NATIONAL BUREAU OF STANDARDS REPORT

10 360

A CURVE OF GROWTH DETERMINATION OF THE F-VALUES FOR THE FOURTH

POSITIVE SYSTEM OF CO AND THE LYMAN-BIRGE-HOPFIELD SYSTEM OF N

2

T echnical Report

to National Aeronautics and Space Administration

Washington, D. C.

NASA Order No. R — 64

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NATIONAL BUREAU OF STANDARDS REPORT

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3160422

NBS REPORT

10 360

A CURVE OF GROWTH DETERMINATION OF THE F-VALUES FOR THE FOURTH

POSITIVE SYSTEM OF CO AND THE IYMAN-BIRGE-HOPFIELD SYSTEM OF N2

by M. J. Pilling, A. M. Bass, and W. Braun

T echnical Report

to National Aeronautics and Space Administration

Washington, D. C.

NASA Order No. R-64

IMPORTANT NOTICE NATIONAL BUREAU OF STA

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U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

A Curve of Growth Determination of the f-values for the Fourth

Positive System of CO and the Lyman-Bir ge-Hopf ield

System of N 2

M. J. Pilling,0 A. M. Bass,* and W. Braun

National Bureau of Standards

Washington, D. C. 2023^-+

Abstract

The curve of growth method has been employed to determine

f-values for the fourth positive system of CO and the magnetic

dipole and electric quadrupole components of the Lyman-BirgeHopfield system of K 2 . The transition moments are, respectively,

1 1 2 0.83 a e, 5.9 x 10 Bohr magnetons and 2.6 a^e. No

o o significant dependence on r-centroid was found. The mean

value of the ratio of the electric quadrupole to magnetic dipole

f-values was 0.076.

*Work Supported in part by NASA

Visiting Scientist, Physical Chemistry Division, 1968-1969; permanent

address: Physical Chemistry Department, Cambridge University,

Cambridge, England.

Introduction

Current interest in elementary processes involving

electronically excited diatomic molecules demands an accurate

knowledge of radiative lifetimes and oscillator strengths.

Several methods are available for their determination.

These include direct measurement of the lifetime by the phase

shift technique'*' , and measurement of the integrated absorption

2 3 coefficient by optical absorption spectroscopy. s The latter

method is severely limited by resolution requirements. In

some instances this has been overcome by the use of very high

U pressures to broaden the rotational fine structure. Alternatively,

if spectrographs of sufficiently high resolving power are

2 3 available, the curve of growth method may be employed. *

Recently, Lassettre and coworkers^ have exploited the technique

of electron impact spectroscopy. Here there is no need to

resolve the individual rotational lines, but the general

applicability of the method has not been thoroughly tested.

This can only be achieved comparing f-numbers derived from

electron impact work with those obtained by other methods.

In the present work, the f-numbers for three electronic

transitions, the fourth positive system of CO, and the magnetic

dipole and electric quadrupole components of the Lyman-BirgeHopfield system of N2» are determined by the curve of growth

method. The equations used for the averaging of f-numbers

,

A-values and lifetimes are clearly defined so that the numbers

derived here can be properly compared with independent

determinations by other methods where slightly different

averaging procedures were employed.

Theory

If a parallel beam of light, intensity I , is incident on

a cell, Z cm long, containing a monatomic gas of density N atoms

per cc, then the light transmitted at frequency v (cm 1

)

2 .

3

is given by

I = I exp ( -o ( v ) ) N

v o where o(v) is the absorption cross section (cmO. The equivalent

width, W( cm *), for an isolated spectral line is defined as

W = f [ 1 -exp ( “O ( v ) N£ )] dv . The relationship between W and the

oscillator strength f is complex, and is dependent on the ratio

of the collision broadened plus natural line width to the Doppler

line width (a). Curves of growth are plots of log (W/ 26 ) against log 1Q (10.6 o c Nl),^ where 6 is the half width at

maximum over e for a Doppler line, and o q

is the peak cross-section

V o , 2RT x 1 / 2

0 = — ( ir) and

^ / o ( v ) d

v

6/

n

= /ne z f = (5 x 10“ 13 f/6) cm 2 me 6

for 6 in cm 1 „ For W /26 ^ 0 . 5 , the plots become linear, and the

dependence on (a) becomes less marked. Valid extrapolation can

then be made to zero optical path length, and the f-value

determined. If the resolving power of the spectrograph is

sufficiently large that the observed spectral line width is not

much larger than the real width, then accurate measurements can

be made in the linear region.

These considerations still apply for all isolated rotational

lines in the electronic spectrum of a diatomic molecule.

However, the relationships between the f-number for a given

line and the overall electronic transition moment, and

between the number of molecules in a given lower rotational

level and the overall gas density, must be considered.

For electric dipole and magnetic dipole transitions, the

oscillator strength for absorption of a rotational line

*T 8

(J*, J") of a vibronic band (n, v'; m, v") is given by *

8 it 2 me v v

? J

1 ^"J 1 * nv'J' ,mv"

J

(

R

nv’J" ,mv" J*

3he 2 (2J"+1) (2-6 » (2S"+l)T ( 1 )

where

^ is the Kronecker delts, and all other symbols have

their usual meanings.

Assuming no interaction between rotational, vibrational

and electronic motions.

R

nv ' J ’ ,mv" J

!

*

j 2 S J'J'iq v'v" ' R

nm / -

e <W (2)

where Sj t j„ is the rotational line strength, q v

, v

„ is the FranckCondon factor and R

nm , - v «' v»v is the electronic transition

9 moment, which may be dependent on the r-centroid r ,

The following summations apply:

Z S TIT „ = 2J' + 1, Z S „ = 2 J

" + 1

j" J J

J'

J J

Z Q • ¥1 ““ Q t ff 1

v

f v

? V

( 3 )

(U)

v

Thus , nv' ,mv" ^nv' J' ,mv" J" f

o 2 I o nm I 2 oir me v , „ R . q v ' v .

1 e1 3h e

2

t v ' v" (5)

(2—6 „ )('2S" + 1 ) o , A

•

For electric quadrupole transitions

,4 3 | n nv ' J

' ,mv"J" | 2 klT mCV „ .T» „»T» l R I f

nv ' J

’ ,mv"j"

v' J' , v"J

5he 2 (2J”+l)(2-6 0 A „)(2S"+l)

( 6 )

The Einstein transition probability for spontaneous emission

is given by

A

nv' J

' ,mv"j"

6Utt 4 v

3

, „ T „ v ' J ' , v J

3h

R

nv'

J

1 ,mv"J"

|

2

(2J’+1) (2-6

o A

, ) ( 2 S ' + 1 ) (T )

for an electric or magnetic dipole transition; and by

6 . A Ml mv ".t "

R2tv°u | nv'J' ,mv"J", 2 3271 V v'J' ,v"j" |R

e

1

( 2 J ' + 1 ) ( 2-6 . . ) (2S'+1)

o , A '

( 8 ) n v ' J

' , mv J 5h

for an electric quadrupole transition.

Thus, for CO, the J independent lifetime of a given excited

vibronic state is given by

(9)

t“ 1

, = v

n v

1

v a 6Utt 4 r / | n nm | 2

3 \ £ A . tj — 0 , . L R I q , ,,v , „)

„ nv',mv 3hw r „

1 e1 v ' v v'v

n v

neglecting the small variation in frequency of the rotational lines

over a vibronic band. For the fourth positive system of CO,

the degeneracy
T

i »

> ,

« \
” 1 nv

w

n

= ‘ 2 -«o.A' ,l2S,+1 > = 2

For the Lyman-Birge-Hopf ield system of N^,

6Un 4 „ / i „nmi 2 ..3 \ . 3211 6 3hw ( I Rnra

| 2

< e D

V) ^ ) + v’v 58 "v ' V 5 hw

n v

E (|

R

nm

| 2 q , „V 5, „ ) ( 10

)

1 01 ^9 V v7 V

Q

where | R^ | Dand | R^ are the magnetic dipole and electric

quadrupole transition moments respectively, and w^ = 2.

1

“5" For a het eronuclear molecule with a E ground state, the

number density of molecules in the J” level is

V

R(2J ,, -4-l) exp[-hB n cJ" ( J" + l ) /kT ] f

( 11 )

where f = kT/hB M c. N is the total number of molecules

and N_„ is the number in a given rotational level, all other

symbols have their usual meanings.

For nitrogen.

N „ = E N (2T + l)(2J M

-frl) exp (°°hB” cJ tl (J tt -«-l)/kT)

J T f

2

In eq. ( 12 ) , f = E ( 2T+1 ) kT /2hB" c

.

T = 0

For even J” „ the total nuclear spin quantum number T can

take the values 2 and 0, while for odd J” it can take the value 1.

In evaluating f, the summation Is taken over all three values of T.

The rotational line strengths for the electric and magnetic

dipole transitions were derived by Honl and London,'*'

0 and

7

have been tabulated by Herzberg, For the electric quadrupole

9 12 transition they are given by Chiu. Nicholls' Morse Franck1

3

Condon factors were used for CO, and Benesch et al '

s
f

i. i
1

2

RKR Franck-Condon factors for N^. Nicholls (Morse) and

Zare et al 1 ^ (RKR) have also calculated Franck-Condon

factors for N^. The differences among the three arrays are

< insignificant {% 2 %) over the range of interest.

Experimental

Spectra were photographed on Kodak SWR plates, using a

6m Eagle spectrograph in the fourth order. The background

was provided by a krypton discharge lamp, powered by a 2^50 Mc/S

power supply, with spectrograph slits of 3 x 10 and 9 x 10 cm. Several background intensities were used, and each plate was

calibrated for density vs. intensity. The absorption cell

was 2 cm long, and was fitted with LiF windows. Pressures less

than 500 Nm” 2 were measured with a calibrated capacitance

micromanometer , while a precision dial gauge was used for

higher pressures. Ultra high purity gases were employed

without further purification.

Results

Log 1() (W/26) was plotted against log 1Q Nj„Sj , /

(

2J" + 1 ) , and

extrapolated to (W/26) = 0.1 to give ( N ,,S , T „ / ( 2J" + 1 ) ) .

«J <J J U • _L At this point, 10.6 = 1.28;

thus f

1 » 2 8mc 6 2 J

" + 1

nv ' ,mv" 10.6 e

^ £/tt NjhSj^,,

q 1

°

Figs, 1-3 show plots for CO ( A

1 II ( v= ^ ) «-X1 ( v=0 ) ) and for the

(0,0) and ( 5 9 0 ) magnetic dipole components and the (2,0) and

(3,0) electric quadrupole components of the Lyman-Bi r ge-Hop f i e 1

d

system of N . 2 Experiments were conducted at three pressures for both

gases, and extrapolations made over the linear range by a least

squares fit. Over this range, there is little dependence on

pressure broadening, and a single composite graph was used for

all three pressures.

Wherever possible the data were extended beyond the linear

region. Some difficulties were, however, encountered in this

respect. With an observed line width of ^0 , H cm the apparent

integrated absorption dropped below the theoretical value as

( A I / I ^ ) at the peak of the absorption line became progressively

greater than ^0 . U ( in the case of CO, the apparent integrated

absorptions dropped significantly below the Doppler curve).

On increasing the slit width by a factor of 3, and thereby reducing

(i/i ) max, the apparent integrated absorption increased to its

15 theoretical value. Oldenburg and Rieke report similar

observations. We believe the explanation for this phenomenon lies

in the finite grain size of the emulsion. At higher densities and

smallest slit settings the grains are of size comparable to the

line width. At low density the grains are smaller. Therefore

two slit widths were used throughout this investigation, the

narrow slit being used for low intensity lines, and the vide slit

for higher intensity lines. The two were found to link satisfactorily with one another.

The CO measurements were made at low pressures (<133 Km 2 ),

and the curves of growth were Doppler. For N , however, much highe

2 pressures were used, which enabled an estimate of ( 6 + 3 ) x 10 15 cm

2

to be made for the pressure broadening cross-section. This is

somewhat less than the value derived by Shemansky ^ ((1.6 +_ 0.5) x

10~ 14

cm

2 ). The gas kinetic cross-section is 1.1 x 10 15 cm

2

.

No f-values were obtained for the N

2 (U,0) band because of

chance overlap of the rotational lines in the region most

suitable for accurate measurements at the optical path lengths

used in this work.

Discussion

The absolute values for I

R

nm

i

I for the three transitions

e

i studied are shown in Tables 1-3. No significant variation of

the electronic transition moment was found. Tables 5, 6 also

show the values obtained for j R | by other methods. For the

fourth positive system of CO, the most extensive previous

1 1 8 19 investigations were by Hesser , Rich , and Meyer et al. y

IT Hesser measured the radiative lifetimes by the phase-shift

JL 8 technique. Rich looked at absorption in shock-heated carbon

monoxide, and in addition to the two (v"=0) bands, he measured

the f-values for several bands in the (v"=l-3) progressions.
* *

l
He found a mean value for |R^ m

| of 0,76 +_ 0.10 au. Meyer et al, 1 ^

studied the electron impact spectrum. This involves measuring

the generalized oscillator strength as a function of the momentum

change of the electrons, and extrapolating to zero momentum

change to give the optical oscillator strength. The data shown

in Table 5 were obtained several years ago, and show some

dependence on upper state vibrational quantum number. Since

then the apparatus has been refined, and the resolution increased,

and the latest relative values show extremely good agreement with

20

Fr anck-Condon factors. However, the dependence on momentum change

has not been investigated. The only other measurements which

21 22 have been made were by Hexter and Brith and Schnepp, who

calculated the f values from Davydov splittings in the solids.

They obtained respectively 0,lU8 for v

? =2 and 0,l6 for v'=0-3.

The Lyman-Bi r ge-Hopf i eld system of nitrogen has been

2 3 2b extensively investigated, Lichten and Olmsted et al.

measured the radiative lifetime of N

2 a

1 II g

by means of a molecular beam technique, using excitation by electron bombardment.

They found T = 1.7 x 10~ 4 sec and (1.2 +_ 0.5) x 10” 4 sec

respectively. These are equivalent to f values of 5 x 10” 6 and

e e

7 x 10 6

, Holland looked at the profile of emission following

excitation by a beam of electrons, and found that it was consistent

with a lifetime < 8 x

10°’ 5 sec (f > 10” 5 ). Jeunehomme /

^

e e investigating the emission from a pulsed discharge, found a strong pressure dependence in the lifetime of N

2 al ^g s and

deduced a radiative lifetime of (5-10) x

10”" 6 sec, corresponding
*

J
to f ^ 10

' 5

. ee —

27 Ching, Cook, and Becker measured the oscillator strengths

for the Lyman-Bi rge-Hopf ield system using pressures of up to

40 atm. to broaden the rotational fine structure, and thus

make the system amenable to low resolution absorption study.

The lR

nm L values deduced from their results are shown in Table 1 e

1 D

6. The data are corrected for the contribution arising from the

electric quadrupole component of the transition, using the

values of (f )a/(f ) D shown in Table 4 . The values are

e e ee

considerably larger than our own, and correspond to overall

radiative lifetimes of (2.7 - 4.1) x 10 5 sec. Ching et al. found

a residual weak dependence of the absorption coefficients on

pressure, and they extrapolated this to zero pressure to obtain

1 ^ the f-values. Recently, Shemansky has shown that this variation

in an artifact, but applying his correction leads to even

larger values for jR

nm

|^.

Shemansky"^ evaluated the f-numbers by fitting theoretical

and experimental curves of growth and band profiles, obtained with

a low resolution spectrograph. The values of |R nm

|_ he

e v obtained are shown in Table 6. They correspond to lifetimes

rising from 1.4 x 10” 4 sec for v - 0 to 1.6 x 10“ 4 sec for v = 6,

with a probable error of ^20 %. He also derived a selfbroadening cross section of 1.6 x

10°° 14

cm

2

, which is again

larger than our own.

The electric quadrupole component of the Lyraan-Bi rge~Hopf ield

2 8 29 system was first investigated by Wilkinson and Mullikent *

Using James and Coolidge ? s^ line strengths for a

1 ^

~

X £

g

transition, they obtained a value of 0.15 for (f ) _ / ( f ) e e Q

aeea D

Following Chiu’s'^'1

' tabulation of line strengths for a

1 IT g

-

, + 31

©2 transition, Vanderslice et al „ reinvestigated the high

§

resolution spectrum of nitrogen, and derived (f ) _ / ( f ) „ = 0.33.

ee Q ee D

Their method was approximate, since they did not use a curve of

growth technique. Thus they compared directly two sets of

absorption lines , which differed substantially in intensity.

Clearly, such a method tends to over-estimate the relative f-value

of the weaker component. Furthermore, they did not apply the

normalization procedure used here (see Appendix and equation ) nm

i

2

, 1 „nm 1 2

1 D

= 1.3 x 10 1 1 with Tables 3,^. This corresponds to |r

1 6 Shemansky compared the profiles of the magnetic dipole and

electric quadrupole components under Doppler conditions, and

found (f ) /(f ) values ranging from 0.08-0.10. These

0 0 0 0 JJ 2 . 2 correspond to j R^

m

j

j R^

m

j

= 5.6 x lOTM 12

, and are in good

agreement with our values. "Once again, his ratio has been

redefined so as to be consistent with the ratio used here.

32 33 Garstang analysed Lassettre and Krasnov's electron

energy loss results for the Lyraan-Birge-Iiopf ield system, and

derived a radiative lifetime for the quadrupole transition of

5 x 10 4 sec., which is about four times shorter than the

lifetimes shown in Table 3 However, this value is based on some
? <
of Lassettre's earlier work in which the vibrational structure

was completely unresolved.

The f-values determined here are, with the exception of those

for the electric quadrupole transition, based on measurements of

the P, Q, and R branches for relatively high J" values (j s, = 8-30).

(For the quadrupole transition, low rotational levels of the

S branch were used,) This raises the question of the relevance

of Franck-Condon factors calculated for rotationless potential

3U

curves in applications of this sort. Learner examined the

influence of vibration-rotation interaction on absorption

intensities for OH, He found some variation, which was most

marked for the weaker bands, where cancellation effects are

important. He also incorporated an r dependence for | R^

m

| , and in this case found a much larger variation of effective

35 Franck-Con don factor with J, More recently, Vi Hare j o et al „ found a large effect for the Lyman transition, for which there

is a large change in r , but little variation for the Fulcher

bands. Several transitions in nitrogen have been examined by

Benesch et al.' and Schumakeri Neither investigation revealed

any significant variation of q , „ with J. The Lyman-BirgeV V Hopfield system, however, was not studied. Any effect is likely

to be most noticeable for lighter molecules, in transitions

with a large change in r . It is, therefore, unlikely to be

of much importance in the transitions studied here.

In addition, the variations found by Learner and by

35 Villarejo et al * were erratic, and would lead to a large

amount of scatter in the curves of growth, particularly as

the pressure is changed. Any large effects can, therefore, be

discounted

,

3 8 Nadler and Kaskan' found a dependence of the collisional

broadening parameter, (a), on J for OH (

A

2 E + -X 2

II ) . This led them

to question the validity of curve of growth procedures for

determining f-values. If such a phenomenon did exist for

and CO, then it would not affect the f-values derived here, since

the linear portion of the curve of growth was used exclusively,

and there is little dependence of the equivalent width on (a)

in this region.

The only other factor which could invalidate the present

work is the possible occurrence of perturbations. Both systems

39 hO have been extensively analysed 9 and perturbations tabulated,

and these rotational lines were avoided. The most prominent

example was the Q(23) line of the ( U s 0 ) band of CO, This line

was in fact slightly weaker than the line to the perburbing

level I

1 ! (v=6, J-23).

Unless a very large data sample is taken, the curve of

growth method is not capable of quite the same accuracy as other

techniques, such as electron energy loss and phase shift

measurements. However, it is the most direct method, and is

dependent only on the assumption of the sepa'-a; ility of

rotational and vibrational motions. At present there

are large uncertainties and inconsistencies in published

f-values . It is, therefore, important that these quantities

are constantly reinvestigated by a variety of experimental

techniques, until consistency is achieved.

Appendix

Two definitions of the degeneracy factors to be used in

equations 1,5-10, and consequently of the absolute transition

moment, have appeared in the literature. While both are internally

consistent, in that experimental observables, f and A, are

related via the ratio of such factors, the out-of-context use of

a previously determined electronic transition moment can lead to

erroneous results if employed with a different definition of

degeneracy

.

7 The convention followed here is that adopted by Herzberg.

Consider transitions between an initial orbital £'\ , which is

one of a degenerate set, and a set of final orbitals £

9

.

.

The

probability of a transition from £

f \ to all £ ’ , is taken as the

total probability of transitions from all levels degenerate with

k to all i, divided by the degeneracy of k. Thus,

nv . mv

87r

2 mc v

v ' V

3he w

m

where |

1 R | e

1 = Z Z

i k

ik

and w = (2-6 . „ ) ( 2 S

" + 1)

m o 5, A

nv ' ,rav

„ is defined as in equation 9.

hi

In Mulliken’s notation, equation 5 is replaced by

8ir 2 mcv , „ v * v In C? “ nv 0 ,mv

and equation 9 by

She

G j R

nm

| n

! e

1 \ » v

"

Z A , „

r , 8 nv” ,mv v

6inT 4 GM Z ( ! R | q . „V 3

. „ ) = - • ‘ e

1 ^-v ' v v*v

3h

If the probability of a transition from to a single

i ik i 2 orbital $! is |R | , then the total probability of a fl

2

number of degenerate final orbitals with which the initial

transition 6" to all is G |r ! , where G is the total

k i n

1 e

1 * n

orbital can combine » |R^ k

1 | is taken

e

' as |

2 R

nm

| . e' Mulliken

discusses in detail the definitions of G

n and G . m In the present cases,s G = 2 , n

5 and w

m

= 1, and the Mulliken

notation therefore leads to values of | R

nm

1 e

2 which are half

those derived in this paper,, The Mulliken notation is used

1 ^ i 6 by both Hesser and Shemansky,

Further difficulties arise in the sum rule employed for

rotational line strengths. In the present work the electronic

transition moments have been directly related to the transition

probabilities, i.e D

Z Z nv* J' ,mv" J"

87T 2 mcv

3 he

R

nm

wm

The Franek-Condon factors and rotational line strengths

have been interpreted simply as branching ratios „ i.e. the sum

rules (3) and (k) have been applied.

Frequently, however, line strengths derived in the

literature have not been normalised in this way. For example,

Shemaasky1 ^ and Vandersliee et a! » 1 directly used Chiu’s 3" 1

line strengths for the quadrupole transition. On

g g

summation , these give V/3(2J M +1). In addition, summation of

their line strengths for the magnetic dipole transition gives

2(2J ra + l). Essentially, we have absorbed the factors k/3

and 2 into the electronic transition moment 9 and this accounts

for the discrepancy in ©ur definitions of |

j ^/ | R^a

| ^.

USC OMM-NBS-DC

References

1. G. M, Lawrence, JQSRT 5_, 359 (1965 ).

2. A. C. G. Mitchell and M. W. Zemansky , Resonance Radiation

and Excited Atoms, Cambridge University Press (193*0 .

3. S. S. Penner, Quantitative Molecular Spectroscopy and Gas

Emis s i vi t ies , Pergamon Press ( 1959 ).

4 . E. B. Wilson Jr. and A. J. Wells, J. Chem. Phys. 1

4

, 578 (1946).

5. E. N. Lassettre, Can. J. Chem. 4_7, 1733 (1969).

6. S. S. Penner and R. W. Kavanagh, J. Opt. Soc. Am. 4_3, 385

(1953)

.

7. G. Herzberg, Molecular Spectra and Molecular Structure. I.

Spectra of Diatomic Molecules, Van Nostrand (1950).

8. A. Schadee, JQSRT 7, 169 ( 1967 ).

9. P. A. Fraser, Can. J. Phys. 32, 515 (195*0.

10 . H. Honl and F. London, Z. Physik J33_, 803 ( 1925 ).

11 . Y. N. Chiu, J. Chem. Phys. 4_2 , 2671 ( 1965 )

12 . R. W. Nicholls, JQSRT 2 , *+33 ( 1962 ).

13. w. Benesch, J , T. Vanderslice, S. G. Tilford

Wilkinson, Astrophys. J. 1 4 3 , 236 ( 1966 ).

, and P. G.

l4 . R. N.

15

Zare , E. 0. Larsson and R. A. Berg, J.

, 117 (1965).

Mol . Spe ct ry

.

15. 0 . Oldenburg and F, F. Rieke, J. Chem. Phys. 6 , 439 ( 1938)

.

16 . D. E. Shemansky , J. Chem. Phys. 5JL, 5487 ( 1 9 6 9 ) .

17. J . E. Hesser, J. Chem. Phys. 48, 2518 ( 1968 ) 9

18 . J . c. Rich, Astrophys. J. 153, 327 (1968).

V. D. Meyer, A. Skerbele, and E. N. Lassettre, J. Chem.

Phys. 4_3 , 805 ( 1965 ).

19 .
*

i

I
References

20c

21 .

22 .

23.

2h 9

25.

2 6 .

27.

28 .

29.

30.

31.

32.

33.

3i».

35.

36.

37.

E. N. Lassettre, A® Skerbele, M. A. Dillon, and K. J.

Ross, J. Chem. Phys. 4J3, 50 66 (1968).

R. M. Hexter, J. Chem. Phys. 3^£, 13^7 (1962).

M. Brith and 0. Schnepp, Mol. Phys. £, U 73 ( 1 9 6 5 )

.

W. Lichten, J. Chem. Phys. 26 . 306 (1957).

J. Olmsted, A. S. Newton, and K, Street, J. Chem. Phys.

42, 2321 (1965).

R. F. Holland, J. Chem. Phys. 5A» 3940 ( 1969 ).

M. Jeunehomme , Air Force Weapons Lab. Rept., AFWL-TR-66-143

,

March 1967 ®

B. K. Ching, G. R. Cook, and R. A. Becker, JQSRT 7_, 323 ( 1967 ).

P. G. Wilkinson, Astrophys. J. 126 . 1 (1957).

P. G. Wilkinson and R. S. Mulliken, Astrophys. J. 126 , 10 (1957).

H. M. James and A. S. Coolidge, Astrophys. J. 85 » 438 (1938).

J. T. Vanderslice , P. G. Wilkinson and S. G. Tilford, J. Chem.

Phys. k2 t 2681 (1965).

R. H. Garstang, J. Chem. Phys. 4

_4 , 1308 ( 1 9 6 6 ) .

E. N. Lassettre and M. E. Krasnov, J. Chem. Phys. 40, 1248

( 196U)

.

R. C. M. Learner, Proc. Roy. Soc. A 269 » 311 (1962).

D, Villarejo, R. Stockbauer, and M. G. Inghram, J. Chem.

Phys. 50, 175*» (1969).

W. Benesch, J. T. Vanderslice, S. G. Tilford, and P. G.

Wilkinson, Astrophys. J. 144 , 408 ( 1966 ).

J. B. Schumaker, JQSRT 9 , 153 ( 1969 ).
V

'T
References

38. M. Nadler and W. E . Kaskan, JQSRT 1J), 2 5 ( 1 9 T 0 ) .

39. J. D. Simmons, A. M. Bass, and S. G. Tilford, Astrophys.

J. 155, 3^5 (1969).

HO. S. G. Tilford, P. G. Wilkinson, V. B. Franklin, R. H. Naber,

W. Benesch and J. T. Vanderslice, Astrophys. J. Suppl.

13, 31 (1966).

Hi. R. S. Mulliken , J. Chesa. Phys. 7, lH (1939).

Figure Captions

Figure 1

Figure 2

: Curve of growth for the (U,0) band of the CO fourth

Positive System,

0 [CO] = 27 Nm" 2 9 [CO] = 66 Nm" 2 ® [ CO ] = 133 Nm" 2

A Q ( J ' =2 3 ) ; [CO] = 27 Nm" 2 A I * z"(V=6, J = 23 ) - X

1 !*

(V=0, J = 2 3 ) ; [CO] = 27 Nm" 2 Least squares fit to points on linear portion

of graph,

Doppler curve for (W126) > 0.7

Curves of growth for the (0,0) and (U,0) bands of the

magnetic dipole component of the Lyman-Birge-Hopf ield

system of nitrogen.

0 [N ] = 2 x 10 4 Nm"* 2

; 0 [N ] = U. 85 x 10 2 Nm" 2

; 2 2 ® [N ] = 10 5 Nm" 2

2 Least squares fit to points on linear portion

of graph. — — Curve of growth for a = 0.55. This correspond

to a self broadening cross-section of U.5 x 10 15 cm 2

.

Curves of growth for the (2,0) and (3,0) bands of the

electric guadrupole component of the Lyman-Birge-Hopf i eld

system of N . Key as for figure 3.

Figure 3:
>4
Table

1.

f-values

for

the

CO

Fourth

Positive

System 3 -f LT\ VO ia 03 VO • o o o o O o

a) • • • • • • — o o o o o o — + 1 + i + 1 + 1 + 1 0 o t— IA VO ao Os c a> CO f— CO ao CO t—

pc • • • • • • — o o o O O o o

a> la aD c— VO On ON m • • • • • • a o O o o o o - + ! + 1 + 1 + 1 + 1 + 1 VO -4 CM CM rH r-l > • • • • • • +> t— ao c- t- On

C\o CM -4* -4 CM -4 o rH rH rH CM rH o o o O o O O o a «t> • • • • • • * o o o o O O > + 1 + 1 + 1 + 1 + 1 + 1 -4 CO VO oo LA OO

II 00 CM U”N vo t- -4

a> rH *H rH rH <H rH

<u « • © • • • o o o o O O

*—•®—

CM CM CM 1 8 1 1 i cn o o O O o o 1 « rH rH rH rH rH O » X X X X X rH > rH as CO t— -4 X

00 rH CO VO 00 On • • • • • • rH HI vo m rH CO

CM CM CH CO 1 1 1 1 O O o CO CO o

rH rHH 1 1 rH

XX

XO o X

r—

.—

X rH rH ^—- LA LA -sf X X oo

O <H rH

H .

- -—V rH

•» • • ao -4 e - O O O • • o > H + | + I o o 1 CM CM t— + 1 + 1 r- -4 LA o o CM CM • • • • • * CM rH H vo 00 rH > 00 -4 ITS vo 0- ao

Table 2 . f-values for the Magnetic Dipole Component of the

21 N Lyman-Bi rge-Hopf i eld System

v* O

1l— 9 i 10 6 f 10 5 f ,( sec) 10 14

1 R

nm

|

% V ' ,0 v

' ,0 e e V e ' D

0 3.9 + 0.3 U.31 X io

"

2 9.0 + 0.6 9.b + 0.6 6.0 + 0 . 6

1 12.8 + 1.6 1.155 X 10 " 1 11.1 + 1 . u 7.9 + 1.0 6.6 + 1.1

2 16.3 + 1.3 1.707 X 10 " 1 9.6 + 0 . 8 9.5 + 0 . 8 6 . 0 + 0.7

3 16.5 + 1.5 1.832 X 10 " 1 9.0 + 0 . 8 10 . u + 1.0 5.8 + 0.7

5 9.8 + 0.7 1.217 X 10" 1 8.1 0.6 12.5 + 0.9 5.^ + 0 . 6

6 7.9 + 1.1 8.30 X 10" 2 9.5 + 1.3 10.9 + 1.5 5.8 + 0.6

aThese measurements were made on the P , Q and R branches

.

The

combinations due to the electric quadrupole component was removed

using Chin's^ line strengths, and taking a mean value of 0.076 for

^ f

ee V^ee D’

*
*•

4
Table 3 f- value s for the Electric Quadrupole Component

a of the N Lyman-Birge-Hopf ield System

2

V’

1

2

3

5

6

6.6 +_ 0,5

ll.l + 0.5

13.0 + 3.6

10.3 + 0.8

6.0 + 0.5

10 7 f

e e

5.7 + 0.U

6.5 + 0,3

7.1 + 2.0

8.5 + 0.7

7.2 + 0.6

t .(msec)

v

’

1.9 + o.i

1.8 + 0.1

1.7 + 0.5

1.6 + 0.1

2.1 + 0.2

i T n m | / \

l R

e

l Q

(a * u)

2.5^ + 0.13

2.59 + 0.07

2.6 +_ 0.5

2.72 + 0.15

2.U2 + O.lU

a All these measurements were made on the S branches of the bands.
r
Table 6. Overall Radiative Lifetime for H a'llg, and the ratios

of the Electric Quadrupole and Magnetic Dipole f-values

y» 10 5 f , ( sec ) 1 °

2 (fV,o ) Q

* f

v' ,o*D

10 1

2

| F

nm

1 ?

{

cm 2

)

1 e ' Q

2D

7.6 + 1.0

9.0 + 0.8

9.8 + l.O

11.6 + 0.9

10.

6

+ 1.5

5.2 + 0.8

6.8 +_ 0.6

8.1 + 2.0

10.5 + 1.2

7.6 + 1.2

3.5 + 0.5

6 . 6 +_ 0.6

6.9 + 1.6

6.1 + 0.7

6.2 + 0.7 6

Table 5 . I

R

nm

I (atomic units) for the CO Fourth Positive System

e

V' a b c

0 0.61 - 0.93

1 0.65 0.78 0.95

2 0.65 0.83 0.98

3 0.61 - 1.03

1+ 0 . 6? - 1.09

5 0.67 “ 1.12

6 - - 1.19

7 - - 1.22

8 - “ 1.23

a 3* 5 n m Phase shift measurements. The |R | values quoted

in reference 15 have been redefined and multiplied by

/If (see appendix).

Shock tube absorption measurements 16

( J = 30 - 60 ) .

c IT Electron impact spectroscopy.

Table 6 |R nm

| x 10 11 (Bohr magnetons) for the Magnetic Dipole

Component of the N

^ Lyman-Bi r ge-Hopf ield System

V’ a

b

0

C\J -V • 10.6

1 5.5 9.7

2

CO

• 9.2

3

b . 5 9.3

b 5.1 10.4

5 4.6 10.3

6

CO

-V » 11.7

a Low resolution, lov pressure absorption spectroscopy

.

The D

2 values given in reference lb have been

multiplied by 4, and converted to | KTM I D ( see appendix).

v * 2 5 b Lov resolution, high pressure spectroscopy.

USCOMM-NBS-DC
>

V

(
§E/M /

(2 J"

-fI)

(cm' 3)
«r
o

x

ID

N-o

<JDo

X

LO

o

“3

S2/M

/(2J"-H)

(cm’ 3)
J
§Z//V\

(2J"+I J)

(2,0)

I

(2J"+I)J

(3,0)

tj l

*