PRINT 261. ICHEAU.(IHEADIN;JI.J=1.2)
READ 10b. (FH0TIJ).NIT(J),J=1,8)
FURNAT(8(FB.4.91.X))

IFIFPGT) 73.82

IFIFROT(?)> 80,81
AZERO=1.EBtFRUT(?)+wTT(2)+FROT(3)w,1
AOhEzFRNTI4)+1.E~b*wTT(4)+1,F-bfiFRQTI5)
IFIA) 77,70

SLPPE : B/AONE

PRINT 79:1L. A,B

00 T0 2

PRINT 79:1Lo AZERO,AONE

lXB=(XB°IB)*1.E5

79 FOPMAT(*0FREOUFNCIES BEGINNING NITH NJMBtR*l4* WERE CALCULATED U81

81
83

73

74
76

106
75

5

00 T0 9

IFIFPNTI3))85,84
CCNT(N,1):FROT(6)
CCVTIN,2)=FR0T(5)
CC»T(N,3)=FROI¢4)
CCVTIN,4)=FEQTI3)
CCNT<N,5):FHUT(7)

00 T0 2

CONTINUE

IFIA) 74,75

00 /6 J=1,8
FRNT(J)=A+(FRUT(JI-AZER0)*SLOPE
PUNCH 106.(FHQTIJ)pWTTIJ).J=1;8)
FORMAT (8(4PF8,R1.X)I

00 12 0:1.8

IF (FRQT (J).E0. 0) GO TO 12

IF (ILT,E0. I) GO TO 1009

IF (FRO(N.ILT ~1) .LE. FROT(J)) GO TO 6
FRO(N,ILT)=FRO¢N.ILT-1>

100*/« THE FULLONINC CONSTANTS, A:*F11,5* b:*F12.10)

 

1009

10
12

2084

3084

710

1762
762

709
711
712
760

761
720

750

WTSIN,ILT)=WTSIN.1LT-1)

ILT = ILT - 1

IF (ILTIEQ. 1) GO TO 6

GO TO 5

FRO(N.ILT):FRQT(J)
NTQINIILT):NTT(J)

GO TO 10

FRQIN:ILT)=FRUT(J)
WTS(N:ILT)=WTTIJ)

IL = IL + 1

ILT = IL

IFIFQQT) GO TO 2

CONTINUE

IFIICAL .NE. 0) GO TO 3084
PRINT ?084.(CCAT(N.J),J=1,5)
FUQMAT (*UNEIGHT-CODE CORRESPONDENCE*/5X* CUDEth,*1*9X,*2*9X,*6*

19x,t4*,7xtaLANK*/* NEIGHTi5F10,4)

CONTINUE

ILT=ILT-I

FTOI:FR0(N.1)

FROIN,IL)=1,E30

ISAME=1

IDQOP=0

”C 750 J=1.ILT

WGT=WTSINIJI

IFIFRQIN,J+1)-FRG(N,J) ,GT. TOLl) GO TO 710
FTGTzFQOIN.J+1)+FT0T

ISAME:ISAME+1

IDPOP=IDROP+1

00 T0 750

AVF=FT01/ISAME

JTT=J-ISAME+1

IF(1PR1NT.LT.50) 00 T0 709

IPRINTzfl

IF(.N0T.A) 00 TO 1762

PRINT 76?,ICHEAU,(IHEAD(NaL).L=1:2):A:5:I0L1
GO TO 709

PRINT 76?,ICHEAD.(IHEAD(N,L),L:1,2),AZERU,AUNE:TUL1
FORMAT(1H1,9A6/1H0:2A8/t0 CALIBRATION CUNSTANTS A=tF11,5

1* P=.F12.10/*0 THESE FREQUENCIES ARE NITHINrF7,3a HAVE N08, 0F
2EACH OTHER AVERAGE*/)

IFIISAME-l) 71?,711
IFIIDDN.NE.1) 00 T0 720
PRINT 760. (FRO(NoK):NTS(N,K),K:JTT,J)
FOPMATI5IF11.4.X.R1))
[PRINT=IPRINT+(JTT-J*4)/5
PRINT 761,AVF
FOPMATI1H+.67XF10.4I
FRO(N,J-IDROP)=AVF
NTS(N.J-IDROP)=NGT
ISAME=1

FTOT:FRQ(N.J+1)

CONTINUE

ILT=ILT~IDRUP

 

2013

15
13

1013

QC
3?

34

66

 

1L9 (N) = ILT

IL=ILT+1

FROIN.IL>=1,E20

NM1:N

I\. z N + 1

GO TO 1001

CONTINUE

00 15 NI=1,NGPS
NILS:ILS(NI)

DO 15 J=1,NIL9
FR0INI.J)=A+B*FRO(NI:J)
Nzfl-T

IFIICAL .NE. 0) GO TO 1013
pRINT 261,ICHEAD

PRINT ?69, (1003(1):IDN (2),(IHEADIIH11),1H=13N))
PRINT 270,(IUN(3).IDN(4):(IHEAD(IH.2),IH=1,N))
PRINT 271

IPQT:0

CONTINUE

IFIA .E0, 0.) A:AZERU
IFIB .FQ. 0.) W=AONE

NMI : M - 1

00 20 J=1.N

IIJI=1
FS=F(1):FRO(1.I(1))
SISTzn,
WIT(1):NTS(1.I(1))

00 34 K=2,N
F(K)=FRU(K.I(K))

IFIFIK) .LT. IS) FS=F(K)
WIT(K)=NTS(K.I(K))
CONTINUE

AVG=AVN=0

ICNT=0

I030 36 K311N

IF(F(K)-FS nLE. TOL2) GO TO 35
F(K)=1.E20

NITIK):48

GO TO 36
XCNT:CNT(K,N1T(K))
AVG:AVG+F(K)*XCNT
AVN=AVN+XCNI

1(K)=1(K)+1

ICNT=ICNT+1

CONTINUE

AVG=AVG/AVW

IAVG=AVG

00 38 K=1.N

IFIF(K) .GT. 1.E10) GO T0 38
IFIICNT .LE- 1) GO TO 37
XCNT=CNT<KIWITIK))
0EVT=<AVG-F(K)I
SIGST=DEVT**2*YCNT
SIG(K)=SIG(K)+SIGST

 

 

157

SICTzSIGT+SIGST
OEVIK):DFV(K)+0EVT*XCNT
SNT(K)=SWT(K)+YCNT

37 F(K)=F(K)-IAVG
IF<F(K) .LT. 0) F(K)=1.+F(K)

38 CONTINUE
SIGT=80RTI(SIGTtICNTI/I(ICNT-l)tAVN))
IPRT:IPRT+1
IFIIPRT .LE. 50) GO To 370
PPINT 262.TOL2
PPTNT 261.10HEAD
PRINT 269. (100(IIII0N (2).(IHEADIIH.1>.1H=1;N))
PAINT 270.(100(3).IDN(4>.IIHEAD(IH.2);IH=1.N)>
PRINT 271
IPPI:1

370 CONTINUE

FPMG=(AVG-A)/R
IFIIPNT) 8250,8300

8250 CALL IIDENTIAVG)

8300 IFIICAL) 2000,2001

2000 NUN:NUN+1
AVGFPEOINUMI=AVG i AWGTCNUM):AVW
GU ID 1270

2001 PRINT210.NAME1(LP)INAME2(LP).FRNG,AVG,AVN.SIOT.(F(JIINIT(J),J=1,N)
IF(IOP(2).NE.2) GO TO 570
IFIIOON.EU.2) 1280:1290

1280 PUNCH 1210. NAMEI<LP),NAME2(LP).AVG
00 T0 570

1290 IFINAMEl<LPI .FQ. 8H ) GO T0 570
PUNCH 1210. NANElILP),NAME2(LP).AVG.AVW

570 CONTINUE

IFCAVG-AVLAST .GT. IOL2) GO TO 1270
IFIABS(AVG-AVLAST) .GT. TOL2) GO TO 1270
PRINT 270

1270 CONTINUE
AVLA§T=AVG

27 DO 28 J = lam
IF (IIJ) .LE. ILSIJ)) GO TO 32

28 CONTINUE
IFIICAL .NE. 0) 00 T0 60
GSIGT=0e
GAVN=0.

NUMH=U

DO 560': 1aN
NUM82N0M0+ILS(J)
DEV(J)=DEV(J)/SNT(J)
GSIGT=GSIGT+SIG(J)
GAVN=GAVN+SNT(J)

56 SIGIJ)=SORT(SIG(J)*ILS(J)/(ILSIJI-1)/SWT(J))

GSIGT=80RTIGSIGT*NUMB/(NUM8~1)/GAVN)
PRINT 235.(DEV(J).J=1,N)
235 FORMAT(*0 AVERAGE DEVIATIONtSOX,8(3XF7.4))
PRINT 230.GSIGT.(SIG(J) ..J=1.N)
23o FORMAT (. STANDARD DEVIATIONt24XF7.4p2XF/.4:7(3xF7.4>)

 

240

5

O

51

52

53

1054

1053

1055

54

60
9500
161
210
261
262

269
270

158

PRINT 240.(ILS(J),J=1.N)

FORMAT (. NO. OF LINES MEASURED*26X.8(6XI4))
PRINT 262.TOL2

GO TO 60

CONTINUE

00 52 K=1IILT

IFIABSIFRO(NM1.K)-A) .GT. TOL) GO TO 52
DO 51 J=K.ILT
NTS<NM1.J)=NTS(NM1:J+1)
FRO<NM1.J)=FROINM1.J+1)
ILS(NM1)=ILS(NMl)-1

ILT=ILS(NM1)

GO TO 1001

CONTINUE

PRINT 280.A.IHEAD(N.2)

GO TO 1001

CONTINUE

DO 54 K=1.ILT

IFIARS<FRO(NM1.K)-A) .GT. TOL) GO TO 54
IFIO .LT. FRC(NM1.K)) GO TO 1053

DO 1054 KOK=K,ILT

IFIB .CT. FRU<NM10KQK+1)) GO TO 1054
WTS(NM1’KQK)=IWT

FPOINM1,KOKI=0

00 TO 1001
FRO(NM1;KOK)=FRO(NM1IKQK*1)
NTSINM1.KOK)=WTS(NM1aKOK+1)
IRQ(NM1,ILT)=B

NTS<NM1;ILT)=INT

00 TO 1001

KMI=K~1

DO 1055 KOK=1,KM1

KQM=K-KOK

IFIB .LT. FRO(NM1.KQM)) GO TO 1055
FRO(NM1.KOM+1)=B

WTS(NM1oKOM+1)=INI

GO TO 1001
FRO(NM1.KOM+1)=FRQ(NM1.KOM)
NTS(NM1.KOM+1)=NTS(NM1.KOM)
FRO<NM1.1)=B

WTS(NM1.1)=INT

GO TO 1001

CONTINUE

PRINT 280.A,IHEAD(N;2)

GO TO 1001

CONTINUE

RETURN

FopNAT (2A8.4x.2E15.10.X.R1)
FORMAT<1H1.10A8/1H02A8/1H0)

FOPMAT (*ONOTE.. LINES ARE ASSUMED TO BE THE SAME IF FREQUENCIESt/

1* ARE NITHthF7.3w NAVE NOS. OF EACH OTHER.w/*5*)

FORMAT (wow2A8.2XrFRINGE AVERAGEt1OX*STD.*2X8A10>
FORMAT (1X2A8,2X*NUMBER FREQUENCY WGT. DEV.*2X8A10)

 

 

A

60
70
90

50

 

159

FOPMAT (1H )

TOPMAT (*+ IDENTIFICATION*)

FOPMAT (*+*35X.1H?)

FORMAT(*FREQUENCY OFrF10.4* NAS NOT PREStNT T0*A8)
FORMAT<2A8.5X.F13,4.7x,F4,2)

IONMAI (1018)

FMD

FUNCTION CNT(IA.IB)
COMMON/9/ CCWT(8.5)
IFTIB.E0.0) GO TO 3
IF(IR.GT.4) GO TO 4
CNT=CCNT<IA,IH)
RETURN

CwT=1.E=20

RETURN
CNT=CCNT(IA;5)
HFTURN

END

SURROUTINE IIDFNT(AVFREQ)
COMMON/1/10P(3),ILS(8),T0L1,T0L2.TOL3,A,B.LP.IDNT.ICAL.IDON,JuMP
COMMON/5/NAME1T2000).NAME2(2000):NUI2000).NMAX
COMMON/7/ LL

TYPE RFAL NU

LP:NMAX+1

X=AVFREQ-NU(LL)

IF(ABS(X).LE.TOL3) 50.60

IFIK) 70.70.90

RETURN

LL=LL+1

IFILL.GT.NMAXJ IDNT=0

GO TO A0

LP=LL

IFTABSTAVFREO—MU(LL+1)),LE.TOL3) LP=NMAX+2
RETURN

END

FILE169
OVERLAYJ404

FILE

END

FTN.L.X

PRnGRAH SEARCH
COMMON/1/10P<3).ILSIB).T0L1.T0L2.T0L5.A.B.LP.IDNT.ICAL.ID0N,JUMP
COMMON/S/NAME1T2000).NAME2(2000>.NU(2000),NMAX

COMMON/4/ FNUMI200)pFREQ(200).NT(200)45UMWHTsNODATA,INDATA
COMMON/S/AVGFREQ(200).AwGTczon).NUM

DIMENSION IDENT1(200).IDENT2(200)

TYPE RFAL NU

READ 2. NUMLINES

SUHNHT=NODATA=INDATA=0.0

L=1

LT=1

 

 

 

50

U‘:

P7

31
32

54
91
33

3am
301
An

4.

.3

49

50
59

6

C)

6?
64

160

READ 1,IIDENT1.IIDENT2,XFNOM
IFIXFNHM,E0,0.0) 00 To 27
IFTL.E0.1) GO TO 6
IFIFNUM(LT-1).LE.XFNUM) Go To 6
FNHM(LTI=FNUM<LT-1)
IDENT1(LT)=IuENT1(LT-1) 5 IDENT2<LT)=IDENT2(LT-1)
LT=LT-1

IFILT-l) 6.0.5 _
FNUM<LT)=XFNUM%IDEN11(LT)=IIDENT1$IDEVT2(LT)=IIDENT2
L=L+1 $ LT:L 5 GO TO 30

LMAX=L-1

IL:LMAX

TFTLMAX,LT.2) GO TO 1000
SUHX=30MY=SUMXY=SUMX2=0.0

11:0

|_[_:1

00 50 L=1.LMAX

Do 49 N=1,NMAX
IF(IDENT1(L).EO.NAME1(N)) 31.49
IFTIDENI2(L).t0.NAMt2(N)) 32.49
X=FJUM(L)-AVGFWEO(LL)
{F(ABS(X).LE.1.U) 36.34

[F(X) 49,49,91

LL=LL+1 T IF<LL.GT.NUM) GO TO 52 S GU T0 62
FNHN<L>=AVOFREO(LL)
WTfL)=ANGT(LL)

FRFU(L)=NU(N)
QU”WHT=SUMWHT+WT(L)

IFTNT(L)) 300.301
NODATA=NOUAIA+1

NUM=NUM-1 0 II=II+1

00 41 K=LL.NUM
AVCFWFO(K)=AVGFRFO(K+1)
ANCT(K)=AWGT(K+1)
SUVX=SUMX+FNUM(L)
SUMV=SUMY+FHE0(L)
SUWXY=SUMXY+FNUMTL)*FREQ(L)
SUMX2=§UMX2+FNUM(L)#FNUM(L)

GO TO 80

CONTINNE

IL=IL’1 $ IFTIL.LT.2) GO TO 1000
CONTINUE

IF!II.LT.2) 00 TO 1000
D:II*SUMX2-SUMX*SUMX
A:(SUMY~SUMx?-SUMX*SUMXY)/D
B=(II*SUMXY-SUMX*SUMY)/D

LL=1

D0 ZUU IT=192

Do 100 1:1,NUM
FRO=A+RiAVGFREO(I)

X=FRO-NU(LL)

IF(ABS(X).LE.TOL3) 76,62

IFTX) 100,100.64

LL=LL+1 $ IF(LL.GT.NMAX) 00 T0 101 $ GO TO 60

 

 

76

400
401

51

80

100
101
200
201

550

1000

500
600
1001

99
110
115
495
501

120

161

II=II+1

FRFU(II)=NU<LL)
FNUMIII)=AVGFRFO(I)
NTIII):ANGT(I)
SUHNHT=SUMHHT+NT(II)
IF(NT(II)) 400.401
NODATA=NODATA+1

NUH=NUM-1

00 51 K=I,NUM
AVCFREQ(K)=AVGFREQ(K+1)
ANGT(K)=ANGT(K+1)

1:1-1

SUMX:SUMX+FNUM(II)
SUMY:50MY+FREO(II)
SUMKY:SUMXY+FNUM(II)*FREQ(II)
SUMX2=5UMX2+FNUM(II)*FNUM(II)
U:II*SUMX2-SUMX*SUMX
A=(SUMY!SUMX2-SUMX*SUMXY)/D
B:(II*SUMXY-SUMX*SUMY)/D
CONTINUE

IFIII.LT.NUMLINES) 200.201
CONTINUE

INnATA:II

CALL CALFIT

PRINT 500.1NUATA,NUMLINES

DO 550 K=1IINDATA

PuNCH 600,FRFO(K),FNUM(K).HT(K)
RETURN

PRINT 1001

RETURN
FORMAT(2A8.13X.F10.53x.A8>
FORMAT (110)

FORMAT (.2 «15* LINES OUT OF ~15. HAVE SEEN FOUND AND ENTERED*)
FORMAT (2F15.4,F15.2)
FORMAT(*2A WRONG IDENTIFICATION 0R FRINGt NUMBER HAS BEEN INPUTw)
END

SURROUTINE CALFIT
COMMON/1/IOPI3I.ILSIa),T0L1,T0L2.T0L5.A.B.LP.IDNT.ICAL.100N.JUMP
COMMON/4/ FRINGEI200I.FREOI200I,wHTI2ooI.suMNHT.NonAIA.INDAIA
DIMENSION coth3I.DATA<s>,IHI1o>.INnex<3>,SIGMAISI,sIGM00I3).
lVECTOR(4.4)pIHEAD(2)

DATA (IHEAD=8H CONST.8H SLOPE)

TYPE DOUBLE COEN,SIGMA.SIGY,VECTOR

PRINT 3

FORMAT(*1*)

PEADZ.IH$IF(IH(10).EQ.8HLAST FITISTOPIIFIIHI1oI-BHEN0 HEAD>110p115
PRINT 2:IH$GO TO 99

PRINTZ.(IH(II.I=1.9)$NDEL=0
DEVMAX=FLEVEL=VAR=0.0$NOIN=K=NOENT=NOMIN=NOMAX=0
AVGNHT=SUMNHTlNODATA

no 120 1:1.16

VECTORCI >=n.0$nATA=1,o

DO?20N=1.INDATA

220

792
794
010
600
830

1000
1002
1010

1017
1020
104?
1060
1080
1100

934
1170
1160
1110
1210
1050

905
1240
1310
1311
1313
1514

71

72
1320
1340
1550

1370
1391
1392
1400
1430
1440
1410

1480

162

wT:NHT(N)/AVGHHT$DATA(2)=FRINGE(N)$DATA(5)=FREO(N)
9072012195$VECTORI1:4)=VECTOR(Ia4I+DATAII)*WI$DOZZUJ=113
VECTOR(I;J)=VECTORII:J)*DATA(I)*DATA(J)*NT

VECTOR(4,4)=NODATA $PRINT900NODATAtAVGWHTJVECTOR<204)l

1VECTOH(3)4)IVECTOR(212)IVECTOR(203)’VECTUR(3Q3)$NOSTEP=’1

0EFR:VECTOR(4,4)-1.0$00800I:1;3$IF(VECTOH(I,1)) 792,794,810
pRINT795.I%GOT0100
PRINT795.I£SIGMA(I)=1.0$GOT0800
SIOMA(I>=0300TIVECT0R<I,I))
VECTORII.II=1.00008301:1.2$IP1=I+1000860J:1P1,5
VEPTORIJ,II=VECTON<1.J)=VECTOR(I.J)/SIGMAI1)/SIGMA<JI
PRINT60;VECTUH(2;1):VECTOR(301):VECTON(3(2)
NORTEP=N05TEP+IIIFIVLCTOR<3.3)31002.1002.101U
NSTPMI:NOSTEP-1$PRINT1004.NSTPM1$GOT01381
SIGY:SIGMA<5)whSORTIVECTORI3.3)/0EFR)IDEFR=0EFR-l.0
.FfflFFR) 1317,1017,1020
pRINT1019,NOSIFP¢GOTOI381
VAIIvaszu.nINOINzoIOOIO5nI=1.2$IF(VECTUR(I:1))
PRI1T1044,I.NOSTLPIOOT01381
IF<VECTUR(I.I)-0.0001) 1050.1000.1080
VAR=VECT0R(I;6)*VECTOR(SII)/VECTOR<I;I)$1F(VAR)1100.1050,1110
NOIN=NOIN+1£INHEXINOINI=I$OOFNINOINI=VECIORII.5)*SIGMA(3>/SIGMAII)
SIQNCO(NUIN)=DSURT(VEcTOR(I.I))tSIGY/SIGMA(I)

IFIVMIN) 1150,1170.904

PRIVT906$GJT0100

VMIN:VAR$NOMIN=I$GOT01050

IFIVAR-VMIN>1080,1050,1170

I?(VAR-VMAX)1050,1050,1210

VWAX:VAR$NDMAX=I

COuTINUEIIFINOIN>903.124U,1310

PRINT907$GOT0100

DQI1T05,SIGY*00T01350

IX=6HENTFRIN0$IF(NOtNT)l511:1311:1313

IxdeRFNOVEU

PRINT91.NO§TEP,IX,IHEAD(K)

PRINT 70.10EA0IK).FLEVEL.SIGY

no 71 J=1.NOIN

JK=INOEX(J)

pRINT 72.IfiEA0(JK)ICOEN(J),SIGMCO(J)

A=COENC1I 6 0=COFN(2)

FORMAT (A17,F10.10,F16.10)
FLEVEL:VMINtnEFR/VECTOR(5:3)$IF(FLEVEL+090000001I1550.1350.1340
K=NOMINONOENT=0$GUT01391

FLEVEL:VMAXw0EFR/(VECTOR<3,6)-VMAX)

IFIFLEVEL=0.0000001I 1380,1370.137n

N0ENT=K=NOMAX

IFI<>1392.1392.1400

PRINT1395,NUSTEP$GOT0100
VK=1.U/VECTOHIK.K>0001410I:1.3$IF<I-KII4éOI1410

001440J=1.5
IFIJ.NF.K)VECT0R(I;J)=VECTOR(I.JI=VECIOR<IoK)*VECTDR(KIJI*VK
CONTINUE

00 1480 1:1.3

IFII.NE.K) VECTORII.K>=-VECTOR(I.KIwVK

10429105091060

 

1520

1.560
1331
1580

1630

1610

1660

1624
1620

100
1

2
60

65
70

90

91
795
795
906
907

1004
1019
1044
1395
1506
9000

9001
9050

1?
75 FQPMAT

163

PO 1520 J3133

IFIJ.NE,K) VECTOR(K.J):vECT0R(K,J)tVK

VECTORIK,KI=VK¢GOT01000

PRINT 79,NOSTEP

CONTINUE
PRINT1506.VECTOR(1:1),VECTOR(2o2)$VFIT=0t$DATA=lI$001600N=1,INDATA
NTszTIN)N0ATAI2)=FHINGE<NI$YPRED=O,050016301:1.NUIN
YP0E0=YPRE0+COENIIIvUATACINDEXTI)ISva=FRE0(N)-YPRED
VFIT:VFIT+NTiDEVtfiEV$PRINT905U,NIDATACZ)oFREU(N)aYPREDIDEV:NT
ADCV=NT*DEV*0EV$IF(ADEV-DEVMAX11660,161011610

NMAX:N

DEVMAX2ADEV

CEJVT'INIIE

VFIT:VFIT«NODATA/<NOUATA-2.0)/VECT0R(4I4)
STOFITzDSORI(VFIT)SPRINT1,VFIT.STDFIT

IFcb-NOEL)100.100,1624

IFIOEVMAx-0,0000?5)100.100,1620
UfifiLzNDEL+l$NODATA=NODATA-1$SUMWHT:SUMWHI-NHI(NMAX)$WHT(NMAX):0,0
PRINT 0001,NMAX

00 T0 495

RETURN

FONAAT (*UVAHIANCE =*F11.0/* STD. DEV. :*F8.4/*7*)

FORWAT (1000)

FORMAT (*OPAHTIAL CORRELATION COEFFICIENTS*9X*CONST FRINGE*/28X*

1FHINGEiFIZ.4/28X*FREQUFNCY*2F9.4)

FQQNAT (*OSTANUARD ERROR OF Y IS*F1225)

FORMATI* F LrVEL OFtR6.E11.2/* STD DEV 0T

COEFFICIENT STD. ERROR*/)
(*OCOMPLETED*12* STEPS 0F REGRESSIONr)

(O'P)*&1192//10X*VARIABL

FJH40T(*-CALIBRATION FIT OF*I4* LINEst/tflwEIGHT NU?MALIZATION:F5.2
1/* SUM OF FRINGE NOS, IStF12.4/~ SUM OF FREQUENCIES ISIF12.4/*0RAN
1 3909 MATRIX FRINGE FREQUENCYt/t FHINOEtF18,2/* FR
ZLQUENCY*?F15.2)

FORMAT (*OSTEP NO,*12* VARIABLEtA9,A8)

FORMAT (*ERROR RESID. SQUARE VAR,*12* IS NEOATIVt. SO LONG.)

(*0VAHIABLE*I2* IS CONSTANTt)
(*UERRUR, VMIN PLUS. 80 LONGi)
(*UtRROR, NOIN MINUS. SO LONGt)
(*OY SOHARE NON=POSITIVE, TERMINATE STEPtlz)
(*UNO MORF DEGREES FREEDOM STEPtIZ>
(*USOUARE Xotllw NEGATIVE. SO L0N0*12v STEPS.)

FOQWAT
FORMAT
FORMAT
FORMAT
FOWMAT
FTHLWAT

FORMAT I*0K=0 STEP*12*, SO LONGt)

FORMAT(*OOIAGONAL ELEMENTS*5X*CONST*F9.4/23X*FRINOE*F8.4/*1*10X*RE
180LTS*/*0 RUN FRINGE FRFQ OBS FREQ CALC OBS-CALC wHTt/I
FORMAT (3F15.27XA8)

FORwAT <*+OELETING LINE NO,*14)

FORMAT II4.F10.4,2F11.4.F9.4,F6,2)

END

 

164

B. DIFF
This program reads and stores punch output from SHAFT
and obtains the A-doublet splittings, and the weighted
average of all possible rotational combination differences,
vibrational differences and spin-orbit differences. Average

A-doublet frequencies are calculated and punched.

STRUCTURE OF DATA DECK

I. Frequencies

 

Up to 600 lines may be input.

 

 

Eel; Field Variable
l I Upper vibrational state of line.
9 R Branch of the line (P, Q, and R).
10 R Subband (l, 2, H, L).

12-13 I Lower state J value times 2.
16 R +/— indicating A-doublet component.
20-33 F Line frequency.
41-44 F Weight of line.
73-80 A "END DATA" signals end of data.
II. Options

1. EBEEE.EE£§L PUNCH in cols. 76-80 indicates that punch
output of difference is desired for input to fitting programs.
2. Heading cards: Cols. 1-72 are printed until END HEAD is
encountered in cols. 73-80. The last card is-printed at the

tOp of each page.

 

165

3. Any of the following may appear:

 

a) RTCOMDIF in cols. 73-80 indicates that rotational
combination differences are desired. In the first 8
cols. of this card a tolerance may be read, equal to
0.001 times the integer number appearing. This is used
to print a flag if two or more differences are averaged
which differ by more than this number.

bl VIBRADIF in cols. 73-80 indicates that Vibrational
differences are desired.

EL SPORDIF1,2 in cols. 73-80 indicate that spin-orbit
differences are desired, for the ground and excited
vibrational states respectively.

d) END CALC in cols. 73—80 terminates execution.

(Note: If A—doublets are present in the input data, a punch
output of the average frequencies is automatically given in
the frequency input format.)

A listing of the program follows.

 

165

3. Any pf the following may appear:
EL RTCOMDIF in cols. 73—80 indicates that rotational

combination differences are desired. In the first 8
cols. of this card a tolerance may be read, equal to
0.001 times the integer number appearing. This is used
to print a flag if two or more differences are averaged
which differ by more than this number.

EL VIBRADIF in cols. 73-80 indicates that vibrational
differences are desired.

21 SPORDIF1,2 in cols. 73—80 indicate that spin-orbit
differences are desired, for the ground and excited
vibrational states respectively.

d) END CALC in cols. 73—80 terminates execution.

(Note: If A-doublets are present in the input data, a punch
output of the average frequencies is automatically given in
the frequency input format.)

A listing of the program follows.

166

PROGRAH “IFF
COMMON/llNU(GDn),NGT(600).JU(600),JL(600),VU(600):SU(600)nSL(600):
1JUHP.N.DSOUIFF(1WO.1).SODIFF(100.5):DNT(100:1):WT(100,3)
COMMON/2l LAMUA(SOO):ISUR(600)
COMMON/SI i“'CUDE(:‘;). IPUN
COMMON/4/ TOL
DIMENSION ICUDF(10)
TYPE REAL MU
TYPE INTEGER VU,SU.SL,RRANCH:5TP
M31
NLINES=NT0TAL=0
1 READ 2,VH(N).HRAACH.ISHB(N1,JLd.rAMDA(N),NU(N).WGT(N),STP
IFtsTP,EQ.nHENn KATA) GO In 20
JLN=(JLN+1)/?
IFCBRAMCH'1R0)3.4.5
3 JUIN)=JLN"
GO TO 6
4 JU(N)=JLW
GO TO 6
6 JUCN)=JLN+1
6 JLIN)=JL4
IFIISUHIN)-2l 8.9111
8 SUKN)=SL(N)=1 ¢ 80 T0 7
9 SUIN):SL(N)=2 ¢ 50 TO 7
11 IFIISUR(N).EU.1RH) 12.13
19 SL(N)=1 % SU(N)=? I GO TO 7
12 SLIN)=? $ SUIN3=1

7 N=N+1
GO TO 1
2a N=M-1

DO 10 LL=1:N
lF‘LAMUA(LL).NF.1R ) 15:10

15 CALL LAMDAWIF
Go To 95

in CONTINUE
GO TO 100

95 pRINT 50
PRINT 51
DO 18 1:1,,“
BRANCH=JU(I)*JL(T)+40
JLOWER=2*JL(I)'1
PRINT 300p VU(I),BRANCH:ISUB(1)pJLOWER,LAMDA(I):NU(1):WGT(I)
PUNCH 301: VU(I),BRANCH:ISUB‘1)1JLONER:LAMDA(I):NU(I)ANGT(I)
NLINEszNLINES+1
NTUTAL=NTOTAL+1 .
IFCNLINES.GE.5n) 17:18

17 PRINT 53
PRINT 51
NLINES=0

1q CONTINUE
pRINT 549 N

100 JUMP=0

IPUN=0
ASSIGN 75 70 N60

-q—‘wfl—fl

70

100”

7:
an
96

20”
201

10?
103

104
105

105
107

103
109

11a
2
5m

51
53
54
101
15“
300
301

16}

READ 1n1. ICDUE

IF‘ICOUE(1D).E0.9H PUNEH) GU ID 1000
GO T0 N60

IPUN=1

so To 70

IF!ICODEI1h)’8HEAD CALC) 6n.110
IFCICOUE(1n) .FQ. RHEND HEAD) 30 T0 200
PRINT 150: (ICODE(I).I=1,9)

GO TO 70

ASSIGN 102 TD NBC

NO 201 181,9

NCODE(I)=ICOHF(I)

GO TO 90
IF(ICODEClh)-UHRTCOMDIF)104.103
TOL=,UU1*ICOUE(1)

CALL RTCOMDIF

GO TO 100
IF(1C0hE(1n)-UHSFORDIF1)106.105
TOL=.001* ICUDF(1)

CALL SPORDIF1

GO TO 100
IFCICUDE(1n)-8HVIBRADIF)1UR.107

CALL VIBRADIF

GO TO 100
IF!ICOUE(1n)-UHSPORDIF2)110,109

JUMP=1

CALL SPORDIF7

GO TO 100

CONTINUE

FORMAT (11:7X17R19X112:2Y’R136x’F1304D7XIF402129X1A8)
FORMATttiTHE FOLLOWING FREQUENCIES ARE THE AVERAGE LAMDA DOUBLFT F

1REOUENGIES¢)

FORMAT(///w v LIVE FREQUENCY NGT*)
FORMAT (*1*)

FORMAT (tOAFTER AVERAGING. IHth ARE*IS* FREQUENCIES*I*5*)

FORMAT (10A8)

FORMAT (9A8)
FORMAT‘4X!11*"n*:7x32R193Xp129*/2*:1x39104XQF10.404XIF1002)
FORMAT(11t-0t5X,2H1,X,12*/?*R1p3XoF13.4:7X:F4o2)

END

SUBRQUTINE LAMDAFIF

C CALCULATES THE LAMBEA SPLITTINGS AND THE AVERAGE FREQUENCIES

T'“T “WW F'j

COMMON/ilNU(600).HGT(600)pJUC600):JL(6OD):VU(600)oSUCéOO).SL(6DO)o

1JUMPnNaUSODIFFfln0p1)aSOnIFF(100p3)oDNT(100:1)oNTC10013)

COMMON/Z/ LAMDA(600)JISUQ(600)
COMMON/3/ NCODE(9)9 IPUN

TYPE INTEGER VU:SU:SL:RRANCH
TYPE REAL NU

PRINT 60

NTQTALflNLINES=n $ NMAX3N

PRINT 51

Do 50 1:11“

3131*1

168

 

no 50 J=II.N
Trcvucl).NE.VUTJT) 00 T0 50
3 TFTJUTT).NE.JU¢JT.UR.JLTT).NE.JL<J)> 00 T0 50
I IFISU(I).NE.SU(J).OR.SL(I).NE.SL(J)) so To 50
I IF(LAMDA(I).E0.1Q~.0R.LAHDA(I).EQ.TR+) 100,50
100 TFTLAMNATJT.E0.1R—.0R.LAN0A<J).E0.1R+a 101.50
‘ 101 XLAMDIP=ABSTNUTIT«NU<JT)
NU(1)=(NU(I)¢NU(J))/2.0
‘ NGT(I)=2*HGT(I)tWGT(J)/(NGT(I)+NGT(J))
LAHDA(!)=1Rw
‘ N=Nvi
‘ DO 30 L=JIN
LAMDA(L)=LAMDA(L+1)
ISUB(L):ISUB(L+1)
vu<L>=vuch1>
JU<L)=JU(L+1) T JL(L)=JL(L+1)
SU<L>=SUTL+1> m SL(L)=SL(L+1)
NUTLT=NUTL+1>
30 weTcL>=wGTTL+T>
JLONER:2oJL<I)-1
BRANCH=JU<T)—JL<T)+40
PRINT 55.VUTI).80ANCH.TSUBT13.0L0NER.NU<I).XLANDTF.NGT(T)
PUNCH SSSoVUfI);BRANCH.ISUR<I).JL0wER.NU(I):XLAMDIF.WGT(IJ
NLINES=NLINE5*1
NTOTAL=NTOTAL*1
TFcNLTNES.GE.5n> 52.50
52 PRINT 53
PRINT 51
NLINES=0
CONTINUE
PRINT 54. NMAX.NTOTAL
RETURN
51 FORMATtll/o v LINE FREQUENCY' DIFF.!gX'HT.*)
53 FORMAT (01¢)
54 FORMAT (tOFROM A TOTAL or .15: FREQUENCIES. A TOTAL or 015/: LAMD
1A DOUBLETS HERE rou~no/*s«)
55 FORMAT(15*-O*.SX.291.3X.IZ.¢/2*.F15.4.F10.4.F10o2)
50 FORMAT (.1TABULATED BELON ARE THE AVERAGE LAMDA DOUBLET FREQUENCIE
isal. AND THE DOUBLET SEPARATIONt)
355 FORMAT(!5¢a0*,2X.291.2X.12.*/2t:2X.F15.4-F10,4n5x.F10.2)
END

5

:3

SUBROUTINE RTCOMDIF
c CALCULATES THE ROTATIONAL CQMRTNATION DIFFERENCES
COHMON/i/NUCéon).HGTCéOO).JU(600).JL(600>.VU(600)eSU(600)oSL(6DD).
1JUMP.N.DSODIFF¢1OOTI)'SODIFF(100a3!
COMMON/Zl LAHDA(600).ISUB(600)
COMMON/SI NCODE(9). IPUN
COMMON/4/ TOL
DIMENSION DcDIFF¢150.2.1).CDTFF4150.2.3).DuTt150.2.1).NT1150.2.3)
DIMENSION DTTEST¢150.2.1).TTEST1150.2,3)
TYRE INTEGER v.s.vu.su.sL
TYaE REAL Nu
TNeo

 

 

2000

21

23

24
25

26
27

35

36

37

38
39

169

BB 2000 14'10150

DO 2000 IBI1o2

DO 2000 1C31N.3

ITEST(!AUIBaIC)31R
PRINT 53
PRINT 51

DO 50 1:1»N
IFILAMDAtli.NE.10*.AND.LAMDA(I).NE.;R ) GO TO 50
1191*1
DO 50 JSlInN
IFCLAHDAIJ)éNE.1R*oAND.LAMDA(J).NE.$R ) 30 T0 50
IF‘SU‘!)9NEOSU‘J)oORQSL‘!)9NEQSL‘J)’ GO TO 50
1F¢VU(X).NE,VU(J)) GO TO 50
IF‘JU(!).NEqJU(J)) GO TO 35
V30
S=SL(I)

IFQJL(I).EQQJL(J)*1)21122
K31
CD!NU(J)3NU(!)
NAT:2.NGT<I)rwGTIJ)/(NGT(II+HGT(J))
JJIJL(J)
GO TO 48

IFtJL(I).ED.JL(J)*1)23024
K31

CD!NU(I)9NU(J)
NAT=2*WGT(!)*NGT(J)/(HGT(I)+dGT(J))
JJIJL(!)

GO TO 48

IF(JL(I).EO.JLlJ)+2)25a26
K=2
CDINU(J)2NU(I)
UAT=2*NGT(I)‘NGTfJ3/(WGT(I)+dGT(J))
JJIJL(J)

GO TO 48

IFCJL‘X).EG.JL(J)-2)27,50

K=2

CD'NU(I)9NU(J)
HAT=2*HGT(I)*NGT(J)/(HGT(II+NGT(J))
JJaJL(1)

GO TO 48

IF!JL(!).EQ.JL(J))36050
V=VU(I)
S:$U(I)
:FIJU(I),E0.JU(J)*1)37038

=1
CD!NU(I)9NU(J)
HATE20HGTC!)*NGT(J)/(HGT(I)+MGT(J))
JJIJU(J)
GO TO 48

IFfJU(!).50.JU(J)‘1)39A40
K81
CDHNU(J)BNU(I)
HAT:2*UG7(!)*HGT(J§/(HGT(l)+dGT(J))
JJ!JU(1)

40
41

42
43

4B

155

49

50

1000

52

60
51

53
54

170

GO TO 48

IF‘JU‘I)UEQoJU¢J§*2)41042

K=2

CD!NU(!}9NU(J)

HAY§2*NGT(I)*NGT(J)/¢NGT(I)*dGT(J)0

JJ!JU(J’

GO To 48

IF‘JU(109500JU¢J392)43;50

K=2

CD!NU‘J)9NU‘!)

WA7§20NGT(I)’NGT(J)/(NGT(IQ+HGT(J)0

JJsJUII)

DELJ!(K~1)*50+JJ

JLONERlzidd'l

PRtNT 155:3;VoKtJLOHERACDAUATaNU‘I):NU(J’

FORMAT10 flax:‘1'6XaliaGXb1136X:I200/2.13XUF3.404X.F4¢2;2F1094’
IF‘NT‘DELJ-ScV)oNE9000) 60 To 49

NT‘DELJ180V0'NAT

CD!FF(DELJOSQV)=CD

GO TO 50

IF¢AB$F(CDIFF(DELJaSnV)'CD)cGTqTOL, ITEST(DELJ15¢V)318*
CD!FF(DELJ;$0V)3(CDIFFQDELJ:5:V).NT(DELJOSgV)¢CD*NAT,Z(HT(DELJ:50V

1’tNAT)

WTCDELJ:S:V)'HT(DELJ050V)*UAT

CONTINUE

PRtNT 53

PRINY 1500 NCODE

PRINT 51

NJCO

NLINESIO

~T0T0L30

DO 60 5:112

00 60 V3NJ03

D0 60 K8102

DO 60 JJ31050

DELJI(K91)NSO+JJ

IF‘CDIFF0DEL4151V),5000900 GO-YO 60

JLOHER a 29JJ-1

PRINT 55:50V0K3JLOVER00DIFW(DELJUSoV)0ITEST‘DELJaSoV)aHTKDELJASJV)
IF!.NOT.!PUN’ GO TO 1000
PUNCH355nSonKnJLOHER9601EP(DELUnSoV)p175370DELU050V’1HT(DELJ950V)
NL!NES'NLINES*1

NTOTAL!NT07AL*1

IFCNLIN55055950) 52:60

FRINT 53

NLlNESIO

PRINT 1500NCODE

PRINT 51

CONTINUE

PRXNT 540N0NTOT‘L

FORMAT (I/IiflXwSUB'4X'VI3*EX.DELTA‘GX*J'7XOCDH*7X*HT.0/9X*STATE*

12X¢STATE*20X*DIFPo*///)

FOfiMAT (.10)
FORMAT (*0 FROM '13: INPUV FREQUENGIES A TOTAL OF «131* COMBINATI

 

55
150
355

C CA

2

O

2

r‘

40

41

42

50

 

171

1°N DIFFERENCES WERE FOUND'I‘5*)

FORMAT(* filoxA11.6X;11.6X.[1:6X.12.'/2*-3X.F8.4,1R1.3X,F4,2)
FORMAT (9A8,

FORMAT(3151161./2*F1304’1R1D4XIF602)

END

SUBROUTINE VIBRADIF

LCULATES THE VIRRATIONAL DIFFERENCES
COMMON/1/Nucéon).NGT(600).JUIboO),JL(600).vutaoo);SU(600)¢SL<600).
1JUMPINDDSODIFF‘10091)ISODIFF‘lOOIS,

COMMON/2! LAMDA(600)-ISUR(600)

COMMON/SI NCODE(9)A IPuN

DIMENSION UVDIFFI200.2.1).VDIFF(200.2.2)oDNT(200o2.1).HT(200.2.2)
TYPE REAL NU

TYPE INTEGER VUOSUOSLISDV

00 5O I=1pN
IFtLAMDAtI).NE.1R0,AND.LAMDA(I).NE.1R ) Go TO 50
1181.1

DO 50 J=!I.N
IFtLAMDA(J).NE.1Rt,AND.LAMDA(J).NE.1R I GO TO 50
IFTSU(I).NE.SU(J).OR.SL<I).NE.SLIU)) GO To 50
IFIJU(I).NE.JUIJI.0R.JL(I).NE.JL(JI) so To 50
K=1

1F(VU(I)!VU(J)) 20.50.21

IFIVUIJ).E0.VU(II*2) K=2

VDENU‘J)HNU(I)

V=VU(I)

JJGJU(J)

S=SU(I)

GO To 40

IFlVUtt).EQ.VU(JI*2) K=2

VDBNU(I>-NU(J)

V=VU(J)

JJnJUIJ)

S:SU(I)

INDEX=(K-1)fi100+JJ
HAY:2*NGT(!)*NGT(J)/(NGT(I)+NGT(J))
IFIUT(INDEX.S.V)I42.41

VDIFF(INDEX)S:V)3VD

UTtINDEXAS.V)=HAT

GO TO 50
VDIFF(INDEX,S.V)I(VDIFF(INDEX:SAV)tNT(INDEX:S.V)+VD*WAT)/(HT(INDEX
1.8.V)*HAT)

NT!INDEX.S.V)=NT(INDEX.S.VI+NAT

CONTINUE

PR!NT 51

NLINES=0

NT0TAL=0

ASSIGN 60 TO NGO

DO 60 8:102

Do an v=1.3

D0 60 K=1I2

DO 60 JJ=1.50

INDEX=(K-1)*100+JJ

 

 

C

172

IF(VDIFF(INDEX.5.V).E0.0.OI GU T0 60

JLOHERaZtJJwi
PRINT 55.5.V1K.JL0WER:VDIFF(INDEX.S.V),NT(INDEX.S.V)
IF(.NOT,IPuN) GO TO 107
PUNCH 355,5,V,K,JLONER.VOIFF(INDEX,S.V).HT(INDEX.S.V)
GO TO 102
60 CONTINUE
ASSIGN 100 TO NGO
DO 100 K31,3
DO 100 3:102
D0 100 1:10N
IFISU(I).NE,SL(II.OR,SU(I).NE.S) 100.5
6 IFCVU(I).NE.K) 100910
10 IFIJU(I).NE.JL(I)) 100.15
15 JLONER=2*JL(I)n1
V=VU(I)
PRINT 55.8.V0K. JLONER.NU(I),WGT(1)
IF(.NOT.IPUN) GO TO 102
PUNCH 355.8.V,K,JLONER.Nu(I).war(1)
GO TO 102
100 CONTINUE
GO TO 105
10? NLINES=NLINES+1
NTDTAL=NTOTAL+1
IFINLINES.GE.50) 52,101
52 PRINT 53
NLINES=0
PRINT 150.NCOUE
PRINT 51
101 GO TO N60
105 PRINT 54DNINT0TAL
51 FORMAT (///1OXtSUB*4X*V1Q*3X*UELTA*6X*Jt7X*VIB'7Xin.t/9X*STATE*
12X‘STATE*ZOX*OIFF.*/l/)
53 FORMAT («1.)
54 FORMAT (*0 FROM +130 IMPUI FREQUENCIES A TOTAL 0F *13/* VIBRATIONA
1L DIFFERENCES WERE FOUNDt/05t)
59 FORMAT (* $10X91116X011:5X911'6X1129*I?*92X3 F9.404X:F492)
150 FURNAT (OAR)
355 FORMAT(4I5,*/2¢7x.F10.4.F10.2)
ENn

SURROUTINE SPORUIFl

CALCULATES TH? SPIN-ORBIT DIFFERENCES FOR THE V=0 STATE

COMMON/i/NUCOUO).NGT(600).JU(600).JLC600)pVU(600);SU(600):SL(600)a
1JUMPANoDSODIFF(10001):SODIFF(100,3IADNT(10001),wT(100,3)
COMMON/ZI LAMUA(600):ISUR(600)

COMMON/SI NCODE(0)o IPUN

COMMON/4/ TOL

DIMENSION DITESTC10091’9 ITE3T(100.3)

TYPE INTEGER V.S:VU.SU.SL

TYPE REAL NU

INflo

DO 2000 IA=10100

DO 2000 IB=IN,3

 

 

‘2000

35

40
41
42

155

40

45

En

100"

52

 

173

ITEST(IA.IR)=1R

PRINT 53

PRINT 61

DO SO 1:1.N
IFILAMOAII).NE.1R0,AND.LAMOA(1).NE.1R ) GO TO 50
1131*1

DO 5n J=IIDN
IFILAMOAIJ).NE.1Rt.AND.LAMOA(J).NE.1R I GO TO 50
IFIJU(I).NE.JU(JI.OR.JL(I).NE.JL<JI) GO TO 50
IFISU(I).NE.SUIJI) GO TO 55

IFCSL(I).EO.SL(J)) GO TO 5O

JJHJLII)

V=D

IF!SL(I).EO.1) 40.41

IFISL(I).NE.SL(J)) GO TO 50

V=VUIII

JJ=JU(I)

IF!SU(I).EO.2) 40.41

SOD:NU(!)-NU(J)

GO TO 42

SOD=NU(J)-NU(I)
NAT=2*NGT(I)*wGT(J)/(NGT(II+NGT(J)I

JM:2*JJ—t

PRINT 156a VoJM.SOO.wAT.NU(l):NU€J)
FORMAT(215¢/2*7X.F10.4,10X,F10.2.2F10.4)
IF‘NT(JJIV,ONEOOIU) 45043

NTIJJ,V)=NAT

SODIFF(JJ.V)=SOD

GO TO 50

IF(ABSF(SOOIFFIJJ.V)rSOU).GT.13L) ITEST(JJ.VJ=1R¢
SODIFF(JJ:V)=(SUEIFF(JJ:V)tWl(JJoV)+SOD'WAT)/(NT(JJ:V)+NAT)
WTIJJAVI=NT(JJ.VI+WAT

CONTINUE

IFIJUMP) RETuRN

PRINT 53

PRINT 150,NcODF

PRINT 81

NJ=0

NLXNES=0

NTDTAL:0

D0 60 V=NJJ1

DO 6O JJ=105U

IFISODIFF(JJ.V).F0.0°0) GO TO 60

JMIZNJJ-i

PRINT 55,V,JM.SOOIFF(JJAV).ITEST(JJ;V),NT(JJ:V)
IFt.NOT. IPUN) GO TO 1000
PUNCH355.V.JM.SOCIFF(JJ.v).ITESTtJJ:V).NT(JJ;VI
NLINESsNLINES+1

”TOTAL=NT0TAL+1

IFINLIHE§.CE,50) 52.60

PRINT 53

NLINESID

PRINT 15UPNCUUE

PRINT 51

 

1
3

C

an

51
51
54

55
5O
55

174

CONTINUE

PRINT 54.N.NTUTAL

FORMAT (ll/14XwVv9XtJtRX*SPIN ORBITiBXtNEIGHTRIS3X*DIFFERENCE~///)
FORMAT (tit)

FORMAT (*0 FHOM 513* INPUT FREQUENCIES A TOTAL OF *IS/w SPIN ORBI

1T DIFFERENCES FOR THE V=n AND V=1*/' STATES HERE FOUND*I*5*)

FORMAT (if t1-‘SX, I197Xo I?:*/9_*'EX:F8041R1’9X:F4.2)
FORMAT (GAR)

FORMAT (215i/2i7Y,F10.4,R1,9X:F10.2)

END

SUBROUTINE SPURDIFZ

CALCULATES THE SPIN-ORBIT DIFFERENCE FOR EXCITED V-STATES

29
21
24
25

26
27

29
40

4'1

45

.50

COMMON/llNU(OUO).NGT(600).JU(600)AJL(600)0VU(600):SU(600)oSL(600)9

1JUMP,N.DSOOIFFI100.1).SOOIFF(100:5),DNTC1OOo1):NT(100:3)

COMMON/z/ LAMUA(‘UD)AIRUR(AOD)

COMMON/s/ NCUDF(9)A IPHN

DIMENSION nNETcanA1):wET(100:3)

TyPE REAL MU

TYPE INTEGER V.S,VU.SU,SL

CALL SPORDIFI

D0 50 1:11“
IFILAMOAII>.NE.1R*.AND.LAM0A(l).NE.1R ) GO TO 50
II=I*1

DO SO J=II,N
IFILAMOAIJ).Nb.1R*.AND.LAMOA(J).NE.1R ) GO TO 50
IFISU(I).EO.SU(JI.OR.SL(I).EJ.SL(J).OR.SU<I).NE.SL(I)) 50122
IFIJU(I).NF.JOIJI.OR.JL(I).NE.JL<J)) 50,23
IFIVH(T).EO.VU(JI.AND.VU(1).Nt.1) 94.50
IFCVU(I).EQ.'/‘) 25,26

V:_7_

GO TO 97

V:3

JJ=JU(I)

IFISU(I).EO.?) 29,29
SOO=Nuc1)-NU(J)+SOOIFF(JJ.0)

GO TO 40

SOD=MU(J)'NU(II+QUDIFF(JJ:O)
NAT:3*NGT(I)*NGTIJ)0NTIJJ.OJI(NGT(I)+NGT(J)+NT(JJ;O))
IFIwFTIJJ.V).NF.n.O) 45.45

HET(JJ,V)=MAT

SOOIFFIJJ.V)=SOD

GO TO 60
SUPIFFIJJ.V)=(SOOIFF(JJ.V)*NEI(JJ,V>+SOD*NAT)/(NET(JJ.V)+NAT>
WET(JJ,V)=NET(JJ,VI+NAT

CONTINUE

PRINT 51

NLINES=0

NTOTAL=U

DO 6” V3213

DO 60 JJalgSn

IFISODIFF(JJIVI.EU.O.0) GO TO 60

JM=2tJJ'1

IFIsODIFF(JJAVI.LT.0.0> 56,57

 

56

57

10°

59

51
53
54

59
7a
15n
355

179

FRINT 75) VitJM

r30 T0 1
- ”0?
pRINT 95 r
- 9 /) JM Sf'
;SféSOT.IPUN) n6 T;D:SZ(JJ'V)' WEI'JJ V)
' N. 355,V’JM Sr. ‘ ’
flL}NES=NL1~Es+; _DIFF(JJ.vx,dtT(JJ.V)
gggTAL=NTOTAL+f
NLINES.G MW v
PRINT 53 "E°90) 52’60
SLINFS=0
RINT 15fi n
pRINT 51 ’!CDUF
CONTINUE
PRINT 54:N.NT0TAL

I ‘ ' - F E R E N ' .-

EORMAT (*1.)
ORmAT (*0 FR"
p U
M .13. Input FREQUENFIFS A TOT
3 , 'AL 0F tlilt

FORMAT (* ‘
tlux,l1;7X.I?:*/Q*:6X:Fb 4 1
. , 0X:F4.2)

SPIN URBI

1T DIFFFRfiNF“‘
_ _____ th F0” T ' "
HE v-2 AND V=$tifi STATFS
L m NERF FOUND:
/*5*)

I E

EORMAT (OAR)

”ORMAT( ‘ "‘

ENG .215.*/:t7!.F10.4.10v Flo P
a .. .,)

 

176

. ROTCONS
ALLFIT
LAMCON
u STEPFIT

*IJDZIUO

Programs in sections C, D, and E use subroutine STEPFIT
(Section F) which is a least squares routine written by M. A.
Efroymson (75). ROTCONS fits rotational combination differ-
ences, ALLFIT fits frequencies and LAMCON fits A—doublet
splittings. All three have essentially the same input and

thus a general description follows.
STRUCTURE OF DATA DECKS

I. Constants cards
CONSTANT in cols. 73-80 indicates that the following
cards have initial or fixed values of the constants.
1. Heading cards: Cols. 1—72 are read and printed until
END HEAD in cols. 73—80 is encountered.
2. Values of the constants: Read in cols. 1—20 in the
following orders:
ROTCONS: 301,302: D01[Doer01[Hoztalraerlrfizrverzr
H6,y'.
ALLFIT: AG(1),H5,y'I10,X,B01,B02,D01,D02,a1,a2,sl,32,
Heeroererzo

LAMCON: pA,qA.

II. Data cards
NEW DATA in cols. 73-80 indicates that the following
cards contain information to be fit. The formats are as

follows:

 

177

Cols. Field Variable

l. ROTCONS

l—S I Substate of difference.
6-10 I Vibration level of difference.
11-15 I AJ
16-21 I 2J
25-36 F Combination difference.
41-46 F Weight.
2. ALLFIT
l I Upper vibrational state.
9 R Branch (P, Q, or R).
10 R Subbranch (l, 2, H, L).
12-13 I 2J
20-33 F Frequency
41—44 F Weight
3. LAMCON
10 R Branch (P, Q, or R).
11 R Subbranch (l, 2, H, L)
l4-15 I 2J
34-49 F A-doublet splitting
50—59 F Weight

"END DATA" in cols. 73-80 signals the end of data.

III. Information card

Col. Field Function
1-5 I #0 indicates statistical infor-

mation from STEPFIT is desired.

Col.

6-10

20-29

30-39

40—49

50-59

70-72

73-80

Field

 

IV. Option card

178

Function

Number of data points to be
deleted if subsequent fits
warrant it.

If the weighted observed minus
predicted value is larger than
this, the line is deleted and

the fit is repeated. The largest
deviation is deleted first.

If the value of the diagonal ele-
ment of the inverse matrix is less
than this number, that variable is
not included in the fit.

Value of the minimum change in the
value of a variable before it will
be entered. Preset to 10's.

Value of the minimum change in the
value of a variable before it will
be removed.

#0 indicates a punch output of the
fit is desired.

Ident field for the molecule.

This card controls which variables will be entered in

the fit.

given in I above.

The order of the variables for each program is as

Starting from column one, a non-zero punch

in the column corresponding to a particular variable will

cause it to be entered in the fit°

V. Heading cards

These cards are read and printed until END HEAD is

encountered in cols.

 

179

VI. Control 2339
This card is read and depending upon the content of
cols. 73-80, control is returned to the appropriate section:
CONSTANT + Section I
NEW DATA + Section II
blank + Section IV (Option card data should appear)

LAST FIT + Ends execution

The listings of ROTCONS, ALLFIT, LAMCON and STEPFIT follow.

 

1000
100
110
120
130
150
160
200
210
230
300
350
360

1200

180
C, ROTCONS

PROGRAM ROTCONS
COMMON/1/NODATA,NOVMI.AVEWHT.STDY,N05TEP.N.NTN.FREGPRD.YPRED.DEV.
1DATA(20:5UO) .
COMMON/ZIFOBS(500)aFCALC(500).NT(500).NK(17).INFO.INDATA.NDELMAX.X
lDEVHAX.N1(25).MOL.CON(17.500).IH(10)aSS(DOO).VV(500).KK(500).JJ(50
20).NUMCON.ISTATE

COMMON/S/ NOVAR.JUMP.CONST(20).EFIN.EFUUT

COMMON/5i TOL

COMMON/IOI IPUNCH

COMMON/Cl NAME(30)
DATAcNAME=3HBo1.3HBO2,3H001,3H002,3HH01.5HH02.6HALPHA1.6HALPHA2,
15HBETA1.SHBETA2.6HGAMMA1.6HGAMMA2.3HH02,6HGAMMA2)

EXTERNAL RDTCONSl.ROTCONSZ.ROTCONS3

TYPE INTEGER SS.VV

TYPE REAL J

U(J.P)=(J¢P+.5)**2

F(J)=(J*.5)**2

NUMCON=14 $ ISTATE=0

JUMP=0

READ 50.1H

IF(IH(10).EQ.8HLAST FIT) 900.110

IF(IH(10),EQ.8HEND DATA) 365.120

IF(1H(10).EQ.8HCONSTANT> 150.130

IF(IH(10),EQ.8HNEW DATA)300.900

JUMP=1

READ SUaIH

PRINT 50.!IHKI).I=1.9)

IF(IH(10),EQ.8HEND HEAD) 200.160

PRINT 53

J1=1

READ 220.CONST(J1).IH(10)

1FtlH<10),NE.8H ) 100,230

PRINT 240.NAME(J1).CONST(J1)

J19J1*1

GO TO 210

M=1

READ 355. SStM).VV(M),KK(M).JJ(M),FOBS(M).WT(M).1H(10)
IF¢IH(10).NE.8H ) 100.360

INDATA=M

JaJJKM3/2.

P=KK(M) _

GO TO (1200.1300) SS(M)

'CON(1.M)=U(J.P)~F(J)

CON(2.H)80.

CON(3.M)=-(U(J.P)**2vF(J)ct2)

CON‘4.M)=0.

CON(5.M)=U(J.P)**3~F(J)**3

CON(6;M’=0.

CON(7.M)a-CON(1.M)*VV(M)

CON‘BgM)‘00

‘MCON(9.M)SCON(3.M)*VV(M)

CPN(109N,30’

 

1300

1400

380
385
390

365
40
20
45

25

900

50
51
53
54
220
240
355

181

C0N(11.M)=-CON(5.M)*VV(M)
CON(12.M>=0.

CON(13.M)::CON(5.M)
CON(14,M)=-CON(11.M)

GO TO 1400

CON(1.M)=0.

CONCZ:M)=U(J.P)2F(J)

CON(3.M)=0.
CON(4.M)=-(U(J.P)**2-F(J)t*2)
CON(5.M)=0.
CON(6.M)=U(J.P)**S9F(J)**3
CON(7.M)=0.
CON(31M)=?C0N(21M)*VV(M)
CON(9.M)=0.
CON(10.N)=CON(4,M)*VV(M)
CON(11.M)=0.
CON(12.M)=-CON¢6.M)tVV<M)
CON‘13.M)=CON(6,M)
CON(14,M)=CON(12.H)

CONTINUE

FCALC(M)=0.

IF¢JUMP) 380.390

00 385 L=1.14
FCALC(M)=FCALC(M)+CONST(L)*CON(L.M)
Mthi

GO TO 350

READ 40: INFO,NDELMAX.XDEVMAX.T0L.EFINaEEOUT;IPUNCH.M0L
FORMATC215.9X,4F10o10X.13,A8)

READ 45: (NKCI’plzlal4):IH(10’
FORMAT(1411158X;A8)
IFCIH(1U),NE.8H ) GO TO 100
READ 50p 1H

PRINT 50. (IH(M).M=1.9)
IF(1H(10),NE.8HEND HEAD) GO TO 25
CALL STEP FIT‘ROTCON31aROTCONSZ.ROTCONSS)
GO TO 20

CONTINUE

PRINT 54

FORMAT (10A8)

FORMAT (*1*/)

FORMAT (///)

FORMAT (.5.)

FORMAT (F20.52X.A8)

FORMAT (A20;F30.107

FORMAT (315016:SXOF12,4pSXQF601125X0A8)
END

 

1000
100
110
120
130
‘ 150
160

200

210

 

182

D, ALLFIT

PROGRAM ALLFIT
COHMON/l/NODATA.NOVMI,AVENHT.STDY,NOSTEPINoNTNoFREOPRD.YPRED.DEV.
1DATA(201500)
COMMON/2/FOBS(500).FCALC(500).NT(500)oNK(17)oINFOaINDATApNDELMAX.
1XDEVMAX.N1(25),MOL.CON(17.500).IH(10).SS(500).VV(500),KK(500).

2JJ(500):NUMCON.ISTATE

COMMON/3/ NOVAR.JUMP.CONST(20),EFIN.EFDUI
COMMON/5/ TOL

COMMON/lfll IPUNCH

COMMON/C/ NAME(30)
DATA(IV1=11030’0(IV2=00100)'(IV3=0a001)
DATA(NAME=7HDELTAG1,3HH02,6HGAMMA2.3HAA0.SHCHI.3H801.
13H802.3HD01.3H002.7HALPHA 1,7HALPHA 2.5H5ETA1,5H6ETA2.3HH01,3HH02,
26HGAMMA1.6HGAMMA2)

DIMENSION Iv1(3).Iv2(3).1v3(5>
EXTERNAL FITALL1.FITALL2.FITALL3

TYPE INTEGER BRANCH.VV.SS

TYPE REAL J.NU.K

U(J.K)=(J+K*.5)t*2

F(J)=(J*.5)**2

JUMP=0 $ NUMCON=17 S lSTATE=0

READ 50a IH

IF(IH(10),E0.8HLAST FIT) 900.110
IF(1H(10).E0.8HEND DATA) 365.120
IF(1H(10).EQ.8HCONSTANTJ 150.130
IF(1H(10).EO.8HNEN DATA) 300.900

JUMP=1

READ 50.1H

FRINT 500 (IH(I)DI=109)
IF(IH(10),E0.8HEND HEAD) 200.160

PRINT 53

J1=1

READ 220. CONST(J1).IH(10)
IFtIHClO).NE.8H ) GO TO 100

IF¢CONSTtJ1).ED.0.0) GO TO 230
PRINT 240, NAME(J1).CONST(J1)
J1=J1*1

GO TO 210

N=1

READ 355.VV(N).BRANCH,SS(N).JJ(N).FOBS(N),NT(N).IH(10)
IFtIH<10).NE.8H ) GO TO 100
INDATA=N

KK(N)=BRANCH-1RO

K=KK(N)

IF(SS(N).EO.1RL)SS(N)=4
IF(SS(N).EO.1RH)SS(N)=3

J=JJ(N)/2,

GO TO (410.420.430a440) 35(N)
C0N‘1QN’3IV1(VV<N))

CON(4.N)=0u

CON‘S:N)=VV(N)/2.

‘ CON(6.N)=U(J.K)-F(J)

 

420

430

440

183

CON(73N)=0.
CON(8.N)=-(U(J1K)**2)+(F‘J)**2)
CON(9.N)=0.
CON(10.N)=-(U(J.K)*.5)*VV(N)
CON(11.N)=-VV(N)/2,
CON(12.N)=-(U(J.K)**2+,5)*VV(N)
CON(13.N)=-VV(N)/2a
CON(14,N)=(U(J.K)**3)-(F(J)t¢3)
CON(15,N)=0.
CON(16.N)=~(U(J.K)**3)*VV(N)
CON(17.N)=0.
CON(2;N)=-CON(14.N)
CON(3,N)=-CON(16.N)

GO TO 450

CON‘1:N)=IV1(VV(N))

CON(4:N)=0.

CON(5:N)=-VV(N)/2q

CON‘pr030.
CON¢7nN)=U(JoK)-F(J)
C0N‘8pN750.
CON<93N)=9(U(JJK)**2)*(F(J)**2)
CON(10.N)=VV(N)/2,
c0~<11.N>=-(U(J.K)-.5)~VV<N)
CON(12.N)=0VV(N)/2u
CON(13.N)=-(U(J.K)**2+,5)tVV(N)
CON<14.N)=0.
CON(15.N)=(U(J.K)**3)r(F(J)**3)
CON(16.N)=0.
CON(17,N)=-(U(J.K)**3)*VV(N)
CON(2:N)=CON(15.N)
CON(3.N)=CON(17.N)

GO TO 450

CON(1:N)=IV1(VV(N))

CON(4)N’31|

CON‘50N73'VV(N’/29
CON‘6:N)=-F(J)

CON(7.N)=U(J.K)
CON‘81N)=F(J,**2
CON<9¢N)=*(U(J.K)**2)
CON(10.N)=VV(N)/2u
CON(11.N)=-<U(J.K)'.5)*VV(N)
CON(12.N)=-VV(N)/2.
CON(13,N)=~(U(J.K)**2+,5)th(N)
CON(14.N)=-(F(J)**3)
CON(15.N)=U(J.K)tt3
CON(16,N)=0.
CON!17.N)8~(U(J.K)**3)*VV(N)
CON‘Z.N)=CON(15.N)'C0N(14.N)
CON(3.N)=CON(17,N>

GO TO 450

CON<1¢N)RIV1(VV(N))
CON‘4ON05'13

CON(5:N)=VV(N)/2.
CON(6.N)=U(J.K)

 

 

450

380
385
390

365
20

25

900

45
so

220
240
355

 

184

CON(7.N)=- F(J)

CON(8.N)=-(U(J.K)**2)
CON(9.N)=F(J)*t2
CON(10.N)=-(U(J.K)+.5)*VV(N)
CON(11.N)=-VV(N)/2.
CON(12,N)=-(U(J.K)*t2+,5):VV(N)
CON(13,N)=—VV(N)/2.
CON<14.N)=U(J.K)'*3
CON<15,N)=-(F(J)**3)
C0N(16.N>=a(U(J.K)tt3).vV(N)
CON(17.N)=0.
CON(2.N)=CON(15.N)~CON(14.N)
CON(3.N)=-CON(16.N)

CONTINUE

FCALC(N)=0.

IF(JUMP) 380.390

00 385 LL:1.NUMCON
FCALC(N)=FCALC(N)+CONST(LL)*CON(LL.N)
N=N+1

GO TO 310

READ 40. INFO,NDELMAX,XDEVMAX.TOL,EFIN.EEOUT.IPUNCH.MOL
READ 45. (NK(II.I=1.17).IH(10)
IFIIH(10),NE.8H ) GO TO 100
READ 500 1H

PRINT 50. (IH(M).M=1.9)
IF!IH(10),NE.8HEND HEAD) GO TO 25
CALL STEP FIT(PITALL1,FITALL2.FITALL3)
GO TO 20

CONTINUE
FORMAT<215.9X,4F10.1OX.16.A8>

FORMAT (1711.55X.A8)

FORMAT<10A8)

F0RMAT(*-t)

FORMAT(F20.52X.A8)

FORMAT!A20.F30.10)
FORMAT(11.7X.2R1.X.12.6X.F13.4.7X.F4.2.29X.A8)
END

 

185
E. LAMCON

PROGRAM LAMCON
COMMON/1/NODATA.NOVMI,AVENHT.STDY,NOSTEP.N.NTN.FREOPRD.YPRED,DEV.
10ATA¢2015UOI ‘
COMMON/Z/Foas<500).FCALC<500).HT(500>.NK<17).INFO.INDATA.NDELMAx.
1XDEVMAX.N1(25).MOL.CON(17.500).IH(10).SS(500).VV(500).KK(500).
2JJ¢500).NUMCON.ISTATE
COMMON/3i NOVAR.JUMP.CONST(20).EFIN,EFDUT
COMMON/El TOL
COMMON/io/ IPUNCH
COMMON/CI NAMEI30)
DATA(NAME:2HPL.2HQL)
EXTERNAL LAMCON1.LAMCON2.LAMCON3
TYPE INTEGER BRANCH.SS
TYPE REAL J
U(J)8(J**2-.25)A(J+1.5)
F(J)=(J*.50)
ISTATE=0 $ NUMCON=2 $ JUMPao
READ 9000, A0,A1.901.802.811.812
9000 FORMAT(6F10)
xL01nA0/801
XXL01=XL01.XL01
XL02uA0/802
XXL02=XL02tXL02
XLlisAl/Bll
XXL11=XL11tXL11
XL12=A1IB12
XXL12=XL12tXL12
1000 READ 50.1H
100 IF(IH<10),EQ.BHLAST FIT) 900.110
110 IF(1H(10),EO.BHEND DATA) 365.120
120 IFIIH(10),EQ.8HCONSTANT) 150.130
130 IF(IH(10).E0.8HNEN DATA) 300.900
150 JUMPci
160 READ 500 IH
PRINT 501 (IHII).I=109)
IF(1H(10).EO.8HEND HEAD) 200.160
200 PRINT 53

Jill .
210 READ 220.00NSTIJ1).IH(10)
IFIIHI10).NE.8H ) 100.230

230 IPCCONST(013.E0.0.0) Go TO 235
PRINT 240 . NAME(01).CONST¢01)
235 Jisdifii
00 To 210
500 Mli' ‘
1350 READ 301.SS(M).KK(M).JJ(M),FOBS(M),HT(M).1H(10)
IFIIH<10).NE.8H )100.360
360 Ja.StJJ(M)
BRANCH:SS(M)9100
_IGO:KK¢M)
IFTIGO.EO.1RH) 100:3
IFIIGO.EO.1RL) 100:4

“flu—...?—

 

 

):

 

370
372

374

380
382

384

386

1370
1372

1374

1376

1380
1582

1384

1386

390
400
500

186

00 To (1370.1380.370.380) 100

GO TO (372.374.376) BRANCH
CON(1.M)=2.'F(J>'2.*U(J31)/XXL12°2.*U(J)/XXL01
00N<2.M>:a<4.«U(Jel)IXL12.4.*U<J)/XL01T

Go To 390
CON(1.M)s-(2.«F(J)*2.'UIJ)/XXL12-2.tU(J)/XXL01)
00N(2.M>=-<1./xL12-1./xL01,.4,.u(J)
F093!M)=.FOBS¢M)

GO To 390
CON<1.M)=2.*F(J)-2.tU(J01)/XXL12=2.*U(J)/XXL01
CONC2.M)=-(4.*U(J*1)/XL12t4.tU(J)/XL01)

Go To 390

00 T0 (382,384,386 ) BRANCH
CON(1.M)=-(2.*P(J)'2.tUtJ-iTIXXL11a2.'U(4)/XXL°2’
CON(2.M)=4.tU(J-1)/XL11*4.*U(J)/XL02
FOBSIMIagFOBS(M)

00 70 390
CON(1.M)=-(2.fi?(J)*2.'U(J)/XXL02=2.*UIJ)/XXL11)
coN<2.M)=(1./XL1121,IxL02>c4.«U(J>
FOBS!M)=-FOBS(M)

00 To 390
00N(1.M)=-(2.tF(J)e2.tU(J+1)/XXL1122.00(J)/XXL02)
CON(2.M)=4.*U(J¢1)IXL11*4,wU(J)/XL02
POBS(M)=-FOBS(N)

GO To 390

Go To (1372.1374.1376) BRANCH
coNt1.H):2.t2..U(J-1)/XXL11~2.oU(J)/XXL01
CON(2.M)=4..U(J-1)le1it4..UtJ)/XL01

00 TO 390
coN<1.M)=-4..F(J)~2.~U(J)/xxL11o2,~U<J)/XXL01
CON(2.MT=4.tt1./XL11+1./X001)*U(J)
roaS¢M)a.FOBS¢M)

GO To 390
CONIi.M)=-2.+2.tUtJ+1)lXXL1122.*U<J)/XXL01
co~¢2.M)=4.ttUlJol)/XL11~U<J)/XL01>
FOBS(M):-F085<M)

00 To 390

00 To (1382.1384.1386) BRANCH
coNt1.M)=~2.tU:J-1i/XXL12~2.wch)/xxL02
00N<2.M>=-4.cU(J-1)/xL1zo4..u(J>/XL02

GO TO 390
CONtl.M):=(1./XXL12*1./XXL02)V2.~U(J)
CON(2.M)=-(1./XL12*1.IXL023t4.tU¢J)
FOBS(M):-FOBS(M)

00 To 390
coN(1.M)==2.v0tJ»1)/xxL12*2.cU¢J)/xxL02
CONI2.M)==4.tU(J*1I/XL12*4.*U(J)/XL02
roas<H>=-F085(M)

FCALC(M)-0.o

IF¢JUMP) 400.500

00 70 K01.NUMCON
PCALCIM)=FCALC¢M>*CON(K.N)fiGONST(K)

Mth1

00 TO 1350

 

 

365
30
340

21
20

187

INDATA=M91

READ 4o. INFO,NDELMAx,XDEVMAx.T0L.EFIN.EEOUT.IPUNCH.M0L
READ 45.(NK{I).I31.2).IH(10)

IP(IH(10),NE.8H )100.21

PRINT 51

READ 50.1H

~PRINT 50.(1H(I).I=1.9)

IFIIHIID).EQ.8HEND HEAD) 350.20

CALL STEP FIT (LAMCON1.LAMCON2.LAMCON3)
GO TO 340

CONTINUE

PRINT 54

FORMAT(215.9X,4F10010X313.A8)

FORMATI 211,70X,A8I

FORMATCIDAB)

FORMATI'l‘I)

FORMATtist)

FORMATIOSi)

FORHATIF20.52X,A8)

FORMAT:A20.F30.10)

FORMATI9X.2R1.2X. 12119X.F15,4,F10,13X,A8)
END

 

_.._.___ -,-_._ _

17%

159
8158

8159
157

251

259

49W

176

Son

511
512

-v——_._—-__. -r—‘ .

188
F. STEPFIT
SURRDUTINE STEP FIT(HEA01:HEAUZ:0UTPUT)

COMMON/1/NHDATA,KUVMIJAVENHTISTDY:NOSTEP:NngNpFREQPRoaYPRED:UEVI
10ATAf20,500)
CONNON/2/F088(Son).FCALC(5n0):AT(500).NK(17):INFOaINDATA.NDELMAX.
1XDEVMAXpN1(25):MnLDCONC17,300):14(10):SS(500)3VV(500):KK‘500)o
2JJ(500).NUMCDN,IQTATE

COMMON/S/ M0VAP,JUMP.C0NST(20).EFIN:EFOUT
COMMON/Cl MAME(6n)

COMMnN/S/ TOL

COMMDN/ln/ IPUNCH

DIMENSION VEC10R(ZC.20).INBEX(20).SIGMA(20)pCOEN¢20):SIGMCO(20).
1MoT1N(?0).~US&(5nU)

DIMENSION XCONST(20)

TYPE IflTEGFR SS.VV

TYPE DOURLE VECTCR;SIGMA.CnEVoSIGMCOoSIGY.DEFRoVAR
IFf.NOT.FFOUT) tFOU1=1.E-8

IF(.NOT.EFIN) FFYNzEFOHT=1.E-6
IFCTOL.ED.H,D) TCL=0o001

MOVAR = 1

no 167 I=1.NUmn0~

IFtNK(I))188»1S7

N1(N0VAR)=NAME(I+ISTATF)

IrtJUMP) 8159,8169

chNST(NDVAR):CUhST(I)

NOVAR=NOVAR+1

COMTINUE

NODATAzo

00954 MHUNDATA

IFCNT(W)i252o2%3

NUSEtN):n

GO TO 254

NUSE(N)=1

NODATA=NODATA+1

CONTINUE

NDEL=0
N0IN=K=N0ENT=N0MIN=N0MAX=VAR=rLEVEL=0.0
LOUP=U

NOVM] : MOVAH - 1

NOVPL = NOVAR + 1

Do 176 1 = 1pNnVPL

D0 176 J = lnNOVpL

VECTORflaJ) 3 n.n

IFtNDEL)BOfl.SOO

SUMHHT=0.0

00626N=1.IHDATA

NUM=0

DO 512 191.NUMCOF

IFCNK(I))5119512

NUM=NUM+1

DATACNUM.N)=CON (I’M)

CONTINUE

DA¥A(NQVAR.N)=F0FS(N)-FCALC(V)

 

 

525
501

146

54a

Sin

58B
1115

601

59°

180

604

1601
609
601

 

SUNwHT=SUMwHT+HT(N)

AVENHTasuMwHY/NOEATA

00510N=1nlMDATA

IFtNUSE(N))146.510

WHT=wT(N)/AVENHT

DO 540 I = 1: NOUAP
VECTOR<I.NOVPL)=VECTOR(I.NOVPL)+DATA(I.N)thT
DO 540 J = InNOVAR
VECTORtI.J)=VECTOR(I.J)+0ATA(I.N)*nATA(JaN)*wHT
VECTOR<NUVPL;NOV¢L) = VECTnR(NOVPL.NOVPL) + WHT
CONTINUE

IFCINF0)58no65n

PRINT 1115

FORMATtiisUM UF VAQtl)

NOMAX=MOVMI

IFCNUVHI.GT,E) NCMAX=8

pRINT 15: (101:1.NOMAX)

PRINT 17. VECTOR(NOVAR,NOVDL).(VECTOR(IoNOVPL).1=1.NOMAX)
IF(NDMAX.EO.NDVMI) GO TO 5&1

NOMAX=N0MA¥+1

PRlNT 1116.(I,!=EOMAX:NOVMY)

PRTNT 17. (VECTOR(I.NOVPL).I=NOMAX,NOVMI)
CONTINUE

NGO=n x M0M1m=1 z NOMAX=N0VMI
IFtNOMAx-6)599.599.601

MOMAX=6

NGU=1

PRINT ‘521fIII=NQMIN1NOMAX5

Do 180 J=NOMIN,NFVM1

JJJ=J ,
IF‘JJJ.GT.N0HA¥.ANU.NGO)JJJ=VUWAX

PRINT 151;J,(VFCTOR(I:J);I=NOMIN:JJJ)
PRINT 154,(VECTOR(I.NOVAR),I=N3MIN.NDMAX)
IFCNG091) 605,604,602

NOM1N:7 x mem:n w NOMAX=NOVMI
IF(NOMAX.GT.12$ 1601:5Q9

NOHAX=12 $ NGO=2 $ GO TO 599

NGU=D R NUMIN=13 $ NOMAX=NOVM1 $ GO TO 599
CONTINUE

PRINTlSS. VECTOR!NOVAR,NOVAR)

NoSTEP = -1

ASSIGN 1320 T0 NUMRER

DEFR = VECTOR(NOVPL.NOVPL) ‘ 1.0

DO eno I = 1.NOVAR

IF!VECTOR(I:I)) 792.794.810

‘ PRINT 793, I

507017?

PRINT 795: I

SIGMA(I) = 190

GO TO 80”

SIGMA(I) =DSUHT (VECTOR (1:1))
VECTOR(I:I) = 1.0

DO 830 I = 1oNOVNI

1P1 = I * 1

 

830

870

1001

100?

101m

1017

10.20

104?

1060
11.08"1

1101

904
1170
1160
1110
1210
1050

903
1240
1300
1310
1311

1313
1314

190

Do 830 J = 1P1. kOVAR
VECTORIIgJ) = VECTOR(I;J) /(
VECTORldalI 3 VECTORII:J)
IFIINFO)R70,1001
PRINT159.(I.I=1.NOVMI)

DO 885 1:2,NUVMI

IM1=I’1
FRINT160’I.IVECTCR(I:JI,J=1,IM1)
PRINT1619(VECIORII:N0VAR):I=1:V0VMI)
NOSTEP = NOSTEP w 1

IF (VECTOR! NOVA:,MOVAP))
NSTPMl = NHSTEP - 1

PRINT 1004. NSTPH

GO TO 1331

SIGY = SIGMA(NOVAQ) *USQRT
DEFR =nEFH'1oU

IF (DEVR ) 1017,1017:
PRINT 1019 :NOSTEP
GO TO 1381
VMIN=VMAX=MOIN:U

DO 1050 I = 1.NUUMI

IF (VECTORII:I)) 1042:
PRINT 1044, I, NCSTEP
GO TO 1391
IFIVECTORII:I)-TCL) 1050: 1080. 1080
VAR=VECTORIIpNnVARItVECTORrNOVAR.I)/VECTOR(I:I)
IF‘VAR)1100a 1n5n, 1110

NOIN = NUIN 1

INDEX(MOIN5 I

CO‘NINHIN) VEKTUR(I.NOVAR) t SIGMAINOVAR) / SIGMA (I)
SIGMCOCNOIN) = (SIGY / SIGMAI1)) *DSQRT (VECTOR(InI))

IF (VMIN) 1160,1170,904

pRINT 906

GOT017?

VMIN = VAR

NOMIN = I

GO TO 1050

IFIvAR - VMIN)1050:1050:1170

IF (VAR - VMAX)1n50.1050»1?10

VMAX = VAR
MOMAX a I
CONTINUE
IF (NOIN)
PRINT 907
GO TO 172
STnYBSIGY
GO TO 1350
IFIINFDI131091320

IF (NOENT) 1311:131111313
PRINT1683 NOSTEPI K

GO TO 1314

PRIN7169: NOSTEP: K
IFILOOP) FLEVEL=FL

pRINT 162pKaFLFVEL:SIGY

SIGMAII)* SIGMA(J))

1002:1002:1010

(VECTOR(N0VAR.NOVAR)/ DEFR)

1020

1050. 1060

I! ll+

 

 

 

1301
8309

8303
8305

8306
8304
132m

1340
1345
1350

1361
1370

1391
139?

1400
1430

146a

 

001301J=1.~OIN

N=INDEX(J)
PRINT163.N.N1(N).COEN(J).STGWCO(J)

IF(JUMP) 830?.8304

IFILUOP) 8303,8304

PRINT 8305

FORMATI¢2FINAL CCNSTANTS AFTER CORRECTIONS WERE ADDED'l)
DO 8306 J=1.NOIN

N=INDEX(J)

XNENCON=COEN(J)+XCONST(N)

PRINT 163.N.N1IN).XNEHCON.QIGMCO(J)

Go T0 NUMBFR.(1320.1580)

FL=FLEVEL
FLEVEL=VMINtEEFRIVECT0n(NOVAR:NOVAR)
IFIEFUHT * FLEVEL) 1350: 1350: 1540

K = NOMIN

NOENT = n

GO TO 1691

FLEVEL = VMAX w CEFR / (venTOR(NDVAR.NOVAR)- VMAX)
IF (EFIN ' FLEVEL) 1370.1361:1380

IF (EFIN) 1380.1180.1370

K = NOMAX

NOFNT = K

IFIK) 1392,1397,14no

PRINT 1395, NOSTFP

GOT017?

DO 1410 I = 1.KOVAR

IF (19K) 1430.1410.1430

00 144m J = 1. NOVAR

IF (J-K) 1460.1440o1460
VECTOR(I.JI=VECTCR(I.J)-VEclDHII.K)*VECTOR(K:J)!VECTOR(K.K)
CONTINUE

CONTINJE

00 14am I = 1, NOVAR

IF (I-K) 1500.1490.1500

VECTOR (1.“) = ‘ VECTOR (I.K) / VECTOR (KIK)
CONTINUE

Do 162n J = 1, NOVAR

IF (J-K) 1540.1520.1540

VECTDRIK.J) = VECTOR (K.J) / VECTOR <K:K)
CONTINUE

VECTORIK.K) = 1.0 / VECTOR(K:KI

GOT01001

CALL HFA01

CONTINUE

ASSIGN 1580 T0 NUMBER

LO0P=1

GO TO 1310

CONTINUE

IFIINFO) PRINT15869‘LJVECTOR‘LDL)!L=1DNOVMI)
CALL HEADZ

VFITHDEVMAX=SNT=XIR=0.0

001660N=1oINDATA

wTNsNUSEINIiWTIN)

 

192

NHT=NTN/AVENHI

YPRED = 0,0

00 1630 I = 1.NOIN
YPRED=YPRED+COFNIIItDATAIIHUEX(I):N)
DEV=FORSINInFCALC(NIPYPRED
IF£1n.ewT(N)I1652.1652.1651
VFIT=VFIT+NTN*OEV**2

x19=x19+1.n

SNT:SWT+WTIN)

FRFOPR0=FCALC(N)+YPRED

NHT=NHT*AVFNPI

CALL OUTPUT

ADEV=ARSFIDEV)tSCRTFINHT)*NUSt(N)
IFIDEVMAY'ADEV)1‘10a1610,1660

NMAx=N

hEVMAstnEv

CONTINUE

vpgravF1T*XIH/((XIR—NOIN)*SHTI
STUFIT=SNRTFIVFIT)

PRINT150. VFIT, RIOFIT
IFfNOELMAX-NFEL)172,177,1694
IFIDFV“A¥'YDEVMA%)172p172:1620

NUSE(NMAX)=O

NDEL=NDEL*1

NOOATAzNOUATA—1

SUMNHT:SUMNHT-NTINMAX)

pRINT 9001.NIAX

GOTO495

RETuRN

FORMATtt Yt8115./)

FORMAT(* *OF15.4.//)

FORMATII7IRlib./T

FORMAT (111.09. NO CORRECTION FOUND*)
FORMATI¢08TAT FROM LINES WHTD LT 10.0*/*0VAR.
1V =«F7.4/*7*)
FORMAT (10A8I
FORMAT(*9RAN SSCP
FORMATIXIZI6F2?.4)
FORMATIt Vt6F22.4)

FORMAT(* Y VS Y¢F15.43

FORMAT (13I1p66XI2.10XI5.FS.2XA8)
FORMAT (t—PAHTIAL OORR. CUFFF.*//1618)
FORMAT (13.10F8.4)

FORMAT It Y*16F3.4)

FoRMAT (* I
1ARIABLE COEFFICIENT
163 FORMAT (111:09.2F17.12)

1630

1651

1659

1610

1660

1624
162n

17?
15
17

111‘
123
15” 3*F10o6* STD-

151

159

153

154

155

156

159

16”

161

16?

MATRIX*/121n5122)

SID ERROR*/)

150 FORMAT (~OSTEP NOtIS/* VIR, REHOVED*13)
169 FORMAT (vDSTEP N0*13/* VAR. ENTERED*IS)
171 FORMATItQRFSULTSw/lt COEFFICIENT OLD VALUE
110M NEW VALUE*//8(9XA6:6F15.8/).4(9XA6:4X3F15.12/)>

701 FORMAT (4F15)
702 FORMAT («ABOVE NCNHEIGENVALUE NOT nIAG. AFTER 10 CYCLESt)
793 FORMAT (* ERROR RESID so VAR*13* Is NEGt)

_._- .___-.. ,-.,

LEVEL OF X**I1pt10.2.9XOSTD DEV 0F (O-P)¢F7.4//10X*V

CORRECT

 

796
85”
904
907
100fi
1004
1019
1044
1395
1586
900m
9001

193

FORMAT (*OVAkttfie IS CUNST»)

FORMAT (X613»F20.F10.23XA83

FORMAT (*OERHOR. VMIN 908*)

FORMAT (*OFRPOP NOIN NFGfi)

FORMAT (*OLINE Nfitl4t “ELETED'5X613,2F10.4)
FORMAT (*DY SQUARE NEG STEP*I5)

FORMAT (*OZEHU DEG FREEDOM 3rE9«13>

FUPMAT («SQUARF x-«IZw NEGATIVE STePtl3)
FORMAT (*K=0 STEp*IS)

FORMAT (*0 DIAG ELEMENTS*/t VAR N0 VALUE*//(I4.F12.6))
FOPMAT (PIS.F10)

FORMAT (*+LIVE Nfitlat REING DELETED FROM FIT')
END

SURROUTINE PRIMTCUT
COMMON/l/NHDATA,h0VMI:AVEHHT:5TDY.NOSTEP:N,NTN:FREQPRD.YPRE09DEV:

inATAtzn.Son)

COMMnN/Z/FNBS(50”)oFCALCt5n0)oATt500).NK(17):INFO:INDATAaNDELMAX:

1XDEVMAX,H1(25),MCL0CQN(17:EUU)p1H(10)p88(500)3VV(500)9KK(500)9
2JJ‘5”U3,NUMCUN,I§TATE

COMMON/SI NOUAR:JUMPpCONST(20).EFIN:EF0UT

COMMON/s/ TOL

COMMON/1P/ IFUNCF

COMMQN/c/ mAkE¢3n)

TYPE INTEGER SS.VV.BRANCH

ENTRY ROTCONsl

PleT 167:M0L.NOPATA.NOVMI,NDtLMAX,XDEVMAX,AVEHHT,3Tny,N05TEp
RETURN

ENTRY ROTCGNSZ

PRINT166

RETURN

ENTRY ROTCON35

PRYNT 166. N.SS<N).VV(N).KK(N).JJ(M).wTN.FOBS(u).FCALc(N),FREQPRD,

lnATA(NUVAR.N>.YPHEW:DEV

IFCIPUNCH) PUNCH 1165nM938(N):VV(N):KK(N):JJ(N)oWTNgFOBS(N)o

1FRFQPRD,DEV

RETURN

ENTRY SPORCON1

PRINT ?67: M0L.NPDAYA.MOVMI.MUELMAx.xDEVMAx,AVEwHT,STDY,NOSTEP
RETURN

ENTRY Sann0N2

PRINT 966

RETuRN

ENTRY SPfiRcohé

PRINT 265. N.vv<m>.JJ(M).HTN.FOBS(N).FCALC¢N).FREUPRD.DATA(N0VAR.N

1,9VPREU,DEV

HETUR‘N

ENTRY PREQFITl

PRINT 367;MOL,NOFATA:NOVMI.NUELMAX,XDEVMAonVENHT:STDY,NOSTEP
RETURN

ENTRY FRFQFITZ

pRINT 366

RETURN

ENTRY FREQFITS

 

194

BRANCH=KK(N)+5n

PRINT 465.N.VV(NI,BRANCH.SR(VI.JJ(N).NTN:FOBS(V).FCALC(N),FREQPRD»
1DATAINflvaH.NI,YPnEn.nEv

RETuRN

ENTRY FITALLI

PRINT 367,M0L,NUPATA.NOVM1.NDELMAX,XDEVMAX.AVEAHT,Spr,NOSTEp
RETuRN

ENTRY FITALL2

PRINT 466

PETURN

ENTRY FITAILA

IFISSIN).tU.3) SS(M)=19H

IFISSIN).EQ.4) SS(N)=lPL

BRANCH=KKINI+1PQ

PRINT 466,N.VV(NI.RRANCH.S§(N).JJ(N).wTN:FOBS(V).FCALC(N).FREQPRD:
iflATAINfiVAR,N),YPREH,DEV

IFIIPUNCH) PUNCH 1465:N.VV(N):BRANCH:SS(N):JJ(N),NTN,FOBS(N),
1FREQPRn,DEV

RETURN

ENTRY LAMCONI

PRINT 667.M0L.NUPAIA.NOVM1,NntLNAx,XDEVMAx,AVEAHr,srny,Nosrep
RETuRN

ENTRY LAMCCN?

PRINT 566

RETURN

ENTRY LAMCON3

PRINT 565:A.SSINIpKKIN).JJ(N):NIN.FOBS(N):FCALC(N).FPEQPRD:
1UATAINOVAH,N),YPHEH,DEV

IFIIPUNCH) PUNCH 1565:“.SSIN):<K(N):JJIN):NTN.FORS(N),FREQPRD.DEV

RETURN

165 FORMAT (Ib.312.13,*/?*.F6.9.6f9.4)

166 FORMAT (*1 H0 8 V K J wHI fiBS CALC PRED O-C
1 P-C n-Ft)

167 FORMAT (*1 CPMPIAATIDN DIIrERtVCES FOR *Aalw FIT *14* DATA POINTS
1T0* 12: VARIABLE9*/t DELEIES UP TO ~12 r POINTS IF (O'P) IS
2 GTcF6,3/* NHT NORMtF¢,2/* STD DEV OF (D-C)* F9,4/* CO

3MPLETEU t19t STEPSV)
26S FORMAT (15:14,I5.*/2*:F6.2,5F9,4)

266 FORMAT (*1 N0 V J NHT URS CALC PRED O‘C
1 P-C O-PY)

267 FORMAT (*1 SPIN CRRIT WIFFFRENCES FOR *AS/t FIT «14* DATA POINTS T
10*Iza VARIABLES*/* DELE'ES UP TO *12* POINTS IF (O-+) IS GT
2*F5.3/* NHT AOPMtF6.2/¢ STD DEV 0F (O'C)* F9.4/* COMPL
3ETF0 :12: QTEPSt)

365 FQPMAT (*lNO V LINE HHT OBS CALC PRED 0-0
1 FCC U'P*)

367 FORMAT (*1 FREQUENCY FIT FnR *AB/t FIT *I4t DATA POINTS T0 *12* VA
1HIABLEStlt DFLETES UP TO *12* POINTS IF (O-P) 18 GT *F6.3/*

2 NHT NORM «F6.2/* STD DEV 0F (O-C) *F9.4/0 COMPLETED *12*
SSTEPS*I

465 FORMATcx.[3.12.1X.2R1o13.*/2*1x,F4.2;3F11.4.3F9.4)

466 FORMAT(*1 N0 V LINE NHT OBS CALC PRED O-C
1 P90 O'P*)

sashFORMATcx,Is.x,7RI.Is.w/2 tF4.2.Xp2F8.4.4F9.4>

 

195

565 FoPMATIti NO LINE NHT OBS CALC PRED O-C
1P-C U!P*)
567 FORMATIti LAMDA PIFFERENCE FII FDRoAB/ * FIT *I4* DATA POINTS
170. 12. VARIABLEStlt DELETES UP TO «12 w POINTS IF (0-P> IS
2 GT¢F6.3/* NPT NORMtFo.2/* STD DEV 0F (Q-C)* F9.4/* CU
3MPLETED «12* STEPS*)
1165 FORMATtl5’3l2:‘3t*/2*9F60203X’SF15¢4)
146a FORMATIIS.13.x.2R1.13.¢/2*.F6-2:3X.3F15.4>
1568 FORMAT!15.2X.291.13.*/?*.F8.2:3Xo3F15.4)
EN n

 

196

G. ZEEPUN

This program calculates the Zeeman splittings for all
branches for the intermediate coupling case and for specified
values of field strength. Punch output of these is provided
for later input to the plotting program. Inputs include the
spin-orbit and rotational constants for the transition under
consideration, the Zeeman splitting constant, the vibration-
rotation band, the fields to be used and the J-values desired.
Also available is the option of adding a fixed value to all

splittings.

STRUCTURE OF DATA DECK

I. Punch Option card

 

 

Col. Field Function
l-9 I #0 indicates punch section is
desired.
10,11,12 R Beginning in col. 10; P, Q, and

R indicates that punch output of
these branches is desired. One
or all may be used.

20-29 I #0 indicates punch output is
desired.

II. Constants card

 

These three cards contain the values of the molecular
constants A and B and the Zeeman splitting constant respect-
ively. The cards are read from left to right and have 8 fields
of 10 columns. The constants A and B are punched on the first
two cards in the order v = 0, l, 2, 3 for 1”N150 and 15N150
respectively. The Zeeman constant is on the third card in

(3015. 1’10.

 

197

III. Band card
The band designation is typed in cols. l-lO of this card.
The codes are: (l—O) = 1, (2-0) = 2, (3-0) = 3, HES = 4, LES = 5.

The format is I10.

IV. Field strength card

Up to 8 values of field may be input and the splitting
is automatically calculated for each. The value is input in
gauss; there are 8 fields of 10 columns starting from the left

of the card. The format is 8(F10.l).

V. J-value card

This card specifies the J-value(s) desired and provides
for adding a constant value to the splittings. The option
of choosing only one subband is also available. As many of

these cards as needed may appear.

Col. Field Function
12—13 I 2J
20-32 F #0 indicates that this value should

be added to all splittings.

41—50 I A value of l or 2 will indicate
that only that subband is desired.
A blank will cause calculation for
both.

73-80 A If the word COMPLETE appears,
splittings of all transitions up to
and including J are calculated.

VI. Return card
If RETURN appears in cols. 75-80, control is returned to I.

VII. New case card

If NEW CASE appears in cols. 73-80, control is returned to

 

 

198

section III.

VIII. StoE card

 

If STOP appears in cols. 77-80, execution is terminated.

A listing of the program follows.

 

10fi

1001

100?
9999
1D03

199

PROGRAM ZEEPUN

COMMON/1/ FREQ!3H0).XIMF(300)

COMMON/4/ IJIM. {BRANCH(3).IPUVCH

READ 1. IJIMo(IBRANCH(M).N:1:5)oIPUNCH

FORMAT (19.3R1.7X.110)

DO 3 L3103

IBRAMCH(L)aIBHANCH<L>-1Rn

CALL ZEEMAN

GO TO ion

END

SURROUTINE ZEEMAN

COMMON/1! FREU(3fl0).XINT(3DU)

COMMON/4/ IJIM, IBRANCH(3).IPUVCH

DIMENSION nA<1n).A(5plu).DR(1G):8(S.10).DG(100p2.1).G(100.2.5),
Htlfl):Y(3)

DIMENSION ISIGN(?).FRQ(50.?.3).lNIt50.2.3)

DATA(ISIGN=1,-1)

TYPE REAL INT

N:O

READ 10((A(19J):J=N:3)n1:1.2):((B(I:J):J=N13)oI=1:2):AMUO

FORMAT (8F1005,/’8F10051/’F10)

READ 3. tMOL

FORMAT {10!}!2)

READ 1001, IBANP

FORMAT (110)

READ 1fi02; (H(I).l=1.8)

FORMAT (RF10.1)

READ 1n03. JMAX.¥NU.ISHBANH.IPLT

FORMAT (11x:12;6¥0F130419Xp110:22X.A8)

IFtlpLT.EU.8H STOP) GO to 5000

IFCIPLT.EO.8HNEW CASE) G0 T0 2

IFCIPLT.EO.8H RFTURN) RETURN

H(9)=0.0

JMOLBIMOL~13

CONTINUE

LHAx=(JMAX+1)/p

JF=8

DO 61 J=12JF

IF(H¢J+1).E0.0.0)JF=J

FLDFAczAMU0*H(J)

FIELD=H(J)

FU=FL=91.D

GO TO (5.6.798.9).IBAND

NJ=2

NU=NL=KU=1

KL=n

EPSU‘EPSL='1ID

GO TO 15

NJ=2

NUQNL=1

KUOZ

KLIO

EPSUaEPSL=-1.0

GO TO 15

200

7 NJ=2
NUBNL=1
KU'S
KLBO
EPSU3E95L=’1QO
60 T0 15
3 NJINL=KU=ITRL=1
NU'Z
KLflO
EPSU=1,0
EPSLB-1.D
1TRO=3
GO TO 15
9 NJINU=KU=ITRU=1
NL'Z
KLfio
EPSquton
EP3L=1.0
ITRL=3
15 CONTINUE
Y(KU)=A(JMOLaKU)/B(JMOL.KUs
Y(KL)=A(JMDLoKL)/B(JMOL.KL)
IFtISURAND) 9100:9200
9100 NBSNT=ISUBAN0
IF¢ISUBAND.E0.2) FU=FL=1.0
GO TO 9000
9200 NB¥1
NTQNJ
9000 DO 61 MzNBpNT
lFtM.Em.2)NUENU*1
IF(M.EQ.2)NLINL+1
FUIFUtEPSU
FLyFLrfiPSL
JJQLMAX*1
160:1
DO 20 LsiaJJ
IFCIPLY.NE.8HCOMPLETE) 202.201
20? IFtIGO) 200.201
200 L=LMAX91
180 I 0
201 A0-L2.5
AM.A0*(AQ*1QO)
G(L.NU.KU)'(1.5+FU*((2.0!(AMec75))91.5wY(KU)*3.ODISORTC4.0tAM¢1.0+
1Y¢KU)*(Y(KU)94,0)))IAM
G(LaNLoKL’3(1q9*FL*(‘2.0*(AM9075))91Q5*Y(KL)*39U)/SQRT(4.0*AM¢1.0+
1Y(KL)t(Y(KL)!4.0)))/AM
20 CONTINUE
DO 61 LainLMAX
IF!!PLT.NE.8HCOMPLETE) 300.301
30g LaLMAx
301 ASSIGN 51 T0 NGOTO
AOHLFOS
J0!2*Lu1
IFCNL.EG.2.AND.L.LT.2)GO To 60

201

IF‘NUoEQoNL) 200012100
2000 ISUB'NU
PR‘NT 31: IMOLoKUoNUIJQ9H(J)
GO TO 50
2100 IrtNU9NE¢NL) 2200:50
2200 IF‘ITRUBITRL’ 2300;230032400
2300 ISUB‘lRL
GO TO 2500
2400 ISUBSlRH
2500 PRINT 41.1M0L.Ku.ITRL.ITRU.JQ.H(J)
50 JH'L‘L
182tJM
SU"P¢1.333*A0*(2o*AQ*1o’*(2q‘AQ91.3
SUMQ'19333*AQ*CA0*1.3.02.*AO*1,)
SUMR310333.(AQ*10)‘(29'A0‘1o)‘(20'AQ‘30’
DO 60 KalaJM
LJBQL+K
AJ‘LJ' g 5
ALPHA:G(L:NL0KL)*FLDFAC*AJ
ZETAR=(AJ9190)*FLDFAC
ZETAL=¢AJ*1.0)tFLDFAC
DNUPLBDNUPRzDNUQL=DNUQR=DNURL=DNURR=RITNPL=RITNPRHRITNQLERITNOR=
1RITNRL8RITNRR=1o¢t10
IFCLcGE.3) GO TO NGOTO
IFCNUoEQo2oAND.LuLTo3) ASSIGN 52 T0 NGOTO
IF‘NUQEQoloANooLILTvZ) ASSIGV 52 TO NGOTO
IFCNUQEQozoAND.L.LTg2) ASSIGN 53 TO NGOTO
IF‘NLOEQ¢ZO‘~DQLQLTQZ’ ASSIGN 53 T0 NGOTO
GO TO NGOTO
51 DNUPR=G(L*1pNU.KU)*ZETAReALPHA
DNUPL‘G‘L‘ioNUoKU)*ZETAL9ALPHA
RITNPR'((AfltflJ)*(AOtAJ51.0))*1009/3UMP
RITNPL=((AOHAJ)*(AOQAJ91.0))Olooo/SUHP
52 DNUQRSGCLpNU:KU)VZETAR2ALPHA
DNUQL=G(LpNU:KU)§ZETAL!ALPHA
RITNQR3‘(A0*AJ,*(A09AJ*1QO,)‘1000/8UMQ
RITNDL3((A0-AJ)*(A0+AJ*1.D))*1009/3UMQ
53 DNURR=G(L*1cNU,KU)*ZETAR9ALPHA
DNURL=G(L*1pNU,KU)‘ZETALGALPHA
RITNRR3((AO!AJ¢1.0)*(AQ-AJ*290))‘1009/SUMR
RITNRL3((00*AJ*1.0)*(AQ*AJ5210))‘1009/SUMR
IF‘RITNPLoEQo0.0)DNUPL8RITNPL310**10
IF(RITNPRoEQ.0.0)DNUPRIRITMPR310**1O
IFCRITNQLoEog0.0)DNUQLIRITNQL510‘*10
IF‘RITNORqfiov0.0)DNU0R3RITNQR‘10**10
IF‘RITNRLQEQO0.0)DNURL'RITNRL310**10
IF(RITNRR.EQ.0.0)DNURR3RITNRR310**10
INDEX=2¢L421
PR1NT55:INDEX:DNUPLaanNPLaDNUPR:RITNPRJDNUQLoRITNQLoDNUQRnfilTNQRo
inNURLianNRLoDNURRaRITNRR
IF(IJIM) 500160
500 PRQ(Kp1:1)flDNUPL*XNU
INYCKt1a1)IR!TNPL
FRQ(K:291)§DNUPR¢XNU

 

60

801

5500

850

799

800

3000

5501
900
61

5000

59
31

41

202

INT(K:2;1)3RITNPR

FRQ(K:1:2)=DNU0L*XNU

INT(K:1:2)=RITNQL

FR0(K:2:2)=DNUDRtXNU

INT(K.2.2)=RITNQR

FRQ(K91:3)=DNURL+XNU

INT(K01:3)=RITNRL

FRQCKa2:3)=DNURR+XNU

INTIK,2.3)=RIT~RA

CONTINUE

TF(IJIM)801o61

DO 900 LI=1a3

IFIIBRANCHILI).GT.5) GO TO 61

NAME=IBRANCH¢LI)+1RO

IF(IPUNCH) PUNCH 5500: NAMEolsdB:JQ:IMOL:FIELD
FORMAT010X.2R13X9120'/2*32X1*N.12*0‘06X:F1091o*GAUSS*)
DO 800 KI=1pJM

DO 800 JI=112

IFIFROIKI:JIaIRRANCHCLID).GT.5000) 799:850
FREQIKI¢(JT91)OJV)=FRQ(KI:JIaIBRANCH(LI))
XINTIKI¢IJ191)*JV)=INTIKIaJI:IBRANCHILI))*ISIGN(JI)
GO TO 800

FREQIKI¢IJ191)*JV)=0.0

XINTIKI+(J191)*JV)=0.0

CONTINUE

NUM:0

DO 3000 N=1,I
IFI.N0T.FREQIN))
NUMsNUM+1
FREOINUM3=FREQ(N)
XINT(NUM)=XINIIN)/100.

CONTINUE

IFIIPUNCH) PUNCH 5501:(FREO(<0):XINT(KQ):K0=1:NUM)
FORMAT (4(?(F7.4o3X)))

CONTINUE

CONTINUE

GO TO 9999

CONTINUE

FORMATII4i/2*dI2(2XF7.4.XF3)X))

GO TO 3000

FORMATIti CALCULATION OF ZEEMAN SPLITTINGS AND RELATIVE INTENSIT
11ES FOR.*/~ NtthO. «law-0. BAND, *Ilt-SUBBAND.t/t J = t12*
2/2, H =¢F5t GAUSS.*I*-*18X*P BRANCHt17xw0 BRANCH017X*R
3 BRANCHt/*n MJt3(t DELM+ I DELM~ ItX)/>

FORMATtti CALCULATION OF ZEEMAN SPLITTINGS AND RELATIVE INTENSIT
1IES FOR,*/v N¢12w0. thweo. tI1*/2 - *Il*/2 BAND.t/t J = .1
22*/2. H = tFSt GAuss.-/t-¢18x*9 BRANCH*17X*O BRANCH*17X
3*R PRANOH*/*0 thatt nELM+ I DELM- [*XII)

END

 

203

H. PLOTPUN
This program accepts input of intensities and splittings
symmetric about the origin, and calculates and plots the absorp-
tion, Zeeman and magnetic rotation signals expected. Gaussian
and intermediate lineshapes are available; Gaussian, triangular
and trapezoidal slit-functions are available. The Doppler,
Lorentz and slit—function HWHM, pressure, polarizer angle and

path lengths are input.

STRUCTURE OF DATA DECK

I. Option card

Col. Field Function
1 I = l, 2, or 3; indicates that a

Gaussian, triangular or trape-
zoidal slit—function is desired.

2 I #0; calculates rotation angle per
unit path length.

3 I #0; calculates the individual
transmission fractions for all
components.
=2; plots the unintegrated CD
pattern.

4 I #0 calculates the unintegrated
circular birefringence.
=2, plots the unintegrated CB

pattern.

5 I #0; plots the transmission frac-
tion for right and left circular
polarizations.

6 I #0; calculates the CD pattern

integrated over the slit-function.
=2; plots the above.

7 I #0; calcualtes the CB integrated
over the slit-function.
=2; plots the above.

Col.

8

9

10

ll

12

l3

14

15

21-30

31-40

41—50

51-60

61—70

71-75

76—80

Field
I

I

204

Function
#0; plots the integrated MR signal.

#0; plots the unintegrated MR
signal.

plots a title according to the
code; l-CIR. DICHROISM, 2—TRANS-
MISSION, 3-ABS. COEFFICIENT, 4-
MAG. ROTATION, 5—ZEEMAN, 6— ABSORP—
TION, 7—blank.

#0; causes all plots above to be
superimposed.

#0; plots the integrated absorption.

#0; prints values of all quantities.
=1; every 5th plotter unit printed.

= - every plotter unit printed.

=3- every 2nd plotter unit printed.

=4; every 10th plotter unit printed.

~

~

#0; suppresses the plot of the experi-
mental conditions.

#0; plots bar graph of the Zeeman
patterns.

Doppler HWHM.

Lorentz HWHM, an intermediate (Dop-
pler) lineshape is used if this is
non—zero (zero).

Range in cm_1/10" of the plot.

Height of the plot in intensity
units/inch.

Slit-function HWHM.

#0; uses trapezoidal slit-function.
This is the halfwidth of the top of
the trapezoid.

A tolerance used to control the in-
tervals of integration in calculating
the lineshape. The intervals are nor-
mally 0.001 times the range in cols.
41-50 above. The tolerance may be set
to some fraction of this value. It is
preset to 1.0.

 

205

II. Pressure gggg
Values of the pressure are read by the format 8F10. The
calculations specified on the option card are automatically
repeated for every pressure.
III. gay 3; Ehg following EEEEE mgy appear
1. Absorption SEEQ‘ The integrated absorption coefficient
for the transition is input in cols. 1—10, the path length
in cm. is in cols. ll-20 and the polarizer angle in degrees
is in cols. 21-30. The splittings and relative intensities
follow this card.
2. Ngw 9353 9339’ If NEW CASE is encountered in cols.
73-80, control is returned to section I.
3) Spgp EEEQ‘ If STOP is encountered in cols. 77-80
execution is terminated.
IV. Splitting EEEEE
These cards follow card III-1 above. The splittings and
intensities must be symmetric about the origin as input.
1. Tiglg 233$: This card is the title card punched in
ZEEPUN. It specifies the transition and field strength.
2. Splitting EEEQE‘ The splittings and fractional inten-
sities from ZEEPUN are input here.
3. E1225 £359: A blank card signifies the end of input data.
V. Control EEEE
Upon completion of all options for the last pressure, con-

trol is returned to section III.

A listing of the program follows.

9%
9n

91
9Q

92
81
82
8%

87
86

85

88

206

PROGRAM PLOTPUN

COMMON/1/ XNU(300).A(300)

COMMON/z/ DABSCOFMIéOl).ABSCOFW(600).DABSCOFPI601).ABSCOFPIbooI
COMMON/SI SY;SX.”AXPOS.GAML.GAAD¢ I0?(20>.NUMBER.XHAX.NUHM
COMMON/4/ nsHAPEcbol).SHAPE(600).IMAX.IMIN.SLITWDTH.P0L.SLIITRAP
COMMON/S/ ILABFL¢4IIFIELU

COMMON/b/ RANGE.HETGHT.SO.O(8).PRES:0PL:XNUZERO:SLITNORM:T0L
common/7; DTRAMSP(601):TRANSW(600).DTRANSP(601):TRANSPC600):

1DCD(601).CD(600)

COMMON/Bl DPHII601).PHI(600)

COMMON/9/ DFARADAYI601):PARADAY(600)

CoMMON/10/ DCDINT(601)aCOIMT(600):DFARINT(601):FARINT(600)
CONNON/11/ DLNSHP<601).XLNSHP(600)

DIMENSION LABELIA)

DIMENSION 11(4).I2t4)

DIMENSION NAMESI10).NAME2(40)

DATA(I1=1)'101.’1)a(l2=0311021)

DATAINAME1=8HCIR. DIC:RHTRANSMIS:8HABS. COE:8HHAG. ROT.8HZEEMAN :

18HABSOWPTI.8H ).(NAME2=8HHROISH .aHSIou .BHFFICIENT.8HA
2TION .aH :BHON .AH I

NUMBFRzo

READ 9n, 10P.GAMP.GAML.RANGE.HEIGHT:SLITNDTH’SLITTRAP.TOL

FORMAT (2011:5F10:2F5)
IFIIUP(15)) IOP(14)=1
IF(.NOT.T0L) TOL=lo0

PLHT=6.

IF‘HEIGHT) PLHT=FEIGHT/100.
KALL=1

PTFSTzn,

IF(.N0T.IOP(10)) IOP(10)=1

READ 91,P

FORMATIBF10)

READ 2.sn.nPL.POLANGLE.XNUZERU.ITEST
FORMAT (3F10:19X,F10917X.A9)
pOL=PULANGLE/57.99575
IF(ITEST.EG.RHNEW CASE) GO TO 95
IF(ITEST.EQ.QH STOP) GO TO 80
READ 9?: ILAHELIFIFLD
FORMAT(1UX.2H1;Xp12:5Xa17:7X1010)
N:1 T NM=4

READ 80: (XNU(J00A(J)1J=N0MM)
FORMAT (4(7F105)

DU 87 J3N1NM

[F(XNUIJ)) GO TO 85

CONTINUE

NzN-j

IFIXNUINI) 80,86

N=N+4

NM=N+3

60 TD 02

IFREQ=N

DO 4 ngnerEQ

L=J+1

 

11

9000

15

17

19

20]

DO 4 K=L91FREQ
IF(XNU(J).LEoXNU(K))4.3
T:XNU(J) 0 S=A<J>
XNU(J)=XNU(K) $ A(J)=A(K)
XNU(K)=T T A(K)=S

CONTINUE

PRINT 200.1LABEL.F1ELD

PRINT ?02

pRINT 201: (XNU(J):AIJ).J=I.IFQED)
NN=1

pRES=P(NN)

NNsNN+1

IFI.N0T.GAML> GU T0 11
IF‘PTEST-PRES) KALL=1
PTEST=PRFS

CONTINUE

PRINT 203. GAME

PRINT 1203, GAML

pRINT 904: SLITNPTH

pRINT 705: Sn

PRINT 706: OPL

PRINT 207. PRES

PRINT 708. POLANGLF

IM=~600

DO 7 IN=IM9600

ABSCOFM(TN)=0. $ ARSCOFPIIM)=0.
TRANSM(IN)=1OU S TRANSP(TN5=100 f CD‘IN)=00
PHI‘IN)=UO

PARADAVIINI=0. $ CUINTCIN)=0. % FARINTIIN)=0.
XLNSHPIIN)=09

CONTINUE

Xth=0

Numm=0

ASSIGN 150 T0 NGC

IFINUMRER) GO TO 16

CALL PLOT(-4..31..0n100..100o)
CALL PLOT(0..0..1)

CALL PL0T(0.9'2..0)

X=O, $ Y=0. T NU“BFR=1 S NHMBER1=1 $ JUM=1 5 GO TO 17
NUMBER=NUMHER+1
NUMBERI:NUMBER/2,+i
NUM=XMODF(NUMBFR,4)+1
JUM=XMODFINUMBER.2)
X=15,*11(NUM)

Y=10.*I2(NUM)

CALL PLOT‘Y,X.2,100.9100.)

CALL PLOT(0..0..0)

IF¢.NOT.JUM) GO TO 19
JU8:20.tNUMBER1

CALL PLOT‘JUB.0..3)

CONTINUE

IFCIOPI15II GO TO 21
XPLHT=PLHT+.1

CALL CHAR(XPLHT.1..NAME1(IOP(10))18.0...2o.2)

 

21

8000

8001

1000
1001

1009

1001

1004

1030

208
CALL CHAR‘XPLHT.3..NAME2(IOP(lD))a8:0.9923.2)

CALL PL0T(PLHI.10..2)
CALL PLOT(PLHT.0..1)
CONTINUE

CALL FLUTIO..5..?)

CALL PLOTIn..0..n)
IFIRANGE) 00 I0 8001
UEL=XNUIIFREO)-XAUI1)
RANGE = OEL+0EL*.1
IFI(RANGE-DEL)/2..GT.6tGAMn) 03 I0 8001
RANGE:RANGE+.1.UPL

GO TO 8000

CONTINUE

XSCALE=10./RANGE
Sx=1000./RANGE

NAXPOS=SX

SygénUO

IFIHEIGHT) SY:HEIGHT

M:fl

TICS=RANGE/20.

Du 1non J=N.6
XTICS=ITICS)*10.**J
IFIXTICS.LT.1.I 00 TO 1000
IFIXTICS.LT.1.5) GO TO 1001
IFIXTICS.LT.2.5) GO TO 1009
GO TO 1003

comTINUE
DELx=1.*(10.*t(-g))

ID=5

Go TO 1004
DELx=2.*(10.**(-g))

ID=5

GO TO 1004
DELx=5.*(1n.**(-q))

ID=2
NUMTICS=RANGF/I2.*0ELX)
0:5.IXSCALE

CALL PLOTIO..-0.7.300..SK)
MAX=NUMTICS*?
X=EINUMTICS)*DFL¥

XNz-X

NUMBIG=NUMTICSIIE
LL=NUMTICS—NUMRIG*ID

CALL PLOT(0.,X,1,100,:SX)
Do 1010 L=N.MAX

YUB.05 $ Y0=-.05
IF<L.NE.LLI 00 TC 1030
Yu=.1 0 YD=~.1 $ LL=LL+10
CALL PLOTIYU.X.1)

CALL PLOT(YD.X.1)

CALL PLOT(0..X.1)
IFCL.E0.MAX) GO TO 1010
X=X¢DELX

CALL PLOT(“.OX:1’

 

1010

2501

2500

5100

5001

300

2502

2503

2504

2600

209

CONTINUE

CALL PLUT(fiooD.1310009SX)
X:¥N-.5125/XSCALE

ENCODE€592501.IX2) XN

FORMAT (F5.3)

CALL CHAR‘-Q2)X)1x205900901tol)
XN=-XN

X=XN'.375/¥SCALE

ENCODEI6.2500.IX1) XN

FORMAT(F6.3)

CALL CHAR(~.2.X.IX1.6.0...1..1)

CALL PLOT (0o.0..2)

IF(IDP(14)) GO TC 2600

CALL PLOT (093-50321100091000)

CALL PLOT (0..0..0)
ENCOOEC1.5100.LAEEL(2)) ILABEL(2)
ENCODEI1.5100.LAEEL(1)I ILABEL(1)
FORMAT(1R1)

ENCODEt2:5001.LAEEL(3)) ILABEL(3)
ENCQOE (2.50“1.LABEL(4)) ILABbL(4)
FORMAT (123

CALL CHAH(-.5.1..LABEL(13.1.0...1..1)
CALL CHAR('.5.1.I:LAREL(2).1:U.:o1.q1)
CALL CHAR('0591ogBOLABELc3’IZ’UoJ01801)
CALL CHAR('.5.1.$.2H/2.2.0...1..1)
CALL CHAQ(905110fi91HN310003019.1)
CALL CHAH(-.5.i.0.LAREL(4),2:0.:.1..1)
CALL CHAR"08190731H091109901,01)
CALL CHARI'.5.9.6.PHH=.2.0.:.1..1)
NFIELD=FIELD

ENCODEI433001LF) NFIELD

FoRmATI14)

CALL CHAH<905:?.prLF1490o,.11.1)
CALL CHARC‘.5.3.45a5HGAUQS,5.0...1..1)
ENCOUEI4.2502.LPRES) PRES
FORMATIF4.1)

CALL CHAR('059403012HP=329n0001901,
CALL CHAR(-05)4Q‘0’LPRESI4D09’01'01)
CALL CHAR('o5.5o?032HMM1290o:011.1)
CALL CHAH('u5:5.7004H09L=’4100:01:.1)
ENCODEI4.2506,LOPL) OPL

FORMATIF4.n)

CALL CHAQ‘FQ59691SDLOPLD4100001:91)
CALL CHAR<?.5.5.7512HCM1210o:013.1)
CALL CHAH(9é3;7.3506HP0L.= .6:0.o.1:.1)
ENCOHEI5.2504.LPOL) POLANGLE
FORMATCF5.1)

CALL CHAR“05970950LP0L353n0001001)
CALL CHAR(~.5.B.65.3HDEG.3.0o:.1..1)
CALL PLOT (0..5..2)

CALL PLOT €0..0..0)

CALL PLOT (0..0..2.100..SX)

CONTINUE

”0 3000 LLalolFREQ

 

210

L=IFREO+1'LL
X:¥NU(L)
IFIIOPI16IT GO Tn 3001
Y1=0.1
CALL PLOT‘”.IX32)
IF‘A‘L).LT.0¢U) Yl=-0.l
GO TO 3200
3001 CALL PLOT‘0o9X1208Y18X)
Y1=AILI
3200 CO0TINUE
CALL PLOT(V1nX.1)
3000 CALL PLOTIO..X.1I
CALL PLOT(0..X.2.SY.SX)
GO TO MGQ
150 IFIKALL) CALL LINESHAP
00 9 K=1.1FREU
CALL ARSCUIK)
9 CONTINuE
IJ=~XMAX*SX
IT=~IJ
CALCULATES SLIT FUNCTIFN
IFCInP(1)) CALL QLITFUNC
CALCULATFS ROTATION ANGLE/UNIT PAT4 LENGTH
IFIIOPI2)) CALL REFRACT
CALCULATES IWDTVTDUAL TRANSMISSIONS: PLOTS C.Do
IF(10P(3)) CALL TRANS

PATTERN

CALCULATES AND/UR PLOTS UNINTEGRATEU FARADAY ROTATION

IFCIOPI43) 6999.7020
699° IFI10PI15>I GO TF 7000
IFIIOPI4).NE.2) 60 TO 7000
IFINUMW) 7010.7000
701m ASSIGN 7non T0 N00
CALL PLOTID..U..9.SY,S¥)
CALL PLOT‘C.:'5.;21100.3100.)
CALL PLOTIn..U..n)
GO TO 9000
7000 CALL FARROT
7020 CONTINuE
c PLOTS INDIVIDUAL TRANSMISSION CJHVES
IFIIOPI53) 30.9300
30 IFIIOPI11I) 00 I0 7100
IFINUMM) 7110.7100
711a ASSIGN 7100 T0 N00
CALL PLOTIU..U..2.SY.SX)
CALL PLOTIn..-5..2.100..100.)
CALL PL0T(0.10.90)
GO TO 9000
71am CONTINUE
X=IJISX
NUMM=1
CALL PL0T(TQJX:238YJSXT
00 31 LITJ.IT
X=X+(1./SX)
YT=TRANSMILI**2

 

 

31

32
930n

211

CALL PLOT(YT.X.1.SY.SXI
X=IJISX

CALL PLOT(1..X.2.SY.SX5
D0 32 L=1JnIT
X=X+(1./SX)
YTETRANSP(L)**7

CALL FLOT‘YT.X.1.SY.SX)
CONTINUE

CALCULATES AND/0H PLOTS INTEGRATED 0.0. PATTERN

940a

500

505

51”
9500

TFfIUPIé)’ 9400:9500
CONTINUE

IFCIDP(11)) GU TC 500
IFIIOP(6).wEo2) GO TO 500
IF€NUMM) 7200,50”

ASSIGN sno TU N00

CALL PLOTC0.:U.:?:SY15X)
CALL PLOT(“.0‘5o.2n100.3100o)
CALL PLOT(0.:0..0)

GO TO 9000

CONTINUE

N831J'IMTN

N =-NB $ Xth/SX
IF‘IOP(6,06002, AUMM=1
CALL PLOT(0..X,2,SV;SX)
00 510 N=NR.“I
X:¥+(1,/SXT

YS=0.

DO 505 M=IM10:TMAX

NM:N+M
vs=y3+sHAPF<M).cr<mM)
YT=YS/SLITNUHM
CDINT(“)=YT
IF‘IOPC6To3002) CALL PL0T(YT9X11:SYISX)
CONTINUE

CONTINUE

CALCULATES AND/OR PLOTS INTEGRATFD TARAUAY ROTATION

9600

7311

7300

IFIIOPI7I) 9000.9700
CONTINUE

IFIIOPI11)) 00 TC 7300
IFIIUPI7).NE.2) GO TO 7300
IFINUMM) 7310.73n0

ASSIGN 7300 TO N00

CALL PLUT‘C.:0.;2:SY:SX)
CALL PL0T(nql“5032:100001009)
CALL PLOT(n..0..0)

00 T0 9000

CONTINUE

NBBPfigg’TMIN

NTarNB

XzNQISX

IF(IOP€7).EQ.2) NUMM=1
CALL PLOTCQoJX3293YISXJ

DO 610 N=N0.NI

X=X+¢1./$X)

 

212

Y8300
DO 605 M=I~IN,IMAX
wM=N+M
605 YS=YS+SHAPF(“)0FARADAYtNM)
YT=YSISLITNORM
FARINTtN5=YT
IF(10P(7).FQ.2) FALL PLOT(VT.Xo1:SY:SX)
610 CONTINUE
970n CONTINUE
c pLoTs INTEGRATED M.G. SIGNAL
IFtlfiP683) 990n.9900
9800 CONTINUE
lFfIOPt11)3 GO T0 9802
IFtNUMM) 9801,6802
9801 ASSIGN 980? T0 N60
CALL PLOT(0.:U..?,SY:SX)
CALL PLOT (0.,-S.:?.100..1n0.)
CALL PLOT(0.:0.:0)
GO TO 9000
9809 NUMM=1
NB=-S9QPIMTN $ NT=-NR f X:MB/bx
CALL PLOT(”.;X,2,SY,SX)
DO 710 N=NR:NT
X=X+(1./SX)
Y:CuINT(N)+FAHINT(N)
710 CALL PLDT(Y,X,1.SY:SX)
9900 CONTINUE
C PLOTS UNINTEGRATED N.R. SIGNAL
1F(10P(9)) 991n.99?0
9910 CONTINUE
IF(10P(11)) GU TF 9915
IF(NUMM) 9011,0915
9911 ASSIGN 9°18 To N00
CALL PLOT(0.:0..$.SY.SK)
CALL PLOT (001'sol?)100011000)
CALL PL0T(0.:0.,0)
GO TO 0000
9918 NUMM=1
.=9500
X=LISX
CALL PLOT (0..Y:2,SY.SX)
DO 810 13L:5“0
X=X+(1./SX)
Y=CD(I)+FARADAY(I)
810 CALL PL0T(Y:X.1:SY:SX)
9920 CONTINUE
C PLOTS ABSORPTION
IFCIOPC12)) 9930,9940
993m CONTINUE
1F£IUP(11)) GO TC 7400
[F(NUMM) 7410,7400
741a ASSIGN 7400 TO NGO
CALL PLOT(0.o0.:?:SYaSX)
CALL PLOT(0.;—5..2n100.:100.)

 

740a

9939

9931
9940

216

CALL PLOT‘D.:0.;0)

Go To 9000

CONTINUE

NB=~599-IMIN f NT=-NB F X=NBISX
NUMM:1

CALL PL0T(0.:X,2.SY.SX)
DO 9931 J=NB,NT
X=X+(1./SX)

YS=0o

DO 993? K=IM1N.INA¥
JK=J+K
TMzTRANSM(JK>tTRANSM(JK)
TP=TRANSP(JK)*TRANSP(JK)
YS:YS+SHAPF(H)*(7.-TM-TP)
YT=YSISLITN0HM

CALL PLOT(YT.X.1.SY,SX)
CONTINUE

C PRINTS VALUFS OF ALL QUANTITIFS

9950

9959

9955
9951
9960

20

80
100
10?
20’1
201
20?
203

1203
204
20%

IF(IUP€13)) 9950,9960

CONTINUE

PRINT 9952

FORMAT(t1 Xt7X*ABSURPIIUV* BXtTRANS.*10X*CD*9X*ROT. ANGLEtlflx

.‘FR*12X*MR*9X*INT. MP*10XtQFt/)

m=n % Y:n.

INDEX=5

IF(IOP(13).EU.?) INDEX:1

IFCIOPC13).EW.3) IMDFX=2

IF(IOP(13).EQ.4) INDEX=10

DO 9951 I=~,bgn,INnex

AB=ARSCOFM(I)+ABSCOFP(1)

TR=TRAHSM(T)tTRAhSP(I)

XMH=CD(I)+FARADAV(I)

XMRI=CWINT¢I)+FAGINT(I)

pRINT 9955.X:AQ.TR:CD(I).PHI(l)pFARADAY(I),XMRpXMRI.SHAPE(I)
FDRMATtF10.4:4X.E10.3.4X,2(F10.4,4X).E1393,4X.4(F10.4.4X))
X=X+(IMDFX/SX)

CONTINUE

CALL PLOT(fio93.:?:SY03x)

CALL PLOT(0.:-5.,2:100..100.)

CALL PLOT(fi.:0.:0)

Y:fi,

X:n,

IFtPtNM)) 00 [n 1

G0 T0 99

CALL PLOT (JUB.0.:-1)

FoflmAT(2F20.2)

FoRMATtSAB) ‘

FORMAT(*1*DZR1:XJI?:*/2 N*12*O*6XIF1001* GAUSS*)
FORMATtt *4X.F10.4,2X:F10.4)
FORMAT¢¢0*30X:12HVALUES INPUT/It *5Xa9HFREQUENCY:4X99HINTENSITY/)
FORmATcanDnPPLER HALFNIDTH *F10.4¢ CM91*)
FORMAT(xwLORENTZ HALFNIDTH *F10,4o Cn-1/ATM,*)
FORMAT¢X¢SPECT. HALFNIDTH *F10.4* CM-1*)
FORMAT(X*INT. ABSOWP. COEF. *F10.5* CM-Z/ATfigt)

 

206
207
209

50”

51m

600

21

20
an

214

FORMAT(X*0PTICAL PATHLENGTH *F10.1r CMt)
FORMAT<X*PPESSURF*llx,F10.?* TORRt)
FORMAT(XwP0LARIZER ANGLEi4pr10.2* DEGREESt)
END

SuRROUTINE LINFSFAP

COMMON/ll XNU(300)aA(300)

COMMON/2/ HAHSCUFM(601).ABQCOF%(600)aDABSCOFP(601):ABSCOFP(600)
COMMON/3, QY,SX,NAXPQSgGAML,GA”D: IOP(20)OVUMBERIXMAX:NUMM
COMMON/4/ HSHAPEc601).SHAPC(600).IMAX.IMIN.SLITHDTH,POL.SLITTRAP
COMMON/s/ ILAdEL!4).FIELU

COMMON/b/ RANGF,0EIGHT,sn,p(8).PRES.OPL.XNUZER0.SLITNORMpTOL
COMMON/7] HTHAMSN(601),TRAMSW(fiUO).DTHANSP(601):TRANSP(600)!

1009(601)p00(fi00)

COMMON/B/ hPPI(601).PHI(60fi)
COMMUN/qx NFARADAY(601).rAmADAY(600)
COMMON/lfi/ DCUTNT(601).C01MT(600).HFARINT(601)oFAHINT(600)
COMMON/lil DLNSHP<601).XLNRHP(600)
IF<.NOT.0A~L) 60 Th 5090

JMAX=700

UEL=1./SY

TLTNE=TOL

MN=1

IF(DFL.GT-TLINF) 500.600
TLINE=?.*TLIWE

NN=2tNM

IFIDFL.GT.TLI~F) 500,510
fiEL:fiEL/NN

JMAx=6norN~+1an

HDFL=0PL*DFL

GL=GAMLtPRES//60, f C0M:0.149ltGL*0EL/GAMD $ GGL=GL*GL
SIG=(.694/(GAMDti2))*DDEL

Nzfl

DO 10 1=N.A0fi

II=I*N“

XL=0.

no 2n J=N,JMAX

DEMOM:GGL+J*0*DDEL
XNHM=EXP(-Slht((q+tI)t*2))
X=XNUMIDFNOM

XszL+X

IF(X0LTo10F’5) GO TO 21

CONTINUE

PRINT ion

no 3n K=1,JMAX

L=9K

DENOMzGGL+JthnDEL
XNUM=EXP(‘SIG*((J+TI)**2))
szNUM/DENOM

XLFXL+X

IFCII*K) 29:30.30

IFCXoLT.1oF-h) GE T0 31

CONTINUE

PRINT 100

 

31
in

4m

50

1000

5000

11”

111

150

100
200

10
1?

215

XLNSHP(1)=XL*CON
IFIXLNSHP(I).LT.1.F-6) Gm T0 40

CONTINUE
PRINT 20o
IIMAX=I

00 SO L=1:TINAX

39L

wasHP(I)=¥LNSHP(L)

KALL=U

PRINT iofiflnCXLMSPPfI):I=N.500:10)
FORMAT(F20.1“)

RETuRN

SIG:.694I((GAMDt*2)tSX)
CON=.47/GA“D

N:fi

DU 110 I=N.5“0
X=EXP(~S!G*(Ito2)>
XLNSHPTI)=V*CUN
IFTXLNSHP(T)0LTo7oF'8) GO TU 111

CONTINME
PRZNT 100
IIMAX=I

DU 150 L=1,IIMAX

I=EL

mesHPc1>=vLRSHPrL)

KALL:0
RETURN

FORMAT<tHAVE EYCFERED no LfiUp')
FORMATttHAVE EXCEEDED MAIN L003.)

ENH

SUQRQUTINE A“SCO(K)

COMmflN/ll
COMMON/Q/
COMMON/S/
COMMON/4l
COMMON/BI
COMMON/bl
CofimnN/7/

YNU(3UQ),A(300)
UAHSCUFMCéDl):ABQCUFW(600)1DABSCOFP(601)pABSCOFP(600)
SY,SY,PAXPOS,GAML,GAWD, IOP(20)oNUMBER:XMAonUMM
DShAPEI601)13HAPF(6OU)DIMAX:IMINoSLITNDTH)P0L:SLITTRAP
TLABFL(4):FIELn
PANGF:HETGHT:SO:P(B’oPRES:OPL:XNUZERD:SLITNORMQTOL
“THAMSW(601);TQAMSW‘fiUO)oDTRANSPC601)oTRANSP(600)9

10c0(501).C0(60n)

QOMMUN/Bl
COMmfiN/9/

HPHI(601).PHI(600)
HFARAUAY¢6015.FAQADAY(600)

COMMON/lfl/ DCDINT(601),CUIMT(600).DFARINT(601)oFARINT(600)
COMMON/ll/ DLNSHP<601).XLN9HP‘600’

AT:A(K)*SO*PRE§/760o

ATXL=ARSF(AT*OPL)

X=XNU(K)

TEST=1./SY

ABCO:ATXL*XLNSHP(J)
TEMP=1.~EXP(-ARCC)
IFTTEMP.LT.TEST) GO TO 12

CONTINUE
xw=x~Jlsx

 

1100

1000

3000

1200

1am

30m
20

in

216

IF‘ARSF(XNT.GT.XVA¥) XMAX=ABSf(XN)

IN=X*SY
Iwzxwwsx

MAX=IH+XABSF(2*(IN'IN))
ITSXABSF(IN)+XABSF(J)
IFTIToGT.600 ) 1100:1200
XMAX3600./SX

IFIIN) 1n0n.10n0.3000

[Na—600

HAX=600+?*IN

GO TO 1200

MAX=500

Iw=-600+9wTN

CONTINUE

no 20 J:Iw,Mnx

IL=JPIN

Y=AT*XLNSHP(IL)

IF‘Y) 1,00:

20:60.0

ABSCOFM(J)=ALSCUFM(J)+AB§F(Y)

00 T0 90

ABSCQFP(J)=AHSCOFP(J)+Y

CONTINUE
RETUPN
END

SURRQUTINE SLITFLNC

COMMfiN/1/
COMMON/z/
COMMON/sl
COMMON/4/
COMMON/SI
COMMUN/b/
COMMON/7/

.J

COMMON/Bl
COMMON/9/

CoMth/1n/

YNU(300).A(300)
”AHSCOFM(601),ABSCOT0(600):DABSCOFP(601).ABSCOFP(600)
SY.5X,~AKPOS.GAML.GAOD. IOP(20).NUMBERaXMAX,NUMM
psuApfifbfil),SHAPF(600).IMAX:IMIN.SLITNDTH.POL;SLITTRAP
TLABFLT4)pFIF’LP}
HANGF,PETGHT.SQ.P(B),P%ES:OPL,XNUZER0:SLITNORM:T0L
FTRAMS~(601),TRAMSW(600).DTRANSP(601).TRANSP(600);

000(601),Ch(bun)

0P01c6n15,PHI(60n)
LFAHADAY(601):FARADAY(600)
UCUINT(fi01).CnJMT(600).DFARINT(601).FARINT(600)

COMMON/11/ DLNSHP<601).XLNSHP(600)

TEST=1./SY

IF(]0P(1).FD.2) 00 T0 500
IFIIUP(1>.#U.$3 00 T0 700
SLITMORM=SX*SLITmDTHt2.13
810:.694/(SL1T001H+*2)

Nzfi

SHAPE(N)=1.0

X=0.

”0 10 1:1:600

X=X+(1,/SX)
SHAPE(I)=EYP(-SIG*(X**?))
IF¢SHAPE(I).LT.TFST) 20:10

CONTINUE
PRINT 100

100 FORmATttiA RANGE T00 SMALL FOR THE SLITNIDTH HAS BEEN USED*)
IMAX=I $ 1M1N:.INAX

20

21/

PRINT 900: X
20m FORMAT (waHE HALF-EXTENT 0F SLIT FUNCTION IS*F8.4w CM-1*)
DU 30 J=1;IMAX
=EJ
SHAPE(L)=SHAPE(J)
30 CONTINUE
GO TO 1000
500 SLITNORM=SX*SLIT00TH*2.
0:0 0 SHAPF(M)=1,0
in.
00 510 1:1.600
X:X+(1./SXJ
SHAPE(I)=l.-<.6t¥/9LIT00TH)
IrtsHAPE(I).LT.T£ST) 520.510
510 CONTINUE
PRINT 100
52% IMAx=I $ IMIN=~I~AY
pRINT 200,x
00 530 J=l.IMAX
L:9J
SHAPE(L)=SHAPL(J)
530 CONTINUE
GO T0 1000
70m SLITNOQM=SxtfiLITwUTH*2.U
0:0 $ x=n. $ ITNAX=SLITTRAP*SX
DU 710 I=N.ITMAX
X=X+(1,/SX)
SHAPF(T)=1.0
71H CONTINUE
IT=ITMAX+1
SLP:SLITHUTH-SLITTRAP
00 720 I=IT.600
X:X+(1./SX)
SHAPE(I)=1.-t.8'x/SLP)
IFtsHAPE(I3.LT.TEST) 730.790
720 CONTINUE
PRINT 100
730 Imhx=l $ HIM-INAx
PRINT 200.x
DO 740 J3131MAY
L=9J
SHAPE(L)=SHAPE(J)
74m CONTINUE
100m CONTTNUE
IOP(1)=0
RETURN
END

SURROUTINE RFFPACT

COMMON/ll XNU(300)oA(300)

COMMON/ZI DABSCOFMK601)aABSCOFM(600)aDABSCOFP(601).ABSCOFPC600)
COMMON/S/ SYQSYnflAXPOS:GAML:GAWD: 109(20):NUMBER:XMAX:NUHM
COMMON/4/ DSHAPE(601)18HAPE(600):IMAX:IMIN.SLITHDTH:P0LaSLITTRAP
COMMON/SI ILABFLt4).FIELD

 

1:"!

29
21

3“

500

600

215

CONMDN/él HANGE,HEIGHT.80,P(8),PRES:0PL;XNUZERO.SLITNORM:TOL
COMMON/7/ DTRAMS~(601).TRAMS%(500).DTRANSP(601):TRANSP(600).
1000(601).C”(000)

COMMON/BI 0PH1(601),PHY(600)

COMMON/9/ fiFARADAY(601).FARAOAY(600)

CONMDN/10/ DCDTNT(601).CUIMT(600),DFAHINT(601):FAHINT(600)
CUMMoN/ljl DLNSHP(601).XLNSHP(600)

iJIV'ENSIOM DDIFcénO).HIF(Aoo)

Isz-XMAX‘SY

IT=~IJ

M30

DO 10 L=IJ,IT

”IF(L)=ABSCOFM(L3'ABSC0FP(L)

co~=1./(4.t3.14159)

00 gm J=N:%99

Prn=.5¢(01£<0+1)-DIF(J-1))

PTsn,

00 26 I:IJ,IT

IF€I.E-’J..J) (50 T0 2‘)

PT=PT+0IV(I)/(Y-J)

CO”TINUE

PHI(J)=CflNv(PT+PT0)

00 3n J=1.H99

Ksz

pHT(K)=PHI!J)

RfiTuRN

ENn

SUHROUTIHE TRANS

COMMON/1/ YNU(Run).A(300)

UOMMHN/Zl ”AhSCOFMtboi).ABQCDFW(600):DABSCQFP(501).ABSCOFP(600)
COWMDN/E/ 3Y15Y9HAYPOS:GAML:GAWDo IOP(2U):NUMBER:XMAX9NUMM
COMMON/4/ “SHAPE(601).SHAPF(600).IMAX.IMIN.SLITWDTH:P0L.SLITIRAP
CUMMnN/S/ ILAHFLc4),FIFLO

COMMON/b/ PA"(:iFAvE:IGHT.80»0<0).Fifi'iFSmPL.XI‘TLJZERL‘J.SLITNORWTOL
000MHN/7/ WThAMSN(601).TRAMSNT600).UTHANSP(601);THANSP(600):
10CU(801),CU(500)

COMmfiN/SI "PHI(601),PHI(600)

COMMnN/Ql “FAHADAY(601):FAPADAY(600)

COMMUN/lfi/ DCUINT<601).CUINT(OOOJ.UFARINT(601)oFARINT<600)
COMMON/11/ ULNSHP(601).XLN9HP(6UU)

IJ=~XMAX*SX

IT=~IJ

X=IJISX

ASSIGN 1n T0 Nno

IFtlflP!3).F0.2> 900:600

CALL PLOTtfi..X.2.SY:SX)

NUMM:1

ASSIGN 110 TV N00

00 10 L=TJ11T

X:X+(1./SX)

TM:(ABSCOFN(L)wOPL)/2o

TP=(ABSCOFP(L)¢0PL)/2.

TRANSM(L)=PXP(-TN)

 

219

TRANSP(L)=FXP(-TP)
IFGTRANSM(L).LT.J.E-100) “HAVSH(L)=0.
IFtTRANSP(L).LT.1.F-100) TRANSD(L)=0.
CDtL)=¢TRAmSM(L)-TRANSP(L))**2/4.
Go To “GO

110 CALL PLOT(CD(L).Y,1)

10 CONTINJE
RETURN
END

SUQRGUTIME FAHPUT
COMMON/1/ XNU(300):A(300)
COMMUN/2/ HAPSCUFM(601).ABSCOF0(600).DABSCDFP(601),ABSCOFP(600)
COHMUN/3/ SY:SY,VAXPOS,GAML:GAWU: IOP(20):NUMBER:XMAX;NUMM
COMMON/4/ HSHAPE’bGl):SHAPE(600)aIMAX.IMINoSLITNDTH:POL;SLITTRAP
COWMflN/S/ TLABFL<4).FIFLO
COMMON/é/ PANGF,HEIGHT.SU.P(8):P4E810PL,XNUZER0:SLITNORMoTOL
UO”MON/7/ ”THAMSV(601).T9AMSW(600).DTRANSP(601)oTHANSPCbOU)u
1000(601).CU(60n)
COMMON/B/ HPHI(6”1):PHT(600)
COWMUN/Q/ ”FARADAY(601):FAQADAY(600)
COMMON/ln/ DCUINT(601),C010T(000).DFARINT(601)nFARINT(600)
COMMON/lfl/ ULNSHP(fi01).XLNSHD(600)
"H g f}
no in ‘=m,a99
X=0PL*PHI(J)+PUL
SN=(SINF(X3)**9
XX=TRANSM(J)*IQARSP(J)
10 FAHAHAY(J)=SW*XX
DO 20 K=13599
=-K
2n PARADAY(J)=FAHADAY(K)
IF'IWP(4).NE.2) RETURN
MUMMal
=9500
X=LISX
CALL PlOT<FAHA0AV(L)3X:2:SY:SX)
00 30 K:L:500
CALL PL0T(FARA0AV(K).X:1.SV.SX)
30 X=X+1./SX
RETURN
END

 

PF‘HH‘F‘HW‘F‘HJJ
'ccnxaownssouvr4c:(>quc>u1acannpn 2:

NNNNNNNNNNNNNNNNNNNNNNNMNMNNNNNNNNN (.0

APPENDIX Vlll-A

GROUND STATE COMBINATION DIFFERENCE TIT FOR 14N160

V

COOOCDOODDCOOCOODQOCOOCOOOCCOOCDCOO

D

E
J

NNNNNNNNNNNNNNNNNNNNNNNNNNNNHHHPHHP

L

7/2

9/2
13/2
15/2
17/2
21/2
23/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
59/2
61/2

HGT.

0.00
0.00
0.45
0.00
0.00
0.00
0.00
0.80
2.00
2.00
2.00
2.00
2.00
3.91
2.40
2.65
2.00
2.00
2.05
2.07
0.00
2.00
2.67
2.00
2.00
1.54
2.00
0.80
1.11
1.03
1.33
1033
1.33
0.00
0.44

OBS.

15.5088
18.8957
25.7884
29.2080
32.6486
39.5050
42.9153
27.5128
34.3930
41.2639
48.1382
55.0015
61.8636
68.7263
75.5783
82.4288
89.2735
96.1112
102.9425
109.7659
116.5903
123.3991
130.2025
137.0010
143.7910
150.5671
157.3424
164.1065
170.8638
177.6128
184.3452
191.0731
197.7962
211.1806
217.8931

220

PRtD.

15.4766
18.9137
25.7838
29.2164
62.6471
39.5018
42.9253
27.5150
64.3906
41.2632
48.1334
35.0003
61.8635
68.7227
/S.5774
02.4271
59.2715
96.1102
102.9428
109.7689
116.5883
123.4005
160.2054
167.0025
143.7916
190.5725
157.3449
164.1086
170.8635
1’7.6U94
184.3462
191.0737
197.7919
211.2003
217.8905

(O-P)

0.0322
20.0180
0.0046
90.0084
0.0015
0.0032
20.0100
20.0022
0.0027
0.0007
0.0048
0.0012
0.0001
0.0036
0.0009
0.0017
0.0020
0.0010
30.0003
90.0030
0.0020
90.0014
90.0029
90.0015
90.0006
90.0054
90.0025
90.0021
0.0003
0.0034
90.0010
30.0006
0.0043
90.0197
0.0026

 

94+5Hw¢+s9+:HHAh5PAAk5Hw¢hsH+4ktHwArtHw*hrpwar5pwarbpw4r5944rtfiwarswwér4944r~H+4t9wwunoNHu

000°CDDCDOOCCCOOOOOCOOOODCOOOODDDOOCDDOCOOOCCDOODOODDO

NNNNNNNNNNNNNNNNNNNNNNNNNNNNMHPPHHHHHHPHPHHPHPPHHPNNNN

63/2
65/2
67/2
69/2

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2

0.46
0.00
0.00
1.44
4.44
7.19
9.29
5.99
4.33
4.38
4.53
3.43
4.53
3.15
4.86
3.37
2.48
4.02
3.43
3.08
0.11
0.59
0.23
0.21
0.00
6.49
4.38
2.00
2.00
3.30
2.00
2.00
2.94
2.67
3.61
2.40
2.80
2.71
2.35
2.00
2.00
2.00
2.40
2.00
0.00
0.00
1.33
1.54
1.54
1.11
1.39
1.33
1.33
1.33

221

224.5773
231.2435
237.8608
244.5585
5.0109
8.3645
11.7037
15.0449
18.3922
21.7368
25.0740
28.4238
31.7664
35.1067
38.4527
41.7943
45.1351
48.4791
51.8164
55.1594
58.5008
61.8383
65.1691
68.5089
71.8436
13.3770
20.0689
26.7511
33.4398
40.1269
46.8150
53.5011
60.1896
66.8753
73.5613
80.2440
86.9284
93.6102
100.2959
106.9757
113.6508
120.3317
127.0052
133.6732
140.3340
147.0000
153.6709
160.3331
166.9848
173.6407
180.2830
186.9201
193.5584
200.1914

224.5713
231.2430
237.9055
294.5591
5.0165
8.3608
11.7050
15.0491
18.3931
21.7369
85.0505
28.4239
51.7669
35.1097
68.4520
41.7939
45.1352
48.4760
21.8161
35.1555
98.4940
61.8315
65.1680
98.5033
71.8372
13.3773
20.0658
26.7541
33.4422
90.1300
96.8174
53.5044
60.1908
66.8766
73.5617
90.2459
86.9291
93.6113
100.2921
106.9716
113.6494
120.3255
126.9995
153.6712
140.3405
147.0069
193.6703
190.3303
106.9365
113.6386
150.2862
166.9288
193.5660
200.1974

0.0060
0.0005
80.0447
90.0006
80.0056
0.0037
20.0013
90.0042
90.0009
:0.0001
10.0065
50.0001
60.0005
90.0030
0.0007
0.0004
90.0001
0.0031
0.0003
0.0039
0.0068
0.0068
0.0011
0.0056
0.0064
90.0003
0.0031
90.0030
90.0024
90.0031
20.0024
90.0033
30.0012
90.0013
90.0004
60.0019
90.0007
30.0011
0.0038
0.0041
0.0014
0.0062
0.0057
0.0020
20.0065
90.0069
0.0006
0.0028
30.0017
0.0021
80.0032
50.0087
90.0076
80.0060

 

90

92
93
94
95

HwAhbwwAkt

OOOC.OCI

NNNNNN

59/2
63/2
65/2
67/2
69/2
71/2

S.D.

0.54
0.00
0.46
0.54
0.00
0.89

= 0.0032

222

206.8169
220.0403
226.6589
233.2465
239.8322
246.4155

206.8224
220.0511
226.6535
263.2472
269.8315
246.4057

90.0055
20.0108
0.0054
90.0007
0.0007
0.0098

 

Z

omuomauww

<

HF‘HW‘HLPF‘HW*H‘HF‘PW‘P‘PF‘HH4htHF¢HWAP‘Rr‘HHJF39*39W4F‘HF‘HW‘P*H+‘HW‘F*HP*FW‘

LINE

91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
91
92
92
92
92
92
92
92
92
92
92
92
92
92

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
61/2
63/2
67/2
69/2
71/2
73/2
75/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2

NGT.

2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
3.00
2.00
0.00
0.00
1.00
1.25
1.25
1.25
1.06
1.00
1.00
1.00
0.31
0.00
0.25
0.31
0.80
0.50
1.25
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00

223

OBSERVED

1871,0621
1867,6678
1864,2372
1860,7738
1857,2751
1853,7426
1850,1777
1846,5784
1842,9420
1839,2729
1835.5705
1831.8345
1828.0622
1824.2581
1820.4175
1816,5447
1812.6403
1808,6959
1804,7237
1800,7203
1796,6884
1792,6158
1788,4977
1784,3583
1780,1857
1775,9811
1771,7412
1767.4719
1763.1680
1758,8344
1754,4648
1745,6376
1741,1611
1736,6771
1732.1552
1727.5964
1867.2154
1863.6850
1860.1206
1856,5204
1852,8884
1849.2157
1845,5164
1841,7786
1838.0078
1834,2044
1830,3675
1826,4956
1822.5922

FREQUENCY FIT FOR 14N16O INPUTING GSCD CONSTANTS

PREULCTED

1571,0644
1967,6686
1864,2387
1560,7745
1957,2761
1853,7436
1850,1769
1846,5761
1642,9412
1939,2722
1535,5692
1831,8322
1528,0612
1824,2563
1820,4175
1816,5449
1812,6386
1808,6985
1804,7249
1800,7177
1796,6771
1792,6031
1788,4960
1784,3558
1780,1826
1775,9767
1771,7382
1767,4673
1763,1641
1758,8290
1754,4621
1/45.6343
1741,1768
1736,6828
1732.1615
1227,6104
1867,2050
1863,6762
1560,1123
1856,5135
1852,8801
1849,2122
1045,5102
1841,7743
1838,0046
1534,2014
1630,3650
1826,4954
1822,5930

(09F)

50.0023
20.0008
90.0015
80.0007
90.0010
60.0010
0,0008
0,0023
0,0008
0.0007
0.0013
0,0023
0.0010
0.0018
90.0000
90.0002
0.0017
80.0026
20.0012
0.0026
0,0113
0,0127
0.0017
0,0025
0.0031
0,0044
0.0030
0.0046
0.0039
0.0054
0.0027
0,0033
90.0127
80.0057
90.0063
30.0140
0.0104
0,0088
0.0083
0.0069
0.0083
0,0035
0,0062
0,0043
0,0032
0,0030
0,0025
0.0002
1”0.0005.

 

 

50

52
53
54
55
56
57
58
59

61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80

82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103

tavtwwar-Hw495uwartpw¢9994;639wa9-FHA».Hwah-H4A+.HwAhtH+‘H-Hwa9=Hw49tww¢9-H449-Hw49594aH-H

31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
63/2
65/2
67/2
69/2
71/2
73/2

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
63/2
65/2
67/2

2.00
2.00
0.00
2.00
4.00
2000
2.00
1.25
2.00
0.50
1,25
1.06
1.00
1.00
1.00
0.00
0.25
0.25
0.25
0.00
0.87
2.00
0.12
2,00
2.00
2,00
2.00
2.00
2.00
4.00
3.00
3.00
3.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
1.00
2,00
2.00
2,00
2.00
2.00
2.00
3.00
2.00

224

1818,6562
1814.6895
1810.6848
1806,6560
1802,5904
1798,4906
1794,3653
1790,2101
1786,0183
1781.7936
1777,5433
1773.2571
1768,9423
1764,5973
1760,2179
1751.3985
1746,9073
1742,4046
1737.8741
1733.3576
1728.7216
1881.0430
1884,3080
1887,5249
1890,7149
1893.8708
1896,9927
1900,0795
1903.1310
1906,1482
1909,1314
1912.0785
1914,9911
1917,8670
1920,7128
1923.5204
1926.2911
1929,0276
1931,7259
1934.3935
1937.0224
1939.6158
1942,1686
1944,6914
1947,1705
1949.6218
1952.0242
1954.3920
1956,7264
1959,0258
1961.2817
1965,6779
1967.8200
1969,9236

1818.6580
1814.6904
1810,6906
1806,6586
1802,5947
1798.4990
1794,3716
1790,2127
1786,0224
1781,8008
1777,5480
1773,2641
1768,9491
1764,6031
1760.2260
1/51,3790
1746,9089
1742,4077
1737,8754
1733,3118
1’28,7168
1681,0459
1884,3044
1587.5286
1890,7183
1693,8765
1696,9943
1900,0804
1903,1320
1906,1488
1909,1308
1912,0781
1914,9903
1917,8676
1920,7097
1923,5165
1926,2880
1929,0240
1931,7244
1934,3889
1937,0176
1939.6101
1942,1663
1944,6861
1947,1691
194919153
1952,0244
1954,3961
1956,7302
1959,0265
1961,2846
1965,6854
1967,8274
1969,9301

80.0018
90.0009
30.0058
90.0026
30.0043
60.0084
30.0063
90.0026
r0,0041
90.0072
30.0047
s0.0070
80.0068
50.0058
80.0081
0.0195
90.0016
80.0031
80.0013
0.0458
0.0048
80.0029
0.0036
60.0037
80.0034
90.0027
80.0016
80.0009
80.0010
90.0006
0.0006
0.0004
0.0008
90.0006
0,0031
0,0039
0,0031
0.0036
0,0045
0,0046
0.0048
0.0057
0,0023
0.0053
0,0014
0.0065
80.0002
80.0041
80.0038
80.0007
80.0029
90.0075
90.0074
90.0065

 

104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157

O‘F‘PW‘H‘H
H4‘P‘HW‘F‘HW‘F‘h‘HJ‘F‘H3HiJP3HJJF‘HW4r4F*HWJF‘“Wflf‘H‘HW‘F‘HJ‘F‘HW‘F‘HWAh‘HJ‘H‘HW‘

R1
R1
R1
R1
R1
R1
R1
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2

R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
PH
PH

PH
PH
PH
PH
PH
PH
OH

69/2
71/2
73/2
77/2
79/2
81/2
83/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
61/2
63/2
67/2
69/2
71/2
73/2
75/2
79/2
81/2

5/2

7/2
13/2
19/2
21/2
23/2
27/2
29/2
31/2

3/2

0.00
4.25
4.06
3.27
1.02
0.25
0.03
0.50
2.00
2.00
2.00
2.00
2.00
4.00
3.00
3.00
2.00
2.00
2.00
2.00
2.00
2,00
2.00
2.00
2.00
2.00
2.00
2.00
1.00
1.00
2.00
2.00
2.00
2.00
2.00
2.00
3,00
5.00
4.25
4.06
4,06
2.52
0.25
0.03
3,50
4.25
0.81
0.59
0.00
0,83
0.22
0.50
0.19
3.44

225

1971,9874
1974,0119
1975.9970
1979,8486
1981,7183
1983.5390
1985,3251
1887.6334
1890.9134
1894.1523
1897.3539
1900,5179
1903,6422
1906.7335
1909,7827
1912.7972
1915.7691
1918,7034
1921,5985
1924.4551
1927.2751
1930.0551
1932,7929
1935,4916
1938,1563
1940,7772
1943,3607
1945,9001
1948,4071
1950.8699
1953.2875
1955,6704
1958,0141
1960,3188
1962.5791
1964,8004
1966,9819
1971,2184
1973.2801
1975,2977
1977,2728
1979,2082
1982,9551
1984,7701
1987,3424
1984,1496
1974,9266
1966.2034
1963.3488
1960,6465
1955,2907
1952,6705
1950,0931
1995,7093

1971,9931
1974,0162
1975,9989
1979,8417
1981,7011
1983,5185
1985,2936
1887.6273
1890,9038
1594,1433
1897,3456
1900.5105
1203:6378
1906,7273
1909,7788
1912,7921
1915,7669
1713.7032
1921,6007
1924,4593
1927,2789
1930,0591
1932,8000
1935,5014
1938,1632
1940,7852
1943,3673
1945,9094
1948,4115
1950,8735
1953,2952
1955,6767
1958,0179
1960,3188
1962,5792
1964,7993
1966,9790
1971,2173
1973,2758
1975,2941
1977,2722
197912101
1982,9656
1984,7834
1987,3585
198411631
1974,9277
1966,1980
1963,3943
1960,6409
1955,2772
1952,6629
1950,0904
199517192

90,0057
50,0043
90,0019
0,0069
0,0172
0,0205
0,0315
0,0061
0,0096
0,0090
0,0083
0,0074
0,0044
0,0062
0,0039
0,0051
0,0022
0,0002
80,0022
80,0042
90,0038
90.0040
90,0071
$0,0098
80.0069
50.0080
80,0066
90,0093
30,0044
'0,0036
90,0077
90,0063
90,0038
0,0000
30,0001
0,0011
0,0029
0,0011
0,0043
0,0036
0,0006
'0,0019
”0,0105
90,0133
80,0161
90,0135
60,0011
0,0054
90,0455
0,0056
0,0135
0,0076
0,0027
90,0099

 

158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211

away-HwnH-H+&
PF‘Hd‘HH‘h‘P
...:
Hw4rsuwartHwAravnHwarah-HwApuserH-HwA
r-Hwah-Hr-HMA
saw-H949w4

0H
0H
OH
OH
0H
0H
0H
0H
0H
0H
OH
OH

OH
OH
0H
0H
0H
0H
0H
0H
0H
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
PL
PL
PL
PL
PL
PL

PL
PL
PL

‘PL

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
29/2

3.44
5.75
5,75
6.50
4.25
6.25
7.25
7.25
5.25
7,25
6.71
5.71
6.25
6.25
6.52
0.06
5.47
2.02
0.75
0.37
0.12
0.02
6.25
4.06
5.25
6.25
3.25
2.25
2.25
2.25
2.25
2.25
2,25
2.25
1.25
2.06
2.02
2.02
0.50
0.31
0.12
0.12
0.00
0.02
0.00
0.33
0.14
0.45
0.00
0.00
0.89
2.35
0,41
0.31

226

1995.8561
1996,0692
1996,3367
1996,6594
1997,0403
1997,4819
1997,9706
1998,5101
1999.1019
1999.7395
2000,4216
2001,1481
2001,9131
2002.7202
2003,5586
2004,4293
2005.3351
2006,2678
2007,2268
2008,2061
2009,2108
2010.2235
2000.7202
2004,2184
2007,7710
2011,3816
2015,0516
2018,7790
2022,5563
2026.3944
2030,2763
2034,2086
2038,1911
2042,2159
2046,2841
2050.3927
2054.5361
2058.7180
2062.9301
2067,1735
2071,4369
2075,7358
2080,0497
1743.7736
1739,8602
1735,8506
1731,7099
1727,4296
1723,0406
1718.5314
1713.8731
1709.1216
1704.2579
1694,1797

 

1995,8681
1996,0758
1996,3416
1996,6646
1997,0437
1997,4776
1997,9649
1998,5039
1999,0928
1999,7297
2000,4125
2001,1389
2001,9065
2002,7131
2003,5559
2004,4324
2005,3399
2006,2757
2007,2372
2008,2214
2009,2259
2010,2478
2000,7357
2004,2289
2007,7808
2011,3907
2015,0577
2018,7806
2022,5581
2026,3888
2030,2709
2034,2025
2038,1817
2042,2064
2046,2741
2050,3826
2054,5292
2058,7113
2062,9263
2067,1714
2071,4437
2075,7404
2080,0587
1743,7518
1739,8601
1735,8411
1731,6960
1727,4259
1723,0325
1718,5175
1713,8825
1709,1298
1104,2613
1694,1865

60,0120
90,0066
90,0049
30.0052
30,0034
0,0043
0,0057
0,0062
0,0091
0,0098
0,0091
0.0092
0,0066
0,0071
0,0027
50,0031
60,0048
“0,0079
90,0104
90,0153
-0,0151
90.0243
80,0155
90,0105
90,0098
n0,0091
90,0061
90,0016
80,0018
0,0056
0,0054
0,0061
0,0094
0,0095
0,0100
0,0101
0,0069
0,0067
0,0038
0,0021
n0,0068
80,0046
20,0090
0,0218
0,0001
0,0095
0,0139
0,0037
0,0081
0,0139
20,0094
«0,0082
90.0034
80,0068

 

212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227

HHHHHRHPHPHPHHFP

PL
PL
PL
0L
CL
CL
0L
0L
0L
0L
0L
RL
RL
RL
RL
RL

31/2
33/2
35/2

3/2

7/2

9/2
13/2
15/2
17/2
21/2
23/2

7/2
17/2
21/2
27/2
29/2

S.D.

0.06
0.31
0.06
0.00
0.37
0.00
0.16
0.00
0.00
0.00
0.00
0.00
2.08
0.18
0.04
0.04

= 0.0065

227

1688.9736
1683,6705
1678,2606
1756.1344
1755,3554
1754,7463
1753,2180
1752,2486
1751,1800
1748,6199
1747,1732
1770,2551
1782,6006
1786,6781
1791,9257
1793,4459

1688,9851
1683,6777
1678,2672
1756,1146
1755,3367
1754,7548
1753,2098
1752,2490
1751,1646
1748,6315
1747,1866
1770,2314
1782,6053
1186,6884
1791,9278
1793,4467

90,0115
20,0072
20,0066
0,0198
0,0187
90.0085
0,0082
«0,0004
0,0154
90,0116
n0,0134
0,0237
90,0047
"0.0103
90.0021
50,0008

 

OQVO‘U‘IAOJNF‘ Z

HtIHMJh-Hrfi
<>UIthnJHw=

Hw-r‘wudhswwartwwdrtHwAthAArnH44r9HwarhuwAb4HwAk4Hwathwa m

APPENDIX VIlIeB

GROUND STATE COMBINATION DIFFERENCE (IT FOR 15N160

V

OOOOOOOOOOOOOOOOOOOOOOOOOOQOOOOOODO

DEL
J

NNNNNNNNNNNNNNNNNHHHHFHHHHHHHHHHHHH

1/2

3/2

5/2

7/2

972
11/2
13/2
15/2
17/2
1912
21/2
23/2
25/2
27/2
29/2
31/2
35/2
37/2

ll?

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
3572

HGT.

1.00
0.68
2.18
3.59
2.67
4.94
2.42
1.49
3.00
2.74
2.67
1.78
0.72
2.67
0.89
0.23
0.04
0.00
2.68
0.80
2.00
1.69
2.00
2.00
2.00
2.14
2.00
2.00
2.00
2.00
2.00
2.40
1.33
0.80
2.00

083.

4.8429
8.0673
11.2901
14.5262
17.7559
20.9792
24.2039
27.4327
30.6579
33.8824
37.1118
40.3365
43.5676
46.7858
50.0139
53.2276
59.6744
62.8878
12.9071
95.8223
32.2769
38.7247
45.1835
51.6308
58.0887
64.5441
71.0020
77.4426
83.9015
90.3481
96.7960
103.2312
109.6903
116.1280
122.5677

228

FRED.

4.8418
8.0696
11.2973
14.5249
17.7523
20.9796
24.2066
27.4334
50.6599
63.8559
07.1116
40.3363
43.5614
46.7355
3000088
93.2314
59.6739
62.8936
12.9114
25.3222
62.2772
68.7320
45.1863
91.6401
3800935
54.5458
70.9975
77.4484
43.8982
90.3469
96.7943
103.2402
109.6345
116.1270
122.5674

(099)

0.0011
“0.0023
90.0072

0.0013

0.0036
«0.0004
'0.0027
90.0007
90.0020
”0.0035

0.0002
90.0003

0.0062

0.0003

0.0051
90.0038

0.0005
90.0058
$0.0043

0.0001
90,0003
90.0073
20.0028
n0.0093
90.0046

.90,0017

0.0045
90.0058
0.0033
0.0012
0.0017
no.0090
0.0058
0.0010
0.0003

 

 

NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNHPHHPF.HPHH.HPHPHPH

OOOOOD
DODOODOOOOOOODOOCQDOOOOOOQCCOOCOOCDOOCQDO-DOODGDO

N
NMNNNNNNNNNNNNNNNNNNMNNNNNNNHPHHHHHHNNNNNNNNMNNNNNNNN

37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
61/2
63/2
67/2
69/2
71/2

5/2

7/2
13/2
15/2
17/2
19/2
21/2
27/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
63/2

1.54
1.39
1.33
0.00
0.80
0.54
1.39
1.03
1.39
0.00
0.00
1.33
0.00
0.00
1.90
0.00
0.19
2.00
0.00
0.00
0.44
0.00
0.38
0.57
0.00
0.00
0.00
2.00
2.00
2.00
2.00
2.00
0.80
2.00
2.00
2.00
2.67
2.40
1.33
2.00
1.54
0.50
0.67
0.44
1.39
0.80
0.54
1.39
0.00
0.54
1.39
0.73
0.32
0.00

229

129.0145
135.4534
141.8769
148.3080
154.7355
161.1580
167.5793
173.9878
180.4014
186.7935
193.2074
199.5898
205.9870
212.3904
225.1080
231.5062
237.8236
11.6097
14.9253
24.7937
28.1714
31.4802
34.7920
38.0861
47.9772
26.5254
33.1269
39.7871
46.4139
53.0349
59.6518
66.2638
72.8835
79.4805
86.0813
92.6750
99.2700
105.8534
112.4393
119.0052
125.5706
132.1308
138.6845
145.2241
151.7599
158.2898
164.8074
171.3214
177.8485
184.3203
190.8109
197.2805
203.7513
216.6528

129.0057
165.4415
141.8746
148.3048
154.7317
161.1550
167.5745
173.9897
190.4003
186.8059
193.2061
199.6004
205.9884
212.3696
225.1092
231.4666
237.8148
11.6074
14.9225
24.8614
28.1715
31.4799
34.7863
68.0905
47.9886
26.5299
33.1592
39.7864
46.4111
23.0329
99.6514
66.2661
72.8768
79.4830
86.0844
92.6805
99.2712
105.8560
112.4346
119.0067
125.5720
152.1303
168.6813
145.2247
191.7604
158.2881
164.8077
171.3189
177.8217
194.3159
190.8015
197.2783
203.7464
216.6562

0.0088
0.0119
0.0023
0.0032
0.0038
0.0030
0.0048
20.0019
0.0011
$0.0124
0.0013
90.0106
90.0014
0.0208
90.0012
0.0396
0.0088
0.0023
0.0028
20.0677
20.0001
0.0003
0.0057
80.0044
30.0114
20.0045
20.0323
0.0007
0.0028
0.0020
0.0004
50.0023
0.0067
30.0025
90.0031
90.0055
60.0012
«0.0026
0.0047
20.0015
«0.0014
0.0005
0.0032
50.0006
50.0005
0.0017
80.0003
0.0025
0.0268
0.0044
0.0094
0.0022
0.0049
30.0034

 

230

90 2 0 2 6712 0.71 229.5218 229.5311 90.0093
91 2 0 2 71/2 0.12 242.3417 242.3713 30.0301

S.D. = 0.0044

Z

O'QNO‘U‘IbCAMH

HW‘F‘PJ‘F‘PW‘F‘P»
‘OGDQCI0156dn3943

NNNNNNNNN
mqousumno

<

LINE

I‘F‘PW‘V‘HW‘PPHW‘r‘Hn‘h‘HW‘r‘HW‘f‘HW‘F.HH‘F‘HW‘t‘HW‘F‘PW‘F‘HH‘F‘HW‘F‘HW‘P‘HW‘H‘HW‘

P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1

77/2
75/2
73/2
71/2
67/2
65/2
63/2
61/2
59/2
57/2
55/2
53/2
51/2
49/2
47/2
45/2
43/2
41/2
39/2
37/2
35/2
33/2
31/2
29/2
27/2
25/2
23/2
21/2
19/2
17/2
15/2
13/2
11/2

9/2

7/2

5/2

3/2

1/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2

HGT.

0.50
0.12
0.00
4.00
0.00
0.00
1.00
0.00
0.00
1.06
1.06
1.06
0.31
0.50
0.00
1.00
1.06
1.25
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
0.50
2.00
0.50
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00

231

OBSERVED

1695,7322
1700.1321
1704,4740
1708.8576
1717.4356
1721.7132
1725.9500
1730,1360
1734,3142
1738.4392
1742.5464
1746.6172
1750.6611
1754,6751
1758.6554
1762.6093
1766,5163
1770.4089
1774,2697
1778.0889
1781,8808
1785,6504
1789,3694
1793,0696
1796.7309
1800.3657
1803.9610
1807,5305
1811.0696
1814,5759
1818.0386
1821.4766
1824,8814
1828.2559
1831.5973
1834.9074
1838.1834
1847.8135
1854.0782
1857.1583
1860.2025
1863.2221
1866.2067
1869,1583
1872.0747
1874.9630
1877.8083
1880.6324
1883,4177

FREQUENCY FIT FOR 15N160 INPUTING GSCD CONSTANTS

PREDICTED

1695,7341
1100,1370
1104.5111
1/03.8562
1717,4584
1721,7151
1725,9419
1730,1385
1734.3048
1738,4407
1142,5459
1/46,6203
1750,6638
1154,6761
1758.6573
1162,6072
1766,5256
1770,4125
1774,2678
1778,0914
1181,8832
1785,6432
1789,3712
1793,0673
1796,7313
1900,3633
1803.9631
1507,5308
1811,0662
1814,5694
1818,0404
1321.4790
1924,8853
1828,2592
1831,6007
1234.909?
1938,1863
1847,8211
1854,0813
1857,1625
1860,2109
1963.2266
1866,2095
1569,1595
1972,0766
1874,9606
1877,3117
1880,6295
1083:0102

(0!?)

90.0019
90.0049
20.0371

0.0014
90.0228
20.0019

0.0081
90.0025

0.0094
60.0015

0.0005
90.0031
30.0027
00.0010
20.0019

0.0021
I0.0093
80.0036

0.0019
90.0025
50.0024

0.0072
90.0018

0.0023
30.0004

0.0024
”0.0021
20.0003

0.0034

0.0065
00.0018
80.0024
20.0039
20.0033
20.0034
90.0023
90.0029
”0.0076
-0.0031
I0.0042
30.0084
R0.0045
!0.0028
90.0012
30.0019

0.0024
80.0034

0.0029

0.0035

HW‘F‘HW‘F‘FW‘F‘HW‘P‘HW‘P‘FH‘P‘H‘HW‘FPHW‘F‘PW‘F‘HW‘P‘HW‘F‘Hfl‘k‘flfl‘Flflwir‘HH‘FIPW‘P‘PW‘F‘HW‘

R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2

P2
P2
P2
P2
P2
P2
P2

27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
61/2
63/2
65/2
67/2
69/2
71/2
75/2
75/2
73/2
71/2
67/2
65/2
63/2
61/2
59/2
57/2
55/2
53/2
51/2
49/2
47/2
45/2
43/2
41/2
39/2
37/2
35/2
33/2
31/2
29/2
27/2
25/2
23/2
21/2
19/2
17/2
15/2

2.00
3.00
1.00
0.50
2.00
2.00
2.00
2,00
2.00
2,00
2.00
2.00
1,00
2.00
2.00
1.00
2.00
2.00
2.00
2,00
1.25
1.25
0.50
0.00
0.12
0,50
0.50
0.00
0.00
0.19
1.37
1.06
0,31
0.00
1.06
0.31
0.50
1.06
0.25
1.00
1.25
1.25
2900
2.00
2,00
2.00
2.00
2.00
2.00
0.50
2.00
2.00
2,00
2,00

232

1886,1654
1888,8816
1891,5711
1894,2169
1896,8374
1899,4234
1901,9697
1904,4862
1906,9634
1909,4106
1911,8191
1914,1965
1916,5342
1918,8406
1921,1077
1923,3434
1925,5398
1927,7002
1929,8260
1931,9140
1933,9656
1935,9802
1937,9557
1941,8065
1696,8332
1701,2654
1705,6775
1714,4074
1718,7343
1723.0202
1727,2815
1731,5179
1735,7232
1739,8789
1744,0501
1748,1706
1752,2571
1756,3202
1760,3483
1764,3489
1768,3187
1772,2598
1776,1782
1780,0440
1783,8990
1787,7169
1791,5102
1795,2653
1798,9888
1802,6814
1806,3468
1809,9735
1813,5698
1817,1362

1886,1655
1888,8833
1891,5677
1894,2183
1696,8352
1899,4182
1901,9671
1?04,4818
1906,9621
1909,4078
1911,8188
1914,1948
1916I5356
1918:3410
1921,1108
1923,3446
1725,5423
1927,7036
1929,8280
1931,9154
1933,9654
1935,9776
1937,9518
1?41,7841
1696,8139
1701,2549
1705,6667
1714,4026
1718,7267
1723,0216
1727,2873
1731,5237
1735,7308
1139,9086
1744,0570
1748,1759
1752,2652
1756:3249
1160,3548
1764,3548
1768:3245
1172.2646
1776,1742
1780,0534
1783,9019
1737,7197
1791,5066
1795,2624
1798,9869
1802,6800
1906,3414
1409,9710
1813,5685
1817,1337

”0,0001
80,0017
0,0034
30,0014
0,0022
0,0052
0.0026
0,0044
0,0013
0,0028
0,0003
0,0017
90,0014
90.0004
90,0031
90,0012
30,0025
00.0034
90,0020
80,0014
0,0002
0,0026
0.0039
0,0224
0,0193
0,0105
0.0108
0,0048
0,0076
90,0014
20,0058
20,0058
90,0076
I0,0297
80,0069
30,0053
«0,0081

‘90100‘7

90.0065
90,0059
90.0061
90,0048
0,0040
l0,0094
u0,0029
90,0028
0,0036
0.0029
0,0019
0,0014
0,0054
0,0025
0,0013
0,0025

 

104
109
104
107
103
109
110
111
112
113
114
119
116
117
119
119
120
121
122
123
124
125
126
127
123
129
139
131
132
133
134
139
134
137
134
139
140
141
142
143
144
149
146
147
145
149
190
151
152
153
154
155
154
157

9+-
tit-Pw3rtuwa+tHH¢FwaavsunartuwfiusuwfiusHwav-HHAp-nwa149wAr-Hw‘hsuuar-Huar-HuAr-uua+-Hw-

13/2
11/2

9/2

7/2

5/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
63/2
65/2
67/2
71/2
29/2
25/2
23/2
21/2
19/2
17/2
15/2
13/2
11/2

9/2

7/2

3/2
31/2
27/2
21/2
19/2
17/2

2,00
0.00
2.00
2.00
2.00
0.00
0.00
2.00
2.00
2,00
2.00
2,00
2.00
2.00
2.00
2.00
4.00
3.00
1.00
2.00
2.00
0.31
0.50
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
0.50
1.00
2.00
1.25
1.25
0.12
0.06
0.25
0.33
0.31
0.50
0.25
0.00
0.00
2.00
0.00
2.00
0.00
0.50
0.00
2.00
0.50
0.00

233

1820,6702
1824,1794
1827,6382
1831,0739
1834,4720
1854,1636
1857,3063
1860,4573
1863,5501
1866,6047
1869,6253
1872,6106
1875,5649
1878,4693
1881-3466
1884,1852
1886,9869
1889,7524
1892,4833
1895,1834
1897,8304
1900,4495
1903,0334
1905,5724
1908,0801
1910,5469
1912,9780
1915.3715
1917,7274
1920,0435
1922.3288
1924,5620
1926,7715
1931,0602
1933,1533
1935,1993
1939,1749
1663,5706
1673,1964
1677,8582
1682,4009
1686,8447
1691,1701
1695,4485
1699,4708
1703,4600
1707,3133
1711,0583
1718,1864
1708,0992
1711,5478
1715,9443
1717,1929
1718,3249

1820,6666
1924,1667
192716340
1831,0683
1834,4692
1954,1639
1857,3259
1060,4530
1963,5449
1966,6014
1§69,6223
1872,6075
1875,5568
1978,4699
1881,3468
1984,1872
1886,9909
1889,7579
199214379
1995,1809
1897,8367
1900,4551
1703,0361
1905,5795
1908,0853
1910,5533
1912,9835
1915,3759
1?17,7303
1?20,0467
1?22,3252
192415959
1926,7680
1931,0588
1?33,1472
1935,1978
1939,1856
1063,5802
1673,2099
1677,8654
1682,4120
1686,8477
1991,1710
1695,3800
1699,4733
1103,4497
140713030
1711,0471
1718,1648
110811137
1711,5688
1715,9559
1717,1982
1113,3276

0,0036
0,0127
0,0042
0,0056
0,0028
90.0003
90.0196
0,0043
0,0052
0,0033
0,0030
0,0031
0,0081
90.0006
90,0002
90.0020
00,0040
60,0055
n0,0046
0.0025
00,0063
00,0056
50,0027
50,0071
00,0052
90,0064
e0,0055
90.0044
20,0029
30,0032
0,0036
90,0036
0,0035
0,0014
0,0061
0,0015
80,0107
80,0096
90,0135
20,0072
20,0111
90.0030
00,0009
0,0685
90,0025
0,0103
0,0053
0,0112
0,0216
30,0145
20,0210
30,0116
30.0053
90,0027

 

158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207

IAPtHw‘HPHwAH-H
HW‘H‘PW‘
HJAP‘HWAPAPPHw‘P-HwAPsHuaPPHWAP-HHAP-HHAPtH-H44k-
F‘HW‘F‘FH‘?‘

CL
CL
CL
0L
RL
RL
PH
PH
PH
PH
PH
PH
PH
PH
0H
OH
OH
OH
OH
OH
OH
OH
OH
OH
OH
0H
0H
0H
0H
0H
OH
OH
OH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH

15/2
13/2

7/2

5/2

7/2
27/2
21/2
19/2
15/2
13/2
11/2

9/2

7/2

5/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
37/2
39/2
41/2

1/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2

S.D.

0.47

0.50
0.12
0.02
0.02
0.00

= 0,0059

234

1719,3415
1720,2422
1722,2386
1722,6680
1736,6579
1757,8669
1931,4675
1934,2000
1939,8185
1942,6763
1945,5907
1948,5692
1951,6154
1954,7006
1962,7679
1962,9055
1963,0996
1963,3476
1963,6441
1963,9958
1964,4011
1964,8510
1965,3521
1965,8982
1966,4860
1967,1174
1967,7831
1968,5015
1969,2411
1970,0260
1971,6784
1972,5484
1973,4387
1967,6108
1977,8723
1981,4000
1984,9774
1988,6050
1992,2837
1996,0100
1999,7806
2003,5978
2007,4539
2011,3507
2015,2872
2019,2551
2023,2536
2027,2882
2031,3528
2035,4363

1119,3425
1120,2414
1722,2305
1122,6545
1736,6089
1157,8816
1931,4602
1934,1894
1939,7941
1942,6722
1945,6023
194815352
1951,6218
1954,7127
1952,7822
1962,9191
1963,1101
1?63,3546
1963,6518
1964,0008
1964,4004
1964,8493
1965,3461
1265,8893
1966,4771
199711077
1967,7791
1968,4893
1969,2362
1970,0174
1971,6737
1972,5441
1973,4394
1997:6240
1977,8795
138114042
1984,9804
1988,6070
1992,2827
1996,0060
1999,7753
2003,5887
2007,4445
2011,3406
2015,2748
2019,2450
2023,2487
2027,2838
2031,3476
2035,4377

20,0010
0,0008
0,0081
0,0135
0,0490

90,0147
0,0073
0,0106
0,0244
0,0041

90,0116

30,0160

60,0064

~0,0121

80,0143

60,0136

$0,0105

50,0070

30,0077

30,0050
0,0007
0,0017
0,0060
0,0089
0,0089
0,0097
0,0040
0,0122
0,0049
0.0047
0,0043

60,0007

30,0132

90,0072

20,0042

.0.0030

e0,0020
0,0010
0,0040
0,0053
0,0091
0,0094
0,0101
0,0124
0,0101
0,0049
0,0044
0,0052
90,0014

 

 

Z

omuamaump

<

tap-94¢PIHwAthwaht944PPHwAPPHwa+4944»-HwérspwfipnnwaP-HwAw-H

LINE

P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1

P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
61/2
63/2
67/2
69/2
71/2
73/2
75/2

APPENDIX IXPA

FREQUENCY FIT FOR 14N160

HGT,

2.00
2.00
2.00
2.00
2.00
2.00
2.00
2,00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2,00
2.00
3.00
2.00
0.00
0.00
1.00
1.25
1.25
1.25
1.06
1.00
1.00
1.00
0,31
0.00
0.25
0.31
0.80
0950

OBSERVED

1871,0621
1867,6678
1864,2372
1860,7738
1857,2751
1853,7426
1850,1777
1846,5784
1842,9420
1839,2729
1835,5705
1831,8345
1828,0622
1824,2581
1820,4175
1816,5447
1812,6403
1808,6959
1804,7237
1800,7203
1796,6884
1792,6158
1788,4977
1784,3583
1780,1857
1775,9811
1771,7412
1767,4719
1763,1680
1758,8344
1754,4648
1745,6376
1741,1611
1736,6771
1732,1552
1727,5964

235

PREDICTED

1871,0603
1867,6650
1864,2355
1860:7719
1857,2742
1653,7423
1850,1763
1846,5762
1842,9420
1939,2736
1835,5712
1331,5346
1828,0640
1524,2593
1320,4206
1816,5479
1012,6412
1808,7007
1904:7264
1800,7183
1796,6767
1792,6016
1(88,4931
1784,3515
1780,1769
1775,9695
1771,7296
1767,4575
1763,1535
1758,8179
1254:4511
1745,6256
1741,1678
1736,6808
1132,1651
1727,6214

(O-P)

0,0018
0,0028
0,0017
0.0019
0,0009
0,0003
0,0014
0,0022
0.0000
90,0007
90,0007
90,0001
60,0018
90,0012
"0,0031
80,0032
20,0009
90,0048
90,0027
0,0020
0.0117
0,0142
0.0068
0,0088
0,0116
0,0116
0,0144
0,0145
0,0165
0,0137
0,0120
90,0067
'000037
80,0099
90,0250

37
38
39
40
41
42
43
44
45
46
47
48
49
50
51

53
54
55
56
57
58
59
60

61'

62
63
64
65
66
67
68
69
7o
71
72
73
74
75
76
77
7e
79
an
81
82

84
85
86
87

89
90

Pf‘FH‘F‘PW‘F‘HW‘P‘HW‘P‘HW‘P‘PWJF3HW‘P‘PM‘F‘Ht‘HH‘F‘HW‘#lHWJF‘HW‘k‘HwathW‘P‘PW‘F‘HH‘F‘PW‘

P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1

R1
R1
R1
91

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
63/2
65/2
67/2
69/2
71/2
73/2

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2

1.25
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2.00
2,00
2,00
2.00
0.00
2,00
4,00
2.00
2.00
1.25
2.00
0.50
1.25
1.06
1.00
1.00
1.00
0.00
0.25
0.25
0.25
0.00
0.87
2.00
0.12
2.00
2,00
2,00
2,00
2.00
2.00
4.00
3.00
3.00
3.00
2.00
2.00
2,00
2.00
2,00
2,00
2.00
2,00

236

1867,2154
1863,6850
1860,1206
1856,5204
1852,8884
1849,2157
1845,5164
1841,7786
1838,0078
1834,2044
1830,3675
1826,4956
1822,5922
1818,6562
1814,6895
1810,6848
1806,6560
1802,5904
1798,4906
1794,3653
1790,2101
1786,0183
1781,7936
1777,5433
1773,2571
1768,9423
1764,5973
1760,2179
1751,3985
1746,9073
1742,4046
1737,8741
1733,3576
1728,7216
1881,0430
1884,3080
1887,5249
1890,7149
1893,8708
1896,9927
1900,0795
1903,1310
1906,1482
1909,1314
1912,0785
1914,9911
1917,8670
1920,7128
1923,5204
1926,2911
1929,0276
1931,7289
1934,3935
1937,0224

1367,2148
1063,6853
1860,1206
1856,5209
1952,8864
1§4912175
1845,5143
1841,7772
1838,0064
1834,2021
1830,3645
1926,4940
1822,5907
1818,6549
1814,6868
1510,6866
1806,6544
1802,5905
1798,4950
1794,3681
1790,2098
1786,0202
1781,7996
1777,5478
1773,2649
1768,9510
1764,6060
1760,2298
1751,3834
1746,9129
1/42,4106
1137,8762
1/33,3094
1728,7099
1881,0413
1884,2999
1837:5242
1090,7142
1093,8698
1896,9911
1900,0778
1903,1301
1906,1476
1909,1305
1912,0785
1914,9916
1?17,5697
1920:7126
1923,5202
1926,2923
1929,0288
1?31,7296
1934,3944
1937,0232

0,0006
90,0003
0,0000
0,0020
"0.0018
0,0021
0,0014
0,0014
0,0023
0,0030
0,0016
0,0015
0,0013
0,0027
20,0018
0,0016
90,0001
90,0044
60,0028
0,0003
ll.060019
R0,0060
20,0045
80,0078
70,0087
90,0087
90,0119
0,0151
90,0056
80,0060
90,0021
0,0482
0,0117
0,0017
0,0081
0,0007
0,0007
0,0010
0,0016
0,0017
0,0009
0,0006
0,0009
90,0000
30,0005
90,0027
0,0002
0,0002
20,0012
9010012
90,0007
£0,0009
90,0008

 

91

92

93

94

95

96

97

98

99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144

PF‘H‘HW‘F‘HW*F‘PW‘H*RF‘HHJP‘HW3F3H4‘HH‘F‘HW‘P‘HJJh699Jh‘HfibHH4F*H+‘HHJP‘HF‘HH4P‘HF*P‘Ht*

R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2

R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2

41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
63/2
65/2
67/2
69/2
71/2
73/2
77/2
79/2
81/2
83/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
61/2
63/2
67/2
69/2
71/2
73/2

2,00
2.00
2.00
2.00
1,00
2.00
2.00
2.00
2.00
2.00
2.00
3.00
2,00
0.00
4,25
4,06
3.27
1.02
0.25
0.03
0.50
2.00
2.00
2,00
2.00
2.00
4.00
3.00
3.00
2,00
2.00
2.00
2.00
2.00
2,00
2.00
2.00
2.00
2.00
2,00
2.00
1.00
1.00
2.00
2.00
2.00
2.00
2.00
2.00
3.00
5.00
4.25
4.06
4.06

237

1939,6158
1942,1686
1944,6914
1947,1705
1949,6218
1952,0242
1954,3920
1956,7264
1959,0258
1961,2817
1965,6779
1967,8200
1969,9236
1971,9874
1974,0119
1975,9970
1979,8486
1983,5390
1985,3251
1887,6334
1890,9134
1894,1523
1897,3539
1900,5179
1903,6422
1906,7335
1909,7827
1912,7972
1915,7691
1918,7034
1921,5985
1924.4551
1927.2751
1930,0551
1932,7929
1935,4916
1938,1563
1940,7772
1943,3607
1945,9001
1948,4071
1950,8699
1953,2875
1955,6704
1958,0141
1960,3188
1962,5791
1964,8004
1966,9819
1971,2134
1973,2801
1975,2977
1977,2728

1939,0156
1942,1716
1944,6910
1947,1734
1949,6189
1952,0270
1954,3977
1?56,7306
1959,0257
1961,2827
1965,6815
1967,8228
1969,9253
1971,9886
1974,0125
1975,9970
1979,8467
1981:7117
1983,5365
1985,3211
1887,6378
1890,9138
1594,1526
1597,3541
190015180
1903,6442
1906,7325
1909,7827
1912,7946
1915,7680
1918,7029
1921,5990
1924,4563
1927,2745
1930,0536
1932,7935
1935,4940
1938,1550
1940,7765
1943,3583
1945,9004
1948,4027
1950,8651
1953,2875
1955,6698
125800121
1960,3141
1962,5759
1964,7974
1966,9784
1971,2190
1973,2783
1975,2968
1977,2745

0,0002
80,0030
0,0004
9'0,0029
0,0029
'0,0028
90,0057
90,0042
0.0001
90,0010
-0,0036
90,0028
10,0017
80,0012
80,0006
'0,0000
0,0019
0,0066
0,0025
0,0040
90,0044
90,0004
90,0003
90,0002
'0,0001
'0,0020
0,0010
0,0000
0,0026
0,0011
0,0005
30.0005
90,0012
0,0006
0,0015
90,0006
90,0024
0,0013
0,0007
0,0024
60,0003
0,0044
0,0048
0,0000
0,0006
0,0020
0,0047
0,0032
0,0030
0,0035
90.0006
0,0018
0,0009
90,0017

 

 

......fi.._——_q.-—— ——v , 7

145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198

l‘b‘Pd‘b‘HW‘F‘P
HwaH-HwaF-H» -
HO‘F‘HW‘FIHWAF‘HHJFiF‘HJJF‘HW4F‘HW‘F‘Hfléhfiflwfih‘
HrAHwAw-Hwah-P
1....

R2
R2
R2
PH
PH
PH
PH
PH
PH
PH
PH
PH
0H
0H
0H
0H
0H
0H
0H
0H
OH
OH
0H
0H
0H
0H
0H
0H
0H
0H
0H
OH

OH
OH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH
RH

RH
RH
RH
RH

75/2
79/2
81/2

5/2

7/2
13/2
19/2
21/2
23/2
27/2
29/2
31/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2

1/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2

2.52
0.25
0.03
3,50
4,25
0.81
0.59
0.00
0.83
0.22
0.50
0.19
3.44
3.44
5.75
5,75
6.50
4,25
6.25
7,25
7.25
5.25
7.25
6.71
5,71
6.25
6.25
6.52
0.06
5.47
2.02
0.75
0.37
0.12
0.02
6,25
4,06
5.25
6,25
3,25
2.25
2.25
2,25
2,25
2.25
2.25
2.25
1.25
2,06
2,02
2.02
0.50
0.31
0.12

238

1979,2082
1982,9551
1984,7701
1987,3424
1984,1496
1974,9266
1966,2034
1963,3488
1960,6465
1955,2907
1952,6705
1950,0931
1995,7093
1995,8561
1996,0692
1996,3367
1996,6594
1997,0403
1997,4819
1997,9706
1998,5101
1999,1019
1999.7395
2000,4216
2001,1481
2001,9131
2002,7202
2003,5586
2004,4293
2005,3351
2006,2678
2007,2268
2008,2061
2009,2108
2010,2235
2000,7202
2004,2154
2007,7710
2011,3816
2015,0516
2018,7790
2022,5563
2026,3944
2030,2763
2034,2086
2038,1911
2042,2159
2046,2841
2050,3927
2054,5361
2058,7150
2062,9301
2067,1735
2071,4369

1979,2112
1982,9610
1984,7739
1987,3497
1984,1554
1974,9249
1966,2010
1963,3990
1960,6472
1955,2855
1952,6714
1950,0986
1995,7098
1995,8596
1996,0685
1996,3358
1996,6605
1997,0414
1997,4773
1997,9666
1998,5074
1999,0981
1999,7364
2000,4202
2001,1471
2001,9148
2002,7207
2003,5621
2004,4364
2005,3409
2006,2728
2007,2293
2008,2077
2009,2055
2010,2198
2000,7259
2004,2197
2007,7726
2011,3838
2015,0524
2018,7770
2022,5565
2026,3890
2030,2730
2034,2065
2038,1873
2042,2132
2046,2818
2050,3905
2054,5369
2058,7181
2062,9314
2067,1740
2071,4429

20,0030
90,0059
90,0038
90,0073
90,0058
0,0017
0.0024
80.0502
90,0007
0,0052
30,0009
10,0055
90,0005
90,0035
0,0007
0,0009
80,0011
90,0011
0,0046
0,0040
0,0027
0,0038
0,0031
0,0014
0,0010
!0,0017
£0,0005
90,0035
90,0071
90,0058
90,0050
90,0025
80,0016
0,0053
0,0037
90,0057
-0,0013
P0,0016
v0.0022
80,0008
-0,0002
0,0054
0,0033
0:0021
0,0038
0,0027
0,0023
0,0022
20,0008
90,0001
90,0013
90,0005
90,0060

199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227

Hk-HwarAHWAFusJHsH+¢HsH+¢HHJ0&HwAFAQWAPus3ktH

RH
RH
PL
PL
PL
PL
PL
PL
PL
PL
PL
PL
PL
PL
PL
PL
0L
CL
CL
CL
CL
0L
0L
0L
RL
RL
RL
RL
RL

39/2
41/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
29/2
31/2
33/2
35/2

3/2

7/2

9/2
13/2
15/2
17/2
21/2
23/2

7/2
17/2
21/2
27/2
29/2

S.D.

0.12
0.00
0.02
0,00
0.33
0.14
0.45
0.00
0.00
0.89
2,35
0,41
0.31
0,06
0.31
0.06
0.00
0.37
0,00
0.16
0.00
0.00
0.00
0.00
0.00
2.08
0.18
0.04
0.04

= 0,0035

239

2075,7358
2080,0497
1743,7736
1739,8602
1735,8506
1731,7099
1727,4296
1723,0406
1718,5314
1713,8731
1709,1216
1704,2579
1694,1797
1688,9736
1683,6705
1678,2606
1756,1344
1755,3554
1754,7463
1753,2180
1752,2486
1751,1800
1748,6199
1747,1732
1770,2551
1782,6006
1786,6781
1791,9257
1793,4459

2075,7353
2080,0483
1743,7655
1739,8721
1135,8512
1131,7039
1727,4315
1723,0357
1715,5182
1’13,8810
1/09,1261
1704,2558
1694,1787
1888,9770
1683,6701
1678,2608
1156,1304
1155,3499
1754,7663
1753,2170
1/52,2539
1751,1670
1748,6294
1747,1825
1770,2441
1782,6071
1786,6858
1791,9211
1/93,4395

0,0005
0,0014
0,0081
-0,0119
90.0006
0.0060
90,0019
0,0049
0,0132
90,0079
90,0045
0,0021
0,0010
-0,0034
0,0004
90,0002
0,0040
0,0055
90,0200
0,0010
50,0053
0,0130
”0,0095
"0.0093
0,0110
“0,0065
50,0077
0,0046
0,0064

Z

CDVOUIAOJNH

<

HranaP-anHwAPsHranAHIH+aHuawsprAHwArsH+4H44hnprfiuwAw-9

LINE

P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1
P1

77/2
75/2
73/2
71/2
67/2
65/2
63/2
61/2
59/2
57/2
55/2
53/2
51/2
49/2
47/2
45/2
43/2
41/2
39/2
37/2
35/2
33/2
31/2
29/2
27/2
25/2
23/2
21/2
19/2
17/2
15/2
13/2
11/2

9/2

7/2

5/2

APPENDIX IXeB

FREQUENCY FIT FOR 150160

HGT,

0.50
0,12
0.00
4.00
0,00
0.00
1.00
0.00
0,00
1,06
1.06
1.06
0.31
0.50
0,00
1.00
1.06
1.25
2,00
2,00
2.00
2,00
2,00
2,00
2.00
2,00
2.00
2,00
2,00
2,00
2,00
2.00
2,00
2.00
2.00
2.00

OBSERVED

1695,7322
1700,1321
1704,4740
1708,8576
1717,4356
1721,7132
1725,9500
1730,1360
1734,3142
1738,4392
1742,5464
1746,6172
1750,6611
1754,6751
1758,6554
1762,6093
1766,5163
1770,4089
1774,2697
1778,0889
1781,8808
1785,6504
1789,3694
1793,0696
1796,7309
1800,3657
1803,9610
1807,5305
1811,0696
1814,5759
1818,0386
1821,4766
1824,8814
1828,2559
1831,5973
1834,9074

240

PREDICTED

1695,7387
1700,1400
1704,5128
1708,8568
1717,4576
1721,7138
1725,9403
1730,1367
1734,3029
1738,4388
1742,5440
1746,6185
1750,6621
1754,6747
1758,6560
1/62,6061
1766,5247
1770,4118
1774,2672
1778,0909
1181,8829
1785,6429
1789,3710
1793,0671
1796,7311
1800,3631
1803,9628
1507,5304
1811,0657
1014,5688
1218:0396
1521,4780
1524,8841
1328,2578
1931,5991
1834,9080

 

(O-P)

30,0065
80,0079
00,0388
0,0008
’010220
30,0006
0,0097
q0,0007
0,0113
0,0004
0,0024
90,0013
60,0010
0,0004
90,0006
0,0032
90,0084
90,0029
0,0025
-0,0020
20,0021
0,0075
90,0016
0,0025
90,0002
0,0026
90,0018
0,0001
0,0039
0,0071
90,0010
90.0014
50,0027
60,0019
*0,0018
20,0006

37
38
39
4o
41
42
43
44
4s
46
47
4a
49
so
51
52
53
54
55
56
57
53
59
60
61
62
63
64
65
66
67
68
69
7o
71
72
73
74
75
76
77
7e
79
an

82
83
84
85
86
87
88
89
90

HW‘F‘HW‘F‘HW‘P‘PW‘F‘Hm‘HH‘F‘HWJF‘HfiihbfiblhfiH)‘h‘HW‘F‘HF‘HW‘F‘HWJPPPt‘h‘HW‘P‘HW‘P‘HH‘P‘H‘H

P1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1

P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2

372

1/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
61/2
63/2
65/2
67/2
69/2
71/2
75/2
75/2
73/2
71/2
67/2
65/2
63/2
61/2
59/2
57/2
55/2
53/2
51/2
49/2
47/2
45/2
43/2
41/2

2.00
2,00
0,50
2,00
0.50
2,00
2,00
2.00
2.00
2,00
2.00
2.00
2.00
2.00
3.00
1,00
0,50
2,00
2,00
2.00
2.00
2.00
2.00
2.00
2,00
1.00
2.00
2.00
1,00
2.00
2.00
2,00
2.00
1.25
1.25
0.50
0.00
0.12
0,50
0,50
0,00
0,00
0.19
1037
1,06
0,31
0,00
1,06
0,31
0,50
1,06
0,25
1,00
1,25

241

1838,1834
1847,8135
1854,0782
1857,1583
1860,2025
1863,2221
1866,2067
1869,1583
1872,0747
1874,9630
1877,8083
1880,6324
1883,4177
1886,1654
1888,8816
1891,5711
1894,2169
1896,8374
1899,4234
1901,9697
1904,4862
1906,9634
1909,4106
1911,8191
1914,1965
1916,5342
1918,8406
1921,1077
1923,3434
1925,5398
1927,7002
1929,8260
1931,9140
1933,9656
1935,9802
1937,9557
1941,8065
1696,8332
1701,2654
1705,6775
1714,4074
1718,7343
1723,0202
1727,2815
1731,5179
1735,7232
1739,8789
1744,0501
1748,1706
1752,2571
1756,3202
1760,3483
1764,3489
1768,3187

 

1538,1844
1847,8187
1854,0787
1957:1598
1560,2032
1563,2238
1866,2068
1569,1568
1872,0740
1874,9583
1877,8095
1880,6276
1583,4125
158601641
1988,8823
1891,5670
1894,2181
1896,8354
1899,4187
1901,9681
1904,4831
1906,9638
1909,4098
1911,8211
1914,1972
1916,5382
1918,8436
1921,1132
1223,3468
1925,5440
1927,7045
1929,8280
1931,9142
1933,9627
1935,9731
1937,9450
1941,7716
1096,8213
1101,2611
1705,6716
1,1404051
1718,7282
1723,0221
1727,2869
1731,5226
1/35,7290
1739,9062
1744,0541
1748,1726
1752,2617
1756,3212
1760,3510
1164,3510
1768,3210

90.0010
90,0052
80,0005
30,0015
-0,0057
20,0017
60,0001
0,0015
0,0007
0,0047
90,0012
0,0048
0,0052
0,0013
90,0007
0,0041
90,0012
0,0020
0,0047
0,0016
0.0031
-0,0004
0,0008
90,0020
20,0007
90,0040
90,0030
40,0055
90,0034
90,0042
90,0043
90,0020
90,0002
0,0029
0,0071
0,0107
0,0349
0,0119
0,0043
0,0059
0,0023
0,0061
20,0019
“0.0054
90,0047
20,0058
90,0273
60,0040
90,0020
90,0046
90,0010
P0,0027
90,0021
60,0023

91
92
93
94
95
96
97
9a
99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

146

141

142

143

144

HH‘E‘F‘PW‘F‘HWJF‘H‘HWJFPHWJP3F3HW4P3F3H43r1F*H%JF‘F‘H44F‘P‘PW‘F‘PW‘F‘HWJFAFPPWJP‘F‘P+3FPPW4F‘

P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
P2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
R2
PL
PL
PL
PL

39/2
37/2
35/2
33/2
31/2
29/2
27/2
25/2
23/2
21/2
19/2
17/2
15/2
13/2
11/2

9/2

7/2

5/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2
41/2
43/2
45/2
47/2
49/2
51/2
53/2
55/2
57/2
59/2
63/2
65/2
67/2
71/2
29/2
25/2
23/2
21/2

1,25
2,00
2,00
2900
2.00
2,00
2,00
2,00
0.50
2,00
2.00
2,00
2.00
2,00
0,00
2.00
2.00
2.00
0,00
0,00
2.00
2,00
2.00
2,00
2.00
2,00
2,00
2,00
2.00
4,00
3,00
1.00
2.00
2.00
0.31
0,50
2.00
2.00
2,00
2,00
2,00
2,00
2.00
2.00
0,50
1,00
2.00
1,25
1,25
0,12
0,06
0,25
0,33
0.31

242

1772,2598
1776,1782
1780,0440
1783,8990
1787,7169
1791,5102
1795,2653
1798,9888
1802,6814
1806,3468
1809,9735
1813,5698
1817,1362
1820,6702
1824,1794
1827,6382
1831,0739
1834,4720
1854,1636
1857,3063
1860,4573
1863,5501
1866,6047
1869,6253
1872,6106
1875,5649
1878,4693
1881,3466
1884,1852
1886,9869
1889,7524
1892,4833
1895,1834
1897,8304
1900,4495
1903,0334
1905,5724
1908,0801
1910,5469
1912,9780
1915,3715
1917,7274
1920,0435
1922,3288
1924,5620
1926,7715
1931,0602
1933,1533
1935,1993
1939,1749
1663,5706
1673,1964
1677,8582
1682,4009

1772,2610
1776,1708
1780,0503
1783,8992
1787,7174
1791,5047
1795,2610
1798,9860
1802,6796
1806,3415
1909,9716
1813,5697
1917,1355
1520,6688
1824,1694
192716372
1531,0718
1934,4731
1854,1687
1957,3306
1960,4575
1863,5491
1866,6053
1869,6258
1872,6105
1875,5592
1878,4718
1981,3480
1884,1876
1086,9907
1889,7569
1892,4862
1895,1784
1997,8334
1900,4511
1903,0314
1905,5743
1908,0796
1910,5473
1912,9773
1915,3697
1917,7243
1920,0412
1922,3204
1924,5619
1926,7657
1931,0607
1933,1520
1935,2060
1939,2024
1663,5676
1973,2011
1677,8589
1682,4079

'0,0012
0,0074
2"0.0063
90,0002
90,0005
0,0055
0,0043
0,0028
0,0018
0,0053
0,0019
0,0001
0,0007
0,0014
0,0100
0,0010
0,0021
90,0011
00,0051
90,0243
90,0002
0,0010
90,0006
90,0005
0,0001
0,0057
90,0025
90,0014
90,0024
90,0038
90,0045
90,0029
0,0050
"0.0030
90,0016
0,0020
90,0019
0,0005
90,0004
0,0007
0,0018
0,0031
0,0023
0.0084
0,0001
0,0058
90,0005
0,0013
90,0067
50,0275
0,0030
«0,0047
90,0007
90,0070

 

145
146
147
140
149
150
151
152
153
154
155
153
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
173
177
170
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
193
197
190

i‘t‘Pfl‘F‘Pfi‘F‘PP‘HflJ
H
14%‘H‘H4¢F‘HW*F‘HH‘F3HH4P‘F‘HWJF‘P‘Hwih39W‘F‘H‘Pfl4f‘HPHW*F*
1artnw¢+~uw¢

PL
PL
PL
PL
PL
PL
PL
PL
0L
0L
0L
0L
0L
0L
0L
0L
0L
RL
RL
PH
PH
PH
PH
PH
PH
PH
PH
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
0H
RH
RH

RH
RH
RH
RH
RH

19/2
17/2
15/2
13/2
1112

9/2

7/2

3/2
31/2
27/2
21/2
19/2
17/2
15/2
13/2

7/2

5/2

7/2
27/2
21/2
19/2
15/2
13/2
11/2

9/2

7/2

5/2

3/2

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
37/2
39/2
41/2

1/2

7/2

9/2
11/2
13/2
15/2
17/2
1972

0.50
0,25
0,00
0,00
2,00
0,00
2.00
0,00
0.50
0,00
2,00
0,50
0,00
2.00
2,00
2.00
2.00
0.00
0.06
0,04
0,00
0,00
0,50
0.00
0,52
1,50
0.52
1,00
4.00
4,00
4,00
4,00
5,00
3,06
1.19
3.00
4,00
4.00
1,60
0,47
4,00
4,00
2.00
0,50
0,12
0,03
1,00
2,00
2,00
2.00
2.00
2.00
2,00
2,00

243

1686,8447
1691,1701
1695,4485
1699,4708
1703,4600
1707,3133
1711,0583
1718,1864
1708,0992
1711,5478
1715,9443
1717,1929
1718,3249
1719,3415
1720,2422
1722,2386
1722,6680
1736,6579
1757,8669
1931,4675
1934,2000
1939,8185
1942,6763
1945,5907
1948,5692
1951,6154
1954,7006
1962,7679
1962,9055
1963,0996
1963,3476
1963,6441
1963,9958
1964,4011
1964,8510
1965,3521
1965,8982
1966,4860
1967,7831
1968,5015
1969,2411
1970,0260
1971,6784
1972,5484
1973,4387
1967,6108
1977,8723
1981,4000
1984,9774
1988,6050
1992,2837
1996,0100
1999,7806

1686,8461
1691,1717
1695,3830
1699,4785
1703,4569
1707,3169
1711,0574
1713,1770
1708,0993
1711,5574
1715,9509
1717,1956
1715,3274
1719,3446
1720,2457
1722,2403
1722,6655
1736,6181
1757,8696
1931,4640
1934,1913
1939,7920
1942,6683
1945,5967
1948,5781
1951,6135
1954,7034
1962,7726
196299102
1963,1023
1963,3481
1963,6469
1963,9977
1964,3991
1964,8501
1965,3489
1965,8941
1966,4837
1967,1161
1967,7890
1968,5004
1969,2481
1970,0298
1971,6858
1972,5553
1973,4492
1967,6141
1977,8723
1981,3984
1984,9763
1988,6047
1992,2824
1996,0077
1999,7789

 

90,0014
90,0016
0,0655
0,0031
90,0036
0,0009
0,0094
20,0001
-0,0096
30,0066
90,0027
90,0025
«0,0031
90,0035
90,0017
0,0025
0,0398
90,0027
0,0035
0,0087
0,0265
0,0080
90,0060
~0,0089
0,0019
90,0028
90,0047
"0,0047
60,0027
30,0005
90,0028
80,0019
0,0020
0,0009
0,0032
0,0041
0,0023
0,0013
90.0059
0,0011
60,0070
90,0038
90,0074
90,0069
90,0105
P0,0033
e0,0000
0,0016
0,0011
0,0003
0,0013
0,0023
0,0017

 

199
200
201
202
203
204
205
206
207

F‘HW‘F‘HW‘F‘HW4

RH

RH

RH
RH
RH
RH
RH
RH
RH

21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2

8,0,

2,00

,0035

244

2003,5978
2007,4539
2011,3507
2015,2872
2019,2551
2023,2536
2027,2882
2031,3528
2035,4363

2003,5943
2007,4519
2011,3496
2015,2852
2019,2564
2023,2609
2027,2962
2031,3599
2035,4494

0,0035
0,0020
0,0011
0,0020
90,0013
60,0073
90,0080
90.0071
20,0131

 

Z

JVVChUWAid339

HLJP‘HF*P*H9*F‘H
0,fl\¢)\flbbw\3973(3

20

tunamronamranm
CID‘JaifilibiMrJ

30
31
32
33
34
35
36

FIT UP THE LAMBDA DnUHLEI

PL
PL
PL
PL
PL
PL
PL
PL
PL
PL
0L
0L
0L
RL
RL
RL
RL
HL
PH
PH
PH
PH
PH
0H
0H
0H
UH
OH
OH
on
0H
OH
OH
0H
0H
0H

LINF

35/2
33/2
31/2
29/2
25/2
23/2
21/2
19/2
17/2
15/2
23/2
21/2
13/2

7/2
17/?
21]?
27/2
29/2
31/2
29/2
27/2
23/2
19/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2
33/2
35/2
37/2
39/2

”GTO

0,06
0,31
0,06
0,31
0.41
7,35
0,89
0,00
0,00
0,33
0,00
0,00
0,08
0.00
0,00
0,18
0.04
0,04
0,19
0,50
0,22
0,83
0,59
0.00
0,00
1,00
3,84
6,10
6.71
5,71
6.25
6,25
6,52
0,06
5,47
2,02

APPPNDIX X-A

085,

“001655
'001639
'0-1200
'0o1316
-0-1204
-0-1151
“001031
'0-1259
“090771
“090677
-0-1545
70,1101
“0.0692
~0-0596
'001045
“091323
“001365
~0,1424

0-1619

0,1543

0,1523

0,1282

0,1042
“090771
“090947
“001123
“091260
'091385
“091530
“0,1626
“091765
“091886
“091995
“092154
“092229
“002350

245

SPLITTINGS FOR 14N160

PREU,

‘0,1590
'0,1556
‘0,1512
“0,1460
'0,1330
“0,1255
'0,1172
“0,1084
“0,0991
“0,0893
“0,1403
“0,0817
"0,0455
“0.0968
“0,1139
“0,1345
'0.1397

0,1514

0.1461

0,1400

0,1255

0,1085
“0,0933
“0,1050
“0,1167
'0,1284
“0,1401
“0,1518
“091636
“0,1753
“0,1571
“0,1988
”0,2106
’0,2224
’0,2342

(O'P)

'090065
‘0,0083
0,0312
0,0144
0,0126
0,0104
0,0141
'0,0175
0,0220
0,0216
“090142
0.0185
0,0125
'0,0138
“0,0077
'0,0184
“0,0020
“0,0027
0,0105
0,0082
0,0123
0,0027
“090043
0,0162
090103
0.0044
0,0024
0,0016
'0,0012
0,0010
“090012
“090015
“000007
“090048
‘0,0005
'0,0008

 

246

37 OH 41/2 0,75 '0,2520 '0,2460 '0,0060
38 GM 43/2 0,37 '0,2638 ”0,2579 "0,0059
39 OH 45/2 0,12 '0-2726 “0,2698 '0,0028
40 0H 47/2 0,02 “092701 ”0,2816 0,0115
41 RH 15/2 0,00 0,0651 0,0874 '0,0223
42 RH 17/2 0,00 0-0764 0,0963 “0,0204
43 RH 19/? 0,00 0,1016 0,1056 -0,0040
44 RH 21/2 0,25 0,1059 0,1138 “0,0079
45 RH 23/2 0,50 0,1170 0,1214 "0,0044
44 RH 27/2 2.06 0.1349 0.1343 0,0006
47 RH 29/2 2,02 0,1383 0,1396 "0,0013
48 RH 31/2 2,02 0,1476 0,1440 0,0036
49 RH 33/2 0.50 001479 0,1474 0,0005
50 RH 35/2 0,31 0,1544 0,1499 0,0045
51 RH 37/2 0,12 0-1542 0,1513 0,0029
5? RH 39/2 0,12 0-1595 0,1516 0,0079
53 RH 41/2 0.00 001789 0,1507 0,0282
54 P1 1/2 0.00 “0,0000 0,0117 “0,0117
55 P1 3/2 0.00 -0.0000 0,0117 '0,0117
56 P1 5/2 0,00 -0,0000 0,0118 “0,0118
57 P1 7/2 0.00 '0-0000 0,0120 "0,0120
58 P1 9/2 0600 “090000 090125 “000125
59 P1 11/2 0.00 ~0,0000 0,0132 '0,0132
6.0 P1 13/2 0,00 “0,0000 0,0142 70,0142
61 P1 15/2 0.00 7000000 0.0156 “0,0156
62 P1 17/2 0,00 '0-0000 0,0173 '0,0173
63 P1 19/2 0.00 -0.0000 0,0196 “0,0196
64 P1 21/2 0.00 7000000 0,0224 '0,0224
66 P? 1/2 0.00 -0,0000 0,0000 "0,0000
66 P? 3/2 0.00 “090000 0,0000 ‘0q0000
67 P9 5/2 0,00 “0,0000 0,0001 "0,0001
68 P9 779 0.00 -o-oooo 0.0002 -o.0002
69 P? 9/2 0.00 70,0000 0,0003 ‘0,0003
70 P2 11/2 0,00 “0,0000 0,0004 “0,0004
71 P2 11/2 0.00 -0.0000 0,0004 ‘0,0004
7? P9 15/2 0,00 '0-0000 0,0008 "0,0008
73 P2 17/2 0,00 "0,0000 0,0011 '0,0011
74 P2 19/2 0,00 '0-0000 0,0014 ‘0,0014
75 P9 21/2 0,00 "0,0000 0,0017 “0,0017
77 R1 3/2 0.00 0-0000 "0,0116 0,0116
78 R1 5/2 0.00 0,0000 ’0,0115 0,0115
79 R1 7/2 0,00 0,0000 ”0,0114 0,0114
80 R1 9/? 0,00 0,0000 ‘0,0112 0,0112
81 R1 11/2 0,00 000000 ’0,0111 0,0111
82 R1 13/2 0,00 0,0000 ”0,0109 0,0109
83 R1 15/2 0.00 0,0000 '0,0107 0,0107
84 R1 17/2 0,00 000000 ‘0,0105 0,0105
85 R1 19/2 0,00 0,0000 “0,0102 0,0102
86 R1 21/2 0,00 0,0000 90,0099 0,0099
87 R2 1/2 0.00 0,0000 ”0,0000 0,0000
88 R? 3/2 0.00 0,0000 90,0001 0,0001
89 R2 5/2 0,00 0.0000 “0,0002 0,0002

 

91

9?

93

94

95

96

97

98

99
10”
101
102
103
104
105
106
107
108
109
11n
111
117
113
114
1.1L3
116
117
118
119
123
121
122
123
124
125
126
127
128

R?
R2
R2
R9
R2
R9
R9
01
Q1
Q1
01
01
U1
01
Q1
Q1
01
01
01
01
01
Q1
Q1
02
U?
U?
Q9
0?
Q2
Q2
02
Q2
09
0?
02
09
Q?
U?

9/2

11/2
13/2
15/2
17/9
19/2
21/2

1/2

3]?

5/2

7/2

9/2
11/2
13/2
15/2
17/2
19/2
21/2
21/2
25/9
27/2
29/?
51/2

3/2

5/7

7/?

Q/?
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
51/2

S.D.

0,00

0.00
0,00
0,00
nfloo
0,00
0,00
0,00
0,00
0,00
0,00
0.00
0,00
0,00
0,00
0.00
0.00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0.00
0,00
0,00
0,00
0,00

0,0043

24/

0,0000

0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
000000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0-0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
000000
0,0000
0,0000
0,0000
0-0000
0,0000
0,0000
0,0000
0,0000

“0,0004

”0,0006
q'0,0008
‘0,0010
'0,0013
‘0,0015
'0.0018
“0,0233
'0,0466
‘0,0697
‘090927
'0,1154
‘0,1379
’0,1601
'0,1818
“0,2031
“0,2240
“0,2442
'0,2638
'0,2825
"0,3011
-005186
‘0,3352
'0,0001
“0,0002
‘000006
‘0.0012
'0,0020
"0,0032
'0,0049
'0,0070
“0,0096
'0,0127
“0,0166
'0,0211
‘0,0264
'0,0324
'0,0394

0,0004

0,0006
0,0008
0,0010
0,0013
0,0015
0,0018
0,0233
0,0466
0,0697
0,0927
0,1154
0,1379
0,1601
0,1818
0,2031
0,2240
0,2442
0,2638
0,2828
0,3011
0,3186
0,3352
0,0001
0,0002
0,0006
0,0012
0,0020
0,0032
0,0049
0,0070
0,0096
0,0127
0,0166
0,0211
0,0264
0,0324
0,0394

 

 

-fi\d)\nh{HNIH

Hf‘F‘HFJP*H+4P‘H
c,B\é®\nbmfl\L423O

20
21
22
23
24
28
26
27
28
29
50
31
39
33
34
35
36

FIT OF THE LAMBDA DOUDLEI

PL
PL
PL
0L
0L
0L
CL
CL
QL
0L
UL
RL
PH
PR
PW
P4
OH
04
UH
OH
0“
OH
OH
QM
UH
0H
0H
QM
OH
OH
OH
R4
RH
RH
RH
RH

LINE

201?
25/2
21/2
31/2
29/2
27/2
25/2
21/2
19/2
17/2
16/2
27/2
21/2
191?
15/2
13/2
16/2
1612
17/2
19/2
21/2
23/?
25/?
27/2
29/2
61/2
33/2
65/2
37/2
39/2
41/?
17/2
10/2
21/2
23/2
25/2

HGT,

0,06
0.25
0,33
0,50
0,00
0,00
0.00
2,00
0,50
0,00
0,50
0,06
0,04
0,00
0,00
0,00
0,00
0,00
0,00
0,75
4,00
4,00
1,60
0,47
4,00
4,00
2,00
0,00
0.50
0,12
0,03
0,00
0,50
2,00
2,00
1.54

APPFNDIX X'R

033,

“001422
“001197
”001182
-0o1785
-002541
'001455
“001227
’001296
”001147
’001042
-000879
“001350

0,1177

0,1099

0,1458

0,0737
"000671
”000823
”000968
-0,1111
”001229
’001335
”001517
”001556
"001713
“001827
"001965
"002335
“002160
-0,2273
~0,2425

0,0909

001028

091117

0.1178

0,1225

248

SPLITTINGS FOR 15N160

PRED,

'0,1440
'0,1307
”0,1231
”0,1825
“0,1595
'0,1480
“0,1251
'0,1137
”091023
'0,0909
‘0,1328

0,1149

0,1061

0,0872

0,0771
“0,0795
'0,0908
'001022
'0,1136
‘0,1250
“0,1564
'0,1478
“0,1592
“0,1706
"0,1520
“0,1935
“0,2049
”0,2164
“0,2279
’0,2394

0,0948

0,1035

0,1117

0,1194

0,1264

(0am

0,0018

090110
090049
0,0040
‘0,0831
0,0130
0,0253
“0,0045
q000010
‘0,0019
0,0030
'000022
0,0028
0,0038
0,0566
”0.0034
0,0124
0,0085
0,0054
0,0025
0,0021
0,0029
‘0,0039
0,0036
”090007
”090007
‘0,0028
”090286
0,0004
0,0006
“0,0031
'0,0039
'090007
”090000
‘0,0016
-000039

37

38
39
40
41
4?
43
44
46
46
47
4P
49
50
51
5?
53
54
SS
56
57
SR
59
6m
61
6?
63
64
65
66
67
68
59
70
71
72
73
74
76
76
77
78
79
an
81
8?
33
84
85
86
87
88
89
9n

RH

RH
RH
RH
RH
RH
P1
P1
P1.
P1
P1
P1
P1
P1
P1
P1
P1
P?
P?
P9
P2
P2
P2
P2
P?
P?
P2
P2
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R1
R?
H?
R?
R?
R?
R?
R2
R2
R2
R2
R2
01
Q1
Q1
01

277?
29/2
31/?
33/2
3572
37/2
1/2
37?
SI?
7/?
9/?
117?
13/7
15/2
17/2
19/2
21/9
1/2
3/2
SI?
7/?
9/7
11/2
11/2
15/2
17/P
10/9
21/2
1/?
3/2
5/2
7/2
9/2
11/?
13/2
16/7
17/?
19/?
21/2
1/2
3/2
5/2
77?
97?
11/2
1372
15/?
17/2
19/2
21/2
1/2
3/2
572
772

2,00

0,50
0,12
0,02
0,02
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0.00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0.00
0.00
0.00
0.00
0,00
3,00
0,00
0.00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0.00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00
0,00

249

0,1357
0,1413
0,1477
0,1583
0,1604
0,1723

“0,0000-

’000000
-0,0000
-0,0000
’000000
-0,0000
-0-0000
“000000
“000000
’000000
"000000
”000000
-0o0000
‘000000
~0-0000
'000000
"000000
“0.0000
-0,0000
'0-0000
"0.0000
"0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
000000
0,0000

0,1327

0,1582
0,1430
0,1469
0,1499
0,1519
0,0113
0,0114
0,0115
0,0117
0,0121
0,0127
0,0136
0,0149
0,0165
0,0185
0,0211
0,0000
0,0000
0,0001
0,0002
0,0003
0,0004
0,0004
0,0008
0,0010
0,0012
0,0015
”0,0113
“0,0113
-000112
’0,0111
“0,0110
'0,0108
'0,0107
‘0,0105
’0,0103
’0,0100
“0,0098
'0,0000
'0,0001
”0,0002
'0.0003
“0,0004
'0,0005
“0,0007
”090009
”0,0011
“0,0014
"0,0017
”0,0227
90,0453
“0.0679
’090903

0.0030

0,0031
0,0047
0,0114
0,0105
0,0204
”000113
‘000114
“0.0115
'0,0117
-000121
“0,0127
“0,0136
‘0-0149
“0,0165
'090185
'0,0211
‘0,0000
'000000
'000001
'000002
‘0,0003
'0,0004
‘0,0004
'0q0008
“090010
’090012
-000015
0.0113
0,0113
0,0112
0,0111
0,0110
090108
0,0107
0,0105
0,0103
0,0100
0,0098
0,0000
0,0001
0,0002
0,0003
0,0004
0,0005
0,0007
0,0009
0,0011
0,0014
0,0017
0,0227
0,0453
0,0679
0,0903

 

 

91
92
93
94
95
96
97
98
99
100
101
102
103
.104
105
10!1
107
110R
109
110
111
112
113
114
115
118
117

01
01
01
Q1
Q1
01
01
01
Q1
01
01
Q1
Q?
Q?
02
02
0?
U?
Q?
02
02
U?
Q?
0?
Q2
09
Q9

9/2
11/2
13/2
15/2
17/2
19/2
21/2
23/2
25/2
27/2
29/2
31/2

3/ 2

5/2

7/2

9/2
11/2
13/2
15/2
17!?
10/2
21/2
23/2
25/2
27/7
29/2
51/2

SOD.

-
..

0.0028

250

000000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000
0,0000

'0,1124

“0.1344
”0,1560
"0,1773
"0,1982
'0,2186
'0,2385
“0,2579
'0,2766
’0,2947
“0,3121
'0,3288
“0,0001
”0,0002
"0,0005
”0,0011
‘0,0018
'0,0029
'0,0044
'0,0063
"0,0087
“0,0116
“0,0150
"0,0191
’0,0239
'0,0294
'0,0357

0,1124

0,1344
0,1560
0,1773
0,1982
0,2186
0,2385
0,2579
0,2766
0,2947
0,3121
0,3288
0,0001
0,0002
0,0005
0,0011
0,0018
0,0029
0,0044
0,0063
0,0087
0,0116
0,0150
0,0191
0,0239
0,0294
0,0357

W

 

111111111
1840

110

1293