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Line-shape asymmetry of water vapor absorption lines in the 720-nm wavelength region
J. Quant. Spectrosc. Radiat. TransferVol. 45, No. 6, pp. 339-348, 1991 Printed in Great Britain.All rights reserved
0022-4073/91 $3.00+ 0.00 Copyright © 1991 PergamonPressplc
LINE-SHAPE ASYMMETRY OF WATER VAPOR ABSORPTION LINES IN THE 720-nm WAVELENGTH REGION BENOIST E. GROSSMANN~" ST Systems Corp., 28 Research Drive, Hampton, VA 23666, U.S.A. EDWARD V. BROWELL NASA Langley Research Center, Atmospheric Sciences Division, Mail Stop 401A, Hampton, VA 23665, U.S.A. (Received 5 September 1990)
Abstract--Spectral line-shape analyses were performed for water vapor lines broadened by argon, oxygen, and xenon in the 720-nm wavelength region. A line-shape asymmetry was observed, which is attributed to statistical dependence or correlation between velocity- and state-changing collisions. The generalized (asymmetric) Galatry profile, which results from the soft-collision profile and includes correlation between velocity- and state-changing collisions, was fitted to the observed line shapes and was found to compare favorably with the observed data. The most prominent asymmetries were observed with xenon as the buffer gas.
INTRODUCTION
In earlier papers, 1'2 we reported high-resolution spectroscopic measurements of water-vapor lines broadened by air, nitrogen, oxygen, and argon. Several spectral profiles, including the Voigt, the soft- and the hard-collision profiles, were used to fit the observed lineshapes. Both Dicke-narrowed spectra (i.e., soft- and hard-collisions) were found to compare favorably with the measured cross-section functions. All these spectral profiles were symmetric about a central (possibly shifted) frequency. Rautian and Sobel'man 3 have shown theoretically that the spectral line shapes become asymmetric if the effect of statistical dependence or correlation between velocity- and statechanging collisions is included and if the line shift is non-negligible. Pine and Looney* have reported in a recent study, asymmetric HF absorption lines broadened by argon, which they attributed to cross-correlations between velocity- and state-changing collisions. In the present study, we report measurements of the pressure-broadening and pressure-shift coefficients for 41 water vapor lines broadened by xenon in the 720-nm wavelength region. We have studied the line shapes and found asymmetric residuals of the order of 2% (expressed in percent of the absorption cross-section at the line center) when compared with either of the Dicke-narrowed spectra. Such asymmetries were observed also for oxygen- and argon-broadening but to a lesser extent (0.5%). The generalized Galatry profile, which results from the soft-collision profile and includes correlations between velocity- and state-changing collisions (i.e., asymmetric profile) was fitted to the observed line shapes and was found to compare very well with the observed spectra. Characteristically, the asymmetry is evident in the strongly narrowed regime for which the pressure-shift is large compared to the pressure-broadening. We have also generated synthetic Voigt, generalized Galatry, and Dicke-narrowed profiles, and the deviations between these profiles were found to be in good agreement with the experimentally observed deviations. EXPERIMENTAL DETAILS Only a brief review of the experimental setup will be presented in this paper since a detailed description was given previously.l'2 The high-resolution spectrometer system consists of a cw ring ~Present address: Thomson CSF/DAO, 78283 Guyancourt Cedex, France. 339
340
BENOIST E. GROSSMANNand EDWARD V. BROWELL ABSORPTION CRO888ECTION :~' I LINEWIOTH :Y J LINE STRENGTH :S I PRESSURE EHIFT :~ i TEMPERATURE COEFFICIENT: n J i
HARD DISK J 40 M BytesI
I
COMPUTER
t
WM'TI IcEL.1
:
compacl 386
PLOTTER
HIGH PRESEURIE PHOTODIOOE8 FILTERS
R SCAN
"k calibration" J
~
-OW EESURE
I I
I
WAVE-Rm
I
t t
oYe LASER J
RGON LASER
J
Fig. 1. Schematic of the simultaneous absorption spectroscopy experiment.
dye laser in conjunction with two multipath absorption cells. The two White cells can be operated in parallel to avoid any laser frequency drift during pressure-induced line shift measurements. Details of the setup are given in Fig. 1. Relative frequency calibration was obtained by using an external Fabry-Perot interferometer with a free spectral range of 0.016 cm-t in parallel with the two absorption cells. The same amount of water vapor (15 torr) was introduced in both White cells by evaporating distilled water contained in a temperature-controlled flask connected to the manifold. Measurements were made with the foreign gas pressure ranging from 50 up to 1000 tort. Each scan of the laser produced three spectral traces (the Fabry-Perot transmission curve and two absorption profiles). We have represented in Fig. 2 a typical recording of xenon-broadened water vapor lines. The water vapor pressure was 15 torr for both White cells with the addition of 420 torr of xenon in one of the cells. Pressure-shift and pressure-broadening due to the buffer gas (e.g., xenon) were easily observable. The Fabry-Perot fringes (bottom trace in Fig. 2) were used to linearize the scan of the dye laser over the scan range (up to 2 cm- 1 ). A least-squares fitting routine was used to extract for each water vapor (H20) absorption line the linewidth and the central frequency. The Lorentzian or pressure-broadening component was deduced for each line through the measured Voigt halfwidth using the expression obtained by Olivero and Longbothum.5 The broadening coefficients were then corrected to take into account the Dicke-narrowing effect. A more complete description of the data reduction process can be found in Refs. 1 and 2. ANALYSIS OF PRESSURE-BROADENING AND PRESSURE-SHIFT COEFFICIENTS Table 1 lists the pressure-broadening and pressure-shift coefficients for 41 water vapor lines between 13,600 and 13,900 cm-l (720-735 nm), normalized to 296 K, with xenon as the buffer gas.
Line-shape asymmetry of water vapor absorption lines
H20 Pressure 3
Spectrum
In Xenon
i3704.180e era--!
Cell #i: 15 t o r t H20 Cell #~ 15 t o r t H20 + 420 torr Xe Febry-Perot FSR = 0.0t6 cm-i
E 0 4J L) q) tn
Shift
341
0.5
(0 @1 O t.. U
~~
R e l a L i v e W8venumber
~13704.5385 cs-t
( FSR ,, 0.016 em-I I
Fig. 2. Simultaneous recording of water vapor absorption lines at two different pressures. The lower trace represents the spectral throughput of a Fabry-Perot interferometer. The spectra have been normalized for clarity. Pressure-broadening and pressure-shift due to xenon are observable.
The broadenings and shiftsin oxygen and argon can be found in Ref. 2. A temperature power law dependence of T -°7 was used to normalize the data to 296 K. Because the measurements were obtained at temperatures close to 296 K (typically 300-305 K), the temperature corrections were very smaU and relatively insensitive to the exponent value. The line-center positions and the rotational and vibrational assignments were taken from Mandin's data 6 and arc specified in the same manner. The xenon pressure-broadening coefficients range from 0.0792 up to 0.0958 crn-I/atm with an average value of 0.0878 era-I/arm. The average value is comparable to the air- and nitrogen-broadening coefficients? W c have represented in Fig. 3 the measured xenon pressure-l~roadening coefficientsas a function of the rotational quantum number J. As indicated in Fig. 3, the decrease of the broadening coefficients as a function of J was not observed, which is in contrast with our previous measurements of self-,air-, nitrogen-, oxygen-, and argon-broadening coefficients? However, we believe this effectcan be attributed to the sample of measured water vapor lines (the measurement was conducted only for the strongest H 2 0 lines with the average line strength investigated in this study being I I x 10 -24 cm~/molecule.cm-~). The pressure-shift coefficients were found to bc negative for all of the lines investigated. The measured values ranged from -0.0269 up to -0.0668 crn-I/atm with an average value of -0.0360cm-~/atm. In order to check the accuracy of our measurements, the broadening and shifts were measured as a function of xenon pressure in the range 130-1000 torr for several H 2 0 absorption lines. N o significant deviations from the expected linear relationship were observed.
COLLISIONAL NARROWING MODELS We have used several spectral profiles to perform least-squares fitting of the observed line shapes. We first used a Voigt profile which results from the convolution of a Gaussian (i.e., Doppler component) and a Lorentzian (i.e., pressure broadening component). We have represented in Fig. 4 the deviations between the fitted Voigt profile and the .measured cross sections functions (left column) for the water vapor line centered at 13,718.5762 crn-' with xenon pressure ranging from 130 to 740 torr. As observed in Fig. 4, the residuals from the (symmetric) Voigt profile
342
BENOIST E. GROSSMANNand EDWARD V. BROWELL Table 1. Spectroscopic data for H20 absorption lines broadened by xenon wavenumber
JKaKc'
JKaKc
v'
cm-i
13,662.5022 13,663.2901 13,688.8686 13,703.1088 13,704.1808 13,704.5385 13,717.1747 13,718.5762 13,728.1798 13,737.4161 13,738.4401 13,741.1540 13,761.5888 13,763.8874 13,764.6747 13,774.2119 13,775.2987 13,783.1795 13,783.8760 13,784.7849 13,797.5367 13,801.2788 13,801.7317 13,815 1226 13,815 7375 13,818 4083 13,819 0491 13,821 9097 13,823 1814 13,839 6550 13,853 2706 13,866 7312 13,872 6818 13,882 7586 13,884 0365 13,884 3369 13,888 0804 13,890 0672 13,890 4020 13,894 6350 13,897 1062
524 221 413 330 331 660 312 322 404 313 313 220 212 414 212 ii0 542 i01 533 iii 431 331 330 633 221 220 321 iii 422 211 i01 212 202 313 322 331 303 615 313 431 414
625 220 514 431 432 661 413 423 303 414 404 321 313 413 303 211 541 202 532 212 432 330 331 532 220 221 322 Ii0 423 212 000 iii i01 212 221 212 202 616 202 330 313
301 221 301 301 301 301 301 301 221 301 202 301 301 301 202 301 301 301 301 301 301 301 301 221 301 301 301 301 301 301 301 301 301 301 301 221 301 301 202 301 301
Gamma
Shift
Xe
Xe
cm-i/atm
cm-I/atm
0.0958 0.0792 0.0937 0.0837 0.0832 0.0846 0.0978 0.0911 0.0891 0.0874 0.0856 0.0881 0.0848 0.0876 0.0851 0.0891 0.0816 0.0864 0.0838 0.0897 0.0844 0.0895 0.0856 0.0834 0.0939 0.0935 0.0917 0.0854 0.0844 0.0866 0.0844 0.0854 0.0935 0.0907 0.0873 0.0895 0.0913 0.0885
-0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0
0386 0331 0353 0430 0439 0668 0379 0359 0348 0300 0374 0392 0296 0290 0290 0345 0512 -0 0284 -0 0410 -0 0291 -0.0433 -0.0431 -0.0439 -0.0431 -0.0335 -0.0343 -0.0369 -0.0269 -0.0359 -0.0307 -0.0296 -0.0293 -0.0332 -0.0329 -0.0317 -0.0321 -0.0332 -0.0337 -0.0327 -0.0408 -0.0274
Note. For each line, we give the wavenumber of the transition (cm-1); the rotational assignment of the upper and lower levels of the transition; the u p p e r s t a t e vibrational assignment and the pressure-broadening and pressure-shift coefficients in xenon (cm-1/atm). Columns 1-4 were taken from Mandin et al. (Ref.6). All results are normalized to T = 296 K.
are asymmetric, which in turn, implies an asymmetric spectral line shape for the absorption line. The asymmetry appears to be less pronounced toward lower xenon pressures. In the limiting case with Px, = 0 (i.e., pure water vapor), the spectral profile is symmetric. Care was taken to ensure that the observed asymmetries were not due to instrumental effects such as laser scan non-linearity [any laser scan non-linearity effects would have produced a similar asymmetry for the low-pressure spectrum (i.e., pure water vapor), and such effects were never observed]. Also, the deviations reported in Fig. 4 were found to be typical of any xenon-broadened water vapor absorption lines. A Galatry profile or soft-collision profile was then used. The analytical expression for the shape of this profile (denoted by G) is given by 7'8
l(fy{
G ( x , y , z ) = - - ~ Re
exp
-ix'r - y r +
[1 - z r - e x p ( - z r ) ]
}) dz
(1)
Line-shape asymmetry of water vapor absorption lines
343
X E N O N - B R O A D E N I N G vs J
0.100 0.098 0.096 A
E
0.094
"7
0.092
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0.090 C O "O
0.088
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0.086
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0.084 i 0.082 0.080
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6
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8
Rotational quantum number J
Fig. 3, Average xenon-broadening coefficients as a function of rotational quantum number J. +3%
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Fig. 4. Results of lcast-squares fitting to the Voigt profile (left) the soft-collision profile (middle), and the generalized Galatry profile (right) for the H20 line centered at 13,718.5762cm -m for various xenon pressures. Deviations are expressed in percent of the absorption cross-section at the line center. The horizontal scale is given for each spectrum by the two vertical bars which correspond to one FWHM.
344
BENOISTE. GRO~MANNand EDWARDV. BROWELL
where x = (w - Wo)/FD, y = F L / F o and z --- [3/Fo. Here w is the frequency or wavenumber referred to the shifted line center frequency w0; Fo represents the Doppler halfwidth at 1/e intensity (~0.024 cm -I); FL is the pressure-broadening component (cm-I), 13 is the effective frequency of velocity-changing collisions (cm- t ), and z is a dummy variable. The parameter y is usually referred as the Voigt parameter. We have represented in Fig. 4 (middle column) the deviations between the fitted Galatry profile and the experimentally-measured profile. The residuals are again asymmetric because the Galatry or soft-collision profile is symmetric. The collisional narrowing coefficient ~ / P was measured to be 0.05 cm-t/atm for the absorption lines under study when using a simple Galatry profile. The coefficient f l i P was measured to be constant as a function of pressure, which is consistent with our previous measurements of self-, nitrogen-, oxygen-, air-, and argon-broadened H 2 0 lines, t'2 It is interesting to note in Fig. 4 that the residuals from the Voigt and soft-collision profiles become similar toward higher pressures. This result is expected since at high pressures the contribution of Doppler broadening will become negligible compared with collision broadening. Hence the reduction of Doppler broadening effected by velocity-changing collisions makes a negligible correction to the line shape. We also used the hard-collision profile for line fitting and it produced similar deviations as compared to the soft-collision profile but with smaller collisional narrowing coefficients ( ~ - 2 0 % ) . These effects were observed and analyzed previously) '2'4 We did not show these deviations because they are indistinguishable from the soft-collision fits. LINE-SHAPE
FITS
TO THE
GENERALIZED
GALATRY
PROFILE
A generalization of the Galatry profile is obtained by including the effects of statistical correlation between velocity- and state-changing collisions, i.e., assuming that velocity and state perturbations occur simultaneously while also assuming that the magnitude of the changes are uncorrelated. 3 The analytical expression for the generalized Galatry profile denoted by H is given by 8 H ( x , y, z , ~ , s) = G ( x , y, Z);
Z = z(1 - y / ~ ) - i s z / ~ .
(2)
Here, s represents the standardized line-shift parameter defined by s = 6/FD where 6 is the line shift of the absorption line (cm-l), and ¢ is an additional parameter defined as the total collision frequency parameter: The asymmetry of the absorption line is caused by the imaginary part of the collisional narrowing parameter Z appearing in the generalized Galatry profile analytical expression [Eq. (2)]. Therefore, the asymmetry will be more prominent for absorption lines associated with large pressure-induced line shifts and large collisional narrowing parameters. This statement explains the rather large asymmetry observed with the xenon-broadened H20 lines as opposed to the nitrogen-, oxygen-, and argon-broadening. 2 For absorption lines for which the line shift is negligible (s = 0), the generalized Galatry profile is mathematically identical to a simple (symmetric) Galatry profile with a reduced narrowing parameter given by Z ( s = O) = z¢rr= z(1 - y l ~ ) .
(3)
We have presented in the right-hand column of Fig. 4 the deviations between the fitted generalized Galatry profile and the measured line shapes. The agreements between these two profiles are satisfactory with the residuals being within the measurement uncertainties for xenon pressure < 530 torr. For pressure > 530 torr, the generalized Galatry profile was unsuitable to fit correctly the observed spectra. No physical reasons were found to explain this behavior. The best-fit routine was rechecked to ensure that the computer codes did not introduce a bias when dealing with the broader absorption lines. Similarly, a generalization of the hard-collision profile can be obtained by including dependence between velocity-changing and state-perturbing collisions. 3's However, this type of profile was not evaluated because it involves additional parameters and lengthy computer calculations.
Line-shape asymmetry o f water vapor absorption lines
345
COLLISION F R E Q U E N C Y P A R A M E T E R / P R E S S U R E 5 -
13718.5762 ¢ m ' I
•e- 3
1
0
I
I
I
I
I
I
0.2
0.4
0.6
0.8
1.0
1.2
X e n o n pressure (atm) Fig. 5. The total collision frequency parameter ~ as a function of xenon pressure. The straight line is a result of a simple linear least-squares fit.
Nevertheless, we believe that the generalized hard-collision profile would yield results quite similar to the generalized Galatry profile. In the least-squares fit routine, the total collision frequency parameter 4} appearing in Eq. (2) was measured to be a linear function of pressure. We have presented in Fig. 5 the measured total collision frequency parameter 4) as a function of xenon pressure. This relationship can be approximated by the following best-fit linear relationship: = 3P + 0.7,
(4)
where P is the xenon pressure (atm). It is not known if the constant appearing in Eq. (4) is real or if it is due to an artifact of the fitting procedure. For a valid collision model, the total collision frequency parameter ¢~ should be proportional to the buffer-gas pressure. 8 When using the generalized Galatry profile, the collision-narrowing coefficients fl/P were found to be much larger than the ones associated with a simple Galatry profile. The coefficient p/P was measured to be 0.24 cm-~/atm as opposed to 0.04 cm-~/atm when using the simple Galatry profile. The coefficient difference for the two models can be explained by examining Eq. (3). In our situation, the use of a simple (symmetric) Galatry profile implies a negligible line shift (s = 0), which in turn yields a reduced narrowing parameter given by Eq. (3). The ratio y/~ averages 0.85 and leads to a theoretical narrowing parameter ratio of 6.7, which agrees with the average experimental ratio of about 6. The measured narrowing coefficients for the generalized Galatry profile were found to decrease systematically with pressure (typical values range from 0.33 to 0.15 cm-I/atm for xenon pressures ranging from 130 to 800 torr), as opposed to the simple Galatry profile where it stays constant. This result indicates that the generalized Galatry profile is not completely valid and may explain the inadequacy of such a profile toward high pressure (Px, > 530 torr) for xenon-broadened H20 lines. The deviations with a Galatry profile reported in Fig. 4 are similar in shape but much larger in magnitude than the ones reported by Pine and Looney4'9 for HF lines broadened by argon and nitrogen. On the other hand, Pine and Looney reported the asymmetry to be the largest in the collisionally-narrowed regime (P ~ 300 tort) and to vanish both in the Gaussian Doppler limit and at higher pressures for which the broadening mechanism dominates. Rautian and Sobel'man 3
346
BENOIST E. GROSSMANNand EDWARD V. BROWELL
have shown theoretically the asymmetry to disappear toward high pressures. This conclusion is in contrast with our high-pressure measurements for which the asymmetries do not vanish and suggests that additional effects may have to be included to explain the line-shape behavior toward high pressures. OXYGEN-
AND
ARGON-H20
LINE-SHAPE
FITS
Asymmetric line shapes were also observed with oxygen- and argon-broadening of water vapor lines but to a lesser extent. We have presented in the upper trace of Fig. 6 the deviations with a Voigt profile of the H20 absorption line centered at 13,909.4088 cm -~ broadened with 430 torr of argon. In the middle trace of Fig. 6, we have presented the deviations with a simple Galatry profile. These deviations are similar in shape but much smaller in magnitude than the ones with xenon as the buffer gas (see Fig. 4). As mentioned earlier, the asymmetry is caused by the ffnaginary part of the collision-narrowing parameter in Eq. (2), which in turn implies a more prominent asymmetry for absorption lines associated with large pressure-induced line shifts and large coUisional-narrowing parameters (the collision-narrowing coefficients fliP were measured in our previous study L2 to be 0.027 and 0.018 cm-~/atm for oxygen and argon, respectively, as compared with 0.24 cm-~/atm for xenon). Also, the line shifts were measured to be slightly larger for xenon as compared to either of the other buffer gases. Hence the maximum asymmetry is expected with xenon. We have presented, in the bottom trace of Fig. 6, the deviations of the experimentally-observed cross section functions with a generalized Galatry profile. The residuals are within the experimental uncertainties. The total collision frequency parameter • was 3.2 for an argon pressure of 430 torr, leading to a coefficient ¢ / P of 5.6 atm- ~. This result is larger than the values associated with xenon, which is expected. According to Eq. (2), a smaller total collision parameter # will correspond to a larger asymmetry. c
I
o
Argon Pressure
-
440
Tort
07
o
6o P ~ O ~ I ~ E
V O I ~ T
+2X 0
--2~g
S O F T - - C O L L I S I O N
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+2X 0
. L
i
.
.
.
.
. -
~111 , , J , , ~ ,-Iw ~ -
•
I C
J
.
Fig. 6. Results of least-squares fitting. The upper trace represents the measured line profile of the line • centered at 13,909.4088 cm -~ broadened with 430 torr of argon. The other trace represent the residuals obtained from the least-squares fitting routine using the Voigt, the soft-collision and the generalized Galatry profiles.
Line-shape asymmetryof water vapor absorptionlines S O P ' T - - t O L L _
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Fig. 7. Results from application of the least-squares fitting routine to the soft-collision profile for the H 2 0 line centered at 13,818.4083 cm-~ for various oxygen pressures. Weak adjacent water vapor lines are responsible for the structures appearing in the residuals. It should be noted that the asymmetry disappears toward low and high oxygen pressures.
On the other hand, we observed the asymmetries to vanish, both in the Doppler Gaussian limit and at higher pressures and to reach maxima in the coUisionally-narrowed regime for buffer-gas pressures of about 300 torr. We have presented in Fig. 7 the deviations with a Voigt profile of the H20 absorption line centered at 13,818.4083 cm-~ for oxygen pressures ranging from 50 to 640 torr. As shown in Fig. 7, the residuals from a Voigt profile are asymmetric only in the collisionallynarrowed regime (intermediate pressure) and become symmetric both toward low and high pressures. As mentioned earlier, such behavior is predicted by Rautian and Sobel'man 3 and was experimentally observed by Pine and Looney. 4'9 Synthetic Voigt, generalized Galatry, and Dicke-narrowed profiles were also generated. We then compared the theoretical deviations between these various profiles with the experimentally observed residuals and found good agreements (cf. Figs. 4, 6, 7). This result indicates that the computer codes used for the line-fitting routines were working properly. In the same fashion, our theoretical deviations were compared with other theoretical deviations, kindly provided by VargheseJ ° Again, the agreement between the two sets of deviations was excellent, giving high confidence in our present measurements. SUMMARY In this paper, asymmetric water vapor absorption-line profiles have been reported for broadening by xenon, oxygen, and argon. The observed asymmetries have been attributed to the statistical dependence between velocity- and state-changing collisions. The generalized Galatry profile, which
348
BE~olsTE. GgOSS~O,NNand EOWAgDV. BROWELL
includes these effects, has been used and was found to compare favorably with the observed deviations. However, in the case of xenon-broadening, the generalized Galatry profile was not suitable to predict correctly the observed water v a p o r spectra for pressures above 530 torr. This observation suggests that additional effects m a y have to be included at high pressures in order to fit correctly the observed line profiles. This feature was observed only with xenon-broadening for which the asymmetries were found to be the largest. To the best of our knowledge, ours are the first reported observations of asymmetric water v a p o r lines. Also, we believe that this is the first time that a generalized Galatry profile has been used in a line-fitting routine to provide the opportunity of testing such profiles with experimental data.
Acknowledgements--The authors thank B. L. Meadows of the NASA Langley Research Center for his technical assistance and P. L. Varghese of the University of Texas at Austin for providing theoretical line fitting information on the generalized Galatry profiles. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
B. E. Grossmann and E. V. Browell, J. Molec. Spectrosc. 136, 264 (1989). B. E. Grossmann and E. V. Browell, J. Molec. Spectrosc. 138, 562 (1989). S. G. Rautian and I. I. Sobel'man, Soviet Phys. Usp. 9, 701 (1967). A. S. Pine and J. P. Looney, J. Molec. Spectrosc. 122, 41 (1987). J. J. Olivero and R. L. Longbothum, JQSRT 17, 233 (1977). J.-Y. Mandin, J.-P. CheviUard, C. Camy-Peyret, J.-M. Flaud, and J. W. Brault, J. Molec. Spectrosc. 116, 167 (1986). L. Galatry, Phys. Rev. 122, 1218 (1961). P. L. Varghese and R. K. Hanson, Appl. Opt. 23, 2376 (1984). A. S. Pine, J. Molec. Spectrosc. 82, 435 (1980). P. L. Varghese, private communication (1989).
0022-4073/91 $3.00+ 0.00 Copyright © 1991 PergamonPressplc
LINE-SHAPE ASYMMETRY OF WATER VAPOR ABSORPTION LINES IN THE 720-nm WAVELENGTH REGION BENOIST E. GROSSMANN~" ST Systems Corp., 28 Research Drive, Hampton, VA 23666, U.S.A. EDWARD V. BROWELL NASA Langley Research Center, Atmospheric Sciences Division, Mail Stop 401A, Hampton, VA 23665, U.S.A. (Received 5 September 1990)
Abstract--Spectral line-shape analyses were performed for water vapor lines broadened by argon, oxygen, and xenon in the 720-nm wavelength region. A line-shape asymmetry was observed, which is attributed to statistical dependence or correlation between velocity- and state-changing collisions. The generalized (asymmetric) Galatry profile, which results from the soft-collision profile and includes correlation between velocity- and state-changing collisions, was fitted to the observed line shapes and was found to compare favorably with the observed data. The most prominent asymmetries were observed with xenon as the buffer gas.
INTRODUCTION
In earlier papers, 1'2 we reported high-resolution spectroscopic measurements of water-vapor lines broadened by air, nitrogen, oxygen, and argon. Several spectral profiles, including the Voigt, the soft- and the hard-collision profiles, were used to fit the observed lineshapes. Both Dicke-narrowed spectra (i.e., soft- and hard-collisions) were found to compare favorably with the measured cross-section functions. All these spectral profiles were symmetric about a central (possibly shifted) frequency. Rautian and Sobel'man 3 have shown theoretically that the spectral line shapes become asymmetric if the effect of statistical dependence or correlation between velocity- and statechanging collisions is included and if the line shift is non-negligible. Pine and Looney* have reported in a recent study, asymmetric HF absorption lines broadened by argon, which they attributed to cross-correlations between velocity- and state-changing collisions. In the present study, we report measurements of the pressure-broadening and pressure-shift coefficients for 41 water vapor lines broadened by xenon in the 720-nm wavelength region. We have studied the line shapes and found asymmetric residuals of the order of 2% (expressed in percent of the absorption cross-section at the line center) when compared with either of the Dicke-narrowed spectra. Such asymmetries were observed also for oxygen- and argon-broadening but to a lesser extent (0.5%). The generalized Galatry profile, which results from the soft-collision profile and includes correlations between velocity- and state-changing collisions (i.e., asymmetric profile) was fitted to the observed line shapes and was found to compare very well with the observed spectra. Characteristically, the asymmetry is evident in the strongly narrowed regime for which the pressure-shift is large compared to the pressure-broadening. We have also generated synthetic Voigt, generalized Galatry, and Dicke-narrowed profiles, and the deviations between these profiles were found to be in good agreement with the experimentally observed deviations. EXPERIMENTAL DETAILS Only a brief review of the experimental setup will be presented in this paper since a detailed description was given previously.l'2 The high-resolution spectrometer system consists of a cw ring ~Present address: Thomson CSF/DAO, 78283 Guyancourt Cedex, France. 339
340
BENOIST E. GROSSMANNand EDWARD V. BROWELL ABSORPTION CRO888ECTION :~' I LINEWIOTH :Y J LINE STRENGTH :S I PRESSURE EHIFT :~ i TEMPERATURE COEFFICIENT: n J i
HARD DISK J 40 M BytesI
I
COMPUTER
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Fig. 1. Schematic of the simultaneous absorption spectroscopy experiment.
dye laser in conjunction with two multipath absorption cells. The two White cells can be operated in parallel to avoid any laser frequency drift during pressure-induced line shift measurements. Details of the setup are given in Fig. 1. Relative frequency calibration was obtained by using an external Fabry-Perot interferometer with a free spectral range of 0.016 cm-t in parallel with the two absorption cells. The same amount of water vapor (15 torr) was introduced in both White cells by evaporating distilled water contained in a temperature-controlled flask connected to the manifold. Measurements were made with the foreign gas pressure ranging from 50 up to 1000 tort. Each scan of the laser produced three spectral traces (the Fabry-Perot transmission curve and two absorption profiles). We have represented in Fig. 2 a typical recording of xenon-broadened water vapor lines. The water vapor pressure was 15 torr for both White cells with the addition of 420 torr of xenon in one of the cells. Pressure-shift and pressure-broadening due to the buffer gas (e.g., xenon) were easily observable. The Fabry-Perot fringes (bottom trace in Fig. 2) were used to linearize the scan of the dye laser over the scan range (up to 2 cm- 1 ). A least-squares fitting routine was used to extract for each water vapor (H20) absorption line the linewidth and the central frequency. The Lorentzian or pressure-broadening component was deduced for each line through the measured Voigt halfwidth using the expression obtained by Olivero and Longbothum.5 The broadening coefficients were then corrected to take into account the Dicke-narrowing effect. A more complete description of the data reduction process can be found in Refs. 1 and 2. ANALYSIS OF PRESSURE-BROADENING AND PRESSURE-SHIFT COEFFICIENTS Table 1 lists the pressure-broadening and pressure-shift coefficients for 41 water vapor lines between 13,600 and 13,900 cm-l (720-735 nm), normalized to 296 K, with xenon as the buffer gas.
Line-shape asymmetry of water vapor absorption lines
H20 Pressure 3
Spectrum
In Xenon
i3704.180e era--!
Cell #i: 15 t o r t H20 Cell #~ 15 t o r t H20 + 420 torr Xe Febry-Perot FSR = 0.0t6 cm-i
E 0 4J L) q) tn
Shift
341
0.5
(0 @1 O t.. U
~~
R e l a L i v e W8venumber
~13704.5385 cs-t
( FSR ,, 0.016 em-I I
Fig. 2. Simultaneous recording of water vapor absorption lines at two different pressures. The lower trace represents the spectral throughput of a Fabry-Perot interferometer. The spectra have been normalized for clarity. Pressure-broadening and pressure-shift due to xenon are observable.
The broadenings and shiftsin oxygen and argon can be found in Ref. 2. A temperature power law dependence of T -°7 was used to normalize the data to 296 K. Because the measurements were obtained at temperatures close to 296 K (typically 300-305 K), the temperature corrections were very smaU and relatively insensitive to the exponent value. The line-center positions and the rotational and vibrational assignments were taken from Mandin's data 6 and arc specified in the same manner. The xenon pressure-broadening coefficients range from 0.0792 up to 0.0958 crn-I/atm with an average value of 0.0878 era-I/arm. The average value is comparable to the air- and nitrogen-broadening coefficients? W c have represented in Fig. 3 the measured xenon pressure-l~roadening coefficientsas a function of the rotational quantum number J. As indicated in Fig. 3, the decrease of the broadening coefficients as a function of J was not observed, which is in contrast with our previous measurements of self-,air-, nitrogen-, oxygen-, and argon-broadening coefficients? However, we believe this effectcan be attributed to the sample of measured water vapor lines (the measurement was conducted only for the strongest H 2 0 lines with the average line strength investigated in this study being I I x 10 -24 cm~/molecule.cm-~). The pressure-shift coefficients were found to bc negative for all of the lines investigated. The measured values ranged from -0.0269 up to -0.0668 crn-I/atm with an average value of -0.0360cm-~/atm. In order to check the accuracy of our measurements, the broadening and shifts were measured as a function of xenon pressure in the range 130-1000 torr for several H 2 0 absorption lines. N o significant deviations from the expected linear relationship were observed.
COLLISIONAL NARROWING MODELS We have used several spectral profiles to perform least-squares fitting of the observed line shapes. We first used a Voigt profile which results from the convolution of a Gaussian (i.e., Doppler component) and a Lorentzian (i.e., pressure broadening component). We have represented in Fig. 4 the deviations between the fitted Voigt profile and the .measured cross sections functions (left column) for the water vapor line centered at 13,718.5762 crn-' with xenon pressure ranging from 130 to 740 torr. As observed in Fig. 4, the residuals from the (symmetric) Voigt profile
342
BENOIST E. GROSSMANNand EDWARD V. BROWELL Table 1. Spectroscopic data for H20 absorption lines broadened by xenon wavenumber
JKaKc'
JKaKc
v'
cm-i
13,662.5022 13,663.2901 13,688.8686 13,703.1088 13,704.1808 13,704.5385 13,717.1747 13,718.5762 13,728.1798 13,737.4161 13,738.4401 13,741.1540 13,761.5888 13,763.8874 13,764.6747 13,774.2119 13,775.2987 13,783.1795 13,783.8760 13,784.7849 13,797.5367 13,801.2788 13,801.7317 13,815 1226 13,815 7375 13,818 4083 13,819 0491 13,821 9097 13,823 1814 13,839 6550 13,853 2706 13,866 7312 13,872 6818 13,882 7586 13,884 0365 13,884 3369 13,888 0804 13,890 0672 13,890 4020 13,894 6350 13,897 1062
524 221 413 330 331 660 312 322 404 313 313 220 212 414 212 ii0 542 i01 533 iii 431 331 330 633 221 220 321 iii 422 211 i01 212 202 313 322 331 303 615 313 431 414
625 220 514 431 432 661 413 423 303 414 404 321 313 413 303 211 541 202 532 212 432 330 331 532 220 221 322 Ii0 423 212 000 iii i01 212 221 212 202 616 202 330 313
301 221 301 301 301 301 301 301 221 301 202 301 301 301 202 301 301 301 301 301 301 301 301 221 301 301 301 301 301 301 301 301 301 301 301 221 301 301 202 301 301
Gamma
Shift
Xe
Xe
cm-i/atm
cm-I/atm
0.0958 0.0792 0.0937 0.0837 0.0832 0.0846 0.0978 0.0911 0.0891 0.0874 0.0856 0.0881 0.0848 0.0876 0.0851 0.0891 0.0816 0.0864 0.0838 0.0897 0.0844 0.0895 0.0856 0.0834 0.0939 0.0935 0.0917 0.0854 0.0844 0.0866 0.0844 0.0854 0.0935 0.0907 0.0873 0.0895 0.0913 0.0885
-0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0 -0
0386 0331 0353 0430 0439 0668 0379 0359 0348 0300 0374 0392 0296 0290 0290 0345 0512 -0 0284 -0 0410 -0 0291 -0.0433 -0.0431 -0.0439 -0.0431 -0.0335 -0.0343 -0.0369 -0.0269 -0.0359 -0.0307 -0.0296 -0.0293 -0.0332 -0.0329 -0.0317 -0.0321 -0.0332 -0.0337 -0.0327 -0.0408 -0.0274
Note. For each line, we give the wavenumber of the transition (cm-1); the rotational assignment of the upper and lower levels of the transition; the u p p e r s t a t e vibrational assignment and the pressure-broadening and pressure-shift coefficients in xenon (cm-1/atm). Columns 1-4 were taken from Mandin et al. (Ref.6). All results are normalized to T = 296 K.
are asymmetric, which in turn, implies an asymmetric spectral line shape for the absorption line. The asymmetry appears to be less pronounced toward lower xenon pressures. In the limiting case with Px, = 0 (i.e., pure water vapor), the spectral profile is symmetric. Care was taken to ensure that the observed asymmetries were not due to instrumental effects such as laser scan non-linearity [any laser scan non-linearity effects would have produced a similar asymmetry for the low-pressure spectrum (i.e., pure water vapor), and such effects were never observed]. Also, the deviations reported in Fig. 4 were found to be typical of any xenon-broadened water vapor absorption lines. A Galatry profile or soft-collision profile was then used. The analytical expression for the shape of this profile (denoted by G) is given by 7'8
l(fy{
G ( x , y , z ) = - - ~ Re
exp
-ix'r - y r +
[1 - z r - e x p ( - z r ) ]
}) dz
(1)
Line-shape asymmetry of water vapor absorption lines
343
X E N O N - B R O A D E N I N G vs J
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Fig. 3, Average xenon-broadening coefficients as a function of rotational quantum number J. +3%
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Fig. 4. Results of lcast-squares fitting to the Voigt profile (left) the soft-collision profile (middle), and the generalized Galatry profile (right) for the H20 line centered at 13,718.5762cm -m for various xenon pressures. Deviations are expressed in percent of the absorption cross-section at the line center. The horizontal scale is given for each spectrum by the two vertical bars which correspond to one FWHM.
344
BENOISTE. GRO~MANNand EDWARDV. BROWELL
where x = (w - Wo)/FD, y = F L / F o and z --- [3/Fo. Here w is the frequency or wavenumber referred to the shifted line center frequency w0; Fo represents the Doppler halfwidth at 1/e intensity (~0.024 cm -I); FL is the pressure-broadening component (cm-I), 13 is the effective frequency of velocity-changing collisions (cm- t ), and z is a dummy variable. The parameter y is usually referred as the Voigt parameter. We have represented in Fig. 4 (middle column) the deviations between the fitted Galatry profile and the experimentally-measured profile. The residuals are again asymmetric because the Galatry or soft-collision profile is symmetric. The collisional narrowing coefficient ~ / P was measured to be 0.05 cm-t/atm for the absorption lines under study when using a simple Galatry profile. The coefficient f l i P was measured to be constant as a function of pressure, which is consistent with our previous measurements of self-, nitrogen-, oxygen-, air-, and argon-broadened H 2 0 lines, t'2 It is interesting to note in Fig. 4 that the residuals from the Voigt and soft-collision profiles become similar toward higher pressures. This result is expected since at high pressures the contribution of Doppler broadening will become negligible compared with collision broadening. Hence the reduction of Doppler broadening effected by velocity-changing collisions makes a negligible correction to the line shape. We also used the hard-collision profile for line fitting and it produced similar deviations as compared to the soft-collision profile but with smaller collisional narrowing coefficients ( ~ - 2 0 % ) . These effects were observed and analyzed previously) '2'4 We did not show these deviations because they are indistinguishable from the soft-collision fits. LINE-SHAPE
FITS
TO THE
GENERALIZED
GALATRY
PROFILE
A generalization of the Galatry profile is obtained by including the effects of statistical correlation between velocity- and state-changing collisions, i.e., assuming that velocity and state perturbations occur simultaneously while also assuming that the magnitude of the changes are uncorrelated. 3 The analytical expression for the generalized Galatry profile denoted by H is given by 8 H ( x , y, z , ~ , s) = G ( x , y, Z);
Z = z(1 - y / ~ ) - i s z / ~ .
(2)
Here, s represents the standardized line-shift parameter defined by s = 6/FD where 6 is the line shift of the absorption line (cm-l), and ¢ is an additional parameter defined as the total collision frequency parameter: The asymmetry of the absorption line is caused by the imaginary part of the collisional narrowing parameter Z appearing in the generalized Galatry profile analytical expression [Eq. (2)]. Therefore, the asymmetry will be more prominent for absorption lines associated with large pressure-induced line shifts and large collisional narrowing parameters. This statement explains the rather large asymmetry observed with the xenon-broadened H20 lines as opposed to the nitrogen-, oxygen-, and argon-broadening. 2 For absorption lines for which the line shift is negligible (s = 0), the generalized Galatry profile is mathematically identical to a simple (symmetric) Galatry profile with a reduced narrowing parameter given by Z ( s = O) = z¢rr= z(1 - y l ~ ) .
(3)
We have presented in the right-hand column of Fig. 4 the deviations between the fitted generalized Galatry profile and the measured line shapes. The agreements between these two profiles are satisfactory with the residuals being within the measurement uncertainties for xenon pressure < 530 torr. For pressure > 530 torr, the generalized Galatry profile was unsuitable to fit correctly the observed spectra. No physical reasons were found to explain this behavior. The best-fit routine was rechecked to ensure that the computer codes did not introduce a bias when dealing with the broader absorption lines. Similarly, a generalization of the hard-collision profile can be obtained by including dependence between velocity-changing and state-perturbing collisions. 3's However, this type of profile was not evaluated because it involves additional parameters and lengthy computer calculations.
Line-shape asymmetry o f water vapor absorption lines
345
COLLISION F R E Q U E N C Y P A R A M E T E R / P R E S S U R E 5 -
13718.5762 ¢ m ' I
•e- 3
1
0
I
I
I
I
I
I
0.2
0.4
0.6
0.8
1.0
1.2
X e n o n pressure (atm) Fig. 5. The total collision frequency parameter ~ as a function of xenon pressure. The straight line is a result of a simple linear least-squares fit.
Nevertheless, we believe that the generalized hard-collision profile would yield results quite similar to the generalized Galatry profile. In the least-squares fit routine, the total collision frequency parameter 4} appearing in Eq. (2) was measured to be a linear function of pressure. We have presented in Fig. 5 the measured total collision frequency parameter 4) as a function of xenon pressure. This relationship can be approximated by the following best-fit linear relationship: = 3P + 0.7,
(4)
where P is the xenon pressure (atm). It is not known if the constant appearing in Eq. (4) is real or if it is due to an artifact of the fitting procedure. For a valid collision model, the total collision frequency parameter ¢~ should be proportional to the buffer-gas pressure. 8 When using the generalized Galatry profile, the collision-narrowing coefficients fl/P were found to be much larger than the ones associated with a simple Galatry profile. The coefficient p/P was measured to be 0.24 cm-~/atm as opposed to 0.04 cm-~/atm when using the simple Galatry profile. The coefficient difference for the two models can be explained by examining Eq. (3). In our situation, the use of a simple (symmetric) Galatry profile implies a negligible line shift (s = 0), which in turn yields a reduced narrowing parameter given by Eq. (3). The ratio y/~ averages 0.85 and leads to a theoretical narrowing parameter ratio of 6.7, which agrees with the average experimental ratio of about 6. The measured narrowing coefficients for the generalized Galatry profile were found to decrease systematically with pressure (typical values range from 0.33 to 0.15 cm-I/atm for xenon pressures ranging from 130 to 800 torr), as opposed to the simple Galatry profile where it stays constant. This result indicates that the generalized Galatry profile is not completely valid and may explain the inadequacy of such a profile toward high pressure (Px, > 530 torr) for xenon-broadened H20 lines. The deviations with a Galatry profile reported in Fig. 4 are similar in shape but much larger in magnitude than the ones reported by Pine and Looney4'9 for HF lines broadened by argon and nitrogen. On the other hand, Pine and Looney reported the asymmetry to be the largest in the collisionally-narrowed regime (P ~ 300 tort) and to vanish both in the Gaussian Doppler limit and at higher pressures for which the broadening mechanism dominates. Rautian and Sobel'man 3
346
BENOIST E. GROSSMANNand EDWARD V. BROWELL
have shown theoretically the asymmetry to disappear toward high pressures. This conclusion is in contrast with our high-pressure measurements for which the asymmetries do not vanish and suggests that additional effects may have to be included to explain the line-shape behavior toward high pressures. OXYGEN-
AND
ARGON-H20
LINE-SHAPE
FITS
Asymmetric line shapes were also observed with oxygen- and argon-broadening of water vapor lines but to a lesser extent. We have presented in the upper trace of Fig. 6 the deviations with a Voigt profile of the H20 absorption line centered at 13,909.4088 cm -~ broadened with 430 torr of argon. In the middle trace of Fig. 6, we have presented the deviations with a simple Galatry profile. These deviations are similar in shape but much smaller in magnitude than the ones with xenon as the buffer gas (see Fig. 4). As mentioned earlier, the asymmetry is caused by the ffnaginary part of the collision-narrowing parameter in Eq. (2), which in turn implies a more prominent asymmetry for absorption lines associated with large pressure-induced line shifts and large coUisional-narrowing parameters (the collision-narrowing coefficients fliP were measured in our previous study L2 to be 0.027 and 0.018 cm-~/atm for oxygen and argon, respectively, as compared with 0.24 cm-~/atm for xenon). Also, the line shifts were measured to be slightly larger for xenon as compared to either of the other buffer gases. Hence the maximum asymmetry is expected with xenon. We have presented, in the bottom trace of Fig. 6, the deviations of the experimentally-observed cross section functions with a generalized Galatry profile. The residuals are within the experimental uncertainties. The total collision frequency parameter • was 3.2 for an argon pressure of 430 torr, leading to a coefficient ¢ / P of 5.6 atm- ~. This result is larger than the values associated with xenon, which is expected. According to Eq. (2), a smaller total collision parameter # will correspond to a larger asymmetry. c
I
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Fig. 6. Results of least-squares fitting. The upper trace represents the measured line profile of the line • centered at 13,909.4088 cm -~ broadened with 430 torr of argon. The other trace represent the residuals obtained from the least-squares fitting routine using the Voigt, the soft-collision and the generalized Galatry profiles.
Line-shape asymmetryof water vapor absorptionlines S O P ' T - - t O L L _
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On the other hand, we observed the asymmetries to vanish, both in the Doppler Gaussian limit and at higher pressures and to reach maxima in the coUisionally-narrowed regime for buffer-gas pressures of about 300 torr. We have presented in Fig. 7 the deviations with a Voigt profile of the H20 absorption line centered at 13,818.4083 cm-~ for oxygen pressures ranging from 50 to 640 torr. As shown in Fig. 7, the residuals from a Voigt profile are asymmetric only in the collisionallynarrowed regime (intermediate pressure) and become symmetric both toward low and high pressures. As mentioned earlier, such behavior is predicted by Rautian and Sobel'man 3 and was experimentally observed by Pine and Looney. 4'9 Synthetic Voigt, generalized Galatry, and Dicke-narrowed profiles were also generated. We then compared the theoretical deviations between these various profiles with the experimentally observed residuals and found good agreements (cf. Figs. 4, 6, 7). This result indicates that the computer codes used for the line-fitting routines were working properly. In the same fashion, our theoretical deviations were compared with other theoretical deviations, kindly provided by VargheseJ ° Again, the agreement between the two sets of deviations was excellent, giving high confidence in our present measurements. SUMMARY In this paper, asymmetric water vapor absorption-line profiles have been reported for broadening by xenon, oxygen, and argon. The observed asymmetries have been attributed to the statistical dependence between velocity- and state-changing collisions. The generalized Galatry profile, which
348
BE~olsTE. GgOSS~O,NNand EOWAgDV. BROWELL
includes these effects, has been used and was found to compare favorably with the observed deviations. However, in the case of xenon-broadening, the generalized Galatry profile was not suitable to predict correctly the observed water v a p o r spectra for pressures above 530 torr. This observation suggests that additional effects m a y have to be included at high pressures in order to fit correctly the observed line profiles. This feature was observed only with xenon-broadening for which the asymmetries were found to be the largest. To the best of our knowledge, ours are the first reported observations of asymmetric water v a p o r lines. Also, we believe that this is the first time that a generalized Galatry profile has been used in a line-fitting routine to provide the opportunity of testing such profiles with experimental data.
Acknowledgements--The authors thank B. L. Meadows of the NASA Langley Research Center for his technical assistance and P. L. Varghese of the University of Texas at Austin for providing theoretical line fitting information on the generalized Galatry profiles. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
B. E. Grossmann and E. V. Browell, J. Molec. Spectrosc. 136, 264 (1989). B. E. Grossmann and E. V. Browell, J. Molec. Spectrosc. 138, 562 (1989). S. G. Rautian and I. I. Sobel'man, Soviet Phys. Usp. 9, 701 (1967). A. S. Pine and J. P. Looney, J. Molec. Spectrosc. 122, 41 (1987). J. J. Olivero and R. L. Longbothum, JQSRT 17, 233 (1977). J.-Y. Mandin, J.-P. CheviUard, C. Camy-Peyret, J.-M. Flaud, and J. W. Brault, J. Molec. Spectrosc. 116, 167 (1986). L. Galatry, Phys. Rev. 122, 1218 (1961). P. L. Varghese and R. K. Hanson, Appl. Opt. 23, 2376 (1984). A. S. Pine, J. Molec. Spectrosc. 82, 435 (1980). P. L. Varghese, private communication (1989).