Resonances in the photodissociation of isotopic molecular oxygen—I. The longest band

J. Quant. Spectrosc. Radiat. Transfer Vol.40, No. 1, pp. 1-13, 1988

0022-4073/88 $3.00+ 0.00 Copyright© 1988PergamonPressplc

Printed in Great Britain. All rights reserved

RESONANCES

IN

ISOTOPIC

THE

PHOTODISSOCIATION

MOLECULAR

THE

LONGEST

OF

OXYGEN--I. BAND

B. R. LEWIS, S. T. GIBSON, M. EMAMI'~,and J. H. CARVER Research School of Physical Sciences, The Australian National University, Canberra, Australia 2600 (Received 8 January 1988)

Abstract--We present detailed photoabsorption cross section measurements of the (0~) and

(0-1) bands of the E327~--X3S£ transition of molecular oxygen. The isotopes ~602, 160180and 1sO2 were studied at 79 and 295 K, with an instrumental resolution of 0.04--0.06/~ FWHM. Our results show clearly that these bands provide one of the rarely observed examples of Beutler-Fano resonances in molecular photodissociation. With the aid of empirical modelling, we show that the widths and asymmetries of individual lines vary significantly with rotation and isotopic mass, but the oscillator strengths show no isotope effect.

INTRODUCTION In the region from the LiF cutoff to the short wavelength side of the Schumann-Runge continuum (1050-1300~), the photoabsorption spectrum of '60 2 consists of a number of strong bands separated by windows of relatively weak absorption. Cross sections in this region have been measured by several investigators, I-4 especially near the solar Lyman-c¢ line) -1° The diffuse bands were first observed spectrographically by Price and Collins." In this and associated works,12'13 we are concerned with Tanaka's progression 1,14consisting of bands at 1244/~ (longest), 1206/~ (second), 1172/~ (third), and 1269 ~ , classified by Tanaka '4 as the hot band associated with the longest band. The assignment of these bands has been in doubt until quite recently. On the basis of isotope shift measurements, Ogawa et aP 5 classified the longest band as the (1-0) transition of a progression with upper state E 3 I f , and the 1269/~ band as the corresponding (0-0) band. Ogawa 16 showed spectrographically that rotational and fine structure was visible in the longest band of 1802, confirming identification of the upper state as 32~-, but he persisted with the vibrational assignments of Ogawa et al) 5 A b initio calculations of the mixing of valence and Rydberg 3~ u s t a t e s of 05, by Buenker and PeyerimhotP 7-19 and Yoshimine, 2° showed that the longest, second and third bands could be explained as transitions to the lowest three vibrational levels of the resulting upper mixed valence-Rydberg state, E3i,, -. Reasonable agreement was found between calculated and observed energy levels, and between calculated 2° and observed 21 oscillator strengths. This reclassification was supported by the arguments of Katayama et al, 22 who suggested that the anomalous isotope shift o f the longest band 15 might be explained by the strong configuration interaction which produced the E32~ - state. Black et a1:3 measured the absorption spectrum of 1602 at 930 K, discovering new hot bands at 1229 and 1195/~, associated with the second and third bands, and confirming the classification o f the 1269/~ band as (0-1). At this time, it is clear that the longest, second, third, and 1269 .~ bands are all part of the same progression, as originally envisaged by Tanaka. la They are the (0-0), (lq)), (2-0), and (0-1) transitions to the mixed valence-Rydberg E3Zu state (labelled B' by some authors2°'22). What remain to be explained are the anomalous isotope shift for the (0-0) band, and the large variations of width with vibration and isotopic mass. Using the methods of Fano, 24 Cimiraglia et a125 showed theoretically that isotopic shifts and widths of the order of 100 cm -I were possible. They 25 noted that this was sufficiently large to explain the observations, but emphasized that their calculations "{'Permanentaddress: Department of Physics, College of Arts and Sciences, Shiraz University, Iran. Q.S.R.T. 40/I--A

l

2

B . R . LEwis et al

were extremely sensitive to the assumed potential curves, and that they had no ambition of fitting the scanty experimental data. Resonances in molecular photodissociation due to absorption into mixed states, such as the E3Z~ state of 02, may be treated theoretically by a full solution of the coupled Schr6dinger equations. This method has been applied, for example, to coupled 2//states in OH by van Dishoeck et al, 26 who also give a brief review of the technique. Torop et a127 have developed a similar treatment which has been applied by Wang et aF 8 to an interpretation of the temperature dependence of the 02 cross section in the region 1300-1600 A. The aim of the present work is to obtain detailed experimental cross sections for the (0-0) and (0-1) E - X bands of 1602, 160180 and 1802, so that accurate potential curves and coupling parameters may be deduced by comparison with the predictions of the coupled-equations model of Torop et al. 27 This fitting procedure will be discussed in detail in an associate work.13 Previously, cross sections have been measured only for 1602, and they are of insufficient detail 25 for an accurate determination of the theoretical parameters. The (1-0) and (24)) E - X bands will be discussed in a future work. 12 EXPERIMENTAL METHOD The experimental apparatus was similar to that used in our study of oscillator strengths and predissociation linewidths for the Schumann-Runge bands of isotopic 02. 29 36 Background radiation was provided by an argon continuum discharge lamp powered by a pulser based on the Argonne design. 37The lamp was operated in the windowless mode at a pressure of 400 torr of argon and a pulse repetition frequency of ~ 80 kHz. The radiation was dispersed by a modified 38 2.2 m scanning VUV monochromator, operating in the first or second order with F W H M resolutions of ,-~0.06 and ,-~0.04 .~, respectively. Radiation was detected photoelectrically before entering and after leaving the 10cm, controlled-temperature absorption cell. The scanning system and data collection were controlled by an IBM AT microcomputer. We studied three gas samples, 99.8% 160, 53% ~80, and 99% 180, the latter two being supplied by ICON. For a previous 20% 180 sample from another manufacturer, 32 it had proved necessary to dissociate the gas with radiation from a mercury lamp in order to achieve a statistical molecular mixture, but this procedure was not required for the ICON samples. The cell was filled from the gas cylinders through an electromagnetic leak valve to pressures in the range 0.01-10torr, monitored by a variable capacitance manometer. Cold traps used with the 1602 sample were not found to alter the measured cross sections, even in regions of low absorption. Their use was abandoned, therefore, for the 53% 180 sample, since repeated observations of the absorption spectrum implied a noticeable variation of the isotopic molecular composition in the cell when the cold traps were used. Scans were performed with cell temperatures of 295 and 79 K and with wavelength increments from 5 to 100 m/~, depending on the scale of the structure being studied. Wavelengths were calibrated by the NI lines present in the lamp spectrum. The longest band was studied at pressures near 0.01 torr, while the weaker structures were measured at pressures up to 10 torr. Corrections to the pressure for the effects of thermal transpiration were necessary at 79 K for pressures <0.05 torr. The magnitude of the correction was determined by measuring the temperature dependence of the effective 1602 Schumann-Runge continuum cross section at 1400 A, a wavelength where the actual cross section is known to have a very small temperature coefficient.39 A stray light correction of 0.4% and a small dark count correction were necessary also. For scans over a small wavelength range, empty-cell background ratios (detector/monitor) were taken at the initial wavelength before the scan, at the final wavelength after the scan, and were linearly interpolated at intermediate wavelengths. For longer scans, empty runs over the wavelength range of interest were taken before and after the full run, and were averaged to provide the reference background ratios. Using the known pressure, temperature, cell length and absolute transmission, absorption cross sections were calculated using Beer's law. Statistical errors in the cross sections, except in the case of very weak absorption, were normally ~<2%, with an extra ~ 2% uncertainty due to uncertainties in cell length, pressure, and temperature. Additional uncertainties arose in the case of the 79 K

Photodissociation of isotopic molecular oxygen--I

3

measurements because of increased temperature measurement error, thermal transpiration correction, and increased background drifts, but every precaution was taken to minimize these. Cross sections of 160180 were deduced from measured total cross sections for the 5 3 0 180 sample by performing a weighted subtraction using the known isotopic enrichments and the previously measured cross sections for the nearly pure 1602 and 1802 samples. This procedure, at some wavelengths, can produce 160180 cross sections with dramatically increased relative uncertainties due to the subtraction, but this occurs only over very limited wavelength ranges, and where the cross section is quite small. EMPIRICAL MODEL Although the E - X bands in 1602 are all diffuse, 14 and thus seem to offer no hope of rotational analysis, the remarkable appearance 15'16of rotational and fine structure in the longest band of 1802, and the rotational analysis o f Ogawa, 16 enable the development of an empirical band model from which it is possible to obtain some information on the behaviour of rotational linewidths and asymmetries, even for the diffuse bands. Spectroscopic constants for the X 3 X g state were taken from Veseth and Lofthus 4° and Steinbach and Gordy, 41'42for 1602, 1802, and 160180, respectively. These were used to generate the manifold of rovibrational levels for the ground state and the corresponding weighted Boltzmann factors. For 1802, except for D', spectroscopic constants for the v' = 0 level of the E3X~- state were taken from Ogawa) 6 The splitting constants 2 and/~ were taken as the same for all isotopes. Band origins for 160180 and 1602 were obtained by fitting the model absorption spectrum to our measurements. The remaining rotational constants B' were obtained from preliminary calculations of Wang, 4a normalized to the measurements of Ogawa 16 for 1802 . Centrifugal distortion constants D ' were calculated from the rotational constants for 1802 and an approximate value for to~, with appropriate isotope correction. 44 Line wavenumbers for v" = 1 were calculated from the v " = 0 wavenumbers and the known ground state energy levels. H f n l - L o n d o n factors were taken from Tatum and Watson 45 for 3X--3X- transitions with coupling intermediate between Hund's cases (a) and (b). The transformation coefficients were determined from the energy levels obtained previously. The forbidden NpI3 branch o f the (ff4)) E3~u-X3~gtransition, seen experimentally by Ogawa, 16 and also studied by us in this work, is well described by the mixed coupling factors. As we shall see later, the longest bands of all three isotopes are asymmetric, and there is clear evidence of absorption minima associated with one wing of each band. Therefore, we described each rotational line by a Fano 24 lineshape, given by F(E)

=

(q + E)/(1 + 22),

(1)

where (2)

E = (v - Vo)/r,

q is an asymmetry parameter, F is the H W H M linewidth, and v0 is the wavenumber of the line centre. Initially, F and q were assumed to be independent of rotation, but it was not possible to fit the experimental cross sections in this way. The model was generalized, therefore, to allow the linewidths and asymmetries to change systematically with rotation so that F ( J ' ) = Fo + F j J ' ( J '

+ 1),

(3)

and q ( J ' ) = qo + q s [ J ' ( J ' + 1)]2.

(4)

In reality, o f course, the variation of F and q with rotation is unlikely to be described by such simple expressions, and we experimented with other forms. Equations (3) and (4) were found to be the most appropriate two parameter expressions which were consistent with the measurements. The model band profile was built up by adding the Fano profiles of individual rotational lines at the positions and with the relative strengths determined by the technique described previously. The effects of interference between resonance profiles, allowed for some pairs of band branches, are expected to be small, for reasons similar to those given by Julienne 46 regarding predissociation

4

B . R . LEWIS et al 1.O

'

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(u-u) ~ ,

~

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g g

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0

0

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.;, i I

/~

t

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--~-*

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295

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79 K

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1244 Wavelength (A)

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u g a w a & Ogawa

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0.0 ,,. 1242

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•

u 2

/,I

"~..

o

'

i+

0.8 E

'

16 ~

x2O

\x

I~:I

1245

1252

1246

Fig. 1. Measured photoabsorption cross sections for the longest band o f t602 at room and liquid nitrogen temperature, together with the measurements of Ogawa and Ogawa, 4 and model cross sections (lines) generated with vo=80,382.8cm-1, f = 0 . 0 0 6 2 5 , F 0 = 5 . 6 c m i, F j = 0 . 0 1 8 c m - t , qo=-19.2, q j = 2 . 8 x 10 -5 .

of the B3Z2 state of 02. The overall band oscillator strength and the width and asymmetry parameters were determined by least-squares fitting the model cross section, after convolution with a Gaussian instrument function, to the experimental measurements. RESULTS AND DISCUSSION In Fig. 1, we present measured cross sections for the longest band of 1602 at 295 and 79 K, together with model cross sections calculated with a fixed set of parameters (v0 = 80,382.8 cm-l, f = 0.00625, F 0 = 5.6cm -I, F j = 0.018 cm -I, q0 = - 1 9 . 2 , q j = 2.8 x 10-5). The measurements of Ogawa and Ogawa 4 are in excellent agreement with ours provided that they are displaced by ~0.07 A towards shorter wavelengths. The observed cross sections are not resolution dependent since the rotational linewidths are larger than the rotational line spacing, but there is a substantial temperature dependence of the cross section since the linewidths are smaller than the extent of the band. The relative enhancement of the R branch at liquid nitrogen temperature occurs essentially because the H 6 n l - L o n d o n factors for the R branch exceed those for the P branch at low rotation. The band profile is noticeably asymmetric, with a stronger long wavelength wing, and structure reminiscent of a Fano minimum is evident near 1241 ~. The model cross sections generated with the single set of parameters listed previously are in excellent agreement with the measurements in all respects. The choice of Fano lineshapes in the model is vindicated by the observed asymmetry and the cross section minimum near 1241 ~, which is correctly reproduced by the model at both temperatures. As mentioned previously, if the linewidth is taken to be independent of rotation there is a noticeable systematic discrepancy between the observed and fitted cross sections. Despite the diffuse nature of this band, there is clear evidence from the model that the linewidth increases strongly with rotation. Although the cross section near the band centre is relatively insensitive to the asymmetry parameter q, it is possible to accurately determine this parameter by fitting in the wings of the band. Using model simulations, the values of q found by this method at each temperature can be associated with an effective rotation. The functional form given previously for the variation of q with rotation, Eq. (4), is then fitted to the results. The value of qj obtained by this technique, while being somewhat uncertain, indicates unambiguously that rotational lines in the longest band of 1602 become more asymmetric for high values of rotation.

Photodissociation of isotopic molecular o x y g e n - - I 1.5

,

,

,

,

[

,

,

,

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I

(0-0) ~802 ~

i!

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--*x--

79 K

'}

1.0

'

5

x50

g ~ 0.5

0 . 0 --L 1~43.5

1244.5

~245.5 Wavelength

t246.5

~47.

(A)

Fig. 2. Measured photoabsorption cross sections for the longest band of !802 at room and liquid nitrogen temperature, together with model cross sections (lines) generated with v0 = 80,286.3 cm -!, f = 0.00629, F 0 = 1.7 cm -t, F j = --0.0028 cm -~, q o = 41, q : = 1.9 x 10 -4. The room temperature spectrum was taken in the second order (0.04 A F W H M ) .

In Fig. 2, we present measured effective cross sections for the longest band of 'so2 at 295 and 7 9 K , together with model cross sections calculated with a fixed set of parameters (v0 = 80,286.3 c m - l , f = 0.00629, F0 = 1.7 cm -1, Fj = --0.0028 cm -l, q0 = 41, qj = 1.9 x 1 0 - 4 ) . The observed cross sections are resolution dependent. The room temperature measurements were taken in the second order (0.04 A, F W H M ) , while the liquid nitrogen temperature results were taken in the first order (0.06/~ F W H M ) . Although the general characteristics of the 1802 cross sections are similar to those for 1602, there are three obvious differences. Firstly, the rotational structure seen in Ogawa's platd 6 is also seen in our cross sections; secondly, the observed asymmetry is smaller than, and in the opposite sense to, that observed in '605; thirdly, the Fano minimum appears on the long wavelength side (,~ 1247/~,), compared with the short wavelength side ( ~ 1241/~) for 1602 . Detailed first order cross sections near the minimum are given in Fig. 3. Part of the forbidden NP13branch also occurs in this region. I

•

!

~

13

m

,z

19

21"p

• I

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c.)

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1246

i

i

i

i

I

I

I

I

1247 Wavelength

I

i

1248 (A)

I

1249

Fig. 3. Measured photoabsorption cross sections near the F a n o m i n i m u m for !sO2 at room and liquid nitrogen temperature. Individual rotational lines from the forbidden NP~3 branch are indicated.

6

B . R . LEw]s et al

I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' '

(o-0) 180 2

•

R

•

branch

R branch N

•

P,3

branch

295

K

79 K 295

K

'E 0 E J== v L

0

, 0

,

,

,

I 5

i

i

J

i

I :10

i

i

t

,

I 15

j'

,

,

,

,

i 20

,

L

I

I

I

I

i

I 25

i

i

i

i 30

Fig. 4. Rotational linewidths for the longest band of ~802, obtained from the R branch structure at room and liquid nitrogen temperature, and the forbidden sP~3 branch at room temperature. The solid line indicates the fitted model rotational linewidth.

The model cross sections generated with the single set of parameters listed previously are in good agreement with the measurements except in the more distant wings. More direct evidence of the variation o f linewidth with rotation is obtainable in the case of 1802. The linewidths in Fig. 4 were obtained by fitting individually to small regions of rotational structure in the R branch, and by deconvoluting the instrument function from first and second order spectra of the NPI3 branch. The lines of the ~¢P13branch are single, and are broader than even the first order instrument function. The solid line in Fig. 4 represents the model width function assumed for the longest band of 1802. The previous functional form, Eq. (3), is used for J'~< 19, and the width is held constant for J ' I> 19. Widths which are significantly less than the instrumental width are difficult to determine accurately, and thus those for J ' t> 19 have a large relative uncertainty. Nevertheless, it is clear that the linewidth decreases strongly with rotation for lSO2, opposite behaviour to that deduced for 1602. Because o f the smaller asymmetries for ~sO2, the values deduced for q are less accurate than those for ~602 but, using the method described previously, we have ascertained that the rotational asymmetry decreases with rotation for ~802, once again opposite behaviour to that observed for 1602 .

It is clear from Fig. 2 that the model overestimates the cross section in the short wavelength wing and underestimates the cross section in the long wavelength wing. The structures near 1238 and 1253/~ are forbidden bands, which we shall ignore for the purposes of this discussion. It is possible to optimize the fit for each wing separately, but the corresponding best values of q exhibit a small systematic difference. This may be interpreted as a breakdown of the applicability in the wings of a Fano lineshape which assumes energy-independent q, F, and continuum. It should be noted that, in the case of the wings for ~802 at _+ ,-~5 ~ from band centre, the dimensionless energy parameter E ~ 200, while for 1602 E ~ 60. We could not find a single set of parameters which resulted in model cross sections in agreement with the observed room and liquid nitrogen temperature cross sections at the minimum near 1247 A, but we could obtain the correct relative behaviour at a level of cross section less than that observed. This suggests that there may be a non-negligible contribution to the cross section in this region from another state, the 3H, valence state, for example. In Fig. 5, we present measured cross sections for the longest band of 160~80 at 295 and 79 K, together with model cross sections calculated with a fixed set of parameters (% -- 80,334.4 cm t, f = 0.0061 l, F0 = 0.90 cm -1, Fj = 0.0064 cm -I, qo = - 4 5 , qa = 6.1 x 10 5). The data have been obtained from raw cross sections for the 53% 1sO mixture, corrected for the previously determined contributions of ]602 and lSO2. As a result, the reduced cross sections are less accurate in some

Photodissociation of isotopic molecular oxygen--I 1.5

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r

,

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1

,

I

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'

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3 - O) ~6 018 0

•

....

,,, E

t

I ~lx

x

i J.235

0 . 0

-

~242

i

.

.

.

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'

'

I

I

;

2

'

x

~

m 0.5 u'l 0

'

~ 'l

g o (D o3

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295 K IJ 79 K'[

I

x50

"1.0

'

7

i

. . . .

J.240

i 1.245

....

;g;..

,

;;

2

"

1243

1245 1244 Wavelength (A)

1246

247

Fig. 5. Measured photoabsorption cross sections for the longest band of 160180 at room and liquid nitrogen temperature, together with model cross sections (lines) generated with v0 = 80,334.4cm-% f=0.00611, F0=0.90cm -t, £ j = 0 . 0 0 6 4 c m - % q o = - 4 5 , q j = 6 . 1 x 10 5.

wavelength regions than those for the homonuclear molecules, and weak artefacts can appear due to uncertainties in wavelength registrations and isotopic abundances. There is no rotational structure visible in the 16OI80 cross sections, and the general characteristics are similar to those for 1602. There is a weak asymmetry, with a stronger long wavelength wing, and a weak Fano minimum near 1243 .~,. The depth of the cross section minimum between the R and P branches is greater for 1601so than for either of the homonuclear molecules. This implies that the rotational linewidth for 16OlSO, at least near the band head, is smaller than that for 1602 and 1802. Rotational structure is not seen in the cross section because, due to the occurrence of even, as well as odd rotational levels in the ground state, there are twice as many rotational lines in the spectrum of 160180 as there are for 1602 or 1802, with a correspondingly closer line spacing. We could not detect rotational structure, even in a second order scan, but such a structure should be readily observable near the band head with a higher resolution experiment. The model cross sections generated with the single set of parameters are in quite good agreement with the measured cross sections except in the more distant wings, as observed for 1so 2. We find that the rotational linewidth increases with rotation, but the values of Fo and Fj are quite uncertain, both because most rotational linewidths are significantly less than the instrumental width, and because of the poorer quality data for 160180. The model overestimates the cross section of the stronger wing, and underestimates that of the weaker wing, just as we observe for 'so 2. The dimensionless energy parameter + ,-, 5 ,~ from band centre is E = 360 for 160180. In Fig. 6, we present the measured cross section in the region of the (0-1) band of ~602 at 295 K, together with the measurements of Ogawa and Ogawa. 4 We fitted a cubic polynomial to the background cross section and subtracted this from the data in order to estimate the contribution due to the (0-1) band alone. This result is given also in Fig. 6, together with a model prediction based on the parameters given earlier for 1602, with the exception that the oscillator strength f = 0.0112. The agreement is seen to be excellent. The asymmetry parameter q for the (0-1) band may be different from that for the (0-4)) band, but it is not possible to obtain a significant value of q by fitting to the (0-1) data since it is difficult to separate the background cross section from the (0-1) band wings. In any case, the difference does not appear to be great. In Fig. 7, we present measured total and reduced first order cross sections in the region of the (0-1) band of 1802 at 295 K, together with a model prediction using the parameters given previously for 1so 2, but with an oscillator strength f = 0.0112. This spectral region is complicated by the adjacent (2-0) band of the f o r b i d d e n f l 3 ~ + - X 3 z ~ g transition, but we were able to determine the oscillator strength by fitting to the P branch only. The degree of structure in the R branch is well predicted by the model.

8

B . R . LEwis et al 2,0

i

,

,

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f

i

(0--t)

,

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1602

i

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i

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~..0 •

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°o.5 (.3

. 0.0 1265

. . . . .

.

1267

.

.

.

.

1269 t271 Wavelength (A)

.

.

.

.

1273

1275

Fig. 6. Measured room temperature photoabsorption cross section near the (0-I) band of J602, together with the measurements of Ogawa and Ogawa. 4 The cross section obtained by subtracting the background is also shown, together with a model cross section (line) generated with the parameters of Fig. 1, but with f = 0.0112.

For completeness, we present in Fig. 8 total and reduced cross sections in the region of the (0-1) band of ~60~80 at 295 K, together with a model prediction based on the parameters given previously for ~60180, but with an oscillator strength f = 0.0105. The necessity to subtract the contributions of the homonuclear molecules, as well as the continuum, from the raw data, leads to a quite scattered reduced cross section, but the agreement between the measurements and the model is good. In particular, the cross section minimum between the P and R branches is deeper than for either of the other isotopes. Figure 9 summarizes the rotational widths obtained from the model fits to the measurements of this work. The experimental points were obtained by fitting a constant width to the strongest parts of the (0~)) bands for 1602 and 1 6 0 1 8 0 at 295 and 79 K. The corresponding effective values of rotation (,~ 5 at 79 K, ~ 10 at 295 K) were deduced by model simulations. The experimental points are consistent with the model widths based on the chosen functional form, Eq. (3). Individual widths for ~sO2 are given in Fig. 4.

dp

(2-0) f3-X E

."".

o

;

x x

"" ~,

.:

02 295 K

:

'C)

.:. j: u3

: : , ,

..

0

I 0 1264

1265

1266

1267 1268 1269 Wavelength (A)

1270

1271

1272

Fig. 7. Measured room temperature photoabsorption cross section near the (0-1) band of ISO2. The background-subtracted cross section includes the (2-0) band of the flLS.+-X3~[ transition and is compared with a model cross section (line) generated with the parameters of Fig. 2, but w i t h f = 0.0112.

9

Photodissociation of isotopic molecular oxygen--I 3

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"-.';,,.-'~,

~.266 ~.267 ~268 ~,269 J.270 ~.27~- 1272 Wavelength (,g,)

Fig. 8. Measured room temperature photoabsorption cross section near the (0-1) band of ~60~80. The background-subtracted cross section is compared with a model cross section (line) generated with the parameters of Fig. 5, but with f = 0.0105.

Figure 10 summarizes the limited amount of data on the variation with rotation of the asymmetry parameter q. In this case, the experimental points are the only data available. Except in the case of J602, where it is possible to obtain a reasonable value for q from the strong region of the band, the points in Fig. 10 result from fits to the wings. The corresponding effective values of rotation, deduced by model simulations, depend both on the actual form of the rotational dependence of q, and also on the distance of the fitting region from the band centre. Equation (4) was fitted to the experimental data to give the model parameters qo and qj. Because of the interaction between the chosen functional form and the effective rotations, the values of qj are very uncertain, but the general behaviour of q with rotation is clear. The most strongly varying asymmetry occurs for ~gO2, where the narrowest lines are nearly symmetric. The systematic difference between q values obtained from the Fano minimum region and the stronger wing, for both ~802 and '60'sO, is clear in Fig. 10. The relative behaviour with rotation, however, is similar for each region. 15

I

I

I

I

I

'E {_}

16

[_

u 18@ / -

5[

) .......... t . 1 0

5

~.0

o 15 j'

20

25

30

Fig. 9. A summary of rotational widths for the longest band of isotopic 02. The lines represent the best model fits to the measurements, with F ( J ' ) = F o + F j J ' ( J ' + l), while the points are effective widths fitted to the 79 and 295 K measurements, with F ( J ' ) = constant. The full data for ~80: are given in Fig. 4.

10

B.R. 70

I

50

..........

LEWlS et al

I

t. . . . . . . .

I

"

L';

~

I

18

"

x wing

0 2

II

• min

30

• band

:10 o-~

...................................

i6 ......................

,

-:10

-30

-50

I 5

-70 0

I '10

I '15

I 20

I 25

30

j'

Fig. 10. A summary of rotational asymmetries for the longest band of isotopic 02. The points are effective values of q fitted to 79 and 295 K cross sections near the band centre, the strong wing, or the Fano minimum, w i t h q ( J ' ) = constant. The lines are best values of the function q ( J ' ) = qo + q J [ J ' ( J ' + 1)]2 fitted to the data points.

From Figs. 9 and 10, we see that F and q vary with rotation in an inverse fashion, and, indeed, the product IqlF°5,,~50cm -°5, within experimental error, independent of isotopic mass or rotation. This type of behaviour is to be expected if a Fano profile with energy-independent parameters is applicable. From Fig. 10 the maximum variation in the effective value of q across the resonance is only ~ 15%. In Table 1, we have summarized the spectroscopic constants, oscillator strengths, widths, and asymmetries obtained from our measurements of the (0-0) and (0-1) bands of the isotopes 1602, 160~sO and 1802. Using the tabulated parameters together with our model, it is possible to generate accurately the (0-0) and (0-1) cross sections for all isotopes to a distance of several/~ from the band centres. Our measured osci!lator strengths show no significant isotope effect for either the (0-0) or (0-1) bands, but the (0-1) oscillator strength is nearly twice that of the (0-0) band. The only previous measurement of oscillator strength for these bands is from the electron energy loss

" ' ' ' 1 ' ' ' ' 1 ' ' ' ' 1

'

I

'

'

,

,

I

'

'

'

'

I

'

'

'

'

16 -

A ~E

3

'o

O3

02 160180 18

. . . . .

0 2

:1260

1270

• i,~~ 2

£D

-

....

295 K

-i', i', i' i

t

i

i

0

Q)

0 12:10

1220

:1230

:1240

Wavelength

1250

1280

(/~)

Fig. 11. Measured room temperature photoabsorption cross sections for isotopic 02 in the range 1210-1280A, emphasizing the isotopic shifts, the Fano minima, and the oscillatory behaviour of the continuum.

Photodissociation of isotopic molecular oxygen--I

11

Table 1. A summary of the results of this work. Band origins, widths, asymmetries, and oscillator strengths which include error estimates have been determined by fitting an empirical model to the measured cross sections. Values refer to the (0-0) band of the E3Z£-X3Z~ transition unless otherwise indicated. Other spectroscopic constants for the upper level of this transition are also given. Units are cm -~, except for qo, q J, and f , which are dimensionless. 1602

160180

1802

vo

80382.8±1.0

80334.4±1.5

80286.3 %

B'

1.470~

1.3838 ~

1.3072

D'

1.93xi0 -6§

1.66xi0 -6§

1.47xi0 -6§

-3.3725 %

-3.3725 %

-3.3725 %

0.045 +

0.045 %

0.045 %

F0

5.6±0.4

0.9±0.4

1.7±0.2

Fj

(1.8±0.3)xi0 -2

(6.4±2.6)xi0 -3

-(2.8±0.3)xi0 -3

qo

-19.2±1.0

-45±8

41±4

qj

(2.8±0.8)xi0 -5

(6.1±3.0)x10 -5

(1.9±0.7)xi0 -4

f(0-0)

(6.25±0.08)xi0 -3

(6.11±0.16)xi0 -3

(6.29±0.08)xi0 -3

f(0-1)

(Ii.2±0.5)xi0 -3

(i0.5±0.8)xi0 -3

(ii.2±0.5)xi0 -3

%

M e a s u r e m e n t s of a s s u m e d for l' t Calculations of (Close to values correction 44 to

%

Ogawa. 16 Zero isotope effect is ~' Wang, 43 normalized to B' for 1802 . obtained by applyin~ an isotope the measured B' for ±~02.)

C a l c u l a t e d from B' for 1802 and aproximate v a l u e for ~e, with appropriate isotope correction. 44 M e a s u r e d D'=l.8xl0 -5 for 1802.16

measurements of Huebner et al, 2~ who obtained the value 0.010 for the oscillator strength of the longest band of '602 . The optical values are to be preferred. R o o m temperature cross sections measured at 1 A intervals for the three isotopes are presented in Fig. 11 from 1210 to 1280 ,~. The Fano minima are apparent in each case, but it is clear that a simple Fano profile model is not consistent with the observed peaked continuum between ~ 1220 and 1270 ,~. Distorted Fano profiles which allow for the energy dependences of F, q and the continuum, such as those discussed by Bandrauk and Laplante, 47'~ will be needed in order to explain the more distant wings of the resonance, and adjacent resonances, such as the (1-0) band, will have to be considered, but we will not pursue these aspects here. A theoretical intepretation of the spectrum in this region, using coupled Schr6dinger equations, will be given in an associate work.'3 CONCLUSIONS We have presented the most detailed photoabsorption cross section measurements available for the (0-0) and (0-1) bands of the E3Z£-X3Z~ - transition of '602, and the first such measurements

12

B.R. LEWISet al

for 1802 and 160180. The bands exhibit significant broadening and asymmetry, strongly dependent on isotopic mass, due to configuration interaction. An empirical band model, based on Beutler-Fano lineshapes, is capable of accurate cross section prediction out to several ,~ from the band centres, including minima observed in the wings of the longest band for all isotopes. Although the resonance phenomenon arising from interacting molecular states is quite general, asymmetric Fano profiles in molecular photodissociation have been observed previously only for H2 in absorption, 49-53 and O D in emission) 4'ss Berkowitz 37 notes this paradox and discusses some possible explanations. It is clear from our work that the longest band of 02 provides a second classical example of a Beutler-Fano resonance due to predissociation in photoabsorption. The rotationally smeared Fano minimum of the band falls fortuitously in a region of the spectrum which allows ready observation. With the aid of our empirical model, we have obtained band origins, oscillator strengths, rotational linewidths and asymmetries. Our measurements provide the first optical oscillator strengths for these bands. We find no isotope effect, and our oscillator strength for the longest band of 1602 is significantly less than the electron-impact value. 21 Directly, in the case of 1802, and from the model otherwise, we find that linewidth changes strongly with rotation, and that the asymmetry parameter changes in an inverse fashion such that I q l F ° S ~ 5 0 c m 0.5, almost independent of isotopic mass or rotation. The (1-0) and (2-0) bands of the E3Z~-X3ff, g transition will be discussed in a future work. 12

Acknowledgements--The authors would like to thank C. Dedman and K. Lonsdale for valuable technical assistance. We are also grateful to A. Dalgarno, A. Blake, D. McCoy, L. Torop, and J. Wang for illuminating discussions on resonances in molecular photodissociation. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.

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Photodissociation of isotopic molecular oxygen--I

13

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