High resolution absorption cross-sections and band oscillator strengths of the Schumann-Runge absorption bands of isotopic oxygen, 18O2, at 79 K

Pher. Space SCL, Vol. 36, No. I I, pp. 1201-1210, Printed in Great Britain.

1988 0

00324633/88 %3.00+0.00 1988 Pergamon Press plc

HIGH RESOLUTION ABSORPTION CROSS-SECTIONS AND BAND OSCILLATOR STRENGTHS OF THE SCHUMANN-RUNGE ABSORPTION BANDS OF ISOTOPIC OXYGEN, “02, AT 79 K K. YOSHINO, D. E. FREEMAN, J. R. ESMOND, R. S. FRIEDMAN* and W. H. PARKINSON Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, U.S.A.

(Receiued 23 June 1988) Abstract-Cross-sections of ‘so2 at 79 K have been obtained from photoabsorption measurements at various pressures throughout the wavelength region 177.8-197.8 nm with a 6.65 m photoelectric scanning spectrometer equipped with a 2400 lines mm-’ grating and having an instrumental width (FWHM) of 0.0013 nm. The measured absorption cross-sections of the Schumann-Runge bands (14,0) through (2,O) are, with the exception of the (12,0) band, independent of the instrumental width. The measured crosssections are presented graphically here and are available at wavenumber intervals of -0.1 cm-’ as numerical compilations stored on magnetic tape, from the National Space Science Data Center, NASA/ Goddard Space Flight Center, Greenbelt, MD 20771, U.S.A. Band oscillator strengths of those bands have been determined by direct numerical integration of the measured absolute cross-sections and are in excellent agreement with our theoretically calculated values.

1. INTRODUCTION

The Schumann-Runge (S-R) absorption bands of O2 at 79 K arise from the transition B(u)~&-X(O)~X; in the wavelength region 175-205 nm. There has recently been interest in the role of the photodissociation and photoabsorption of isotopic oxygen through the Schumann-Runge bands, especially those of ‘60’80. The abundance of ‘60’80 is only 0.41% of that of atmospheric oxygen, but ‘60’80 is the sixth most abundant molecule in the atmosphere. Cicerone and McCrumb (1980) did the first calculation on atmospheric isotopic oxygen effects, in an attempt to account for the abundance of ozone observed in the atmosphere. Blake et al. (1984) performed more detailed and realistic calculations concerning the effects of ‘60’80 in the atmosphere. Recently, Omidvar and Frederick (1987) did a line by line calculation of the Schumann-Runge bands of ordinary and isotopic oxygen to obtain the contributions from the photodissociation of these molecules at different altitudes. On the other hand, the only recent experimental results for the band oscillator strengths for the S-R bands, other than those for “jO*, are the results of Lewis et al. (1987a,b) for “0, and ‘60’80 ; these were obtained with medium resolution (- 0.005 nm), and not directly from absolute cross-section measurements. Our present studies contain the first absolute *Also, Department U.S.A.

of Chemistry, Harvard University,

absorption cross-section measurements of the S-R bands of ‘*02 and ‘60’80. Our high resolution permits absolute cross-section measurements of ‘*02 to be made in the usual way, i.e. from measured optical depths of known column densities (pressures) of essentially pure “OZ. However, isotopically pure ‘60180 is unavailable for absolute cross-section measurements of ‘60’80, which must be derived from measurements of available isotopic mixtures of 1602, ‘60’80 and ‘*O,, in which all three sets of S-R absorption bands are simultaneously present. To obtain the cross-sections of ‘60180, which will be published later, from studies of such mixtures, we need detailed absorption wavelengths and cross-sections of 1602 and “‘OZ. For 1602, we have previously published high resolution photographic wavelength measurements (Yoshino et al., 1984) their spectroscopic analysis (Cheung et al., 1986), and absorption cross-section measurements at 300 K (Yoshino et al., 1983 ; Cheung et al., 1984) and at 79 K (Yoshino et al., 1987). We have recently completed similar wavelength measurements and spectroscopic analyses for ‘*02 (Cheung et al., 1988b) and for ‘60’80 (Cheung et al., 1988a). In the present paper, we report absolute cross-section measurements of the (2,0)-(l l, O), (13,0) and (14,0) S-R bands of ‘*OZat 79 K. Of the bands (2,0)(14,0) of ‘*02 located in the wavelength region 177.8197.8 nm, only the (12,0) band is too sharp for its absolute absorption cross-section to be measured with our current instrumental width (FWHM) of 0.0013 nm ( - 0.4 cm ‘) . We have also determined band oscil-

1201

K. YOSHINO et al.

1202

lator strengths of the (2,0)-(ll,O), (13,O) and (14,O) bands of “02 by numerical integration of the absolute cross-sections measured at 79 K, and we have compared these experimental band oscillator strengths to our theoretical values.

2. EXPERIMENTAL

PROCEDURE

The apparatus and procedure for this work are the same as described in our previous paper (Yoshino et al., 1987). A 6.65 m vacuum spectrometer (Yoshino et al., 1980) is used in the first order of a 2400 lines mm-’ grating to provide a reciprocal linear dispersion of 0.06 nm mm-‘. The entrance and exit slit widths are 10 +2 pm, and the resulting instrumental band width (FWHM) is 0.0013 nm. The continuous background for the photoabsorption measurements of “02 is provided by a hydrogen continuum discharge source. The absorption cell is made of stainless steel tubing, of internal diameter 25 mm and length 81 cm, with Cajon fittings on both ends. Two Pyrex tubes, each 25 mm in diameter and 23 cm in length, and each with a silica (Suprasil-1) window on one end, are inserted, window first, through Cajon fittings into opposite ends of the stainless steel tubing. This arrangement provides an optical pathlength of 50.3 cm between the two silica windows. The cell is immersed in a liquid-nitrogen bath, 58 cm in internal length and 17 cm in internal depth. The isotopic oxygen (Stohler Isotope Chemicals, 99% atomic “0) is introduced into the absorption cell. The oxygen pressure is varied from 0.18 to 150 Torr, providing column densities of 1.08 x 10” to 9.03 x 102’ cmp2, for photoabsorption measurements of the (14,0)-(2,0) bands. The photoelectric scanning is continuous ; in this spectral region the counting period is set at 0.225 s which corresponds to accumulating counts at intervals of 4 pm in length or 0.00024 mn in wavelength (-0.1 cm-‘) in the focal surface of the spectrometer. The background continuum is obtained by scanning before and after the photoabsorption measurements ; the small decrease in the intensity of the background continuum during a scan is taken into account by interpolation. The Fourth Positive bands of CO (Yoshino and Freeman, 1984) excited by a dc discharge through carbon dioxide, are used to obtain a dispersion for each scan and the absolute wavenumber scale is established by the use of the known wavelengths of rotational lines of the S-R bands (Cheung et al., 1988b). The ratio of the incident intensity lo(v) to the intensity transmitted Z(v) through a medium of column density N (cm-2) is related to the absorption cross section a(v) (cm”) by the formula :

In [Zo(v)/Z(v)] = No(v).

(1)

This expression applies strictly for monochromatic radiation, and effectively for radiation for which the instrumental width is negligible compared with the width of the spectral feature being measured. With respect to the present instrumental width (FWHM = 0.0013 nm), the spectral features of the S-R bands with u’ = 2-l 1, 13 and 14 prove broad enough for the measured cross-sections to be absolute, as discussed in our previous papers (Yoshino et al., 1983 ; Cheung et al., 1984). However, the (12,O) band of ‘*02 is so sharp that we could not measure its absolute cross-section. 3. CROSS-SECTIONS

OF THE SCHUMANN-RUNGE

BANDS OF “0,

AT 79 K

Absolute absorption cross-section measurements of ‘*02 at 79 K have been obtained for the first time for the S-R bands (2,0)-(ll,O), (13,O) and (14,0) which occur within the wavelength region 177.8-197.8 mn. The cross-sections of these bands are available at wavenumber intervals of -0.1 cm-’ as numerical compilations stored on magnetic tape, from the National Space Science Data Center, NASA/ Goddard Space Flight Center, Greenbelt, MD 20771, U.S.A. In this paper, we present the cross-sections in graphical format. In Figs la through 11, the measured cross-sections of the S-R bands of ‘*02 at 79 K are shown as separate linear plots, one per band, for the (2,0)-(ll,O), (13,O) and (14,O) bands. The rotational assignment of lines belonging to the main branches can be deduced from the few explicitly given as Z?(N) or P(N). The complete assignment of the observed lines and their wavenumbers measured from photographic spectra are presented in a separate publication (Cheung et al., 1988b). The (12,O) band is too sharp for its absolute cross-section to be measured with the present resolution. The experimental error in an absolute cross-section o(v) derived from equation (1) depends on the errors in the column density N and the optical depth In [Zo(v)/Z(v)]. An uncertainty of -3% in N results from estimated errors of 1% in the l8O2 pressure measurements and of f2 K in the temperature estimation for “02 derived from rotational intensity distributions; the error in the optical path length, + 1 mm in 50.3 cm, is negligible. Errors in the final values of the absolute absorption cross-sections are estimated to be -4% in regions of the principal absorption peaks. Errors in the range below 5 x 1O-22 cm* are somewhat greater as a result of the limited column densities available at the highest pressures we have used.

Schumann-Runge bands of "02 at 79 K

1203

2.0 5 f

0 3 4 0

50800

Wavenumber 2

tb) 3.0

_I

b

0 51050

51400

Wavenumber S~~~-RUNGE BANDS(~',~)WI~ v'=2-11,13 AND 140~ FIG. 1. A~OL~CR~-~CTIONSO~T~ '*O,AT~~KARESHOWNINFIGS 1aTHRoUoH lI,ReSPECTIvELY.

4. BAND OSCILLATORSTRENGTHSOF THE ‘“0, SCHUMANN-RUNGE BANDS B(u’)-X(O),

d = Z-11,13sod 14

The band oscillator strength is given by (Yoshino et al., 1983) mc2 1 f(u’, V”) = 2 -==--,F c(v) dv 7re N(v ) s

rotational lines belonging to the (~‘,a”) band. The constants m, e, and care the electronic mass, electronic charge and velocity of light, respectively: mc2/rce2 = 1.130x lOi cm-‘. For IgO,, AG’;,, = 1468.5 cm-’ (Huber and Herzberg, 1979), so that B(O) = 1.000 at 79 K, and equation (2) yields for the band oscillator strength of the (Y’,0) band,

(2)

in which @(v“) is the fractional Boltzmann population of the absorbing vibrational level, and the integration of the cross-section a(v) is performed over all of the

f(u’, 0) = 1.130 x 1012 a(v) dv. s

(3)

Band oscillator strengths f(u’, 0) with v’ = 2-l 1, 13

1204

K.

b

YOSHINO et al.

1

I

51600

Wavenumber

52550.

Wavenumber

and 14 have been determined from equation (3) by direct numerical integration of the measured crosssections and are shown in the third column of Table 1. The uncertainty introduced into the band oscillator strength by the integration procedure itself is negligible, so that our estimated uncertainty of 4% in the measured cross-section represents an upper limit to the uncertainty in the band oscillator strength. Also presented in Table 1 are theoretical band oscillator strengths~(~‘, 0). They were determined by summing rotational line oscillator strengths weighted by the Boltzmann popufation of the initial rotational

level. The oscillator strengths presented in Table 1 correspond to transitions emanating from the F2component of the X?Z; state, but it is expected that the variation of the oscillator strength with the fine-structure component will be small (Lewis et al., 1987b). The HonkLondon factors corresponding to AN = + 1 were assumed to be appropriate to a coupling case intermediate between Hund’s cases (a) and (b) (Tatum and Watson, 1971) and were calculated using the accurate molecular parameters of j602 and “02 for the .X3X; state (Steinbach and Gordy, 1975) and the B3’C,; state (Cheung et al., 1986; 1988b). In

Schumann-Runge

1205

bands of ‘*O, at 79 K

6.0

P9

b 1

A

,

I

53050

52700

Wavenumber 8-

(f)

I P9

$ z2

RII 4

b

I l-

\, LJb I 53200

53550

Wavenumber FIG.

1 (cminued).

the absence of accurate parameters for u’ = 0 and 1 of the “02 B3C; state, case (b) Ho&London factors were adopted ; however, even for high vibrational levels u’, oscillator strengths f(u’, 0) calculated using case (b) and intermediate case rotational line strengths differed by less than 0.5%. The X3X; state potential was constructed from the RKR data of Krupenie (1972) and for the B’C; state an RKR potential was calculated using the vibrational-rotational term values of Cheung et al. (1986). For the B3C;-X3X; dipole moment, we adopted the function calculated by Allison et al. (1986) but shifted by -0.049 a, since the excited state eigenfunction used in the evaluation

of D(R) corresponded to an electronic potential with an equilibrium separation too large by 0.049 a,,. Due to the very different equilibrium separations of the X and B states, only values of the dipole moment between about 2.5 and 2.9 a0 are significant to the calculation off(u’, 0). Within the BornOppenheimer approximation, the ground and excited state potentials as well as the dipole moment are isotopically invariant. 5.

DISCUSSION

The principal benefit of studying the absolute absorption cross-section at 79 K, rather than at room

1206

K. Yosnmo

et al.

P7

R9

I I

54100

Wavenumber

415i0

54500

Wavenumber FIG.1 (continued).

temperature, is that the integration of the cross-section over the spectral range of any particular (u’, 0) band is simplified by the absence of contributions from bands with v” > 0 and the absence of contributions from rotational lines of high N”(N” > 17’)of the (v’, 0) band, which if present, would overlap the band-head region of the (a’- I, 0) band. Thus, the integrated cross-section obtained at 79 K, over the spectral range of a particular (u’, 0) band, consists solely of all the rotational contributions from that band. In Table I, our band oscillator strengths for r802 and 1602, obtained from cross-sections measured at

79 K, are compared with the values we obtained from theoretical calculations. The agreement between our experimental and theoretical oscillator strengths is excellent, especially considering the 4% experimental uncertainty and the uncertainty in the calculated dipole moment. Due to the decrease in rotational oscillator strengths within a given band with increasing N, band oscillator strengths for 1602 at 300 K are calculated to be about 3% smaller than those at 79 K, an effect too small to be seen experimentally because of the approximately 4% uncertainties in each of the experimental values for 1602at 79 and 300 K.

Schumann-Runge

bands of “0, at 79 K

1207

(i)

Wavenumber

r:

25

2-

b lo-

Wavenumber FIG. 1 (continued).

The present band oscillator strengths for “Oz are also compared with the recent results of Lewis et al. (1987a) in Table 1 where the band oscillator strengths of 1602 are also listed. The band oscillator strengths of “Or in our work are results at 79 K, while the results of Lewis et al. in our Table 1 are for N = 0 and are therefore expected to be close to our results for 79 K. The band oscillator strengths for 1602 of Lewis et al. (1986) are Boltzmann weighted averages at room temperature (300 K) and they are in quite good agreement with our experimental and theoretical

results at 300 K. On the other hand, the N = 0 values for ‘*02 of Lewis et al. (1987a) are higher than our 79 K results by 13-25%, which is much higher than our experimental errors. The earlier measurements (Halmann and Laulicht, 1965 ; Halmann, 1966) were quoted by Lewis ef al. (1987a) as being about 15% lower than theirs, but our results agree with those of Halmann and Laulicht reasonably well. Halmann and Laulicht (1965,1966,1967) have calculated isotope effects for Franck-Condon factors for the Schumann-Runge absorption bands of oxygen.

K. Yosm~o et al.

1208

55950

Wavenumber 91

(I)

a-

14,o

;?0,

b 6H

';; 5Y. 2 45 $ 3;3zb 11 o1

559;

58250

Wavenumber Frc. I (continued).

They first used Morse potential functions to compute Franck-Condon factors, but Morse potential functions are not realistic for the higher vibrational levels. They later calculated Franck-Condon factors from RKR potential functions and those results are also shown in Table 2. Our experimental and theoretical ratios of the band oscillator strengths of 1602to those of ‘*02, obtained from Table 1, are given in Table 2. The experimental and theoretical ratios agree closely with each other and with the ratios of the FranckCondon factors, showing that the effect of the dipole

moment function on the ratios is small. 6. CONCLUDING

REMARK

High resolution absorption cross-section measurements that are independent of the spectrometer function have been made on ‘*02 at 79 K in the wavelength region 177.8-197.8 nm of the Schumann-Runge bands (v’, 0) with v’ = 2-11,13 and 14, for which band oscillator strengths have been obtained. Theoretical results are also obtained in excellent agreement with

Schumann-Runge bands of “02 at 79 K

1209

TABLE 1. BANDOSCILLAM~R STRENGTHS, j”fv’, 0) IN UNITSOF lo-“, OF TUESCHUMANN-RUNGE BANDSOF ‘*O2 AND L60,

Present (CfA) Experiment Theory 79 K 79 K

VI

x

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

10 9 8 8 7 7 6 6 6 6 5 5 5 5 5

0.775 0.995 0.656 2.96 I .02 2.91 0.701 1.48 2.19 4.75 0.742 1.07 1.43 1.76 2.00

0.586 2.86 1.01 2.85 0.682 1.51 2.79 4.61 0.747 1.04 1.66 1.90

Lewis Experiment*

Present (CfA) Experiment? Experimentt 300 K 79 K

0.737 3.30 1.14 3.22 0.815 1.73 3.28 5.75 0.898 1.21 1.60 2.09 2.23

2.59 2.90 1.81 8.30 2.77 7.29 1.60 3.37 6.11 9.31 1.36 2.00 2.38

1.90 8.36 2.71 7.39

1.63 3.36 5.92 9.06 1.39 1.91 2.24

Present (CfA) Theory Theory 19 K 300 K 2.53 3.06 1.90 8.12 2.66 7.15 1.63 3.27 5.84 9.44 1.39 1.90 2.31 2.12 2.89

Lewis Experiment$ 300K

2.47 2.99 1.86 7.92 2.59 6.95 1.59 3.17 5.66 9.12 1.34 1.82 2.27 2.58 2.72

3.04 I.94 8.14 2.74 7.42 1.67 3.44 6.08 9.65 1.47 1.96 2.44 2.73 2.82

*Lewis ef af. (1987a), rotationless (N = 0) values. t Yoshino et al. (1987), Table 2. $ Lewis ef al. (1986).

TABLE2. THE RATIOOF THEABSORPTION INTENSITIES OF 1602vs “0, IN THESCHUMANN-RUNGE BANDS Band oscillator strengths present ratios d

2 3 4 5 6 7 8 9 10 11 12 13 14

Franck-Condon

Experiment*

Theory*

Presentt

3.24 2.92 2.68 2.59 2.39 2.23 2.12 1.97 1.86 1.84

2.90 2.74 2.61 2.46 2.33 2.21 2.09 1.99 1.87 1.78 1.66 1.55 1.44

2.90 2.74 2.58 2.44 2.31 2.19 2.08 1.97 1.86 1.76 1.65 1.54 1.43

I-IL (1967)$

2.59 2.31 2.03 1.84 1.56 1.40

* From our results (CfA) at 79 K in Table 1. t Our results using RKR potentials. $ From Halmann and LauIicht (1967), using RKR potentials. §From Hahnann and Laulicht (1966), using Morse potentials. I/From Halrnann and Laulicht (1965), using Morse potentials.

factor ratios HL (1966)s 2.89 2.73 2.60 2.47 2.35 2.24 2.14 2.05 1.96 1.89 1.82 1.76 1.69

HL (1965) 3.85 3.25 3.14 2.12 2.75 2.30 2.45 2.25 2.38 1.72

11

1210

K.

the experimental results. Cross-section of ‘60180 at 79 K have been completed will be published soon.

YOSHIIvo et al.

measurements and the results

Acknowledgement-We are pleased to acknowledge the valuable discussions with Professor A. Dalgamo. The work reported was supported by the NASA Upper Atmospheric Research Program under Grant NAG 5-484 to Smithsonian Astrophysical Observatory and by NSF under Grant ATM87-13204 to Harvard University. REFERENCES

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Yoshino, K., Freeman, D. E., Esmond, J. R. and Parkinson, W. H. (1987) High resolution absorption cross-sections and band oscillator strengths of the Schumann-Runge bands of O2 at 79 K. Planet. Space Sci. 35, 1067. Yoshino, K., Freeman, D. E. and Parkinson, W. H. (1980) Photoelectric scanning (6.65 m) spectrometer for vuv cross-section measurements. Appl. optics 19,66. Yoshino, K., Freeman, D. E. and Parkinson, W. H. (1984) Atlas of the Schumann-Runge absorption bands of O2 in the wavelength region 175-205 nm. J. phys. Chem. (Ref Data) 13, 207.