THE msr AND SECOND ovsaroue BAND-S
or N150 {N THE 51am grammes:

““8 g” flw Dom. as M. s.
MECHKGAH SMTE UNEVERSET‘!
Sister Mary

Dominic McNeIis. O. P.
1962

THESIS

llulwnfi'tlzil’fllfi‘flmfl‘ 11111111111111

17640131

 

ABS TRAC T

THE FIRST AND SECOND OVERTONE BANDS
OF N150 IN THE NEAR INFRARED

by Sister Mary Dominic McNelis, O. P.

The 2-0 and 3—0 absorption bands of N150 have been observed
in the near infrared at Z. 7 and 1.8 microns respectively by means of
a vacuum recording infrared spectrometer. A system of Edser-Butler
bands, obtained with a Fabry- Perot etalon and recorded simultaneously
with the absorption spectra, was used as a calibration system for this
study. The records obtained were carefully analyzed and an evaluation
of the molecular constants was made using MISTIC, the Michigan
State University digital computer. The determination yielded the follow-

. . . __1 . . .
2mg results, where the units are in cm , unless spec1f1ed.

B0 1.63613 4 0.00004

B2 :1.60284 4 0.00001
133 21.5861; 4 0.00002

D0 = (4.5 i- 0.5) x10'6

Dz : (4.7 4 0.1) x10"6

D3 : (4.7 4 0.3) x 10-6

Ho = {-5.8 4 0.6) x 10"10
H; = (-4.9 4 0.1) x 10-10
Be: 1.64447 4 0.00004

ae : -0.01667 4: 0.00004
De: (4.4 4 0.4) x 10-6

Ie : 17.016 x 10""‘0 gm-cmZ

re: (1.1506 4. .0005) x 10»8 cm.

Sister Mary Dominic McNelis, O. P.

an/uwe : 1870.075 4 0.002
wexe 213.529 4 0.002
Brahma 2: 1869.874 4 0.001

13.532 :1: 0.001

wexe

These constants were compared with the molecular parameters
of N140 by means of an isotope calculation and found to be in good agree-

ment.

To further examine their significance, the N150 constants above
were compared with those obtained by Fletcher and Begun for the
fundamental of N150 and those obtained from microwave data of Gallagher

and Johnson. The agreement was found to be quite good.

THE FIRST AND SECOND OVERTONE BANDS
OF N150. IN THE NEAR INFRARED

By

Sister Mary Dominic McNelis, O. P.

A THESIS

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

MASTER OF SCIENCE

Department of Physics and Astronomy

1962

Approved CD. [0. W,

ACKNOWLEDGMENTS

The author wishes to express her gratitude to Professor
C. D. Hause for his very kind and helpful assistance. His guidance
and encouragement are sincerely appreciated. She would like to
thank Mr. John Boyd whose computer program ”Dalcevac" was used
extensively in this analysis. The author also wishes to express her
gratitude to the Arthur J. Schmitt Foundation of Lemont, Illinois,
for its very generous financial support during the years 1961-1962.

>1: >:< >1: >:< >:< >:< >1: >§< >:< >1: >§< >§< z}:

ii

TABLE OF CONTENTS

Page
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 1
THEORY . 3
Angular Momentum Coupling Cases. 3
Energy Relations 4
Band Branches. . . . . . . . . . . 8
Molecular Constants and Isotope Effect. . . . . . . . . 10
EXPERIMENTAL PROCEDURES . . . . . . . . . . . . . . . l3
DATAANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . 14
Observed Spectra and the Fringe System. . . 14
Determination of Bv, DV, HV and v0 for the (2- 0) Band 18
Determination of BV, Dv, and v0 for the (3- 0) Band . . 27
Determination of Be, ae, Ie, re, and De . . . . . . . . 28
Calculation of the (2- Branch . . . . . . . . . . . . . 30
Determination of the Vibrational Constants: we, and
exe 30
COMPARISON OF N150 WITH OTHER WORK. . . . . . . . . 33
SUMMARY AND CONCLUSION . . . . . . . . . . . . . . . . . 36
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . 37

iii

LIST OF TABLES

TAJKLE
I. Lines Deleted from the Overtone Bands .

II. Argon and Neon Standards .
III. Calculated and Observed Frequencies for the 2-0 Band
IV. Calculated and Observed Frequencies for the 3-0 Band
V. Effective Rotational Constants .
VI. Rotational and Vibrational Constants for N150.

VII. Calculated and Observed Q Branch Lines .

VIII. Comparison Of N150 Constants .

iv

Page

16

19

20

23

26

31

32

34

LIST OF FIGURES

FIGURE

1. Hund's Coupling Cases . .

2. Formation of P, Q, and R Branches . .

3. 2-0 Band and 3-0 Band of N150 .

4. Graphical Determination of Be and “e .

Page

15

29

INTRODUCTION

Nitric Oxide is a diatomic molecule which has been of consider-
able interest in spectroscopy for some time. It is the only stable
diatomic molecule with an unpaired electron having both non-zero spin
and orbital angular momentum and a normal an ground state. The two
substates of the ground state, designated as 2171/; and 2113/2, are separated
by only 122.14 cm"1 [1] and for this reason are both appreciably popu-
lated at room temperature.

N140 has been quite thoroughly studied and a history of the investi-
gations made to 1953 is presented by N. L. Nichols [Z]. W. H. Fletcher
and G. M. Begun [3] also give a resume of the more recent experimental
work done on N140. They list the first high resolution observation of
the fundamental made simultaneously by Neilsen and Gordy [4] and
Gillette and Eyster [5] in 1939, Nichols, Hause and Noble's [6] study of
the first and second overtones in 1955, the microwave analysis done by
Burrus and Gordy [7] in 1953 and Gallagher, Bedard and Johnson [8] in
1954, and Shaw's [9] re-examination of the fundamental in 1956.

In 1955 Gallagher, King and Johnson [10] reported preliminary
results on the microwave spectrum of N150. Coupling this information
with the microwave studies [7,8] done on N140, Gallagher and Johnson
[11] in 1956 presented a comparison of the microwave observations of
these two isotopes along with a completed list of all the molecular and
nuclear parameters then determined. Fletcher and Begun's [3] work
in 1957 was an analysis of the fundamental of N150 made with a grating
spectrometer.

The first and second overtone bands of N150 analyzed here were

obtained with a vacuum recording infrared spectrometer, the bands

occurring at Z. 7 and 1. 8p. respectively. The rotational and vibrational
constants Of the molecule were determined and as an additional check
on their accuracy, these constants were compared with the molecular

constants [12] of N140 by means of an isotope calculation.

THEORY

Angular Momentum CouplingCases. In a diatomic molecule the

 

electrons move in a field axially symmetric about the internuclear axis.
As a result only the projection of the orbital angular momentum on the
internuclear axis is constant, i. e. , L, the total orbital angular momentum
precesses about the internuclear axis with a constant component desig-
nated as A. . The electronic states of diatomic molecules are classified
according to_/\. . Thus, in the case of N150 whereA = 1, it is a TI state
and because/\can be 1' l, the TT state is doubly degenerate.

The orbital motion of the electrons causes an internal magnetic
field in the direction of the internuclear axis which in turn causes a
precession of S, the resultant of the spins of the individual electrons,
about the field direction. The projection of S on the internuclear axis is
designated as 2 which for N150, because of the odd electron, may be t 1/2.
The total angular momentum of electronic origin along the internuclear

axis is denoted by!) where
.0. = IA + z I (1)

Because./\. and Z are both along the internuclear axis, their sum may
be taken directly. For each value ofA, there are (ZS +1) possible
2 values, (28 +1) being the multiplicity. For N150 the multiplicity is 2,
and .0. may be 1/2 or 3/2.. Consequently, the substates are designated
as 2171/2 and 713/2, the former being lower in energy.

If one next considers the angular momentum of nuclear rotation
as well as the orbital and spin angular momenta of the electrons, several
possible modes of coupling are possible--all of which are treated in

detail by Hund [13]. In case "a", Hund assumes that the total electronic

momentum is strongly coupled to the internuclear axis and that the inter-
action of nuclear rotation with the electronic motion is weak. In terms
of Figure l-A, A and Z are strongly coupled to form n which in turn is
weakly coupled with N to form J, a vector fixed in space which is the
resultant of the different momenta neglecting nuclear spin. In case "b",
the spin 5 is only weakly coupled to the internuclear axis. A and N are
coupled directly to form K, the total angular momentum apart from spin.
K and S then form the resultant J. See Figure l-B. The molecule NO
exhibits a coupling which is intermediate between case ”a“ and case "b",
being just slightly removed from case "a". We have evidence of this
because the doublet separation is large (122.14 cm'l) compared to the
rotational constant (~2 cm‘l). As rotational speed increases, rotational
velocity becomes comparable to the precessional velocity of S and
eventually the molecular rotation dominates. S then uncouples from the

molecular axis and case "b" is approached.

Enefly Relations. The case "a” coupling described above is

 

entirely similar to that of the symmetric top whose energy levels to

a first approximation are given by:

F(J) : BJ(J + 1) + (A - B)flz (2)
,h h
Here B = -*2—-—- and A = ——2-—
8w CIB 817 CIA

1B is the moment of inertia of the molecule about an axis perpendicular
to the internuclear axis and is much larger than IA, the moment of
inertia of the electrons about the internuclear axis.

If this simple case is extended to that of a non— rigid, vibrating

symmetric top, the rotational term values then become

F

V(

J) = BVJ(J + 1) + (A - 13,0112 - DVJZ(J +1)’- + (3)

 

 

w

 

 

 

(B)

 

HUND' S COU PLING CASES

FIGURE I.

The term D accounts for the influence of the centrifugal force and higher
order correction terms may be added as needed. The subscripts on

the rotational constants indicate that effective values of B and D must be
used which Show the slight dependence of these constants on the vibra-
tional level. For a given vibrational level of a given electronic state,
the term in [12 is constant and can be neglected in the computation of
rotational transitions if the band origin is chosen properly.

Equation (3) is essentially that used in this analysis of N150.

It was mentioned above, however, that N150 is only close to case a
actually being intermediate between cases "a" and "b".

Hill and Van Vleck [14] derived a general expression for any
magnitude of coupling between S and A . This relation is given below

along with the centrifugal distortion term arrived at by Almy and

Horsfall [11].

E = BV[(J + 1/2)2 - A2] 4 1/2 BV[>. A20. - 4) + 4(J + 1/2)~"]‘/Z

2 Z
- DV[J (J +1) - J(J +1)+ 13/16] (4)
12:
BV
sign to the 3171/; state.

where A = , the upper Sign refers to the 2173/; state, and the lower

When spin uncoupling is small, i. e. , A >> 1 as it is in the case
of N150 where A 2 75, the radical may be expanded and an equation of

the form
E : (Bi/)effu + l/Z)z - (DV)(J + 1/2)4 + constant (5)

is obtained, where

 

 

BV
B 4
D = D i V (7)

V V [AAZ(A .. 4Bv)]"
constant = .13v AZ 41/2[AA 2(A - 4BV)]}’2 - DV + AA 2

+ BV[L(L + 1) .. A211“ BV [5(5 + 1) - 272] (8)

If to these effects of spin uncoupling, one also takes account of 1 un-

coupling, an additional term is added to the (By)eff’ namely:

 

' allE v(Tr——> 2)
states

The value listed by Gallagher and Johnson [ll] for this term is 0. 71
Mc/sec. It is now evident that Equations (3) and (5) are essentially the
same; (J + 1/2)2 and J(J + l) differing by only 1/4 which is accounted for
in the constant term. Thus we see that when the spin uncoupling is
small, A >> 1, the general equation for the energy levels in the inter-
mediate coupling case may be represented by the symmetric top form
where the B's and D's are interpreted as Beff and Deff'

Equation (3) was therefore used in the form:
FV(J): BVJ(J + 1) - DVJZU + 1)" (10)
for the analysis of the 3-0 band and in the form
FV(J) = BVJ(J + l) - DVJ2(J + 1)7‘ + HVJ3(J + 1)3 (11)

for the 2-0 band where the higher order term was found to be significant.
These bands are rotation-vibration bands of a single electronic state.
For the 2-0 band or first overtone, the vibrational transition occurs
between the zero vibrational level, v = 0, and the second vibrational
level, v = 2. For the 3-0 band or second overtone, the transition occurs
between v = O and v = 3. These vibrational transitions show a fine
structure due to the rotation of the molecule and therefore the bands are
called rotation-vibration bands.

The anharmonic approximation for the vibration terms is given

by

(3(0) = we(v + 1/2) - wexe(v + 1/2)‘2 + weye(v + 1/2)3 + (12)
Therefore a rotation-vibration term T, is:
T 4 O(V) + FV(J) (13)
and a rotation-vibration transition is given by:
v : G'(v) — G”(v) + Fjv,(J) - F{,'(J) (14)

where (') refers to the upper state and (") refers to the lower state.
If G'(v) - G"(v) be represented as v0, the band origin, then by a substi-

tution in Equation (14):
v = v0 + ij - F30) (15)

Band Branches. The spectrum of N150 consists of two almost

 

superimposed bands each having three branches called P, Q, and R.
When A = 1, as it does for NO, the allowed transitions must follow the
selection rule AJ = 0, =1: 1. The P branch consists of those lines for
which AJ 2 -l, the Q branch those for which AJ = 0, and the R branch
those for which AJ = +1. See Figure 2. It will be noted that the line
designation corresponds to the lower state J value. When A = O, (the
23 state) the selection rule becomes AJ = i 1, and therefore no Q branch
results. This is the case with most diatomic molecules.

For P and R branches the frequencies in cm"1 of the transitions

may be represented by
P(J) 2 v0 + R} (J - 1) - F3”) (16)

R(J) = v0 4 F“; (J + 1) - F3(J) (17)

respectively. These may be written collectively as

J1

 

. /2
¢ 5

 

. 3/2

 

 

 

 

P(5/2)

 

PCS/2)

 

 

 

0(1/2)

 

Q(3/2)

 

 

Q(5/Z)

 

 

R(l/2)

 

R(3/Z)

 

 

 

 

 

FIGURE 2.

 

 

1/2 0 V”

 

FORMATION OF P, Q, R BRANCHES

10

”P, R = v0 + (B), + Binm + (B1, - B3 - D; + D{;)ma
+ (H1, + H3 - 2D)v - 2D;;)m3 + (3H), — 3H3 - DEV + Dwm“
5 6
+ 3(H; + me + (H1, _ me (18)
after appropriate substitutions from Equation (10) or (11) are made for
F{,(J) and F",'(J). To use the single relation, (-J) must be substituted

for m to obtain P branch lines, and (J + l) to Obtain R branch lines.

For Q branch lines:

v0 2 v0 + (B'V - B3)J + (B1, - B;,')Jz (19)

and from this relation, using the band origin and the determined B

values, the frequencies of the Q branch lines were calculated.

Molecular Constants and Isotope Effect. The effective rotational

 

constants, B3, Di}, H3, Blv, D1,, and H' along with v0, the band origin,

v,
were obtained from a least squares determination following methods
suggested by Rank [15]. This method will be explained in the section
labeled Data Analysis.

Using these effective constants and the relations given above in
Equations (6), (7), and (9). the actual rotational constants Bv and Dv
were obtained. HV was evaluated by averaging the two effective H values
obtained experimentally. In Equation (6) for example, a(B3)efi was
substituted for the ground state Of each Of the substates Of one band.
When combined the result is immediately obtained:

2 (B3). + (By);

Bv 2

— Dv - 0.71 Mc/sec (20)

Next by plotting the BV values versus (v + 1/2) the equilibrium
B(Be) was determined as the intercept, and ae determined as the slope
of the straight line obtained. ae is a measure of the change in BV with

changes in vibration, i. e. ,

11

BV 2 Be - ae(v + 1/2) (21)
Be is given by
h
Be _ 8n cle (22)

where 1e = P re?‘ is the moment Of inertia for the equilibrium separation
of the atom, r is the equilibrium separation and u is the reduced mass

e
of N0 (=

m m -
—-1-—-7‘——) By an analogous method De can be determined and
m1 '1' m2

also B which is a measure of the change in De as the vibration changes:

DV 4 D8 + B(v+1/2) (23)

The vibrational anharmonic constants given above in Equation (12)
were determined from a knowledge of the band origins by means of the

following relations:

0(3) - 6(0) (24)

V3-0

v24, C(2) - G(0) (25)

When isotopic species are involved, it is usual to relate their constants

in terms Of a factor p which may be defined as follows:

p = ’_1-_Li__ (26)

u

where the heavier isotope, distinguished by the superscript i, has the
smaller frequency. It can be shown from Equation (12) that to a first

approximation the vibrational term may be written as

C(v) = 008(v + 1/2) (27)

for the "ordinary" molecule, and one may also write

Gi(v) = wei(v + 1/2) (28)

12

for the heavier molecule. This assumes the vibrations are harmonic

and it follows that

.3 = pwe (29)

By similar calculations the relation between the higher order vibra-
tional constants, wexe and “eye: for the "ordinary" molecule and their

counterparts for the isotope are found to be:

I)

424: Pzwexe (30)

“Eve p3were (31)
The rotational constant B was defined in Equation (22). This equation

may also be written as

Be = mL—z- (32)
8w cure

by substitution Of the value of Ie. For the heavier molecule this

becomes
Bi - —-2—-—-zh (33)
e‘ 1
811 cu re

However, from Equation (26) pi equals 7911;— and therefore Equation

(33) may be written as:

. 2
B81 = W =: sze (34)
Similarly:
(lei - p3ae (35)
and
D31: “Be (36)

By means of these relations between the constants of the two isotopes
the rotational and vibrational constants of N150 were compared with those

Of N140.

EX PERIMENTAL PR OC EDURES

The first and second overtone bands Of N150 analyzed here were
Obtained by Professor T. H. Edwards and Professor C. D. Hause with
a vacuum recording infrared spectrometer. The spectrometer was
equipped with a Bausch and Lomb precision grating in a Littrow mounting
having 600 grooves per mm and a 6" x 8" ruled surface.

The source of radiation was a 300-watt Zirconium arc, and the
detector used was a PbS type P. The N150 gas was placed in a Multiple
Traverse Cell which was designed by T. H.. Edwards [16]. For both
the 2-0 band and the 3-0 band the path length of the radiation in the cell
was eight meters. The pressure maintained in the cell was 3 cm for
the 2-0 band and 15 cm for the 3-0 band.

Calibration of the absorption bands was accomplished by means
Of Edser-Butler bands. These bands were produced by visible radiation
in higher orders traversing the monochromator and a 3 mm Fabry-Perot
etalon. Their maxima were detected by a 1P21 photo-multiplier and
phase sensitive amplifier. The Edser-Butler bands and the spectra
we re recorded simultaneously with a Leeds and Northrup two pen
recorder. Neon and Argon lines were inserted and/or superimposed

in the spectra as standard lines.

13

DATA ANALYSIS

Observed Spectra and the Fringe System. The Observed absorption

 

spectra of the 2—0 and the 3-0 bands of N150 at 2.7 and 1.8 h respectively
are shown in Figure 3. Because B‘ is less than B", the bands degrade
toward low frequencies. This is seen as a spreading of the lines in the
P branch and a drawing together of the lines in the R branch. Since the
selection rule AJ 2 0 is allowed and a may be 1/2 or 3/2, the lowest J
value for the 2171/; state is J = 1/2 and for the 273/3 state is J: 3/2.
This then means that the PI and P2 branches start with P1(3/2) and
P2(5/2), respectively, and the R1 and R2 branches start with R1(1/2) and
Rz(3/2) respectively. The subscript 1 denotes the 2171,; state and sub-
script 2 denotes the 2TT3/z state. Because the separation of the substates
is small the Q branches almost coincide, the P and R branches spreading
and overlapping as indicated above. No transitions between substates
are Observed so the stronger P and R lines are a result Of the 211]]; -
ZTl'l/z transition and the weaker lines of these branches from the 2173/; -
2173/2 transition.

As can be noted in Figure 3-A, the high J region of the R branch
of the 2-0 band is somewhat overlapped by the 101 band of the linear
polyatomic molecule C02. The presence of this band did not hinder the
identification of the various components of the N150 spectrum, but it did
render some Of the lines useless in the determination of the molecular
constants. The lines not used and the reasons for their disregard are
given in Table I. The P1 and P2 branch lines were identified to J = 53/2,
and the R1 and R2 branch lines to J = 55/2. Only two of the Q1 branch
lines were observed and identified: J = 1/2 and J = 5/2. The Q; branch
is particularly well resolved, the lines J = 3/2 to J = 27/2 being identified

and measured. The R; branch lines are well resolved for J = 3/2 and 5/2,

14

.1... 4

032 .mO Qz<m 01m Q24 Qz<m cum .m HmDUHh

 

 

15

 

 

 

 

 

. 1....) e an a...
g
L- 44 _ 4 - .. .
: 34444444443...

 

0::

l6

 

 

 

Table I. Lines deleted from the Overtone Bands
Line Reason* Line Reason Line Reason
2-0 Band
P1(15/2) l R1(11/2) 3 PZ(51/Z) 2
P1(43/Z) l R1(55/2) 2 Pz(53/2) 2
Pl(47/2) 1 P219/Z) 1 Rz(7/2) 3
131(51/2) 2 P2(11/Z) 1 R2(9/2) 3
131(53/2) 2 132(13/2) 1 R2(11/2) 3
R1(7/2) 3 132(35/2) 1 R2(37/2) 1
Ri(9/2) 3 P2(45/2) 1 Rz(55/Z) 2
3-0 Band
P1(11/2) l R1(15/2) 3 R1(45/2) 2
P1(17/2) 1 R1(17/Z) 3 R1(47/2) 2
P1(41/2) 2 R1(19/Z) 3 R1(49/Z) 2
P1(43/2) 2 R1(35/Z) 1 132(27/2) 1
P1(45/Z) 2 R,(41/2) l Pz(37/2)-P2(47/2) 2
131(47/2) 2 R1(43/Z) 2 Rz(15/Z)-Rz(49/2) 3
*Reasons:

1. Overlapped or distorted by an impurity.
2. Identified, but not well enough resolved for measurement.
3. Overlapped by component of the other substate.

17

but as J increases the components of the two R branches draw closer
together so that at J = 7/2 the two are not resolved. The second com-
ponent appears again at J : 13/2 but is then on the other side of the

R1 branch lines.

The 3—0 band appearing in Figure 3 was overlapped by HZO lines
and the effect was comparable to the effect of the C02 lines on the 2-0
band. Here the P1 and P2 branch lines were identified through J = 47/2,
and the R branches through J : 49/2. Again the resolution Of the Q7,
branCh was better than the resolution of the Q1 branch. , In the Q1 branch
only the J = 1/2 to J = 5/2 lines were identified whereas in the Q2
branch, lines for J = 3/2 to J = 13/2 were measured. The R1 and R2
branches in this band are fairly well resolved to J = 13/2. From this
point to the end of the R branch the two components are overlapped and
no indication of the R2 lines appearing on the other side of the R1 lines
is in evidence.

In order to determine the frequencies Of these observed spectral
lines a set of calibration fringes obtained by means of a Fabry-Perot
etalon was employed. The construction of this system is described in
detail by Van Home [17]. The etalon follows the exit slit of the mono-
chromator and is illuminated with higher order visible radiation.

Fringe maxima occur at those wave lengths for which:
2d : noxo (37)

In wave numbers this relation becomes

no : 2d V0 (38)

where no may be an arbitrary number assigned to the first fringe,
the fringe corresponding to a definite wave number v0. If the fringes

are numbered consecutively we may represent any later fringe by:

n0+n=2dv0+n=2dvn (39)

18

By subtracting Equations (38) and (39) a linear relation is obtained

between the wave number of a fringe and the number of the fringe.
v 2: v0 + B— (40)

Although Figure 3 shows only the ove rtone bands, the charts actually
measured were a simultaneous record of the overtone band and the
fringe system. A series of Neon and Argon lines whose frequencies
are well established were inserted at the proper angle of the grating
rotation as a means of calibration.

A least squares fit was made based on Equation (40) using the
fringe number, n, assigned to each standard and the corresponding
known frequency of the Neon or Argon line. The lines used for this
calibration appear in Table II. The slope of the straight line obtained
is L- where d is the etalon spacing. A 3 mm spacer was used and

2d
therefore the spacing between adjacent fringes was approximately 1. 6

cm‘l. The slopes actually obtained for the 2-0 and 3-0 bands were
0. 3215 cm-1 and 0.4019 cm"1 respectively. These correspond to fifth
order fringes for the first overtone band and 4th order fringes for the
2nd overtone band. The intercepts obtained were v0 = 3523. 848 cm"1
and v0 = 5308. 361 cm‘1 respectively.

By use of Equation (40) and the values for v0 and igiven above,
the frequency of each observed spectral line was determined. The
measured fringe number which corresponds to an absorption line was

substituted for n and vn was then evaluated. The Observed frequencies

thus determined are listed in Tables III and IV.

Determination of By, Dy, HV and v0 for the 2-0 Band. The wave

 

numbers thus determined for the 2-0 band were fit to a set Of least
mean squares equations based on Equation (18). This equation is essen-

tially of the same form as the first equation in the following block:

19

Table II. Argon and Neon Standards

 

 

 

Vacuum Vac Wave.No.
Gas Wavelength (R) Wavel No. Order .Order (cm'l)
(cm' )
2-0 Band
Neon 7032.413 14215.951 4 3553.988
Neon 6929.467 14427.145 4 3606.786
Argon 13718.576 7287. 394 2 3643.696
Argon 13622.658 7338.705 2 3669. 352
Argon 13504.190 7403.085 2 3701.542
Argon 13367.111 7479.003 2 3739.502
3-0 Band
Neon 6266.495 15953.472 3 5317.824
Neon 6143.062 16274.024 3 5424.675
Argon 9122.966 10958.340 2 5479.170
Neon 6029.997 16579.166 3 5526. 388

 

20

 

 

 

 

 

 

 

Table III. Calculated and Observed Frequencies for the 2-0 Band
J Wt . Calc. v(cm'1) Obs. v(cm’1) Calc. -Obs. (cm'l)
ZTTIIZ State, P Branch
1.5 1 3654.111 3654.112 -.001
2.5 2/3 3650.786 3650.784 +.002
3. 5 2/3 3647. 399 3647. 399 .000
4.5 1 3643.942 3643.943 -.001
5.5 1 3640.423 3640.425 -.002
6.5 1 3636.838 3636.839 -.001
8.5 1 3629.474 3629.475 —.001
9.5 1 3625.695 3625.695 .000
10.5 1 3621.850 3621.850 .000
11.5 1 3617.941 3617.944 -.003
12.5 1 3613.966 3613.954 +.012
13.5 1 3609.926 3609.929 -.003
14.5 1 3605.821 3605.827 -.006
15.5 1 3601.652 3601.650 +.002
16.5 1 3597.417 3597.410 +.007
17.5 1 3593.117 3593.123 -.006
18.5 1 3588.753 3588.752 +.001
19.5 1 3584.324 3584.328 -.004
20.5 1 3579.831 3579.831 .000
22.5 1 3570.652 3570.649 +.003
24.5 1 3561.219 3561.220 -.001
217112 State, R Branch
0.5 2/3 3663.696 3663.699 -.003
1.5 1 3666.760 3666.755 +.005
2.5 1 3669.760 3669.754 +.006
6.5 1 3681.110 3681.120 -.010
7.5 1 3683.784 3683.789 -.005
8.5 1 3686.392 3686.392 .000
9.5 1 3688.936 3688.932 +.004
10.5 1/3 3691.413 3691.400 +.013
11.5 1 3693.824 3693.825 -.001
12.5 1 3696.170 3696.164 +.006
13.5 1 3698.450 3698.451 -.001
14.5 1 3700.662 3700.664 -.002

 

Continued

21

Table III - Continued

 

J Wt, Calc.v(cm-1) Obs. v(cm'1) Calc. -Obs. (cm’l)

 

ZTTIIZ State, R Branch

 

 

15.5 1 3702.809 3702.814 -.005
16.5 2/3 3704.889 3704.888 +.001
17.5 1 3706.901 3706.893 +.008
18.5 1 3708.847 3708.853 -.006
19.5 1 3710.725 3710.723 +.002
20.5 1 3712.536 3712.538 —.002
21.5 1 3714.278 3714.280 -.002
22.5 1 3715.953 3715.960 -.007
23.5 1 3717.559 3717.552 +.007
24.5 2/3 3719.097 3719.088 +.009
25.5 1 3720.566 3720.569 -.003
26.5 1 3721.966 3721.967 —.001
277312 State, P Branch

2.5 1 3650.137 3650.139 -.002
3.5 1 3646.650 3646.657 -.007
7.5 1 3632.030 3632.031 -.001
8.5 2/3 3628.208 3628.214 -.006
9.5 1 3624.320 3624.318 +.002
10.5 1 3620.365 3620.366 —.001
11.5 1 3616.345 3616.327 +.018
12.5 1 3612.259 3612.264 -.005
13.5 2/3 3608.107 3608.095 +.012
14.5 1 3603.891 3603.897 -.006
15.5 2/3 3599.609 3599.611 —.002
16.5 1 3595.262 3595.273 -.011
18.5 1 3586.376 3586.375 +.001
19,5 1 3581.837 3581.835 + 002
20.5 1 3577.233 3577.231 +.002
21.5 1 3572.567 3572.566 +.001
23.5 1 3563.044 3563.044 .000
24.5 2/3 3558.188 3558.188 .000

 

22

Table III - Continued

 

 

J Wt. Calc. v(cm'1) Obs . v(cm‘1) Calc. -Obs. (cm-l)
273/; State, R Branch
1. 5 1 3666. 550 3666.548 +.002
2.5 /3 3669.628 3669.628 .000
6.5 1 3681.246 3681.230 +.016
7.5 1 3683.977 3683.978 —.001
8.5 1 3686.637 3686.655 -.018
9.5 1 3689.228 3689.226 +.002
10.5 1 3691.749 3691.744 +.005
11.5 /3 3694.199 3694.196 +.003
12.5 1 3696.579 3696.578 +.001
13.5 1 3698.888 3698.888 .000
14.5 1 3701.126 3701.119 +.007
15.5 /3 3703.293 3703.319 -.026
16.5 1 3705.390 3705.390 .000
17.5 1 3707.415 3707.412 +.003
19.5 1 3711.252 3711.246 +.006
20.5 1 3713.064 3713.065 -.001
21.5 1 3714.804 3714.809 -.005
22.5 1 3716.472 3716.468 +.004
23.5 1 3718.070 3718.065 +.005
24.5 1 3719.596 3719.595 +.001
25.5 1 3721.050 3721.059 -.009
26.5 1 3722.433 3722.429 +.004

 

23

Table IV. Calculated and Observed Frequencies for the 3-0 Band

 

 

 

 

 

J Wt. Ca1c.v(cm"1) Obs. v(cm'1) Calc. -Obs. (cm-l)
2171/2 State, P Branch
1.5 2/3 5443.000 5443.000 .000
2.5 1 5439.627 5439.638 -.011
3.5 1 5436.156 5436.157 —.001
4.5 1 5432.588 5432.594 -.006
6.5 1 5425.160 5425.163 -.003
7.5 1 5421.300 5421.306 -.006
9.5 1 5413.285 5413.281 +.004
10.5 2/3 5409.131 5409.117 +.014
11.5 1 5404.879 5404.869 +.010
12.5 1 5400.528 5400.519 +.009
13.5 1 5396.079 5396.081 -.002
14.5 1 5391.530 5391.539 —.009
15.5 1 5386.883 5386.878 +.005
16.5 1 5382.136 5382.138 -.002
17.5 1 5377.290 5377.303 -.013
18.5 2/3 5372.343 5372.362 -.019
19.5 2/3 5367.296 5367.320 -.024
2171/2 State, R Branch

0.5 1 5452.536 5452.536 +.001
1.5 1 5455.520 5455.524 -.004
2.5 1 5458.406 5458.409 -.003
3.5 1 5461.196 5461.191 +.005
4.5 1 5463.887 5463.891 —.004
5.5 1 5466.481 5466.467 +.014
6.5 2/3 5468.977 5468.975 + 002
10.5 1 5477.980 5477.976 +.004
11.5 1 5479.984 5479.974 +.010
12.5 1 5481.890 5481.893 -.003
13.5 1 5483.695 5483.701 -.006
14.5 1 5485.402 5485.394 +.008
15.5 1 5487.008 5487.015 —.007
16.5 1 5488.514 5488.509 +.005
18.5 1 5491.224 5491.215 +.009
19.5 2/3 5492.427~ 5492.408 +.019

 

Continued

24

Table IV - Continued

 

J Wt. Calc.v(cm'1) Obs. v(cm'1) Calc. -ObS- (cm'l)

 

2773/2 State, P Branch

 

 

2.5 1/3 5438.756 5438.756 .000
3.5 1/3 5435.182 5435.185 -.003
4.5 1 5431.508 5431.510 -.002
5.5 1 5427.731 5427.733 -.002
6.5 1 5423.853 5423.853 .000
7.5 l 5419 874 5419.874 .000
8.5 1 5415.794 5415.782 +.012
9.5 1 5411.613 5411.611 +.002
10.5 1 5407.332 5407.327 +.005
11.5 1 5402.952 5402.957 -.005
12.5 1 5398.471 5398.478 -.007
14.5 1 5389.214 5389.208 + 006
15.5 1 5384.437 5384.436 +.001
16.5 2/3 5379.562 5379.571 -.009
17.5 1/3 5374.590 5374.583 +.007
277312 State, R Branch
1.5 1/3 5455.083 5455.075 +.008
2.5 2/3 5458.040 5458.033 + 007
3.5 2/3 5460.893 5460.895 -.002
4.5 2/3 5463.643 5463.656 -.013
5.5 2/3 5466.289 5466.286 +.003
6.5 1/3 5468.831 5468.845 -.014

 

25

an + bei + czxiz + dei3 + eri4 + fo15 + gZXi6 = 2Y1

ain + bzxi‘2 + chi3 + dei4 + eEx-l5 + foi6 + gin7 2‘ Exiyi

azxi6 + bei7 + chie + deig + erilo + foi“ + gin12 = xiéyi (41)

This set was evaluated on the Michigan State University digital computer
MISTIC. The program used was one entitled "Dalcevac" and was written
by Mr. John Boyd. Actually in the use Of this program the basic

Equation (18) was rewritten as

v :. v0 + B],(m + m2) + B3(m - m2) + D'V(-mz - 2m3 - m4)
+ D"’,'(m2 - 2m3 + m4) + H1/(m3 + 3m4 + 3m5 + me)
+ H3(m3 - 3m4 + 3m5 - m6) . (42)

in order to Obtain the desired constants directly. For the 2-0 band,
2771/2 state, forty-five lines were used; and for the 2773/; state, forty
lines were used. If the relation had been left in the form Of Equation
(18), the constants would have been composite constants, i. e. , a = v0;
b =(B' + B"); c = (B' — B" - D' + D"); etc. The values of the molecular
constants found by this means for the 2-0 band are listed in Table V.
This table also contains the standard deviation for each constant as was
determined in the "Dalcevac" program. The subscripts 01 and 21 refer
to the zero and second vibrational levels Of the first substate and the
02 and 22 refer to the same vibrational levels of the second substate.
The constants evaluated by the method above were used in Equation
(18) to Calculate the frequency in wave numbers of each Observed line.

These calculated values are given in Table 111 where they are compared

26

Table V. Effective Rotational Constants for NISO’P

 

B0121.61365 4 0.00003
B21:1.58119 i 0.00001
B31: 1.56500 3+- 0.00001
D01: (2.4 :1: 0.8) x 10-7
D21: (6.5 4 0.2) x 10-7
D31 2 (1.1 :1: 0.1) x 10-6
H01: (—1.56 4 0.01) x 10-9

H21:(-1.4 4 0.3) x 10-9

241,2sz = 3658.976 4 0.001
v3-0 = 5447.877 4 0.002
243,412., = 3658.55. 4 0.001

v3-0 = 5447.240 :1: 0.001

1.65856 4 0.00004
1.62444 4 0.00001
1.60718 4 0.00002

(8.8
(8.7
(8.3

(3.9
(4.2

:t 0.4)x10"6
4 0.1)x10'6
4 0. 3) x 10-6

:1: 0.6) x 10'10
4 0.1)x10'lo

 

=:<
. . .1
All constants are given in cm .

 

27

to the Observed values. Only two lines in the first substate and five
lines in the second substate show a variation greater than 0. 010 cm'l'
The lines used for the determination of the constants were weighted
on a basis of 1, 2/3, and 1/3. The magnitude of weighting was determined
by the amount Of the distortion or disturbance of a particular line. The
weight given each line is also tabulated in Table III.
The effective B values, B01, B02, B21, and B22, listed in Table V
were used in relation (20) to Obtain the actual rotational constants B0
and 52,. The actual values of D0, D2, H0, and Hz were evaluated by

averaging the effective D's and H's. These actual rotational constants

are collected in Table VI.

Determination of BV, Dv and vaor the 3-0 Band. Only thirty-

 

three lines of the first substate of the 3-0 band and twenty-one lines of
the second substate were usable so the following method was employed
in the evaluation of the parameters of this band. The 2-0 and 3-0 bands
of the same electronic state have their ground states in common, so
the ground state constants of the 2-0 band were accepted and used as
the ground state constants of the 3-0 band. This, then, left only four
constants to be Obtained from the data: va, Di], H{,, and v0, rather
than the seven required from the more numerous data of the 2—0 band.
When this computation was carried out, it became Obvious from the
standard deviations that the H1, evaluated was not significant so the
determination was repeated using the B3 and D{,' from the ground state
of the first overtone and requiring just three constants from the data,

namely, B1,, DEV, and v0. The program "Dalcevac"

was again used
and the equation being fit was a modification of Equation (18) with the H's

deleted. The actual form used in the analysis was

v' v0 + Bv'v(m + m2) + D{/.(--mz - 2m3 - m4) (431

where
v' : v - B"(m - m2) - D"(mz - 2m3 + m4)

28

The constants thus obtained and their standard deviations are listed

in Table V with those Obtained from the 2-0 band. The subscripts 01
and 31 refer to the zero and third vibrational levels of the first substate
and 02 and 32 refer to the same vibrational levels of the second sub-
state. These effective constants were substituted in the modified form
Of Equation (18) and the line frequencies in wave numbers were calcu—
lated. A comparison of the Observed and calculated frequencies of the
spectral lines of the 3-0 band is made in Table' IV. Here seven lines Of
the first substate differ from the observed values by slightly more than
0. 010 cm'l. The method Of using weights described above was also
employed, and the weights are given in Table IV. The actual B3 value
was Obtained by using B31 and B33 in Equation (20). D3 was evaluated by
a numerical averaging of D31 and D33. These actual rotational constants

are listed in Table V1 with those obtained from the 2-0 band.

Determination of Be, 06,, If, and re. The values for B0, B2, and

 

B3 as listed in Table VI were plotted versus (v +. 1/2) following the

relation given in Equation (21) to obtain the intercept, B and the slope

e'
68. See Figure 4. The values Obtained were Be = 1.64447 cm'1 and
Ce 2 0. 0167 cm'l. The values were checked by a least squares calcu-
lation.

By use of Equation (22) and the value of Be given above, the
equilibrium moment of inertia, Ie was calculated and found to be 17. 016
x 10-40 gm-cmz. This constant was then used with the reduced mass,

(1, equal to 7. 743235 amu [18] to compute r the equilibrium separation

e)

of the atoms. The value obtained for r was 1.1506 x 10"8 cm.

e
It can be noted from Table VI that the value for D3 seems some-

what in error in relation to D0 and D2. These latter constants were

obtained along with values for H0 and H2 whereas D3 was obtained without

this higher order correction constant. Because of this it was felt that

29

 

 

 

Bvcm‘
EV: Be - 68 (v + 1/2)
Be: 1.64447 cm-1

1'64" (18 = .0167 cm"1

1.63-

1.62—

1.61~

1.60—

1.59-

1.58 I l I J l I I

0 1/2 1-1/2 2-1/2 3—1/2 (v+1/2)

FIGURE 4. GRAPHICAL DETERMINATION OF Be AND (16

30

Do and D; were more reliable constants and consequently the value Of
De quoted in Table VI is a result of a computation using these two
alone.

Calculation of the Q Branch. It was stated in the theory that Q

 

branch lines can be calculated by use of Equation (19) and the constants
B and v0, already determined. This was done for each band and the
results of these calculations are given in Table VII. For the 2-0 band
the lines Q1(5/2) and Q3(15/2) were not measured or calculated although
they could be identified. Q1(5/2) is not well resolved and Qz(15/2) is
overlapped by an impurity making it much too intense. In the case of the
3-0 band, the lines 01(3/2), 02(11/2), and 02(13/2) although identifiable
were not well enough resolved for measurement. The differences be-
tween the Observed and calculated values are stated in Table VII where it
can be seen that the accuracy here is comparable to that of the P and R

branches.

Determination of the Vibrational Constants, we and weXe- The

 

band origins as given in Table V were used in Equations (24) and (25)
to evaluate the anharmonic vibrational constants, we and wexe. After
appropriate substitutions for G(3), G(Z), and G(O), the relations used

for each substate were:
v3_o = 3.88 - 121.1631e (44)
V2-0 : 2608 - 6wexe (45)

The constants evaluated by the simultaneous solution of these two

equations are given in Table VI.

31

>:<

Table VI. Rotational and Vibrational Constants for N150.

 

B0 21.63612 4 0.00004
Ba 21.60284 4 0.00001
B3 =1.5861z 4 0.00002
D0 = (4.5 4 0.4)x10'6
D2 = (4.7 4 0.1)x10-6
D3 = (4.7 4 0.3)x10'6
I—I0 = (-5.8 4 0.6)x10”10
H2 2 (-4.9 4 0.1)3410-10

Be = 1.64447 4 0.00004
(1e =-0.0166-,:1: 0.00004
D8 = (4.4 4 0.4)x10'6

Ie : 17-016 x10’4o gm-cm2

r =(1.1506 :1: .0005)x10"8 cm
2171/2sz = 1870,0754 0.002
006x

6 3:13.529 :1: 0.002

2"m: we = 1869.87. 4 0.001

wexe 213.532 :1; 0.001

 

>1<
All constants are in cm"1 except in cases where the appropriate units

are specified.

32

Table VII. Calculated and Observed Q Branch Lines.

 

 

 

Line Calc .(cm-l) Obs . (cm'l) Calc. -Obs. (cm'l)
2-0 Band
Q1(1/2) 3658.952 3658.943 +.009
02(3/2) 3658.429 3658.439 —.010
02(5/2) 3658.259 3658.257 +.002
Qz(7/Z) 3658.020 3658.026 -.006
02(9/2) 3657.713 3657.719 -.006
02(11/2) 3657.337 3657.329 +.008
02(13/2) 3656.894 3656.883 +.011
02(17/2) 3655.802 3655.793 +.009
02(19/2) 3655.154 3655.155 -.001
02(21/2) 3654.437 3654.428 +.009
(12(23/2) 3653.653 3653.653 .000
02(25/2) 3652.800 3652.808 -.008
02(27/2) 3651.878 3651.880 -.002
3—0 Band
01(1/2) 5447.841 5447.842 -.001
01(5/2) 5447.451 5447.446 +.005
02(3/2) 5447.047 5447.053 -.006
02(5/2) 5446. 790 5446.792 -. 002
02(7/2) 5446.431 5446.425 +. 006
02(9/2) 5445.969 5445.971 —.002

 

33

COMPARISON OF N150 WITH OTHER WORK

To check on the accuracy of the rotational and vibrational con-
stants determined for N150 several comparisons were made, the first
of which was the isotope Calculation.

Hause and Olman [12] have re-evaluated the molecular constants
of the 2-0 band of N140 and these were used as a basis for comparison
with the N150 constants determined here. The N140 constants from this
computation that were used are Be 2: 1.70477 cm'l, “e = .0173 cm'l,
and the band origins for each substate; namely, v0 = 3724. 100 cm'1 for
2171/; state and v0 = 3723. 676 cm'1 for the 2173/; state. In order to
calculate we and wexe for N140, another set of band origins was needed
so those Obtained by Van Horne [17] for the 3-0 band were employed.
Equations (44) and (45) were then used as described above to evaluate
we and wexe for N140. The reduced mass 11, for N140 was taken to be
7.4688067 amu and for N150, pi was taken as 7. 7432348 amu. According
to Equation (26) then, p equals 0. 9821196 and this was the value used in
Equations (29), (30), (34), and (35) to calculate the N150 constants on
the basis Of N140. The results are given in Table VIII.

As can be seen from this table the agreement is particularly good
for the vibrational constants we and wexe. The values of Be are only

in fair agreement differing by 0. 00012 cm‘l.

It is felt that the presently
evaluated N150 constants are correct to six significant digits whereas
this variation occurs in the fifth place. Perhaps this is due to the fact
that the B6 of N150 was determined on the basis of three B values while
the B8 of N140 was found using only two.

As a second check, a comparison was made with the constants

given by Fletcher and Begun [3], and Gallagher and Johnson [11].

These values are listed in Table VIII.

34

Table VIII. Comparison of N150 Constants

 

 

 

 

N140 [12] N150 N150
(Isotope Calc.) (Present Evaluation)
Isotope Comparison

Be 1. 70477 1. 64435 1. 64447
0.8 0.0173 0.0164 0.0167
68(1) 1904.09 1870.04 1870.075
wexe(l) 14.01 13.53 13.529
we(2) 1903.92 1869.83 1896.87,,
wexe(2) 14.03 13.53 13.532

Comparison with Other Studies

 

Present Gallagher and
Evaluation Johns on
Be 1. 64447 1. 64450
Ge 0.0167 0.0171
18 17-016 x 10"” gcm‘2 17.01., x10"40 gcm2
0
re 1.150618 1.1508A
we(1) 1870.075 __-
we(2) 1869.874 ___
wexe(1) 1.3.529 --...
B0 1.63612 1.6358;
130 4.5 x 1076 4.6 x 10-6
0
r0 1.1539 A.

Fletcher and
Begun

l. 6446
0.0170

 

* . . -1 . .
All constants are given in cm except in cases where the appropriate

units are specified.

35

The equilibrium B seems to be in better agreement with the micro-
wave value Obtained by Gallagher and Johnson than with the infrared
value Obtained by Fletcher and Begun. The differences are 0.00003 cm“1
and 0.0001 cm“1 respectively. The Ge values are fairly comparable,
but the value obtained here is slightly lower than either of the values
quoted for comparison. Fletcher and Begun state in their paper that the
experimental value they obtained for tie was 0. 0166 em“1 but because
it was based only on the fundamental they felt the value 0. 0170 cm'1
Obtained by the isotopic relation was more reliable. The experimental
value Of 9e in this paper is in closer agreement with their experimental
value than with the value they actually quoted.

It will also be noted that the values Of Ie and re given by Gallagher
and Johnson are in excellent agreement with those given here. As would
be expected, Ie for N150 is slightly larger than 1e for N140. The value
listed for N140 by Van Horne [17] is 16.422 x 10"“'0 gm. cmz. The

variation between the re value given here and that of N140 by Van Horne,

1.15096 x 10'8 cm, is within experimental error.

SUMMARY AND CONCLUSION

It is felt that the data Obtained from the records of the two over-
tone bands Of N150 was quite good. In previous work done on these
bands in this laboratory the resolution was not as high as it is now with
the revised optical system. The computer analysis to determine the
constants also gave a measure of their accuracy and it is not probable
that a more refined set of constants can be Obtained without a higher
resolution instrument.

It would be of considerable interest to observe the fundamental
of N150 under the resolution available here in the infrared and re-

evaluate the rotation-vibration constants of the band.

36

10.

11.

12.

l3.

14.

15.

16.

BIBLIOGRAPHY

. P. G. Favero, A. M. Mirri, and W. Gordy. Phys. Rev. 114,

1534 (1959).

. N. L. Nichols. The near infrared spectrum Of nitric oxide. Ph. D.

Thesis, Michigan State University (1953).

. W. H. Fletcher and G. M. Begun. Jour. Chem. Phys. 21, 579 (1957).

A. H. Neilsen and W. Gordy. Phys. Rev. 26, 781 (1939).

. R. H. Gillette and E. H. Eyster. Phys. Rev. _5_6_, 1113 (1939).

. N. L. Nichols, C. D. Hause, and R. H. Noble. Jour. Chem. Phys.

2_3_, 57 (1955).

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

J. J. Gallagher, F. D. Bedard, and C. M. Johnson. Phys. Rev.
23, 729 (1954).

. J. H. Shaw. Jour. Chem. Phys. _2_4_, 399 (1956).

J. J. Gallagher, W. C. King, and C. M. Johnson. Phys. Rev. 28,
1551(A) (1955).

J. J. Gallagher and C. M. Johnson. Phys. Rev. 103, 1727 (1956).
C. D. Hause and M. D. Olman. Unpublished work.

G. Herzberg. Spectra of Diatomic Molecules, ed. 2, (D. VanNostrand
CO., Inc., New York, 1950), p. 232.

 

E. Hill and J. H. Van Vleck. Phys. Rev. _3_2, 250(1928).
D. H. Rank. Jour. Chem. Phy. 203, 1975 (1952).

T. H. Edwards. J.O.S.A. _5_1_, 98 (1961).

37

l7.

18.

38

B. H. VanHorne. The near infrared spectra Of deuterium chloride
and nitric oxide. Ph. D. Thesis. Michigan State University (1957).

W. H. Johnson, Jr., K. S. Quisenberry, and A. O. Nier.
"Measurements of Nuclear Masses. " Part 9. Handbook of Physics
Ch. 2, p. 55. Edited by E. U. Condon and H. Odishaw. 1958.
McGraw-Hill Book Co. , Inc., New York.

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