Measured Radiative Lifetimes and Electronic Quenching Cross Sections ofBaO(A 1Σ)S. E. Johnson Citation: The Journal of Chemical Physics 56, 149 (1972); doi: 10.1063/1.1676841 View online: http://dx.doi.org/10.1063/1.1676841 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/56/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Polarized laser induced fluorescence of BaO (X 1Σ+) produced in a crossedbeam reaction of Ba+SO2 J. Chem. Phys. 97, 991 (1992); 10.1063/1.463201 Electronic properties of BaO on W(001) J. Vac. Sci. Technol. A 6, 1063 (1988); 10.1116/1.575636 Lifetimes and transition moments among excited electronic states of BaO J. Chem. Phys. 72, 6437 (1980); 10.1063/1.439143 A microwave optical double resonance Stark effect measurement of the dipole moment of A 1Σ+BaO J. Chem. Phys. 66, 2745 (1977); 10.1063/1.434223 CrossSection Measurements for the Quenching of the 2537Å Resonance Radiation of Mercury J. Chem. Phys. 41, 768 (1964); 10.1063/1.1725959

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THE JOURNAL OF CHE~ICAL PHYSICS VOLUME 56, NUMBER 1 1 JANUARY 1972

Measured Radiative Lifetimes and Electronic Quenching Cross Sections of BaO(A 12:)*

S. E. JOHNSONt

Department of Physics, University of California, Santa Barbara, California 93106

(Received 1 July 1971)

Lifetimes of the A 1 ~ state of BaO have been measured for the vibrational levels v' = 0 to 11 from the fluorescence decay excited by a short-pulsed (10 nsec) tunable dye laser. Radiative lifetimes were found to vary with vibrational level from 0.275±0.022 to 0.389±0.016 j.lsec, with a value of 0.356±0.OO7 j.lsec for v' =0. Electronic transition moments and absorption oscillator strengths have been calculated from the measured lifetimes. Measured quenching cross sections of BaO(A l!) by helium vary with vibra­tionallevel by nearly an order of magnitude from 0.28 to 2.28X 10-16 cm2, suggesting that part of the elec­tronic quenching is through collisional transfer into a perturbing state. Consistent with this model of quenching is the fact that a second fluorescence decay, with a lifetime of 10±2 j.lsec, was observed at high helium pressures from vibrational levels exhibiting strong quenching.

INTRODUCTION

There has been considerable interest in the A 12:­X 12: system of BaO, especially among astronomers and those concerned with the properties of the upper

proposed in the discussion section to explain the existence of this second lifetime.

EXPERIMENTAL

atmosphere. Emission from this band system has been Figure 1 shows a schematic diagram of the barium seen in M-type stars1 and has been used diagnostically oxide furnace. Barium oxide was produced in a flowing to measure upper atmosphere temperatures following gas system by first vaporizing barium in an aluminum the release of barium from rockets.2 An important oxide crucible heated to about 1300 K by a tungsten property of molecular transitions is the electronic heater. Barium vapor was cooled and carried by an oscillator strength, or the closely related quantity, the inert gas to the reaction chamber where it was mixed radiative lifetime. Oscillator strengths are useful, with molecular oxygen. The carrier gas pressure could perhaps necessary, for determining molecular abundan- be varied between about O.S and 20 torr. The O2

cies in astrophysical objects, and are important in concentration needed to produce the brightest fluores­understanding the electronic structure of molecular cence was at least 1000 times less than that of the carrier states. gas.

Despite the importance, few attempts have been A sketch of the experimental arrangement used to made to determine the electronic oscillator strengths measure the lifetimes of BaO is shown in Fig. 2. The and radiative lifetimes of BaO. In a paper on the output from a dye laser excited by a pulsed nitrogen fluorescence of BaO excited by an argon ion laser, the laser passed through the fluorescence cell where it lifetime was reported to be 12±3 J.lsec.3 This value pumped BaO from the ground state to a selected vibra­implies a transition moment of 0.3 Debye, a value tional level of the A 12: state. Fluorescence decay characteristic of reasonably weak bands. The lifetime following the excitation pulse was detected with a of this state has been calculated to be on the order of 1 phototube and displayed on a fast rise-time oscillo­J.lsec, using an electronic transition moment of 1 scope. A short-wavelength cutoff filter between the Debye.4 In an experiment involving "laser blowoff" cell and the phototube protected the phototube from from solid BaO, the lifetime has been measured to be directly scattered laser light. approximately O.S J.lsec.5 The only other measurement The dye laser7 used a nitrogen laser of 100 to 200 found for the radiative lifetime of the A 12: state was kW peak power at 337 nm to pump a dye solution con­in the form of a measured oscillator strength.6 From the tained in a cavity made tunable with a Littrow mounted measured value of the oscillator strength of the (2, 0) reflection grating as one of the cavity mirrors. The transition, 1.3X 10-a, we calculate the radiative lifetime peak power from the dye laser varied from 1 to 4 of v' = 2 to be 0.68 J.lsec. kW with wavelength, and the pulse width at half-

In light of the need for accurate absolute transition maximum was about 10-8 sec. With the appropriate constants for BaO and the lack of agreement in the dyes, the laser could be tuned to almost any wave­measured values, an experiment was undertaken to length in the visible with a full spectral width at half­systematically measure the lifetimes of the A 12: maximum of 0.2 to 0.8 nm. state as a function of vibrational level. Radiative life- In a typical experiment, the dye laser was tuned to times and quenching cross sections for v' = 0 to 11 excite BaO molecules from the Oth vibrational level of of BaO(A 12:) have been measured, and absolute the X l~ state to a selected level of the A 12: state. The oscillator strengths have been calculated. In addition fluorescence decay curve from a single exciting pulse to these lifetimes, a second, longer lifetime has been was displayed and photographed along with the curve measured for certain vibrational levels. A model is of the exciting pulse on a dual trace oscilloscope. This

149

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150 S. E. JOHNSON

METAL OXIDE

FURNACE

FIG. 1. BaO is produced by mixing barium vapor with molecular oxygen. An inert gas carries the barium vapor to the reaction chamber after barium is vaporized in an alumina crucible heated by a tungsten heater.

process was repeated for several values of helium pressures in the range 1-15 torr. To determine that the fluorescence was from BaO rather than an impurity, the dye laser was tuned through the transition wave­length for several (v',O) bands of BaO while monitor­ing the fluorescence intensity on the oscilloscope. In all cases, the intensity maxima occurred within a laser linewidth from measured bandhead wavelengths.s

Fortunately, three factors helped to reduce the possibility of exciting more than a single vibrational level at anyone time: (i) The molecular constantsS•9

of BaO are such that only the v" = 3 and v" = 5 pro­gressions are sufficiently close to the v" = 0 progression to be excited by the 0.5 nm wide pumping pulse; (ii) The transition probabilities, as indicated by cal­culated Franck-Condon factors,4 are considerably weaker for most of the transitions of the v" = 3 and 5 progressions compared with the v" = 0 progression; (iii) Finally, since the BaO molecules are immersed in a room temperature helium bath, nearly 65% of the BaO molecules are in the Oth vibrational level.

Theoretical Relationships

The measurements described in this paper directly give T", the radiative lifetime of the v' vibrational level of the excited state as it spontaneously decays to the various vibrational levels of the ground state. It is possible and often quite useful to convert radiative lifetimes into quantities such as absolute transition probabilities, electronic transition moments, and ab­solute absorption oscillator strengths. Relationships necessary to effect such conversions are outlined below.

The absolute transition probability A., from a given

vibrational level is given by

I/Tv,=A v'= LA v"'" .11

(1)

Individual A V'v" can be obtained from A v' and experi­mentally measured vibrational band intensities Iv'v'" smce

Avl v"/ A v' = Ivf v"/ L Iv'v". vII

(2)

An absorption oscillator strength, iv"'" can then be computed fromlo

iv'v" = (mc/8re2) (g' / gil) A "v,;>'v'v,,2

= 1.499(g'/g")A"v"Av'v,,2, (3)

where A is in centimeters, A is sec\ g' / gil is the ratio of the electronic statistical weights [g is (2s+1) for ~ states and 2(2s+ 1) for states with A21], and m, c, and e have their usual meanings.

The conversion of a lifetime Tv' to an absolute ab­sorption oscillator strength iv'v" using Eqs. 1, 2, and 3 requires the experimentally measured values of vibra­tional band intensity ratios. However, it is possible, in cases where certain approximations are valid, to use calculated Franck-Condon factors rather than meas­ured band intensities in computing iv"'" These ap­proximations are summarized below.

(i) In the Born-Oppenheimer approximation for an electric dipole transition, the absolute transition probability Av'v" is given byll

Av'v"= (32r3/3fi)Av'v,,-3 1 J'Jrv,*Re(r)'Jrv"dr 12, (4)

where Re(r) is the electronic transition moment, 'Jr. is vibrational wavefunction, and r is the internuclear separation.

(ii) In the Fraser approximation,12 which is valid where Re varies slowly with internuclear separation,

MIRROR

DIELECTRIC MIRROR---c:=I=::o

SPHERICAL MIRROR-...... ~

NOT TO SCALE

WALL (ElECTRIC SHIELD)

,,~~ DUAL BEAM OSCILLOSCOPE

ChI Ch2

FIG. 2. Schematic diagram of the experimental arrangement for measuring lifetimes of BaO with a pulsed tunable dye laser.

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QUENCHING CROSS SECTIONS OF BaO(A l~) 151

the variable Re(r) is replaced by the fixed value of Re at f, the r-centroid of the v'-v" transition:

A.,.,,= (32r/3fi) Av'v,,-3Re2 (r) qv'v", (5)

where gv'v", the Franck-Condon factor, is the square of the vibrational overlap integral:

g.,v" = [J'lF v'*'lF v"dr J2. (6)

(iii) If it is further assumed that Re(r) is constant for all v'v" transitions in a given band system, vibra­tional branching ratios Av'v,,/A v' can be expressed in terms of Franck-Condon factors:

(7)

When the approximations leading to Eq. 7 are ac­ceptable, Eqs. 1, 3, and 7 can be combined to give an expression for the absorption oscillator strength in terms of the lifetimes Tv' and the calculated Franck­Condon factors:

(8)

It must be emphasized that Eq. 8 is meaningful only if the electronic transition moment Re is constant over the range of v', v" combinations being considered. From Eqs. 1, 5, and 7, Re, in terms of the lifetime Tv', IS

Re2( v') = (3fi/32r) /[T" L: (g.,."A.,.,,-3)]. (9) v"

The degree to which R.2(V' ) in Eq. 9 is independent of v' indicates the amount of confidence which can be placed in the use of Eq. 8 to convert from radiative lifetimes to absorption oscillator strengths.

>­!::IO ~ '" ~ ~

5

0- 2 TORR 6-10 TORR

o

o

IO~~~~~~~~~I~.0~~~~1.5 TIME (jLSEC)

FIG. 3. Plot of fluorescence decay from v'=O at two helium pressures: T(2 torr) =0.326 I'sec; T(lO torr) =0.248 I'sec.

20r----,----,-----r----.----,

TIME (I'SEC)

FIG. 4. Plot of fluorescence decay from v'= 1 at P(He) = 18.4 torr. Circles indicate data points. Curve A is a least-squares fit to data using Eq. lO with T2 fixed at lO I'sec; Tl =0.0825 !/osec. Curve B is "best" straight line through initial points only; T= 0.118 !/osec. Curve C is a straight line through first data point with T=0.0825 !/osec, the value of Tl in curve A.

Data Reduction

Radiative lifetimes were determined by measuring the intensity of the fluorescence decay as a function of time and pressure from photographs of oscilloscope tracings. Computer analysis was utilized to aid the conversion of fluorescence decay data to lifetimes.

Initially, the emission intensity versus time curves were plotted on semilog paper as shown in Figs. 3 and 4. For certain v', the resulting plots were straight, as in Fig. 3, over a time interval as long as four lifetimes, indicating a simple exponential decay with a single lifetime (the reciprocal of the slope). Many of the curves however were like that in Fig. 4 which could not be fit to a single lifetime except over only a limited portion of the curve, implying that a second lifetime was involved. Radiation from certain vibrational levels at high helium pressures was made up of a suf­ficient amount of the longer fluorescence decay to measure the second lifetime, which was found to be 1O±2 ~sec. To correct for the influence of a second lifetime, a least-squares fitting program!3 was adapted to fit the intensity decay data to a curve of the form

I =A[ (1-B) exp( -tiT!) +B exp( -t/T2) J, (10)

where Tl and T2 are the two decay lifetimes. In actual use, only three parameters of Eq. 10 were

allowed to vary in fitting a given set of data. Since the second lifetime was a factor of 10 larger than the length of time over which the fluorescence decay was gen­erally measured, the term A2 exp( -t/T2) was nearly

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152 S. E. JOHNSON

TABLE I. Measured radiative lifetimes and electronic quenching rates and resulting electronic transition moments and oscillator strengths for v' = 0 to 11 of BaO (A 12; - X 12;) •

Fractional v' T(sec) • K(cm3 sec-I) u(cm2) Re(D) b.c jV/to b errord

0 3.56Xlo-7 0.35X1O-U 0.28XlO-16 1.79 0.26XlO-3 0.02 3.63 1.55 1.24

2 3.35 1.14 0.91 3 2.93 2.86 2.28 4 2.75 1.26 1.01 5 3.03 1.89 1. 51 6 3.38 1.83 1.46 7 3.26 3.12 2.49 8 3.89 2.32 1.85 9 3.80 1. 94 1.55

10 3.60 1.77 1.41 11 3.65 1. 69 1.35

• A second lifetime, T2 = 10 ±2 X 10-' sec, was observed for certain vibra­tionallevels. See text.

b Calculated from measured lifetimes using Rydberg-Klein-Rees Franck-

constant and insensitive to changes in 'T2 by as much as a factor of 2. A typical set of data and the least-squares fit of Eq. 10 to the data is shown in Fig. 4. Also shown in Fig. 4 are two straight lines; one, a best fit by eye to the first few data points, and the other, the line ob­tained by plotting a single exponential with the cor­rected lifetime 'Tl taken from the least-squares fit of Eq. 10. In this particular case, the corrected decay lifetime is about 30% shorter than that obtained by fitting a straight line to the first part of the data.

The actual radiative lifetime is related to the meas­ured lifetime of BaO in helium through the Stern­Volmer equation

(11)

where 'T.m and 'Tv are the measured and actual radiative lifetimes, respectively, and K[HeJ is the electronic quenching rate due to collisions with helium at a concentration [He]. The quenching rate constant K is often written in terms of a quenching cross section 0'.

For BaO quenched by helium at a temperature T= 300 K, 0' and K are related through

1. 76 1.07 0.02 1.82 2.56 0.04 1. 93 4.50 0.08 1. 98 5.72 0.08 1.88 5.15 0.04 1.77 3.95 0.05 1. 79 3.08 0.05 1.64 1.76 0.04 1.64 1.10 0.10 1.68 0.66 0.04

0.10

Condon factors from Ref. 4 (qv',v" given only through v' =10) . c 1 D = 10-18 statcoulomb ·cm. d Fractional errors for Re are! the values listed.

near 1 torr, the fluorescence decay could be well repre­sented with a single exponential and a single lifetime. Thus, the use of Eq. 10 to correct for the influence of a second lifetime had little effect on the extrapolated radiative lifetime. It did, however, have a large effect on the measured quenching rate.

RESULTS

Radiative lifetimes and electronic quenching rates and cross sections are listed in the first three columns of Table I. Fractional errors listed in the last column of Table I reflect the estimated precision of these

HELIUM CONCENTRATION (oloms/cm3) x 10'7

o 2 3 4 5 6

10

e

I-

0'(cm2) = (1I"JL!8kT)1/2K=8.0XI0-<lK(cm3 sec1). (12) :::: 5

Stern-Volmer plots of measured lifetimes versus helium concentration (and pressure) are illustrated in Fig. 5 for v' = 0 and 1 along with linear least-squares fits. Notice that although the radiative lifetimes of v' = 0 and 1 are nearly equal, the electronic quenching rates are quite different.

It should be pointed out that in fitting Eg. 10 to the fluorescence decay data, the connecting parameter B was found to be strongly pressure dependent, that is, the decay characterized by the longer lifetime became more apparent at higher pressures. At pressures

HELIUM PRESSURE (TORR)

O-V'=O

e-v'= I

FIG. 5. Stern-Volmer plots of measured lifetimes versus helium pressure (and concentration) for vibrational levels 0 and 1 of BaO(A 12;). The straight lines through the data points are least-squares fits. The radiative lifetimes are found from the intercepts to be To=0.363::1::0.007 "sec and Tl =0.356::1::0.007 "sec. Quenching cross sections from the slopes are Uo = 0.28 and Ul = 1.24X 10-16 cm2•

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QUENCHING CROSS SECTIONS OF BaO(A 1I:) 153

measurements and are equal to two standard devia­tions in the statistical fluctuation. The larger errors generally followed from the fact that fewer points were used in the Stern-Volmer plots, rather than from the fact that the data were more scattered. The relative accuracy is estimated to be nearly equal to the listed precision. The absolute accuracy of the more precise points is judged to be about 8%.

Three important features of the listed results should be noted: (i) the lifetimes differ only slightly (about 40%) in going from v' = 0 to 11, (ii) the variation in lifetimes, although relatively smooth, does not follow a simple pattern, and (iii) the electronic quenching rate of BaO(A 1~) by helium has almost an order of mag­nitude variation, depending on vibrational level. Of less importance if> the fact that the helium quenching rate is relatively small; the ratio of the gas kinetic collision rate to the quenching rate varies from about 20 to 200, depending on vibrational level.

Absolute absorption oscillator strengths jv' ,0 and electronic transition moments Re( v'), calculated from Eqs. 8 and 9 using measured lifetimes and recently cal­culated Rydberg-Klein-Rees Franck-Condon factors,4 are listed in Columns 5 and 6 of Table 1. As pointed out earlier in the paper, the criteria for calculating absorption oscillator strengths from emission lifetimes is that Re remain constant, which is not the case ac­cording to the present data. However, since the total variation in Re( v') is less than 20%, the values of jv' ,0

listed in Table I should agree to within about 20% of actual measured oscillator strengths. For comparison, Linevsky6 measured the oscillator strengths of the (2, 0) and (3, 0) transitions to be 1.3X 10-a and 2.0X 10-a

compared to our values of 2.56X 10-a and 4.5X 10-a, respectively.

DISCUSSION

Radiative Lifetimes

In finding the radiative lifetimes· by extrapolating to zero helium pressure, it was tacitly assumed that the only quenching of BaO(A 1~) was through collisions with helium atoms. No mention has yet been made of the two other possible quenchers, BaO and O2 • BaO­BaO interactions are quite strong, by evidence of the fact that barium oxide particles are formed downstream from our reaction zone. The actual quenching of BaO by BaO, however, was assumed negligible since the BaO density, as monitored by the fluorescence intensity, could be varied by about a factor of 5 without measur­ably changing the lifetime. Oxygen, when added in excess, strongly quenched BaO, as noted by a reduction in intensity of both fluorescence and chemilumines­cence. All experiments,. however, were carried out with the amount of added oxygen adjusted to give the strongest signal. Under these conditions, a decrease in added oxygen caused no apparent lengthing of the BaO

lifetime, indicating that under the conditions of strongest signal nearly all the added oxygen went into forming BaO, leaving little or no O2 for quenching.

Two other possible sources of error which need to be considered when measuring molecular lifetimes are vibrational relaxation and radiation entrapment. Vibrational relaxation, which does occur in the pressure range used in the present experiment,a presents a problem since the somewhat crude detection system (photomultiplier plus filter) does not discriminate as to which vibrational level emits during a given transi­tion. Vibrational relaxation should therefore have an averaging effect on the lifetime data since the fluo­rescence from each laser excited level will be accom­panied, to a small extent, by emission from adjacent levels. However, since the relaxation process is pressure dependent, it will affect only the quenching rate and not the extrapolated lifetimes.

A check must also be made to determine the extent to which radiation entrapment affects the measured lifetimes and quenching rates. If present, the radiation entrapment would cause an increase in the measured lifetime and a nonexponential fluorescence decay. Some of our results did show a nonexponential decay; however, its dependence on helium pressure indicated that it could not be due to radiation entrapment, which should depend only on the BaO density. The fluorescence decay at low helium pressures was a simple exponential with no indication of radiation entrapment.

In summary, the lifetimes found in this experiment by extrapolating to zero helium pressure are evidently the natural radiative lifetimes of BaO. In going from v' = 0 to 11 of the A 1 ~ state, the lifetimes first de­crease from about 3.6 to 2.8 then increase to about 3.9X 10-7 sec. The variation in lifetimes does indeed seem real as reflected by the precision. However, if forced to quote a single value for the radiative lifetime of the BaO(A 1~), the best value would probably be the weighted average, (3.46±0.3)X 10-7 sec.

Transition Moments and Oscillator Strength

The conversion of emission lifetimes to absorption oscillator strengths, as derived in this paper, require that the transition moment Re be constant. Since this is seldom the case, attempts have been made to find analytical expressions for Re(r) in order to derive more accurate conversions.l4 Two such expressions for BaO(A 1~_X 1~) derived from intensity data are ReCi-) = (const) exp( -6.07r)15 and R.(r) =kl(1-0.536r) .16 The present results disagree with both ex­pressions and could not be fit to any simple analytical function.

Quenching Rates and the Second Lifetime

One of the interesting results of this work is that the quenching rate of BaO(A 1~) by helium varies strongly

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154 S. E. JOHNSON

with vibrational level. Indeed, the variation may be even greater than indicated since no corrections have been made for any averaging effects on the quenching rate due to vibrational relaxation. It is quite possible that some of the quenching is due to direct conversion of BaO(A I};) electronic energy into translational energy through collisions with helium. However, this mechanism should show a small and smooth change (if any) in the quenching rate as a function of vibra­tional level.

A clue to another pos~ible quenching mechanism comes from a study of the perturbations in the BaO spectrum.9 ,17 Sixteen perturbations have been found in the upper state levels, v' = 1 to v' = 5; none has been detected in v' = O. An analysis of these perturbations has shown that they are due to four overlapping electronic states, most likely, 3IT, 3ITo, 3};J+l, and 3};J_C,17 A possible quenching mechanism is an ir­reversible transfer of energy from the A I}; state to one or more of the overlapping perturbing states during collisions with helium. Such a method is supported by the fact that v' = 0 is both unperturbed and has a quenching rate which is considerably less than the quenching rates of levels known to be perturbed. Ad­ditional support for this view is obtained from the large variation in the quenching rates, which is similar to the large variation one would expect in the strengths of the perturbations.

A quenching mechanism whereby a BaO molecule in the A I}; state is collisionally transferred into a molecule in some other overlapping electronic state is particularly appealing since it allows for the possibility of observing a second radiative lifetime in the fluo­rescence decay, as has been observed in the present work. Furthermore, if the coupled differential equa­tions derived for this type of quenching are solved, the intensity decay is found to be exactly in the form of Eq. 10, where B is now related to the collisional transfer rate from the A I}; state to the perturbing state. To be consistent with this model, B must be larger for those levels with larger quenching rates, as is the case.

The model described above stands as a possible explanation for the second lifetime observed in the

present work, T2= 10±2 /-Isec, and perhaps the lifetime reported in an earlier paper, 12±3 /-Isec.3 If this model is indeed correct, weak transitions from the perturbing state should be seen in the region of the A-X system. None has yet been reported. We are currently analyzing several new transitions which we have detected in the BaO spectrum.

ACKNOWLEDGMENTS

I would like to express my appreciation for the help and encouragement of Professor H. P. Broida in whose laboratory this work was conducted. I would also like to thank Dr. Katsumi Sakurai for many stimulating discussions and useful suggestions and Gene Capelle who assembled the dye laser and assisted in its use.

* Work supported in part by the Air Force Office of Scientific Research Office of Aerospace Research, USAF, under Grant No. AFOSR-70-1851.

t Present address: AeroChem Research Laboratories, Princeton, New Jersey 08540.

1 D. N. Davis, Astrophys. J. 106, 28 (1947). 2 G. Haerendel and R. Liist, Sci. Am. 219, 81 (1968); Planetary

Space Sci. 15, 1, 357 (1967). 3 K. Sakurai, S. E. Johnson, and H. P. Broida, J. Chern. Phys.

52, 1625 (1970). 4 T. Wentink, Jr. and R. J. Spindler, Jr., J. Quant. Spectry.

Radiative Transfer (to be published). 6 G. Diebold and T. Went ink, Jr., Panametrics, Waltham,

Mass.; pending Boston College doctoral thesis of Diebold. , M. J. Linevsky, General Electric Co., Technical Report No.

RADC-TR-70-212, 1970, presented at A.G.U. Meeting, Washing­ton, D.C., April, 1971.

7 G. Capelle and D. Phillips, App!. Opt. 9, 2742 (1970). 8 P. C. Mahanti, Proc. Phys. Soc. 46, 51 (1934). 9 A. Lagerqvist, E. Lind, and R. F. Barrow, Proc. Phys. Soc.

68, 1132 (1950). 10 C. W. Allen, Astrophysical Quantities (Athlone, London,

1963), 2nd ed. 11 G. Herzberg, Molecular Spectra and Molecular Structure

(Van Nostrand, New York, 1950), 2nd ed., Vol. 1, p. 200. 12 P. A. Fraser, Can. J. Phys. 32,515 (1954). 13 P. R. Bevington, Data Reduction and Error Analysis for the

Physical Sciences (McGraw-Hill, New York, 1969), p. 237. 14 R. W. Nicholls and A. L. Steward, Atomic and Molecular

Processes, edited by D. R. Bates (Academic, New York, 1962), p.58.

16 F. S. Ortenberg, dissertation, Moscow, 1961, quoted in Ref. 4.

16 A. P. Walvekar and V. M. Korwar, J. Phys. B 2,115 (1969). 171. Kovacs and A. Lagerqvist, J. Chern. Phys. 18, 1683

(1950).

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