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Experimentally determined oscillator strengths and linewidths for the Schumann-Runge band system of molecular oxygen—II. The (2-0) to (5-0) bands
1. Quonf. Sp~c~rosc. Rodiar. Tronsjer Vol. 22, PP. 213-221 0 Pergamon Prcw Ltd.. 1979. Printed in Great Britain
EXPERIMENTALLY DETERMINED OSCILLATOR STRENGTHS AND LINEWIDTHS FOR THE SCHUMANN-RUNGE BAND SYSTEM OF MOLECULAR OXYGEN-II. THE (2-O) TO (5-o) BANDS B. R. LEWIS,? J. H. CARVER,$ T. I. HOBBS, D. G. MCCOY, and H. P. F. GOES Department of Physics, University of Adelaide, Adelaide, Australia 5001 (Received 19 January 1979)
Abstraft-Experimental oscillator strengths and predissoclation linewidths have been measured at room temperature for the (2-O) to (5-O) Schumann-Runge bands of molecular oxygen using the Adelaide 6m vacuum ultraviolet monochromator operated at a resolution of about 0.06A. Photoelectric detectors were used to measure the ultraviolet absorption at normally two different gas pressures for 37 groups of rotational lines, and the resulting data were interpreted using an equivalent width type of analysis. The variation with N” of the oscillator strengths within each band was found to be smaller than that measured earlier for the higher vibrational bands. Measured oscillator strengths agree well with previously accepted values except for the (3-O)band, while the linewidths of the present work agree well with recent theoretical values for the (M) and (4-O) bands but are larger for the (2-O) and (5-O) bands. A modification was performed on the parameters of a recent theoretical predissociation model to produce excellent overall agreement between experimental and theoretical linewidths from v’ = 2 to 14. The present work provides results which can be used to construct accurate synthetic absorption profiles for studies of the atmospheric absorption of ultraviolet radiation by the Schumann-Runge bands. INTRODUCTION
THE SCHUMANN-RUNGE band system of molecular oxygen (B32,- - X3&-) has been studied extensively in absorption.“-‘4’ Oscillator strengths have been measured optically’“*4’and can also be inferred from electron-impact studies. “5’These results are fully discussed by LEWIS et ~1,~‘~) who present new photoelectrically determined oscillator strengths for u’ = 6-14. Their high resolution work includes the first experimental measurements of the variation of band oscillator strength with IV”.This effect has been predicted theoretically by ALLISON,(“) and its importance in relation to the atmospheric absorption problem has been noted by FANGet uf.(“) This paper, an extension of the previous work,(*6)presents high resolution photoelectric oscillator strength measurements for the (2-O) to (5-O) Schumann-Runge bands of molecular oxygen. Several groups of lines were studied in each band and the variation of band oscillator strength with N” is discussed. Evidence for the predissociation of the B38,- state of molecular oxygen is well known.‘*s25’ The associated line broadening has been measured quantitatively by ACKERMAN and BIAUME,‘~) who made photographic estimates of linewidths for the (O-O)to (19-O) bands, and by HUDSON and MAHLE(‘~’ who applied a fitting procedure to the photoelectric results of HUBONand CARTER”’ to obtain linewidths for the (2-O) to (16-O) bands. The theoretical linewidths of JULIENNE and KRAUSS’~~’ have been compared with the experimental values”4*26’by LEWS et N’.,(‘@who also presented new mean linewidth measurements for the (6-O) to (14-O) bands obtained by making both high and low pressure absorption measurements and applying a fitting procedure.
This paper presents mean linewidths for the (2-O) to (5-O) bands obtained by the fitting procedure described elsewhere. w The (2-O) to (14-O) linewidths measured by the authors are compared with the most recent theoretical values of JULIENNE/~and it is found that his model parameters must be varied to obtain good overall agreement. The model linewidths of BLAKE(“) are also in good general agreement with the results of this work. This paper continues the thorough line by line study of the Schumann-Runge bands started earlieP’ and provides data . Wresent address: Departmentof Physics, BendigoCollegeof Advanced Education, Bendigo, Australia, 3550. *Presentaddress: The Institute of AdvancedS&dies, The Australian National University, Canberra, Australia, 2600.
213
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B. R.
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which will facilitate more accurate studies of the atmospheric absorption of radiation from 1750 to 2000 A, a problem already considered by ACKERMAN et al.!‘3) FANGet u/.,“*’ and BLAKE.‘~~’ Measurements of the 2r”= 0 series of Schumann-Runge bands with u’ > 14 will be performed with a new absorption cell which is optimized for the lower pressures and temperatures needed for study in this wavelength region. The results will be published in a later work. EXPERIMENTAL METHOD The apparatus and experimental method have been described in detail elsewhere.“6’ Background radiation (1750-2000 A) provided by a thyratron triggered hydrogen discharge was dispersed by the Adelaide 6m monochromator’28’ and monitored by a gated photomultiplier detection system before entering and after leaving the windowed absorption call. Typical exp.erimental wavelength resolution was O&A;. The pressure of oxygen in the absorption cell was servo-controlled and ranged from 6 to 750 torr for the lines studied in this work. In normal operation, after the absorption line of interest had been located, wavelength scans were performed both with the cell evacuated and filled with a suitable pressure of oxygen. The programmable calculator which controlled the whole scanning and counting sequence then calculated absolute transmission values as a function of wavelength and the results were stored in a multichannel store. The calculator automatically evaluated the equivalent width associated with each absorption line together with its statistical error. Measurements were normally made at two widely differing pressures in order to allow the determination of both oscillator strength and linewidth.“@ ANALYSIS OF DATA The theory relating the experimentally measured equivalent width of an absorption line to its associated oscillator strength has been discussed in detail elsewhere,“@and the notation used here will follow that used earlier!16’ after PENNER.“‘) Rotational absorption lines in the Schumann-Runge system exhibit both thermal and predissociation broadening, (7)the relative importance of these two effects being expressed in terms of the mixing parameter a.W) The line equivalent width is related to the quantity P'X (where P’ is the true absorption coefficient at the line centre and X is the amount of absorbing gas@‘))through the well known curves of growth for a mixed lineshape.‘29’If a value for the mixing parameter is known, the appropriate curve of growth can be selected and the corresponding value of P’X read off. The band oscillator strength f(N”, v’) for the line of interest follows from”@ f(N,,, v,) = 1.577 x 1o-3 T3'*P'x
plA~ffs where T(K) is the temperature of the absorbing gas, p (micron of Hg) is its pressure, I(cm) is the absorbing path length, (Yis the weighted Boltzmann factor for the ground state rotational level giving rise to the line of interest, and S is the correctly normalized Hiinl-London factor for the line. In this work, line centre wavelengths A,&) were taken from ACKERMAN and BIAUME!~and weighted Boltzmann factors a were calculated from the accurate X3x,- energy levels of VESETHand L~FI’Iws,@~including allowance for u” = 1 levels. H&&I&ndon factors S were taken from TATUM,(“)who considered pure Hund’s case (b) coupling. Deviations from intermediate coupling Hiinl-London factorsC3*’were found to be negligible for the bands under consideration. Several important experimental factors are omitted from the above discussion. Firstly, the finite instrumental resolution must be considered. A Gaussian slit function of 0.06A FWHM was adopted after examination of scans over some of the narrow lines of the (14-O) band.“@ The lines studied from the (2-O) to (s-;ij bands were invariably scanned as unresolved PR doublets, each component of this doublet consisting of a basic triplet structure. Hence, no individual lines were scanned in this work. Interference from adjacent lines also complicated matters. The single line analysis remains valid as long as the single line, wavelength dependent absorption coefficient is replaced by the sum of the absorption coefficients for all the sign&ant lines of interest in the scanned region. (“) Hence, a knowledge of accurate line positions and
Oscillatorstrengths and linewidths for the Schumann-Runge band system of molecular oxygen-11
215
relative strengths is required. The line separations of ACKERMAN and BIAIJME,‘~) the theoretical oscillator strengths of ALLISON”~and the normalized Ho&London factors of TAIXJJ+&~” were used, together with the weighted Boltzmann factors, to estimate the contributions to the measured absorption due to undesired lines within the experimental scan range. The theoretical oscillator strengths”‘) are only necessary for estimating the strengths of weak lines from other bands, or to allow for the small rotational variation of band oscillator strength. Hence they only enter the calculation as a second order effect. As mentioned earlier for the higher bands>‘@a continuum underlies the lines of interest. In the wavelength region of the (2-O) to (5-O) bands the temperature-dependent Schumann-Runge continuum”” is relatively unimportant. The Herzberg continuum, although weak, is significant when compared with the lower Schumann-Runge bands. As noted for example by BLAKEet al (3)the continuum cross section in the Herzberg region exhibits a linear pressure dependence which has been attributed to the formation of 04. Since pressures of up to one atmosphere have been used in this work, this effect is significant and the pressure corrected continuum cross section values of SHARLMNAND and PRASAD RAO(33)have been used to correct the experimental background. There is also an effective continuum at the centre of the line of interest due to the sum of the Lorentzian wings of neighbouring Schumann-Runge lines not included in the scan range.‘r4)This contribution was calculated for all lines within ? 100cm-’ of the scan region, and converted to an effective cross section at the centre of the line of interest. Wavelengths for all Schumann-Runge lines were calculated from the spectroscopic constants of BERGEMANand WOFSY,‘~) relative strengths were calculated as above, and approximate linewidths were taken (14)Together these parameters enabled effective wing contributions to from HUDSON and MAHLE. be calculated. All the above factors were combined into a large computer program in which the basic routine numerically integrated a convolution of the instrument slit function and the Voigt lineshapes of the absorption lines. The value of P'X for a reference line in a scan group was generated given the total experimental equivalent width for the whole scan (lines and continuum). This was then converted to a band oscillator strength using Eq. (1). The normal experimental method was to perform a scan at a comparatively low pressure (approaching the linear region of the curve of growth) where the curves of growth for different values of the mixing parameter a bunch together. (29)An initial approximation for a was calculated using the predissociation linewidth values of HUDSONand MAHLE,“~’and the corresponding oscillator strength f(N”, u’) was calculated as above. A second scan was performed over the same wavelength range at a much higher pressure where the observed absorption is more dependent on Q. The value of f(N”, u’) obtained from the previous scan was then assumed, and a new value of ~1 was obtained from the program using the second scan results. This calculational loop was then repeated until the pair of results
cf(N”, v’), a} converged to values consistent with the result of each scan. The above technique was used in this work to obtain values for the band oscillator strength f(N”, u’) and the mixing parameter a (and hence predissociation linewidth) for as many rotational lines as possible for the (2-O) to (5-O) Schumann-Runge bands. It was not possible to obtain linewidths for the higher rotational lines in the (2-O) band since the largest experimentally feasibly pressure ratio between the high and low pressure scans was too small to produce sensible convergence of the f(iV”, v’) and a values. In practice, it was found that a pressure ratio greater than about 4: 1 was needed for sensible determination of a values. The amount of pressure broadening present at the highest pressures used was insignificant when compared with both the expected and obtained values of the predissociation linewidths.
RESULTS (i) Oscillator strengths The band oscillator strengths measured in this work are presented in Table 1 as a function of the rotational and vibrational quantum numbers. All measurements were performed on unresolved P(W) R(N"+2) doublets and hence the basic experimental result is an oscillator strength averaged over the P and R branches. The P/R oscillator strength ratios of ALLISON(‘~ were used to separate this data into P and R branch oscillator strengths. The errors shown in
216
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R.
LEWIS
et
al.
Oscillatorstrengthsand linewidths for the Schumann-Rungeband system of molecularoxygen-II
217
Table 1 are standard deviations arising mainly from the counting statistics of the measured equivalent width values. Errors due to uncertainties in pressure, temperature and cell length total about 1%. Due to practical considerations, it was not possible to obtain a 4: 1 pressure ratio between the high and low pressure scans for P(N”)R(N”+2) doublets in the (2-O) band with N”> 11. This made it diflkult to obtain accurate a values for these lines. In practice, the a values for the lines with IV’ s 11 were averaged and assumed to be applicable to the higher rotational lines. As mentioned previously,06) no experimental evidence has been found of a systematic variation in linewidth within a given band, although some variation has been predicted by JULIENNE.~~ The oscillator strengths for the (2-O) band with N” > 11 will thus tend to be more inaccurate than indicated by the tabled statistical errors if the above assumption is not strictly true. It is intended to study in detail the variation of a value across a suitable band and the results will be the subject of a future publication. The results for the (5-O) band are shown in Fig. 1, and it can be seen that the oscillator strengths fall off with increasing N” in a manner consistent with the bands of higher u’.(‘@In fact if we express the band oscillator strengths deduced from each rotational line in the form(‘@ f(N”, 0’) = fCJ(u’)- /.?(u’)N”(N”+ 1).
(2)
we find that f0 = (7.98kO.20) x lo-‘, j3 = (1.93 50.83) x lo-” (P branch) and f0 = (7.82 -C0.20) x lo-‘, /3 = (2.37 f 0.83) x lo-” (R branch). These are in excellent agreement with the theoretical values of ALLISON”’ for the (5-O) band, 7.88 X lo-‘, 1.75 X lo-” (P branch) and 7.85 x lo-‘, 2.13 x lo-” (R branch). It should be noted that, despite the large number of individual scans performed on the band, the experimental values of /3 are still quite inaccurate. In fact the relative variation of oscillator strength with N” becomes smaller as u’ decreases, and for u’ < 5 we are looking for a variation of less than 8%“‘) over the whole of the studied area of a band. The results for the (4-O) band are relatively constant, the (3-O) band shows a slight decrease as N” increases, and the (2-O) band results should be interpreted with care in view of the earlier discussion. Slopes /3 deduced from these bands are not sufficiently accurate for any real conclusions to be drawn. Mean band oscillator strength were calculated by averaging the present values over all levels of rotation and combining the P and R branches. (“) The results are presented in Table 2 and
0.5
I
1-
,
5-o band I
0
0.e
+ -----
thiswork ,jllison""
Fii. 1. Band oscillatorstrengthsmeasuredin this work for rotationallines in the P branchof the (5-0) band plotted as a function of N”(iV”+ 1). A least squares linear fit is also shown together with the theoretical predictionsof ALLISON.(‘~
218
B.R.LEWISet01.
compared with other experimental values. The random errors quoted do not include any contribution arising from assuming a linear dependence of oscillator strength on W(W + 1). BETHKE’~’ and HALMANN used photoelectric detection and a low resolution pressure broadening technique to obtain their results. FARMER et aI. employed a photoelectric technique at a resolution of 0.3 8, which enabled some separation of adjacent triplets, but oscillator strengths were calculated from overall integrated band absorption coefficients. HUEBNER et al.‘“’ used low resolution electron impact methods to deduce oscillator strengths, while ACKERMAN et CZI!‘~) employed a fitting procedure. All the above results have a low enough resolution to be validly compared with the mean oscillator strengths of this work presented in Table 2. The results of FARMER et al.(“) are in clear disagreement with the others for u’ = 3-5, while those of HUEBNER et aLon become very inaccurate below U’= 4. The present results agree well with those of BETHKE”)and HALMANN”‘) except for u’ = 3 where the higher value of ACKERMAN et ~1.“~’is favoured. Basically the overall trend continues towards better agreement between the experimental oscillator strengths of this work and previously accepted experimental and theoretical values as u’ decreases. This is in agreement with the pattern observed previously”‘j) for u’ = 6-14. HUDSONand MAHLE(‘~) examined individual lines optically at high resolution and used an analytical technique similar to that of this work. No details are given of the particular lines studied in their work. This comment also applies to HASSONet al.“” who used a very high resolution photographic technique to directly obtain absorption coefficients and hence oscillator strengths of lines in the (O-O) to (3-O) bands. Nevertheless, in view of the small rotational variation seen for u’ < 5, their values should be valid for comparison. (ii) Linewidths Average measured linewidths for each band studied in this and the previous”@ work are presented in Table 3 and Fig. 2, with the restriction of considering only lines with N” s 11. Although the mean linewidths have an uncertainty of typically lo%, individual widths are considerably less accurate and it is not possible to detect a statistically significant rotational variation of linewidth from the current results. The errors in Table 3 are standard errors of the mean arising mainly from counting statistical errors in the equivalent widths of both the low and high pressure scans. Only lines with N s 11 were considered in order to enable a correct comparison with the most recent theoretical model of JULIENNE,“~ who presents mean linewidths averaged over the three triplet components and not considering rotation. JULIENNE’*~) gives results for several bands predicting the change in the 3&+ partial width as a function of rotation due to centrifugal distortion, but for N ” G 11 there is minimal variation. The results of ACKERMAN and BUUME@~) were measured photographically, include blended lines, and are clearly too large for the narrower lines.‘24’HUDSON and MAEILE”~) used an optical technique similar to that of this work but their results show generally poor agreement with the present widths, especially in the range I)’= 5-11. The model linewidths adopted by BLAKE'~~in his atmospheric absorption model for the Schumann-Runge bands are in excellent agreement with the present results except for u’ = 2,7. His model reproduces measured absorption profiles well, but his widths depend on his adopted values of oscillator strength, and should only be regarded as model parameters.‘2V The original theoretical widths of JULIENNEand KRAUSS’~) are shown for completeness. Agreement with the present results is poorest in the range u’ = 5-10, the dip at u’ = 7 not being reproduced by any of the experimental measurements. In order to improve the agreement between theory and experimento4*26’near u’ = 7, a refined model was introduced by JULIENNE.'~~' Itcan be seen that agreement with the data of HUDSON and MAHLE('~) is much closer in the range u’ = 5- 11 than previously, w but for u’ = 12-14 agreement has worsened considerably. As the present results are regarded as being the most reliable experimental values, it was decided to slightly vary the parameters of the latest model of JULIENNE’~~’ to optimize agreement with this work. The matrix elements, crossing points and slopes adopted are shown in Table 4, (25)All parameters are still within the range of the notation adopted being that of JULIENNE. (u) The resultant widths are shown in Table 3 and Fig. 2, and possibilities as defined by JULIENNE. it is seen that the agreement with the present work is excellent, except for a large discrepancy at u’ = 2 and a lesser one at u’ = 5. The (2-O) band is on the edge of the possible measurement
219
Oscillator strengths and linewidths for the Schumann-Runge band system of molecular oxygen-II Table 3. Measured predissociation Iinewidths, WL (FWHM, cm-‘), compared with other experimental and theoretical values. The values in column 1represent the averages of experimentally measured widths with N” G 11. The (2-O) to (5-O) band results are those of this work, while the (6-O)to (14-O)band results are obtained from the raw data of LEWISet al.“” Julienne (a) represents the published theoretical widths of JULISNNE!~while Iuhenne (b) represents new values obtained from his work by a slight variation of parameters, as described in the text. v’
THIS
wow
(27)
BIAKE
ACKERMAN 6
HUDSON 6
BIAUKB (26)
MAHLE (14)
JULIENNE 6 KBAUSS (24)
JULIENNE (25 (a)
(b)
I
_
Juliem8” (modified)
----
Julieme and
L
o
2
4
6
a
IO
12
14
16
V’
Fig. 2. Predissociation linewidths WL(cm-‘, FWHhf) measured in this work and previously”” compared with recent model predictions.
range with the present apparatus and efforts will be made to perform measurements optimized for the (O-O)to (2-O) bands at a later date. The results clearly show that JULIENNEt2%has gone too far in his effort to improve agreement with HUDSONand MAHLE(‘~)and ACKERMANand BLCJME(~ around u’ = 7. While it is certainly true that the dip at u’ = 7 had to be eliminated from the results of JULIENNE and Ka~uss,(~) the absolute widths in this region are not as high as indicated by previous experimental measurements.“4S26’We also feel that widths of 0.2 cm-ran are too high for u’ = 13, 14, considering the accurate low values obtained in this work, supported to a certain extent by the even lower values of HUDSON and MAHLE.(‘~) The only slight discrepancy between the modified JULIENNE?~
220
B. R. LEWISet al.
Table 4. Model parameters for the predissociation of molecular oxygen. The notation follows tbat of JULIENNE.“”
-
Matrix A,
crossing point
Element (cm-‘)
R,
Adopted
in
this
Slope Hx(cm-lR-l)
&I work.
65
1 .a775
40,000
55
1.99
45,000
20
1.425
75,000
1.73
23,000
25
=_~---
-_--..._I_ Adopted
by
JULIENNE.(25)
65
1.875
t
0.0025
55
2.000
+ 0.010
40,000 45,000
30
1.425
80,000
25
1.73
23,000
model (ignoring u’ = 2) is at u’ = 5 where it is difficult to bring the model width up to the higher value favoured experimentally without creating greater discrepancies elsewhere. CONCLUSIONS
The present work completes a detailed study of the Schumann-Runge bands between u’ = 2-14. Rotational variation of oscillator strength, measured for the tirst time in the Schumann-Runge bands as described in the previous paper in this series,“@ is observed to decrease as II’ decreases. Average band oscillator strengths are seen to agree better with previously accepted values as u’ decreases, and excellent agreement has now been obtained between measured predissociation linewidths and a modification of the latest theoretical model.‘29 Although more work needs to be done for u’ < 2 and u’ > 14, the present and previouP results enable the construction of much more accurate Schumann-Runge atmospheric absorption profiles than have hitherto been available. As predicted previously”@ the comprehensive linewidth study has enabled a more accurate molecular oxygen predissociation model to be obtained. Acknowledgements-The authors would like to thank Dr. A. C. hLl.WN for communication of his oscillator strength calculations for molecular oxygen, S. GIBWN for MShelp in modifying the calculational program, and F. A. Sa~rmfor his valuable assistance. One of us (B.R.L.) held a Queen Elizabeth II Fellowship during part of this work.
REFERENCES 1. K. WATANABE, E. C. V. INN,and M. ZELIKOFF, I. Chem. Phys. 21,1026 (1953). 2. B. A. THOMPSON,P. HARTECK, and R. R. REEVES Jr., .I. Geophys. Res. 68,643l (1%3). 3. A. J. BLAKE,J. H. CARVER, and G. N. HADDAD, JQRST 6,451(1966). 4. J. CURRY and G. HERZBERG, Ann. Phys. 19,808 (1934). 5. H. P. b4AUSS and S. S. BALLARD,Phys. Reu. 48,7% (1935). 6. P. Btux and G. HJXBERG,Can. J. Phys. 32, 110(1954). 7. R. D. HUDSON and V. L. CARTER, J. Opt. Sot. Amer. 58, 1621(1968). 8. R. W. Drrc~eu~~ and D. W. 0. HEDDLE, Proc. Roy. Sm. WA, 509 (1954). 9. G. W. Bm, J. Chem. Phys. 31,669 (1959). 10. A. J. D. FARMER, W. F~~sllw,B. R. LEWIS,K. H. LOGAN, and G. N. HADDAD, JQRST 8, 1739(1968). 11. V. HASSON, G. R. H@BERT, and R. W. Nicrtous, .I. Phys. B.: Atom. Molec. Phys. 3, 1188(1970). 12. M. HALMANN, J. Chem. Phjs. 44,2486 (1966). 13. M. AC-, F. BIAUME, and G. KOCKARTS, Planet. Space. Sci. 18, 1639(1970). 14. R. D. H~JDSON and S. H. MAHLE,J. Geophys. Res. 77,2902 (1972). 15. R. H. HUEBNER, R. J. CELOITA, S. R. MIELCZAR~ZK, and C. E.-KUYATT, 1. Chem. Phys. 63,241 (1975). 16. B. R. LEWIS, J. H. CARVER,T. I. HOBBS, D. G. MCCOY,and H. P. F. Gms, JQRST #), 191(1978).
Oscillator strengths and linewidths for the Schumann-Runge 17. 18. 19. 20. 21.
A. T. P. P. P.
band system of molecular oxygen-II.
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C. ALLISON,Private communication (1975). M. FANG, S. C. WOFSY,and A. DALGARNO,Planer. Space Sci. 2,413 (1974). KRUPENIE,.I. Phys. Chem. Ref. Dafa 1,423 (1972). G. WILKINSONand R. S. MULLIKEN,Aslrophys. J. 125, 594 (1957). K. CARROLL,Aslrophys. J. 129, 794 (1959). 22. H. F. SCHAEFERand w. H. MILLER,J. Chem. Phys. 55,4107 (1971). 23. J. N. MURRELLand J. M. TAYLOR,Molec. Phvs. 16,609 (1%9). 24. P. S. JULIENNEand M. KRAUSS,J. Molec. Sp&t&. 56, .270 (1975). 25. P. S. JULIENNE,J. Molec. Spedrosc. 63, 60 (1976). 26. M. ACKERMANand F. BIAUME,J. Molec. Spectrosc. X,73 (1970). 27. A. J. BLAKE,J. Geophys. Res. accepted for publication (1979). 28. J. H. CARVER,G. N. HADDAD,T. 1. HOBBS,B. R. LEWIS,and D. G. MCCGY, Appl. Opt. 17,420 (1978). 29. S. S. PENNER,Quantitative Molecular Spectroscopy and Gas Emissiuities. Addison-Wesley, Reading, Mass. (1959). 30. L. VESETHand A. LOFTHUS,Molec. Phys. 27,511 (1974). 31. J. B. TATUM,Can. J. Phys. 442944 (1966). 32. J. B. TATUMand J. K. G. WATSON,Can. J. Phys. 49, 2693(1971). 33. SHARDANAND and A. D. PRASADRAO, JQRST 17,433 (1977). 34. T. H. BERGEMANand S. C. WOFSY,Chem. Phys. Left. 15, 104(1972).
EXPERIMENTALLY DETERMINED OSCILLATOR STRENGTHS AND LINEWIDTHS FOR THE SCHUMANN-RUNGE BAND SYSTEM OF MOLECULAR OXYGEN-II. THE (2-O) TO (5-o) BANDS B. R. LEWIS,? J. H. CARVER,$ T. I. HOBBS, D. G. MCCOY, and H. P. F. GOES Department of Physics, University of Adelaide, Adelaide, Australia 5001 (Received 19 January 1979)
Abstraft-Experimental oscillator strengths and predissoclation linewidths have been measured at room temperature for the (2-O) to (5-O) Schumann-Runge bands of molecular oxygen using the Adelaide 6m vacuum ultraviolet monochromator operated at a resolution of about 0.06A. Photoelectric detectors were used to measure the ultraviolet absorption at normally two different gas pressures for 37 groups of rotational lines, and the resulting data were interpreted using an equivalent width type of analysis. The variation with N” of the oscillator strengths within each band was found to be smaller than that measured earlier for the higher vibrational bands. Measured oscillator strengths agree well with previously accepted values except for the (3-O)band, while the linewidths of the present work agree well with recent theoretical values for the (M) and (4-O) bands but are larger for the (2-O) and (5-O) bands. A modification was performed on the parameters of a recent theoretical predissociation model to produce excellent overall agreement between experimental and theoretical linewidths from v’ = 2 to 14. The present work provides results which can be used to construct accurate synthetic absorption profiles for studies of the atmospheric absorption of ultraviolet radiation by the Schumann-Runge bands. INTRODUCTION
THE SCHUMANN-RUNGE band system of molecular oxygen (B32,- - X3&-) has been studied extensively in absorption.“-‘4’ Oscillator strengths have been measured optically’“*4’and can also be inferred from electron-impact studies. “5’These results are fully discussed by LEWIS et ~1,~‘~) who present new photoelectrically determined oscillator strengths for u’ = 6-14. Their high resolution work includes the first experimental measurements of the variation of band oscillator strength with IV”.This effect has been predicted theoretically by ALLISON,(“) and its importance in relation to the atmospheric absorption problem has been noted by FANGet uf.(“) This paper, an extension of the previous work,(*6)presents high resolution photoelectric oscillator strength measurements for the (2-O) to (5-O) Schumann-Runge bands of molecular oxygen. Several groups of lines were studied in each band and the variation of band oscillator strength with N” is discussed. Evidence for the predissociation of the B38,- state of molecular oxygen is well known.‘*s25’ The associated line broadening has been measured quantitatively by ACKERMAN and BIAUME,‘~) who made photographic estimates of linewidths for the (O-O)to (19-O) bands, and by HUDSON and MAHLE(‘~’ who applied a fitting procedure to the photoelectric results of HUBONand CARTER”’ to obtain linewidths for the (2-O) to (16-O) bands. The theoretical linewidths of JULIENNE and KRAUSS’~~’ have been compared with the experimental values”4*26’by LEWS et N’.,(‘@who also presented new mean linewidth measurements for the (6-O) to (14-O) bands obtained by making both high and low pressure absorption measurements and applying a fitting procedure.
This paper presents mean linewidths for the (2-O) to (5-O) bands obtained by the fitting procedure described elsewhere. w The (2-O) to (14-O) linewidths measured by the authors are compared with the most recent theoretical values of JULIENNE/~and it is found that his model parameters must be varied to obtain good overall agreement. The model linewidths of BLAKE(“) are also in good general agreement with the results of this work. This paper continues the thorough line by line study of the Schumann-Runge bands started earlieP’ and provides data . Wresent address: Departmentof Physics, BendigoCollegeof Advanced Education, Bendigo, Australia, 3550. *Presentaddress: The Institute of AdvancedS&dies, The Australian National University, Canberra, Australia, 2600.
213
214
B. R.
LEWISet al.
which will facilitate more accurate studies of the atmospheric absorption of radiation from 1750 to 2000 A, a problem already considered by ACKERMAN et al.!‘3) FANGet u/.,“*’ and BLAKE.‘~~’ Measurements of the 2r”= 0 series of Schumann-Runge bands with u’ > 14 will be performed with a new absorption cell which is optimized for the lower pressures and temperatures needed for study in this wavelength region. The results will be published in a later work. EXPERIMENTAL METHOD The apparatus and experimental method have been described in detail elsewhere.“6’ Background radiation (1750-2000 A) provided by a thyratron triggered hydrogen discharge was dispersed by the Adelaide 6m monochromator’28’ and monitored by a gated photomultiplier detection system before entering and after leaving the windowed absorption call. Typical exp.erimental wavelength resolution was O&A;. The pressure of oxygen in the absorption cell was servo-controlled and ranged from 6 to 750 torr for the lines studied in this work. In normal operation, after the absorption line of interest had been located, wavelength scans were performed both with the cell evacuated and filled with a suitable pressure of oxygen. The programmable calculator which controlled the whole scanning and counting sequence then calculated absolute transmission values as a function of wavelength and the results were stored in a multichannel store. The calculator automatically evaluated the equivalent width associated with each absorption line together with its statistical error. Measurements were normally made at two widely differing pressures in order to allow the determination of both oscillator strength and linewidth.“@ ANALYSIS OF DATA The theory relating the experimentally measured equivalent width of an absorption line to its associated oscillator strength has been discussed in detail elsewhere,“@and the notation used here will follow that used earlier!16’ after PENNER.“‘) Rotational absorption lines in the Schumann-Runge system exhibit both thermal and predissociation broadening, (7)the relative importance of these two effects being expressed in terms of the mixing parameter a.W) The line equivalent width is related to the quantity P'X (where P’ is the true absorption coefficient at the line centre and X is the amount of absorbing gas@‘))through the well known curves of growth for a mixed lineshape.‘29’If a value for the mixing parameter is known, the appropriate curve of growth can be selected and the corresponding value of P’X read off. The band oscillator strength f(N”, v’) for the line of interest follows from”@ f(N,,, v,) = 1.577 x 1o-3 T3'*P'x
plA~ffs where T(K) is the temperature of the absorbing gas, p (micron of Hg) is its pressure, I(cm) is the absorbing path length, (Yis the weighted Boltzmann factor for the ground state rotational level giving rise to the line of interest, and S is the correctly normalized Hiinl-London factor for the line. In this work, line centre wavelengths A,&) were taken from ACKERMAN and BIAUME!~and weighted Boltzmann factors a were calculated from the accurate X3x,- energy levels of VESETHand L~FI’Iws,@~including allowance for u” = 1 levels. H&&I&ndon factors S were taken from TATUM,(“)who considered pure Hund’s case (b) coupling. Deviations from intermediate coupling Hiinl-London factorsC3*’were found to be negligible for the bands under consideration. Several important experimental factors are omitted from the above discussion. Firstly, the finite instrumental resolution must be considered. A Gaussian slit function of 0.06A FWHM was adopted after examination of scans over some of the narrow lines of the (14-O) band.“@ The lines studied from the (2-O) to (s-;ij bands were invariably scanned as unresolved PR doublets, each component of this doublet consisting of a basic triplet structure. Hence, no individual lines were scanned in this work. Interference from adjacent lines also complicated matters. The single line analysis remains valid as long as the single line, wavelength dependent absorption coefficient is replaced by the sum of the absorption coefficients for all the sign&ant lines of interest in the scanned region. (“) Hence, a knowledge of accurate line positions and
Oscillatorstrengths and linewidths for the Schumann-Runge band system of molecular oxygen-11
215
relative strengths is required. The line separations of ACKERMAN and BIAIJME,‘~) the theoretical oscillator strengths of ALLISON”~and the normalized Ho&London factors of TAIXJJ+&~” were used, together with the weighted Boltzmann factors, to estimate the contributions to the measured absorption due to undesired lines within the experimental scan range. The theoretical oscillator strengths”‘) are only necessary for estimating the strengths of weak lines from other bands, or to allow for the small rotational variation of band oscillator strength. Hence they only enter the calculation as a second order effect. As mentioned earlier for the higher bands>‘@a continuum underlies the lines of interest. In the wavelength region of the (2-O) to (5-O) bands the temperature-dependent Schumann-Runge continuum”” is relatively unimportant. The Herzberg continuum, although weak, is significant when compared with the lower Schumann-Runge bands. As noted for example by BLAKEet al (3)the continuum cross section in the Herzberg region exhibits a linear pressure dependence which has been attributed to the formation of 04. Since pressures of up to one atmosphere have been used in this work, this effect is significant and the pressure corrected continuum cross section values of SHARLMNAND and PRASAD RAO(33)have been used to correct the experimental background. There is also an effective continuum at the centre of the line of interest due to the sum of the Lorentzian wings of neighbouring Schumann-Runge lines not included in the scan range.‘r4)This contribution was calculated for all lines within ? 100cm-’ of the scan region, and converted to an effective cross section at the centre of the line of interest. Wavelengths for all Schumann-Runge lines were calculated from the spectroscopic constants of BERGEMANand WOFSY,‘~) relative strengths were calculated as above, and approximate linewidths were taken (14)Together these parameters enabled effective wing contributions to from HUDSON and MAHLE. be calculated. All the above factors were combined into a large computer program in which the basic routine numerically integrated a convolution of the instrument slit function and the Voigt lineshapes of the absorption lines. The value of P'X for a reference line in a scan group was generated given the total experimental equivalent width for the whole scan (lines and continuum). This was then converted to a band oscillator strength using Eq. (1). The normal experimental method was to perform a scan at a comparatively low pressure (approaching the linear region of the curve of growth) where the curves of growth for different values of the mixing parameter a bunch together. (29)An initial approximation for a was calculated using the predissociation linewidth values of HUDSONand MAHLE,“~’and the corresponding oscillator strength f(N”, u’) was calculated as above. A second scan was performed over the same wavelength range at a much higher pressure where the observed absorption is more dependent on Q. The value of f(N”, u’) obtained from the previous scan was then assumed, and a new value of ~1 was obtained from the program using the second scan results. This calculational loop was then repeated until the pair of results
cf(N”, v’), a} converged to values consistent with the result of each scan. The above technique was used in this work to obtain values for the band oscillator strength f(N”, u’) and the mixing parameter a (and hence predissociation linewidth) for as many rotational lines as possible for the (2-O) to (5-O) Schumann-Runge bands. It was not possible to obtain linewidths for the higher rotational lines in the (2-O) band since the largest experimentally feasibly pressure ratio between the high and low pressure scans was too small to produce sensible convergence of the f(iV”, v’) and a values. In practice, it was found that a pressure ratio greater than about 4: 1 was needed for sensible determination of a values. The amount of pressure broadening present at the highest pressures used was insignificant when compared with both the expected and obtained values of the predissociation linewidths.
RESULTS (i) Oscillator strengths The band oscillator strengths measured in this work are presented in Table 1 as a function of the rotational and vibrational quantum numbers. All measurements were performed on unresolved P(W) R(N"+2) doublets and hence the basic experimental result is an oscillator strength averaged over the P and R branches. The P/R oscillator strength ratios of ALLISON(‘~ were used to separate this data into P and R branch oscillator strengths. The errors shown in
216
B.
R.
LEWIS
et
al.
Oscillatorstrengthsand linewidths for the Schumann-Rungeband system of molecularoxygen-II
217
Table 1 are standard deviations arising mainly from the counting statistics of the measured equivalent width values. Errors due to uncertainties in pressure, temperature and cell length total about 1%. Due to practical considerations, it was not possible to obtain a 4: 1 pressure ratio between the high and low pressure scans for P(N”)R(N”+2) doublets in the (2-O) band with N”> 11. This made it diflkult to obtain accurate a values for these lines. In practice, the a values for the lines with IV’ s 11 were averaged and assumed to be applicable to the higher rotational lines. As mentioned previously,06) no experimental evidence has been found of a systematic variation in linewidth within a given band, although some variation has been predicted by JULIENNE.~~ The oscillator strengths for the (2-O) band with N” > 11 will thus tend to be more inaccurate than indicated by the tabled statistical errors if the above assumption is not strictly true. It is intended to study in detail the variation of a value across a suitable band and the results will be the subject of a future publication. The results for the (5-O) band are shown in Fig. 1, and it can be seen that the oscillator strengths fall off with increasing N” in a manner consistent with the bands of higher u’.(‘@In fact if we express the band oscillator strengths deduced from each rotational line in the form(‘@ f(N”, 0’) = fCJ(u’)- /.?(u’)N”(N”+ 1).
(2)
we find that f0 = (7.98kO.20) x lo-‘, j3 = (1.93 50.83) x lo-” (P branch) and f0 = (7.82 -C0.20) x lo-‘, /3 = (2.37 f 0.83) x lo-” (R branch). These are in excellent agreement with the theoretical values of ALLISON”’ for the (5-O) band, 7.88 X lo-‘, 1.75 X lo-” (P branch) and 7.85 x lo-‘, 2.13 x lo-” (R branch). It should be noted that, despite the large number of individual scans performed on the band, the experimental values of /3 are still quite inaccurate. In fact the relative variation of oscillator strength with N” becomes smaller as u’ decreases, and for u’ < 5 we are looking for a variation of less than 8%“‘) over the whole of the studied area of a band. The results for the (4-O) band are relatively constant, the (3-O) band shows a slight decrease as N” increases, and the (2-O) band results should be interpreted with care in view of the earlier discussion. Slopes /3 deduced from these bands are not sufficiently accurate for any real conclusions to be drawn. Mean band oscillator strength were calculated by averaging the present values over all levels of rotation and combining the P and R branches. (“) The results are presented in Table 2 and
0.5
I
1-
,
5-o band I
0
0.e
+ -----
thiswork ,jllison""
Fii. 1. Band oscillatorstrengthsmeasuredin this work for rotationallines in the P branchof the (5-0) band plotted as a function of N”(iV”+ 1). A least squares linear fit is also shown together with the theoretical predictionsof ALLISON.(‘~
218
B.R.LEWISet01.
compared with other experimental values. The random errors quoted do not include any contribution arising from assuming a linear dependence of oscillator strength on W(W + 1). BETHKE’~’ and HALMANN used photoelectric detection and a low resolution pressure broadening technique to obtain their results. FARMER et aI. employed a photoelectric technique at a resolution of 0.3 8, which enabled some separation of adjacent triplets, but oscillator strengths were calculated from overall integrated band absorption coefficients. HUEBNER et al.‘“’ used low resolution electron impact methods to deduce oscillator strengths, while ACKERMAN et CZI!‘~) employed a fitting procedure. All the above results have a low enough resolution to be validly compared with the mean oscillator strengths of this work presented in Table 2. The results of FARMER et al.(“) are in clear disagreement with the others for u’ = 3-5, while those of HUEBNER et aLon become very inaccurate below U’= 4. The present results agree well with those of BETHKE”)and HALMANN”‘) except for u’ = 3 where the higher value of ACKERMAN et ~1.“~’is favoured. Basically the overall trend continues towards better agreement between the experimental oscillator strengths of this work and previously accepted experimental and theoretical values as u’ decreases. This is in agreement with the pattern observed previously”‘j) for u’ = 6-14. HUDSONand MAHLE(‘~) examined individual lines optically at high resolution and used an analytical technique similar to that of this work. No details are given of the particular lines studied in their work. This comment also applies to HASSONet al.“” who used a very high resolution photographic technique to directly obtain absorption coefficients and hence oscillator strengths of lines in the (O-O) to (3-O) bands. Nevertheless, in view of the small rotational variation seen for u’ < 5, their values should be valid for comparison. (ii) Linewidths Average measured linewidths for each band studied in this and the previous”@ work are presented in Table 3 and Fig. 2, with the restriction of considering only lines with N” s 11. Although the mean linewidths have an uncertainty of typically lo%, individual widths are considerably less accurate and it is not possible to detect a statistically significant rotational variation of linewidth from the current results. The errors in Table 3 are standard errors of the mean arising mainly from counting statistical errors in the equivalent widths of both the low and high pressure scans. Only lines with N s 11 were considered in order to enable a correct comparison with the most recent theoretical model of JULIENNE,“~ who presents mean linewidths averaged over the three triplet components and not considering rotation. JULIENNE’*~) gives results for several bands predicting the change in the 3&+ partial width as a function of rotation due to centrifugal distortion, but for N ” G 11 there is minimal variation. The results of ACKERMAN and BUUME@~) were measured photographically, include blended lines, and are clearly too large for the narrower lines.‘24’HUDSON and MAEILE”~) used an optical technique similar to that of this work but their results show generally poor agreement with the present widths, especially in the range I)’= 5-11. The model linewidths adopted by BLAKE'~~in his atmospheric absorption model for the Schumann-Runge bands are in excellent agreement with the present results except for u’ = 2,7. His model reproduces measured absorption profiles well, but his widths depend on his adopted values of oscillator strength, and should only be regarded as model parameters.‘2V The original theoretical widths of JULIENNEand KRAUSS’~) are shown for completeness. Agreement with the present results is poorest in the range u’ = 5-10, the dip at u’ = 7 not being reproduced by any of the experimental measurements. In order to improve the agreement between theory and experimento4*26’near u’ = 7, a refined model was introduced by JULIENNE.'~~' Itcan be seen that agreement with the data of HUDSON and MAHLE('~) is much closer in the range u’ = 5- 11 than previously, w but for u’ = 12-14 agreement has worsened considerably. As the present results are regarded as being the most reliable experimental values, it was decided to slightly vary the parameters of the latest model of JULIENNE’~~’ to optimize agreement with this work. The matrix elements, crossing points and slopes adopted are shown in Table 4, (25)All parameters are still within the range of the notation adopted being that of JULIENNE. (u) The resultant widths are shown in Table 3 and Fig. 2, and possibilities as defined by JULIENNE. it is seen that the agreement with the present work is excellent, except for a large discrepancy at u’ = 2 and a lesser one at u’ = 5. The (2-O) band is on the edge of the possible measurement
219
Oscillator strengths and linewidths for the Schumann-Runge band system of molecular oxygen-II Table 3. Measured predissociation Iinewidths, WL (FWHM, cm-‘), compared with other experimental and theoretical values. The values in column 1represent the averages of experimentally measured widths with N” G 11. The (2-O) to (5-O) band results are those of this work, while the (6-O)to (14-O)band results are obtained from the raw data of LEWISet al.“” Julienne (a) represents the published theoretical widths of JULISNNE!~while Iuhenne (b) represents new values obtained from his work by a slight variation of parameters, as described in the text. v’
THIS
wow
(27)
BIAKE
ACKERMAN 6
HUDSON 6
BIAUKB (26)
MAHLE (14)
JULIENNE 6 KBAUSS (24)
JULIENNE (25 (a)
(b)
I
_
Juliem8” (modified)
----
Julieme and
L
o
2
4
6
a
IO
12
14
16
V’
Fig. 2. Predissociation linewidths WL(cm-‘, FWHhf) measured in this work and previously”” compared with recent model predictions.
range with the present apparatus and efforts will be made to perform measurements optimized for the (O-O)to (2-O) bands at a later date. The results clearly show that JULIENNEt2%has gone too far in his effort to improve agreement with HUDSONand MAHLE(‘~)and ACKERMANand BLCJME(~ around u’ = 7. While it is certainly true that the dip at u’ = 7 had to be eliminated from the results of JULIENNE and Ka~uss,(~) the absolute widths in this region are not as high as indicated by previous experimental measurements.“4S26’We also feel that widths of 0.2 cm-ran are too high for u’ = 13, 14, considering the accurate low values obtained in this work, supported to a certain extent by the even lower values of HUDSON and MAHLE.(‘~) The only slight discrepancy between the modified JULIENNE?~
220
B. R. LEWISet al.
Table 4. Model parameters for the predissociation of molecular oxygen. The notation follows tbat of JULIENNE.“”
-
Matrix A,
crossing point
Element (cm-‘)
R,
Adopted
in
this
Slope Hx(cm-lR-l)
&I work.
65
1 .a775
40,000
55
1.99
45,000
20
1.425
75,000
1.73
23,000
25
=_~---
-_--..._I_ Adopted
by
JULIENNE.(25)
65
1.875
t
0.0025
55
2.000
+ 0.010
40,000 45,000
30
1.425
80,000
25
1.73
23,000
model (ignoring u’ = 2) is at u’ = 5 where it is difficult to bring the model width up to the higher value favoured experimentally without creating greater discrepancies elsewhere. CONCLUSIONS
The present work completes a detailed study of the Schumann-Runge bands between u’ = 2-14. Rotational variation of oscillator strength, measured for the tirst time in the Schumann-Runge bands as described in the previous paper in this series,“@ is observed to decrease as II’ decreases. Average band oscillator strengths are seen to agree better with previously accepted values as u’ decreases, and excellent agreement has now been obtained between measured predissociation linewidths and a modification of the latest theoretical model.‘29 Although more work needs to be done for u’ < 2 and u’ > 14, the present and previouP results enable the construction of much more accurate Schumann-Runge atmospheric absorption profiles than have hitherto been available. As predicted previously”@ the comprehensive linewidth study has enabled a more accurate molecular oxygen predissociation model to be obtained. Acknowledgements-The authors would like to thank Dr. A. C. hLl.WN for communication of his oscillator strength calculations for molecular oxygen, S. GIBWN for MShelp in modifying the calculational program, and F. A. Sa~rmfor his valuable assistance. One of us (B.R.L.) held a Queen Elizabeth II Fellowship during part of this work.
REFERENCES 1. K. WATANABE, E. C. V. INN,and M. ZELIKOFF, I. Chem. Phys. 21,1026 (1953). 2. B. A. THOMPSON,P. HARTECK, and R. R. REEVES Jr., .I. Geophys. Res. 68,643l (1%3). 3. A. J. BLAKE,J. H. CARVER, and G. N. HADDAD, JQRST 6,451(1966). 4. J. CURRY and G. HERZBERG, Ann. Phys. 19,808 (1934). 5. H. P. b4AUSS and S. S. BALLARD,Phys. Reu. 48,7% (1935). 6. P. Btux and G. HJXBERG,Can. J. Phys. 32, 110(1954). 7. R. D. HUDSON and V. L. CARTER, J. Opt. Sot. Amer. 58, 1621(1968). 8. R. W. Drrc~eu~~ and D. W. 0. HEDDLE, Proc. Roy. Sm. WA, 509 (1954). 9. G. W. Bm, J. Chem. Phys. 31,669 (1959). 10. A. J. D. FARMER, W. F~~sllw,B. R. LEWIS,K. H. LOGAN, and G. N. HADDAD, JQRST 8, 1739(1968). 11. V. HASSON, G. R. H@BERT, and R. W. Nicrtous, .I. Phys. B.: Atom. Molec. Phys. 3, 1188(1970). 12. M. HALMANN, J. Chem. Phjs. 44,2486 (1966). 13. M. AC-, F. BIAUME, and G. KOCKARTS, Planet. Space. Sci. 18, 1639(1970). 14. R. D. H~JDSON and S. H. MAHLE,J. Geophys. Res. 77,2902 (1972). 15. R. H. HUEBNER, R. J. CELOITA, S. R. MIELCZAR~ZK, and C. E.-KUYATT, 1. Chem. Phys. 63,241 (1975). 16. B. R. LEWIS, J. H. CARVER,T. I. HOBBS, D. G. MCCOY,and H. P. F. Gms, JQRST #), 191(1978).
Oscillator strengths and linewidths for the Schumann-Runge 17. 18. 19. 20. 21.
A. T. P. P. P.
band system of molecular oxygen-II.
221
C. ALLISON,Private communication (1975). M. FANG, S. C. WOFSY,and A. DALGARNO,Planer. Space Sci. 2,413 (1974). KRUPENIE,.I. Phys. Chem. Ref. Dafa 1,423 (1972). G. WILKINSONand R. S. MULLIKEN,Aslrophys. J. 125, 594 (1957). K. CARROLL,Aslrophys. J. 129, 794 (1959). 22. H. F. SCHAEFERand w. H. MILLER,J. Chem. Phys. 55,4107 (1971). 23. J. N. MURRELLand J. M. TAYLOR,Molec. Phvs. 16,609 (1%9). 24. P. S. JULIENNEand M. KRAUSS,J. Molec. Sp&t&. 56, .270 (1975). 25. P. S. JULIENNE,J. Molec. Spedrosc. 63, 60 (1976). 26. M. ACKERMANand F. BIAUME,J. Molec. Spectrosc. X,73 (1970). 27. A. J. BLAKE,J. Geophys. Res. accepted for publication (1979). 28. J. H. CARVER,G. N. HADDAD,T. 1. HOBBS,B. R. LEWIS,and D. G. MCCGY, Appl. Opt. 17,420 (1978). 29. S. S. PENNER,Quantitative Molecular Spectroscopy and Gas Emissiuities. Addison-Wesley, Reading, Mass. (1959). 30. L. VESETHand A. LOFTHUS,Molec. Phys. 27,511 (1974). 31. J. B. TATUM,Can. J. Phys. 442944 (1966). 32. J. B. TATUMand J. K. G. WATSON,Can. J. Phys. 49, 2693(1971). 33. SHARDANAND and A. D. PRASADRAO, JQRST 17,433 (1977). 34. T. H. BERGEMANand S. C. WOFSY,Chem. Phys. Left. 15, 104(1972).