Multispectrum analysis of pressure broadening and pressure shift coefficients in the 12C16O2 and 13C16O2 laser bands

Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

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Multispectrum analysis of pressure broadening and pressure shift coe+cients in the 12C16O2 and 13C16O2 laser bands V. Malathy Devia;∗ , D. Chris Bennera , Mary Ann H. Smithb , Linda R. Brownc , Michael Dulickd a

Department of Physics, The College of William and Mary, Box 8795, Williamsburg, VA 23187-8795, USA Atmospheric Sciences, NASA Langley Research Center, Mail Stop 401A, Hampton, VA 23681-2199, USA c Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA d National Optical Astronomy Observatories, National Solar Observatory, P.O. Box 26732, Tucson, AZ 85726-6732, USA

b

Received 28 March 2002; accepted 14 May 2002

Abstract Extensive high-resolution experimental determination is provided for air- and N2 -broadening and pressure shift coe+cients for the two 13 C16 O2 laser bands (located at 913.4 and 1017:6 cm−1 , respectively), in addition to new measurements of self-broadening and self-shift coe+cients for the 12 C16 O2 laser bands. These parameters were determined from analysis of spectra recorded with the McMath–Pierce Fourier transform spectrometer (FTS) of the National Solar Observatory on Kitt Peak, Arizona. We used a multispectrum nonlinear least-squares Btting technique to analyze 30 long path, room temperature absorption spectra. By combining the spectra of 12 CO2 and 13 CO2 in the same Bt we were able to obtain a consistent set of line parameters for both molecules. The results obtained for the 12 CO2 and 13 CO2 laser bands were compared with each other, with values in the HITRAN database, and with values reported in the literature for CO2 bands. Comparisons revealed no signiBcant diDerences in the broadening or shift coe+cients between the two laser bands. The coe+cients determined for the two isotopomers agreed closely. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: CO2 ; CO2 isotopomers; CO2 laser bands; Infrared spectra; Fourier transform infrared (FTIR) spectroscopy; Spectral line shape

1. Introduction Although several studies ([1] and the papers cited therein) pertaining to air and N2 -broadening and shifts in the 12 C16 O2 laser bands [3 − 1 is the laser band I and 3 − 202 is the laser band II] ∗

Corresponding author. Tel.: +1-757-864-5521; fax: +1-757-864-7790. E-mail address: [email protected] (V. Malathy Devi).

0022-4073/02/$ - see front matter ? 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 2 - 4 0 7 3 ( 0 2 ) 0 0 0 6 8 - 7

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have been reported in the literature, no measurements of air and N2 -broadening or shift coe+cients have thus far been published for the 13 C16 O2 laser bands. Mandin et al. [2] have published intensities and self-broadening coe+cients of 13 C16 O2 laser lines by analyzing spectra obtained with a Fourier transform spectrometer. In contrast to large numbers of pressure-broadening measurements reported for various CO2 bands, results on pressure-shift coe+cients, especially for the laser bands, are very few. Most of the previously published pressure-shift values in 12 C16 O2 laser bands are self-shift coe+cients [3–5]. Freed et al. [3] and Woods and JolliDe [4] reported self-shift coe+cients for a few laser band transitions in 12 C16 O2 . Using a nonlinear laser heterodyne spectroscopic technique, SooHoo and co-workers [5,6] published average values of self-shift coe+cients obtained from measurements performed over a range of J

values for diDerent vibrational levels of four CO2 isotopomers (12 C16 O2 , 13 16 C O2 , 12 C18 O2 and 13 C18 O2 ). Kou and Guelachvili [7] measured self shifts for over 40 transitions in each 12 C16 O2 laser band but reported only the mean value. There are a few studies reporting the temperature dependence of self- and foreign-gas broadened 12 16 C O2 laser lines (e.g. [8–11]). In most of these studies, however, measurements are obtained only for a small number of CO2 transitions. Similar to 12 C16 O2 laser bands, parameters for the 13 C16 O2 laser bands are of great interest for atmospheric spectral analyses, particularly as atmospheric scientists seek to quantify regional and global sources and sinks of atmospheric carbon dioxide. As discussed above, measurements of broadening and shift coe+cients of the 13 C16 O2 laser bands are very sparse. With this need in mind we have made measurements of line broadening and shifts in the two 13 C16 O2 laser bands from spectra recorded with 13 C-enriched CO2 sample. 2. Experimental details and data analysis In addition to the 10 spectra used in Ref. [1], 20 more spectra were added in the present analysis. The experimental conditions of all spectra used in the present analysis are summarized in Table 1 of the CO2 laser bands intensity paper [12]. Additional details about the McMath–Pierce FTS, data recording procedure and other experimental details are given in Refs. [1,12]. For retrieving accurate pressure-induced shift coe+cients using the multispectrum technique it is important that a good relative calibration of the wavenumber scales of all of the spectra be performed prior to starting the least-squares Bts. The main purpose of performing absolute calibration in our study was to also determine accurate line center positions of the 12 C16 O2 and the 13 C16 O2 laser lines. The wavelength scales of all the spectra included in the analysis were aligned using several (∼20) 2 water vapor lines. These water vapor lines appeared in the spectra due to the residual water present in the “evacuated” FTS tank and the nitrogen-purged atmospheric paths between the source and the entrance aperture of the interferometer. Absolute calibration was performed after the multispectrum Bts by forcing agreement between the derived zero pressure CO2 positions with those of Refs. [13,14]. The recent absolute frequency measurements for 20 12 C16 O2 laser transitions by Bernard and co-workers [15] conBrm the results of Refs. [13,14]. Each spectral line in the Btted interval was modeled assuming the Voigt line shape function convolved with the instrument line shape function appropriate for the McMath–Pierce FTS. In the least-squares solution the Doppler width of each line was Bxed to the theoretical value calculated

V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

413

using the following expression:
T −7 : (1) bD = 3:581 × 10 0 M In the above equation, 0 is the position of the center of the line in cm−1 , T is the gas temperature in degrees Kelvin and M is the molecular weight of the absorbing gas in atomic mass units. Initial values of the spectral line parameters were taken from the HITRAN database [16,17]. A total of 22 spectra [two low-pressure spectra of a natural CO2 sample, two low-pressure spectra with 13 C-enriched CO2 , four spectra each with either CO2 (or 13 CO2 ) in air or CO2 (or 13 CO2 ) in nitrogen and 10 self-broadened spectra obtained with the natural CO2 sample] were Btted simultaneously using our nonlinear least-squares spectrum Btting technique [18]. The following expressions were used to determine the broadening and shift coe+cients.  = 0 + 0 × p; bL (p; T ) = b0L (p0 ; T0 ) × p ×



T0 T

n

(2) :

(3)

In the above equations, 0 is the zero-pressure line position (in cm−1 ), 0 , the pressure-induced line shift coe+cient (in cm−1 =atm at the temperature of the spectra) and  is the line position corresponding to the pressure p. bL (p; T ) is the pressure-broadened Lorentz halfwidth (in cm−1 ) of the line at pressure p and temperature T and b0L (p0 ; T0 ) is the pressure-broadened halfwidth of the line at the reference pressure p0 (1 atm) and temperature T0 (296 K). The temperature dependence exponent of the pressure-broadened halfwidth coe+cient is deBned by n. The value of n listed for each line in the HITRAN spectral line parameters compilation [16,17] was adopted in the least-squares Bts. For the range of J observed in our study, the n values vary from 0.70 to 0.78. In our measurements the temperature corrections were small because T was close to T0 and the maximum correction was only about 1%. Fig. 1 shows an example of a multispectrum Btted interval near 1037 cm−1 in the 3 − 202 laser band with three P-branch transitions of 12 C16 O2 and several R-branch transitions of the 13 C16 O2 isotopomer. Weak features due to 2 +3 −312 and the 202 +3 −402 ‘hot’ bands are also identiBed in this Bgure. In addition, transitions belonging to the laser bands of 16 O12 C18 O, 16 O12 C17 O, 16 O13 C18 O and 13 C18 O2 (not marked in the Bgure) also appear in this spectral interval. Line parameters (such as position and intensity) for many of the weak lines were unconstrained in the least-squares solutions. In the lower panel (b) we show the 22 calculated spectra while the magniBed residuals (observed minus calculated) resulting from the least-squares Bt to the observed spectra are shown in the upper plot (a). There are 14 self-broadened spectra of CO2 and eight nitrogen-broadened spectra (four each for 12 C16 O2 and 13 C16 O2 ) included in this example. The channeling appearing in some of these spectra caused by unwedged windows from the 1.37-m (84:85 m pathlength) multipass cell was satisfactorily modeled in the least-squares Bts. In Fig. 2, a small section (expanded) of the Btted interval shown in Fig. 1 is re-plotted to show details. Some of the weak absorption features mentioned earlier (in Fig. 1) are identiBed in Fig. 2(b). The self-broadened and N2 -broadened P(30) transition of the 12 C16 O2 laser band and the N2 -broadened R(28) line of the 13 C16 O2 laser band are prominent in this plot. Without the multispectrum Btting technique it would require 22 separate least-squares Bttings of this same spectral region and processing all the resulting values in order to obtain the spectral line parameters.

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Fig. 1. Twenty-two calculated spectra (lower panel) and the corresponding residuals (observed minus calculated on an expanded scale; top panel) resulting from a multispectrum Bt. There are 14 self-broadened CO2 spectra and eight N2 -broadened spectra (four spectra each for 12 C16 O2 and 13 C16 O2 ) included in the Bt. The channeling appearing in some of these spectra can be clearly seen. In addition to the 12 C16 O2 and 13 C16 O2 laser lines, laser lines belonging to 16 O12 C18 O, 16 12 17 O C O and 16 O13 C18 O isotopomers are also visible. Several weak transitions belonging to the P branch of the hot band lines (2 + 3 − 312 and 202 + 3 − 402 ) of 12 C16 O2 and (2 + 3 − 312 ) of 13 C16 O2 also appear in this spectral region. Tick marks shown in the bottom panel indicate positions of spectral lines included in the least-squares calculations.

For several of the spectra, the zero-level was noticeably oDset. When strong lines are present in the spectrum, the program Bts this oDset and the residuals due to it are removed. For weak lines, an error of 1% in zero-level corresponds to an intensity error of 1%. The majority of these spectra have zero-level oDsets less than 1.0 % and the zero-level is very well determined in our analysis, typically to 0.002% of the continuum. This causes only a negligible error in intensity determinations compared to errors resulting from other sources. In all cases a constant oDset for a given spectrum within a given Btted interval was su+cient. Details about the zero-level oDsets in the recorded spectra and the eDect of zero-level oDsets on the parameters determined in a multispectrum Btting technique are described by Benner [19]. Phase errors were small (6 0:01 rad), but measurable, and were also successfully modeled in our analysis. We were aware of the possibility of observing collisional narrowing eDects in our analysis. However, no evidence of such eDects was seen in the residuals of our least-squares Bts.

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Fig. 2. A portion of Fig. 1 is re-plotted on an expanded scale to show detail. P(30) transition in the 12 C16 O2 3 − 202 laser band and the R(28) line of the 13 C16 O2 3 − 202 laser band are the prominent absorbing features in this interval. With the multispectrum Btting technique we were able to determine the N2 broadening of 12 C16 O2 and 13 C16 O2 lines and the self-broadening coe+cients of the 12 C16 O2 lines simultaneously. The nominal 100% absorption level is indicated in the Bgure by the horizontal dashed line.

3. Results and discussion The values determined from the multispectrum least-squares Bts for zero pressure spectral line position 0 , the Lorentz pressure-broadening coe+cients b0L (air), b0L (N2 ), b0L (self ), and the pressureinduced shift coe+cients 0 (air), 0 (N2 ) and 0 (self ) for 12 C16 O2 lines for laser bands I and II are listed in Tables 1 and 2, respectively. The results for 0 , b0L (air), b0L (N2 ), 0 (air) and 0 (N2 ) for the 13 C16 O2 laser transitions for band I and band II are listed in Tables 3 and 4, respectively. The uncertainty given in parentheses represents one standard deviation in the measured quantity as determined by the least-squares spectrum Bt in units of the last digit quoted. The mean zero-pressure line center positions for each transition retrieved from air-, N2 - and self-broadened spectra for 12 C16 O2 and air- and N2 -broadened spectra in the case of 13 C16 O2 are listed in these tables. The line positions obtained from least-squares Bts involving diDerent broadening gases (e.g., air and N2 ) were within their measurement uncertainties.

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Table 1 Zero-pressure line center positions, air-, N2 -, and self-broadened width and shift coe+cients for the 3 −1 band of Line

 (cm−1 )

P(60) P(58) P(54) P(52) P(50) P(48) P(46) P(44) P(42) P(40) P(38) P(36) P(34) P(32) P(30) P(28) P(26) P(24) P(22) P(20) P(18) P(16) P(14) P(12) P(10) P( 8) P( 6) P( 4) P( 2) R( 0) R( 2) R( 4) R( 6) R( 8) R(10) R(12) R(14) R(16) R(18) R(20) R(22) R(24) R(26) R(28) R(30) R(32) R(34)

903.21184(7) 905.50659(5) 910.01589(3) 912.23076(2) 914.41933(2) 916.58180(2) 918.71832(1) 920.82914(1) 922.91428(1) 924.97397(1) 927.00828(1) 929.01743(1) 931.00143(1) 932.96044(1) 934.89446(1) 936.80376(1) 938.68823(1) 940.54809(1) 942.38330(1) 944.19401(1) 945.98019(1) 947.74196(1) 949.47927(1) 951.19223(1) 952.88084(1) 954.54507(1) 956.18496(1) 957.80053(1) 959.39175(1) 961.73287(1) 963.26313(1) 964.76895(1) 966.25035(1) 967.70723(1) 969.13953(1) 970.54722(1) 971.93025(1) 973.28850(1) 974.62197(1) 975.93040(1) 977.21390(1) 978.47225(1) 979.70539(1) 980.91316(1) 982.09551(1) 983.25223(1) 984.38319(1)

b0L (air)a

0.0628(16) 0.0638(12) 0.0665( 9) 0.0703( 8) 0.0678( 6) 0.0667( 5) 0.0676( 4) 0.0685( 3) 0.0678( 3) 0.0696( 3) 0.0697( 2) 0.0701( 2) 0.0710( 2) 0.0718( 2) 0.0731( 2) 0.0740( 2) 0.0758( 2) 0.0763( 2) 0.0778( 2) 0.0793( 2) 0.0823( 2) 0.0830( 3) 0.0845( 3) 0.0895( 6) 0.0979(13) 0.0872( 4) 0.0851( 3) 0.0823( 2) 0.0804( 2) 0.0780( 2) 0.0770( 2) 0.0761( 2) 0.0751( 2) 0.0732( 2) 0.0717( 2) 0.0710( 2) 0.0699( 2) 0.0697( 2) 0.0690( 2) 0.0692( 2) 0.0687( 2) 0.0684( 2)

b0L (N2 )a

b0L (self )a

0.0641(18) 0.0663(14) 0.0647( 9) 0.0724( 8) 0.0713( 6) 0.0673( 5) 0.0699( 4) 0.0708( 3) 0.0707( 3) 0.0731( 3) 0.0725( 3) 0.0728( 2) 0.0728( 2) 0.0743( 2) 0.0755( 2) 0.0764( 2) 0.0784( 2) 0.0792( 2) 0.0807( 2) 0.0826( 2) 0.0839( 2) 0.0853( 3) 0.0890( 4) 0.0938( 7) 0.0970(13) 0.0900( 4) 0.0875( 3) 0.0846( 2) 0.0828( 2) 0.0805( 2) 0.0794( 2) 0.0783( 2) 0.0777( 2) 0.0761( 2) 0.0739( 2) 0.0746( 2) 0.0731( 2) 0.0735( 2) 0.0716( 2) 0.0720( 2) 0.0726( 2) 0.0712( 3)

0.0640( 0.0660( 0.0681( 0.0711( 0.0722( 0.0752( 0.0760( 0.0789( 0.0780( 0.0810( 0.0846( 0.0845( 0.0871( 0.0899( 0.0906( 0.0926( 0.0949( 0.0963( 0.0976( 0.0993( 0.1009( 0.1017( 0.1050( 0.1071( 0.1087( 0.1108( 0.1145( 0.1172( 0.1199( 0.1272( 0.1177( 0.1148( 0.1127( 0.1096( 0.1073( 0.1045( 0.1022( 0.1002( 0.0990( 0.0980( 0.0956( 0.0948( 0.0923( 0.0909( 0.0891( 0.0864( 0.0847(

8) 6) 3) 2) 2) 2) 2) 2) 2) 2) 3) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 1) 1) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2)

0 (air)b

0 (N2 )b

−0.0012(17) −0.0015(13) +0.0001(10) −0.0010( 8) −0.0018( 6) −0.0039( 5) −0.0023( 4) −0.0005( 3) −0.0018( 3) −0.0018( 2) −0.0014( 2) −0.0017( 2) −0.0020( 2) −0.0018( 2) −0.0017( 2) −0.0017( 1) −0.0020( 1) −0.0020( 1) −0.0020( 2) −0.0021( 2) −0.0016( 2) −0.0010( 2) −0.0018( 3) −0.0011( 6) +0.0000( −0.0008( −0.0006( +0.0007( −0.0012( −0.0009( −0.0009( −0.0012( −0.0013( −0.0006( −0.0008( −0.0014( −0.0012( −0.0013( −0.0018( −0.0016( −0.0023(

4) 3) 2) 2) 1) 1) 1) 1) 1) 1) 1) 1) 1) 2) 2) 2) 2)

+0.0009(18) −0.0039(14) −0.0030(10) −0.0011( 9) −0.0004( 7) −0.0034( 5) −0.0022( 4) −0.0020( 3) −0.0011( 3) −0.0022( 2) −0.0010( 2) −0.0020( 2) −0.0015( 2) −0.0022( 2) −0.0016( 2) −0.0014( 2) −0.0018( 2) −0.0019( 2) −0.0015( 2) −0.0011( 2) −0.0013( 2) −0.0011( 2) −0.0003( 3) −0.0003( 6) −0.0013(13) +0.0000( 4) −0.0015( 3) −0.0008( 2) +0.0003( 2) −0.0004( 2) 0.0002( 1) −0.0005( 1) −0.0006( 1) −0.0009( 1) −0.0012( 1) −0.0007( 1) −0.0007( 1) −0.0009( 2) −0.0009( 2) −0.0008( 2) −0.0021( 2) −0.0024( 2)

12

C16 O2

0 (self )b −0.0039( −0.0016( −0.0024( −0.0026( −0.0023( −0.0029(

7) 5) 3) 2) 2) 2)

−0.0020( −0.0023( −0.0022( −0.0019( −0.0026( −0.0024( −0.0031(

1) 1) 1) 1) 1) 1) 1)

−0.0027( −0.0026( −0.0029( −0.0028( −0.0030( −0.0007( −0.0006( −0.0012( −0.0014( −0.0022( −0.0023( −0.0025( −0.0022( −0.0023( −0.0013( −0.0006( −0.0012( −0.0007( −0.0021( −0.0026( −0.0024( −0.0032( −0.0035( −0.0048( −0.0006( −0.0011( −0.0011( −0.0015( −0.0017( −0.0019( −0.0022( −0.0020(

1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1)

V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

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Table 1 (continued) Line

 (cm−1 )

b0L (air)a

b0L (N2 )a

R(36) R(38) R(40) R(42) R(44) R(46) R(48) R(50) R(52) R(54) R(56) R(58)

985.48829(1) 986.56736(1) 987.62015(1) 988.64669(1) 989.64654(1) 990.61965(1) 991.56583(1) 992.48483(1) 993.37648(1) 994.24046(2) 995.07667(3) 995.88464(4)

0.0681( 3) 0.0689( 3) 0.0683( 4) 0.0671( 5) 0.0680( 7) 0.0689(10) 0.0662(13)

0.0712( 0.0709( 0.0720( 0.0698(

3) 4) 4) 5)

0.0673(10) 0.0670(13)

b0L (self )a

0 (air)b

0.0821( 1) 0.0800( 1) 0.0782( 1) 0.0760( 1) 0.0745( 1) 0.0726(11) 0.0712(11) 0.0703(13) 0.0686(16) 0.0681(19) 0.0666(28) 0.0667(39)

−0.0026( −0.0007( −0.0019( −0.0021( −0.0024(

0 (N2 )b 3) 3) 4) 5) 7)

−0.0008( −0.0016( −0.0003( −0.0005(

0 (self )b 3) 3) 4) 5)

−0.0009( 1)

−0.0021( −0.0018( −0.0021( −0.0024( −0.0028( −0.0027( −0.0026( −0.0025( −0.0034( −0.0030( −0.0028( −0.0016(

1) 1) 1) 1) 1) 1) 1) 1) 2) 2) 3) 3)

The uncertainties listed in parentheses are one standard deviation in units of the last quoted digit. a The broadening coe+cients are in cm−1 =atm at 296 K. The value of n for each line was taken from the HITRAN database [16,17]. b The shift coe+cients are in cm−1 =atm at the corresponding temperature of the spectra.

3.1. Pressure-broadening coe@cients For 12 C16 O2 , self-broadening and self-shift coe+cients were determined for 59 transitions in laser band I and 61 transitions in laser band II with assignments between P(60)-R(58) and P(62)-R(58), respectively. Because of smaller optical densities used in recording the air- and N2 -broadened spectra compared to self-broadened spectra (see Table 1), air- and N2 -broadening and shift coe+cients were determinable for only 49 transitions in each laser band. For the 13 C16 O2 isotopomer, air-, and N2 -broadening and shift coe+cients were determined for only 41 transitions each in laser band I and laser band II covering P(40)-R(40). The values of air- and self-broadening coe+cients listed in Tables 1 and 2 for the two 12 C16 O2 bands are plotted as a function of m in Fig. 3. The self-broadening coe+cients from present measurements are compared to results of Dana et al. [20], and also to air-broadening coe+cients reported in the HITRAN line parameters compilation [16,17]. Dana et al. [20] in 1992 published self-broadening coe+cients of 90 lines in the two laser bands from analyzing spectra recorded with the Fourier transform spectrometer of the Laboratoire de Physique MolUeculaire et Applications, at the UniversitUe Paris-Sud. It is clear from Fig. 3(a) and (b), that for many CO2 transitions, self-broadening is larger than air-broadening by about 30%. Also, self-broadening coe+cients fall oD more rapidly with m than air-broadening coe+cients. However, as can be seen in Fig. 3(a) and (b), the ratio of self- to air-broadening is not same for all transitions. The ratio of self-broadening to air-broadening (or to N2 -broadening), depending upon the transition involved, varies from about 1.10 to 1.35. It is interesting to note that unlike the ratio of self- to foreign-gas (air or N2 ) broadening, the ratio of air-broadening to N2 -broadening is nearly the same for all measured transitions. Dana and co-workers [20] did not Bnd any vibrational dependence of the self-broadening coe+cients between the two laser bands. Our present measurements also did not reveal any

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V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

Table 2 Zero-pressure line center positions, air-, N2 -, and self-broadened width and shift coe+cients for the 3 − 202 band of 12 16 C O2 Line

 (cm−1 )

P(62) P(60) P(58) P(56) P(54) P(52) P(50) P(48) P(46) P(44) P(42) P(40) P(38) P(36) P(34) P(32) P(30) P(28) P(26) P(24) P(22) P(20) P(18) P(16) P(14) P(12) P(10) P( 8) P( 6) P( 4) P( 2) R( 0) R( 2) R( 4) R( 6) R( 8) R(10) R(12) R(14) R(16) R(18) R(20) R(22) R(24) R(26) R(28)

1003.16156(4) 1005.47752(3) 1007.77133(2) 1010.04286(2) 1012.29184(2) 1014.51793(2) 1016.72099(1) 1018.90069(1) 1021.05691(1) 1023.18940(1) 1025.29785(1) 1027.38215(1) 1029.44208(1) 1031.47743(1) 1033.48800(1) 1035.47360(1) 1037.43410(1) 1039.36931(1) 1041.27904(1) 1043.16324(1) 1045.02167(1) 1046.85423(1) 1048.66079(1) 1050.44125(1) 1052.19551(1) 1053.92347(1) 1055.62498(1) 1057.30015(1) 1058.94869(1) 1060.57063(1) 1062.16599(1) 1064.50886(1) 1066.03731(1) 1067.53909(1) 1069.01408(1) 1070.46227(1) 1071.88376(1) 1073.27841(1) 1074.64644(1) 1075.98776(1) 1077.30249(1) 1078.59061(1) 1079.85221(1) 1081.08736(1) 1082.29621(1) 1083.47875(1)

b0L (air)a

0.0624(15) 0.0657(11) 0.0684( 9) 0.0689( 7) 0.0691( 5) 0.0669( 4) 0.0675( 3) 0.0677( 3) 0.0680( 3) 0.0681( 2) 0.0687( 2) 0.0691( 2) 0.0695( 2) 0.0709( 2) 0.0713( 2) 0.0720( 1) 0.0727( 1) 0.0743( 1) 0.0759( 1) 0.0766( 1) 0.0774( 2) 0.0804( 2) 0.0819( 2) 0.0833( 2) 0.0852( 3) 0.0895( 5) 0.0922( 9) 0.0876( 3) 0.0852( 3) 0.0831( 2) 0.0818( 2) 0.0789( 2) 0.0774( 2) 0.0760( 1) 0.0747( 1) 0.0727( 1) 0.0742( 1) 0.0714( 1) 0.0707( 1) 0.0726( 1) 0.0682( 2)

b0L (N2 )a

b0L (self )a

0.0672(16) 0.0724(13) 0.0719(10) 0.0717( 7) 0.0713( 6) 0.0696( 4) 0.0706( 4) 0.0711( 3) 0.0714( 3) 0.0707( 2) 0.0718( 2) 0.0722( 2) 0.0718( 2) 0.0735( 2) 0.0742( 2) 0.0748( 2) 0.0756( 2) 0.0764( 2) 0.0786( 2) 0.0795( 2) 0.0806( 2) 0.0832( 2) 0.0843( 2) 0.0868( 3) 0.0887( 3) 0.0913( 5) 0.0984(10) 0.0883( 4) 0.0868( 3) 0.0862( 2) 0.0834( 2) 0.0817( 2) 0.0801( 2) 0.0790( 2) 0.0774( 2) 0.0758( 2) 0.0748( 1) 0.0740( 2) 0.0736( 2) 0.0738( 2) 0.0715( 2)

0.0636( 0.0651( 0.0677( 0.0681( 0.0687( 0.0709( 0.0717( 0.0724( 0.0742( 0.0762( 0.0780( 0.0802( 0.0824( 0.0842( 0.0870( 0.0878( 0.0895( 0.0925( 0.0936( 0.0956( 0.0981( 0.0998( 0.1009( 0.1016( 0.1032( 0.1057( 0.1073( 0.1095( 0.1128( 0.1160( 0.1204( 0.1267( 0.1180( 0.1134( 0.1098( 0.1072( 0.1056( 0.1037( 0.1015( 0.0998( 0.0987( 0.0956( 0.0948( 0.0938( 0.0893( 0.0905(

4) 3) 3) 2) 1) 1) 1) 1) 1) 1) 1) 2) 2) 2) 2) 2) 2) 2) 2) 2) 1) 2) 2) 2) 2) 2) 2) 2) 2) 3) 2) 1) 3) 3) 2) 2) 2) 2) 1) 1) 1) 1) 1) 1) 2) 2)

0 (air)b

−0.0002(12) −0.0037(10) −0.0024( 8) −0.0017( 6) −0.0011( 4) −0.0021( 3) −0.0017( 3) −0.0021( 2) −0.0016( 2) −0.0018( 2) −0.0023( 2) −0.0022( 1) −0.0019( 1) −0.0015( 1) −0.0020( 1) −0.0020( 1) −0.0024( 1) −0.0021( 1) −0.0018( 1) −0.0020( 1) −0.0016( 1) −0.0022( 2) −0.0018( 2) −0.0010( 2) +0.0002( 5) −0.0000( 9) −0.0020( 3) +0.0006( 2) −0.0005( 2) −0.0007( 1) −0.0008( 1) −0.0005( 1) −0.0003( 1) −0.0008( 1) −0.0009( 1) −0.0007( 1) −0.0013( 1) −0.0011( 1) −0.0010( 1) −0.0005( 1)

0 (N2 )b

0 (self )b

+0.0012(14) −0.0049(10) −0.0037( 8) −0.0017( 6) −0.0025( 4) −0.0021( 3) −0.0019( 3) −0.0018( 2) −0.0014( 2) −0.0013( 2) −0.0018( 2) −0.0018( 2) −0.0018( 1) −0.0013( 1) −0.0017( 1) −0.0021( 1) −0.0017( 1) −0.0024( 1) −0.0016( 1) −0.0012( 1) −0.0015( 2) −0.0012( 2) −0.0013( 2) −0.0010( 3) −0.0011( 5) +0.0005(10) −0.0004( 3) −0.0007( 2) −0.0003( 2) −0.0009( 2) −0.0006( 1) −0.0002( 1) −0.0002( 1) −0.0004( 1) −0.0008( 1) −0.0009( 1) −0.0008( 1) −0.0006( 1) −0.0009( 1) −0.0007( 2)

−0.0018(4) −0.0023(3) −0.0011(3) −0.0017(2) −0.0033(1) −0.0027(1) −0.0028(1) −0.0026(1) −0.0025(1) −0.0021(1) −0.0022(1) −0.0023(1) −0.0020(1) −0.0023(1) −0.0023(1) −0.0020(1) −0.0025(1) −0.0023(1) −0.0022(2) −0.0024(2) −0.0023(2) −0.0024(2) −0.0031(2) −0.0034(2) −0.0009(2) −0.0010(2) −0.0010(2) −0.0007(2) −0.0022(2) −0.0022(1) −0.0026(1) −0.0021(1) −0.0015(2) −0.0015(2) −0.0019(2) −0.0030(2) −0.0027(2) −0.0007(2) −0.0011(2) −0.0016(2) −0.0015(2) −0.0020(1) −0.0022(2) −0.0029(1) −0.0026(2) −0.0025(1)

V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

419

Table 2 (continued) Line

 (cm−1 )

b0L (air)a

R(30) R(32) R(34) R(36) R(38) R(40) R(42) R(44) R(46) R(48) R(50) R(52) R(54) R(56) R(58)

1084.63509(1) 1085.76537(1) 1086.86977(1) 1087.94829(1) 1089.00108(1) 1090.02835(1) 1091.03017(1) 1092.00675(1) 1092.95818(1) 1093.88473(1) 1094.78647(1) 1095.66364(1) 1096.51640(2) 1097.34489(2) 1098.14946(2)

0.0704( 0.0677( 0.0672( 0.0669( 0.0663( 0.0679( 0.0664( 0.0670(

b0L (N2 )a 2) 2) 2) 2) 3) 3) 4) 4)

0.0719( 0.0718( 0.0702( 0.0698( 0.0700( 0.0702( 0.0689( 0.0690(

2) 2) 2) 3) 3) 3) 4) 5)

b0L (self )a

0 (air)b

0.0866( 0.0861( 0.0845( 0.0829( 0.0802( 0.0795( 0.0770( 0.0756( 0.0730( 0.0715( 0.0705( 0.0704( 0.0696( 0.0676( 0.0660(

−0.0005( −0.0005( −0.0028( −0.0029( −0.0027( −0.0027( −0.0042( −0.0034(

2) 2) 2) 2) 2) 2) 1) 1) 1) 1) 1) 1) 1) 1) 2)

0 (N2 )b 2) 2) 2) 2) 2) 3) 3) 4)

−0.0004( −0.0014( −0.0005( −0.0007( −0.0009( −0.0014( −0.0019( −0.0027(

0 (self )b 2) 2) 2) 2) 3) 3) 4) 5)

−0.0027(2) −0.0020(2) −0.0023(1) −0.0022(1) −0.0024(1) −0.0023(1) −0.0021(1) −0.0022(1) −0.0023(1) −0.0020(1) −0.0022(1) −0.0019(1) −0.0028(1) −0.0023(1) −0.0031(2)

The uncertainties listed in parentheses are one standard deviation in units of the last quoted digit. a The broadening coe+cients are in cm−1 =atm at 296 K. The value of n for each line was taken from the HITRAN database [16,17]. b The shift coe+cients are in cm−1 =atm at the corresponding temperature of the spectra.

signiBcant diDerence (1% or less) between the two laser bands for air-, N2 - or self-broadening coe+cients. The measurements of air- and N2 -broadening coe+cients obtained for the 12 C16 O2 and 13 C16 O2 isotopomers listed in Tables 1–4 are plotted as a function of m in Fig. 4. The results for laser band I are plotted in Fig. 4(a) and those for laser band II in 4(b). The uncertainties for the weaker lines (low |m| and high |m|) are larger compared to those for stronger transitions with intermediate m values. Similar to our previous study [1], the measured air-broadening coe+cients are 2– 4% smaller compared to corresponding N2 -broadening coe+cients. The absorption features with |m| ¿ 40 were weak and the results obtained for those weak transitions were less accurate. Except for our previous work [1] there are no other extensive measurements of either air or N2 -broadening reported for the CO2 laser bands with which our present results could be compared. Our present results for air- and N2 -broadened widths agree well with results from our previous work [1]. Comparison of the N2 -broadening coe+cients in 12 C16 O2 laser bands with other published values has been previously reported (Table 4 of Ref. [1]) and will not be repeated here. The high-resolution spectra combined with the multispectrum analysis technique used in the present study surpass all previous measurements in quantity and quality for these CO2 laser bands. In the HITRAN database [16,17] it is assumed that the pressure broadening of CO2 is independent of vibrational transition [21]. The calculated self-broadening coe+cients (for all CO2 bands) listed in the database [16,17] are based upon the experimental results of Johns [22] and Dana and co-workers [20,23]. For the calculations of air-broadening coe+cients listed in the database, the results of Dana et al. [20] provided N2 - and O2 -broadening, Johns [22] provided N2 -broadening (in addition to self-broadening) and data from Devi et al. [24] and Margottin-Maclou et al. [25] provided additional

420

V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

Table 3 Zero-pressure line center positions, air- and N2 -broadened width and shift coe+cients for the 3 − 1 band of Line

 (cm−1 )

b0L (air)a

b0L (N2 )a

0 (air)b

P(40) P(38) P(36) P(34) P(32) P(30) P(28) P(26) P(24) P(22) P(20) P(18) P(16) P(14) P(12) P(10) P( 8) P( 6) P( 4) P( 2) R( 0) R( 2) R( 4) R( 6) R( 8) R(10) R(12) R(14) R(16) R(18) R(20) R(22) R(24) R(26) R(28) R(30) R(32) R(34) R(36) R(38) R(40)

878.43349(3) 880.37043(3) 882.28729(3) 884.18426(2) 886.06126(2) 887.91857(2) 889.75613(2) 891.57384(2) 893.37202(1) 895.15053(1) 896.90946(1) 898.64879(1) 900.36865(1) 902.06890(1) 903.74969(2) 905.41100(1) 907.05283(1) 908.67506(2) 910.27799(2) 911.86113(2) 914.19960(4) 915.73389(2) 917.24879(2) 918.74394(2) 920.21947(1) 921.67526(1) 923.11126(1) 924.52752(1) 925.92391(1) 927.30013(1) 928.65669(1) 929.99296(1) 931.30921(1) 932.60507(1) 933.88066(1) 935.13576(1) 936.37037(1) 937.58435(2) 938.77749(2) 939.94986(2) 941.10124(2)

0.0689( 7) 0.0674( 5) 0.0694( 4) 0.0691( 4) 0.0687( 3) 0.0693( 3) 0.0694( 3) 0.0713( 2) 0.0711( 2) 0.0724( 2) 0.0742( 2) 0.0757( 2) 0.0757( 2) 0.0772( 2) 0.0786( 2) 0.0815( 2) 0.0825( 3) 0.0849( 3) 0.0859( 4) 0.0891( 6) 0.0908(12) 0.0856( 4) 0.0852( 3) 0.0824( 2) 0.0803( 2) 0.0792( 2) 0.0780( 2) 0.0774( 2) 0.0754( 2) 0.0738( 2) 0.0725( 2) 0.0722( 2) 0.0715( 2) 0.0696( 2) 0.0694( 2) 0.0687( 2) 0.0684( 2) 0.0684( 2) 0.0666( 3) 0.0670( 3) 0.0656( 4)

0.0697(11) 0.0704( 8) 0.0713( 7) 0.0707( 5) 0.0719( 5) 0.0722( 4) 0.0712( 4) 0.0736( 3) 0.0728( 3) 0.0739( 3) 0.0750( 3) 0.0768( 3) 0.0774( 3) 0.0780( 3) 0.0794( 3) 0.0813( 3) 0.0831( 4) 0.0864( 4) 0.0900( 6) 0.0938(10) 0.0923(19) 0.0863( 7) 0.0872( 4) 0.0851( 4) 0.0819( 3) 0.0811( 3) 0.0797( 2) 0.0783( 2) 0.0763( 2) 0.0750( 2) 0.0742( 2) 0.0738( 2) 0.0720( 2) 0.0709( 2) 0.0721( 3) 0.0703( 3) 0.0702( 3) 0.0696( 4) 0.0689( 4) 0.0668( 5) 0.0678( 6)

−0.0017( −0.0017( −0.0007( −0.0016( −0.0013( −0.0012( −0.0024( −0.0010( −0.0023( −0.0018( −0.0022( −0.0021( −0.0021( −0.0020( −0.0019( −0.0025( −0.0015( −0.0015( −0.0021( −0.0027( +0.0002( +0.0003( −0.0005( −0.0006( −0.0005( −0.0004( −0.0007( −0.0012( −0.0011( −0.0009( −0.0015( −0.0010( −0.0013( −0.0018( −0.0015( −0.0014( −0.0014( −0.0012( −0.0013( −0.0018( −0.0025(

13

C16 O2

0 (N2 )b 6) 4) 3) 3) 2) 2) 2) 2) 2) 2) 2) 1) 2) 2) 2) 2) 2) 2) 3) 5) 9) 3) 2) 2) 1) 1) 1) 1) 1) 2) 1) 1) 1) 1) 1) 1) 2) 2) 2) 2) 3)

−0.0018( −0.0017( −0.0030( +0.0000( −0.0023( −0.0013( −0.0017( −0.0015( −0.0020( −0.0019( −0.0025( −0.0029( −0.0025( −0.0015( −0.0021( −0.0016( −0.0016( −0.0010(

6) 5) 4) 4) 3) 3) 3) 3) 2) 2) 2) 2) 2) 2) 3) 3) 3) 4)

+0.0002( −0.0012( +0.0002( −0.0014( +0.0000( +0.0005( −0.0008( +0.0001( +0.0001( −0.0015( −0.0009( −0.0013( −0.0013( −0.0011( −0.0011( −0.0012( −0.0022( −0.0021( −0.0027( −0.0017(

5) 3) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 3) 3) 4) 5)

The uncertainties listed in parentheses are one standard deviation in units of the last digit quoted. a The broadening coe+cients are in cm−1 =atm at 296 K. The value of n for each line was taken from the HITRAN database [16,17]. b The shift coe+cients are in cm−1 =atm at the corresponding temperature of the spectra.

V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434 Table 4 Zero-pressure line center positions, air- and N2 -broadened width and shift coe+cients for the 3 − 202 band of

13

421

C16 O2

Line

 (cm−1 )

b0L (air)a

b0L (N2 )a

0 (air)b

0 (N2 )b

P(40) P(38) P(36) P(34) P(32) P(30) P(28) P(26) P(24) P(22) P(20) P(18) P(16) P(14) P(12) P(10) P( 8) P( 6) P( 4) P( 2) R( 0) R( 2) R( 4) R( 6) R( 8) R(10) R(12) R(14) R(16) R(18) R(20) R(22) R(24) R(26) R(28) R(30) R(32) R(34) R(36) R(38) R(40)

980.80500(2) 982.91252(2) 984.99304(2) 987.04652(1) 989.07271(1) 991.07148(1) 993.04251(1) 994.98581(1) 996.90107(1) 998.78821(1) 1000.64720(1) 1002.47774(1) 1004.27986(1) 1006.05326(1) 1007.79801(1) 1009.51395(1) 1011.20104(1) 1012.85916(1) 1014.48833(2) 1016.08820(2) 1018.43379(4) 1019.96114(2) 1021.45911(1) 1022.92799(1) 1024.36769(1) 1025.77822(1) 1027.15962(1) 1028.51186(1) 1029.83508(1) 1031.12925(1) 1032.39443(1) 1033.63074(1) 1034.83821(1) 1036.01693(1) 1037.16703(1) 1038.28863(1) 1039.38176(2) 1040.44661(2) 1041.48331(2) 1042.49188(2) 1043.47259(2)

0.0634( 4) 0.0671( 4) 0.0680( 3) 0.0673( 2) 0.0680( 2) 0.0680( 2) 0.0693( 2) 0.0706( 2) 0.0705( 2) 0.0718( 2) 0.0723( 2) 0.0733( 2) 0.0775( 2) 0.0758( 2) 0.0781( 2) 0.0791( 2) 0.0814( 2) 0.0815( 3) 0.0848( 4) 0.0846( 6) 0.0930(13) 0.0871( 5) 0.0844( 3) 0.0814( 2) 0.0796( 2) 0.0784( 2) 0.0771( 2) 0.0755( 2) 0.0738( 2) 0.0731( 2) 0.0718( 2) 0.0714( 2) 0.0699( 2) 0.0691( 2) 0.0683( 2) 0.0693( 2) 0.0682( 3) 0.0680( 3) 0.0671( 3) 0.0658( 4) 0.0654( 5)

0.0693( 7) 0.0689( 5) 0.0695( 5) 0.0690( 4) 0.0702( 3) 0.0706( 3) 0.0713( 3) 0.0721( 3) 0.0716( 2) 0.0740( 2) 0.0740( 2) 0.0744( 2) 0.0798( 3) 0.0770( 2) 0.0797( 3) 0.0818( 3) 0.0820( 3) 0.0854( 4) 0.0855( 6) 0.0888(10) 0.0927(20) 0.0867( 7) 0.0844( 5) 0.0835( 4) 0.0811( 3) 0.0797( 3) 0.0789( 2) 0.0766( 2) 0.0761( 2) 0.0751( 2) 0.0730( 2) 0.0732( 2) 0.0730( 3) 0.0709( 3) 0.0711( 3) 0.0717( 3) 0.0707( 4) 0.0695( 5) 0.0681( 5) 0.0679( 6) 0.0673( 7)

−0.0013( −0.0017( −0.0015( −0.0015( −0.0020( −0.0017( −0.0014( −0.0018( −0.0019( −0.0020( −0.0017( −0.0018( −0.0021( −0.0014( −0.0016( −0.0018( −0.0008( −0.0018( −0.0023( +0.0016(

3) 3) 2) 2) 2) 2) 1) 1) 1) 1) 1) 1) 1) 1) 1) 1) 2) 2) 3) 5)

−0.0030( −0.0028( −0.0009( −0.0016( −0.0014( −0.0020( −0.0009( −0.0013( −0.0018( −0.0012( −0.0022( −0.0015( −0.0028( −0.0013( −0.0020( −0.0011( −0.0009( −0.0023( −0.0017( −0.0011(

6) 4) 4) 3) 3) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 3) 4) 9)

+0.0002( +0.0001( +0.0001( −0.0001( +0.0003( −0.0002( −0.0003( −0.0007( −0.0013( −0.0003( −0.0008( −0.0011( −0.0004( −0.0009( −0.0012( −0.0005( −0.0006( −0.0017( −0.0013( −0.0020(

4) 2) 2) 2) 1) 1) 1) 1) 1) 1) 1) 1) 1) 2) 2) 2) 2) 2) 3) 4)

+0.0011( +0.0007( +0.0004( +0.0006( −0.0000( −0.0002( +0.0000( −0.0003( −0.0010( −0.0007( −0.0006( −0.0010( −0.0009( −0.0006( −0.0013( −0.0017( −0.0017( −0.0011( −0.0008( −0.0021(

6) 4) 3) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 2) 3) 3) 3) 4) 5) 6)

The uncertainties listed in parentheses are one standard deviation in units of the last digit quoted. a The broadening coe+cients are in cm−1 =atm at 296 K. The value of n for each line was taken from the HITRAN database [16,17]. b The shift coe+cients are in cm−1 =atm at the corresponding temperature of the spectra.

422

V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

Fig. 3. Measured self- and air-broadening coe+cients at 296 K plotted as a function of m for the 12 C16 O2 laser bands. Results for band I are plotted in (a) and those for band II are shown in panel (b). The self-broadening coe+cients plotted in both (a) and (b) decrease more rapidly with m compared to the air-broadening coe+cients that decrease very slowly with m. Where error bars are not visible the measurement uncertainties are smaller than the size of the symbol used.

nitrogen-broadening coe+cients. In the HITRAN database pressure shifts (air-induced shifts) are available only for a few CO2 transitions and the values are based upon the results (N2 -induced shifts) provided for the 3 fundamental by Devi et al. [24]. The following comparisons of the measured broadening and shift coe+cients were made: (a) between bands (b) between broadening gases and (c) between isotopomers (13 C16 O2 versus 12 C16 O2 ). The results are summarized below and also listed in Table 5.

V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

423

Fig. 4. Measured air- and N2 -broadening coe+cients, b0L (air) and b0L (N2 ), in cm−1 =atm at 296 K as a function of m for 12 16 C O2 and 13 C16 O2 plotted for (a) laser band I (b) laser band II. Where error bars are not visible the measurement uncertainties are smaller than the size of the symbol used.

(a) In 12 C16 O2 , within our experimental uncertainties, the broadening coe+cients (for all three gases) for the 9.4- and 10:4-m laser bands were found to be close. However, in the case of 13 CO2 , the air- and N2 -broadening coe+cients in the 9:4-m band were slightly (∼1%) larger than the corresponding values in the 10:4-m band. More studies involving spectra obtained with higher optical densities and signal-to-noise ratios could verify this observation. (b) For both laser bands in both isotopomers, air-broadening is about 2– 4% smaller than N2 -broadening. As mentioned earlier in the discussion of Fig. 3, in the case of 12 C16 O2 , self-broadening

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V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

coe+cients are about 10 –35% larger (depending upon the transition) than the corresponding air-broadening coe+cients, and the ratio of self- to air-broadening (and self- to N2 -broadening) is not same for all transitions. (c) Although the diDerences between corresponding broadening coe+cients for 12 C16 O2 and 13 C16 O2 are small, there is marginal evidence that N2 -broadening parameters for 12 C16 O2 may be 1–2% larger than those for 13 C16 O2 . For both the 9.4- and 10:4-m bands, the air-broadening coe+cients for 12 C16 O2 and 13 C16 O2 as well as the self-broadening coe+cients measured for 12 C16 O2 compare well (within ±1% on average) with the corresponding values in the HITRAN line parameters compilation [16,17]. In the HITRAN database [16,17] the broadening coe+cients are assumed to be identical for all isotopomers. Accuracy of our measured broadening coe+cients is estimated based upon the following sources of errors. Uncertainties listed in the broadening coe+cients in Tables 1–4 take into account only those derived by the multispectrum Bts. Systematic errors caused by other sources such as measurement of sample temperatures and pressures, volume mixing ratios of 13 C16 O2 and 12 C16 O2 determined in the sample mixtures, amounts of 12 C16 O2 in the nitrogen purged atmospheric paths and within the evacuated FTS tank may contribute an additional 1% error to listed broadening parameters. Instrumental errors caused by the instability of the source or detector nonlinearity and errors from line parameters that were constrained (for weak transitions) in the least-squares solution may also contribute to values listed in Tables 1–4. These errors are rather di+cult to quantify. Errors arising from uncertainties in spectrum parameters such as zero-level oDsets, zero absorption level of each spectrum and the FTS phase errors were minimized by treating these quantities as free (unconstrained) parameters in our multispectrum Bts. Finally, the accuracy of the broadening coe+cients determined using Eq. (3) is also dependent upon the accuracy of the n values used in computing the measured broadening coe+cients to 296 K. For small temperature diDerences between 296 K and the temperature of the spectra, error introduced by using two n values diDering as much as 0.1 corresponds to [0.1/296] times the temperature diDerence. As an example, for a temperature diDerence of 5 K between 296 K and the sample temperature, the error introduced in the broadening coe+cient is still less than 0.2%. Consolidating all known errors we estimate the total uncertainty in our broadening coe+cients to be ∼2% plus the uncertainty listed in Tables 1–4. The measured broadening coe+cients were Bt to a cubic polynomial using nonlinear regression. The polynomial has the form: b0L = c0 + c1 M + c2 M 2 + c3 M 3 ;

(4)

where M = |m|, and m = −J

in the P branch and J

+ 1 in the R branch. The coe+cients of the above cubic polynomial determined from the measurements are listed in Table 6 and the units of b0L are cm−1 =atm at 296 K. The use of these empirical models to determine the broadening coe+cients far outside the quantum number range of the present measurements may not yield reliable values and therefore should be avoided. In our comparisons for self-broadening coe+cients, we have included only the results of Dana et al. [20], but none of the measurements prior to 1990 (since calculations of self-broadening in the HITRAN are based upon the results of Dana et al.). The mean and standard deviation of ratios of self-broadening coe+cients between Dana et al. [20] and the present measurements are 0.990 and 0.023 for laser band I and 1.001 and 0.023 for laser band II, respectively.

V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434 Table 5 Comparison of broadening and shift coe+cients in the 9.4- and 10:4-m laser bands of (1) Comparison between Band I and Band II



BandI BandII

Isotopomer

Broadening gas

b0L Ratio

12

Air N2 Self Air N2

0:997 ± 0:025 0:993 ± 0:028 1:005 ± 0:017 1:011 ± 0:015 1:011 ± 0:018

C16 O2 C16 O2 12 16 C O2 13 16 C O2 13 16 C O2 12

12

C16 O2 and

13

C16 O2

 0 DiDerencea (Band I-Band II) (cm−1 =atm) −0:0002 ± 0:0009; −0:0001 ± 0:0011; −0:0001 ± 0:0012; −0:0004 ± 0:0008; −0:0002 ± 0:0009;

[0.0001] [0.0002] [0.0002] [0.0001] [0.0001]

(2) Comparison of results between broadening gases Isotopomer

Broadening gases A/B

Band

b0L Ratio A/B

12

N2 =air N2 =air Self/air Self/N2 Self/air Self/N2 N2 =air N2 =air

I II I I II II I II

1:033 ± 0:017 1:038 ± 0:012 1:287 ± 0:092 1:250 ± 0:082 1:263 ± 0:096 1:227 ± 0:090 1:023 ± 0:012 1:026 ± 0:016

C16 O2 C16 O2 12 16 C O2 12 16 C O2 12 16 C O2 12 16 C O2 13 16 C O2 13 16 C O2 12

(3) Comparison of results between

13

C16 O2 and

12

0 DiDerencea (A − B) (cm−1 =atm) 0:0002 ± 0:0010; 0:0003 ± 0:0008; −0:0007 ± 0:0010; −0:0009 ± 0:0013; −0:0004 ± 0:0011; −0:0007 ± 0:0010; 0:0002 ± 0:0009; −0:0000 ± 0:0008;

[0.0002] [0.0001] [0.0002] [0.0002] [0.0002] [0.0002] [0.0002] [0.0001]

C16 O2  13

C16 O2 12 C16 O 2

Broadening Gas

Band

b0L Ratio

Air b0L (Air) N2 N2

I II I II

1:002 ± 0:020 0:989 ± 0:018 0:990 ± 0:020 0:978 ± 0:013

 0 DiDerencea (13 C16 O2 − 12 C16 O2 ) (cm−1 =atm) 0:0000 ± 0:0007; 0:0004 ± 0:0007; −0:0001 ± 0:0007; 0:0001 ± 0:0007;

[0.0001] [0.0001] [0.0001] [0.0001]

(4) Comparison of results between HITRAN and present work Isotopomer

Parameter

Band

Ratio (present work/HITRAN)

C16 O2 C16 O2 12 16 C O2 12 16 C O2 13 16 C O2 13 16 C O2

b0L (Air) b0L (Self ) b0L (Air) b0L (Self ) b0L (Air) b0L (Air)

I I II II I II

0:993 ± 0:017 1:000 ± 0:020 0:993 ± 0:018 1:005 ± 0:017 0:989 ± 0:017 1:002 ± 0:018

12 12

No pressure shift coe+cients are listed for the CO2 laser bands in the HITRAN database [16,17]. a Mean and standard deviation. The values in [] represent standard deviation of the mean (standard error).

425

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Fig. 5. Measured N2 -broadening coe+cients in the laser bands, the 3 bands [26], and the 33 band [27] of 12 C16 O2 (lower panel) and 13 C16 O2 [upper panel; laser bands and the 3 bands (26)]. Values for both the P- and R-branches are plotted as a function of |m|.

We have recently reported measurements of N2 -broadening coe+cients in the 3 bands of 12 C16 O2 and 13 C16 O2 [26]. Those broadening coe+cients are plotted in Fig. 5 along with the values measured for the laser bands in the present work and in the 33 band by Thibault et al. [27]. We note that for 13 16 C O2 it appears that the 3 N2 -broadening coe+cients are slightly larger than the values of laser bands, while the reverse is true for the 12 C16 O2 isotopomer. However, these diDerences are small compared to the absolute uncertainties of the measurements, so we cannot be sure that there is a real vibrational dependence of the N2 -broadening between the laser bands and the 3 fundamental. As seen in Fig. 5, a stronger case can be made for the vibrational dependence of broadening between the 3 and 33 bands. However, such a comparison would be more appropriate if both the 3 and the 33 bands were recorded by the same group of investigators with the same instrument and measured using the same analysis technique.

2

0.0013 101 1 6 |m| 6 54 0:09331 ± 0:00053 −(1:750 ± 0:085) × 10−3 (4:37 ± 0:37) × 10−5 −(3:98 ± 0:47) × 10−7

0.0007 86 2 6 |m| 6 48 −(1:50 ± 3:87) × 10−4 −(2:38 ± 0:67) × 10−4 (1:04 ± 0:32) × 10−5 −(1:40 ± 0:43) × 10−7

2

0.0007 58 1 6 |m| 6 47 −(2:13 ± 0:39) × 10−3 (3:80 ± 5:31) × 10−5 −(2:18 ± 1:94) × 10−6 (2:56 ± 2:02) × 10−8

P branch

0 (Self )a

0.0011 81 1 6 |m| 6 41 0:09315 ± 0:00053 −(1:539 ± 0:108) × 10−3 (3:81 ± 0:59) × 10−5 −(3:75 ± 0:93) × 10−7

13 C16 O

0.0008 87 1 6 |m| 6 47 −(2:74 ± 2:81) × 10−4 (4:56 ± 4:99) × 10−5 −(4:74 ± 2:42) × 10−6 (6:32 ± 3:37) × 10−8

R branch

0.0013 97 1 6 |m| 6 49 0:09593 ± 0:00059 −(1:752 ± 0:101) × 10−3 (4:43 ± 0:46) × 10−5 −(4:13 ± 0:61) × 10−7

2

2

0.0009 61 1 6 |m| 6 47 −(1:35 ± 0:44) × 10−3 −(5:11 ± 6:26) × 10−5 (1:35 ± 2:38) × 10−6 −(1:52 ± 2:56) × 10−8

R branch

0.0015 120 1 6 |m| 6 62 0:1223 ± 0:00057 −(1:409 ± 0:080) × 10−3 (1:26 ± 0:30) × 10−5 −(8:74 ± 3:20) × 10−8

12 C16 O

b0L (Self )a

Pressure shift coe+cients are in cm−1 =atm at the corresponding temperature of the spectra. a Self-shift coe+cients were measured for only 12 C16 O2 bands. In both branches and both laser bands, use measured values rather than Btted values [for computing shift coe+cients] for 10 6 |m| 6 20. b Standard error of estimate (in cm−1 =atm).

0.0006 87 1 6 |m| 6 47 (0:970 ± 27:1) × 10−5 −(8:93 ± 4:87) × 10−5 (3:58 ± 2:39) × 10−6 −(6:62 ± 3:36) × 10−8

P branch

P branch

R branch

0 (N2 )

C16 O2 bands.

0 (Air)

SEEb 0.0007 No. of points 90 Range in M 2 6 |m| 6 54 −(7:52 ± 3:08) × 10−4 c0 −(1:59 ± 0:50) × 10−4 c1 c2 (6:33 ± 2:18) × 10−6 c3 −(7:13 ± 2:76) × 10−8

Constant

Table 7 Polynomial Bts to measured pressure shift coe+cients

12

0.0011 83 1 6 |m| 6 42 0:09075 ± 0:00054 −(1:329 ± 0:108) × 10−3 (2:60 ± 0:58) × 10−5 −(1:93 ± 0:89) × 10−7

12 C16 O

13 C16 O

12 C16 O

2

b0L (N2 )

b0L (Air)

Broadening coe+cients are in cm−1 =atm at 296 K. a Self-broadening coe+cients were measured for only b Standard error of estimate (in cm−1 =atm).

No. of points Range in M c0 c1 c2 c3

SEEb

Constant

Table 6 Polynomial Bts to measured broadening coe+cients

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3.2. Pressure-induced shift coe@cients The pressure-induced line shift coe+cients determined for air-, N2 - and self-broadening for the C16 O2 laser bands are listed in the last three columns in Tables 1 and 2. The air- and N2 -induced shift coe+cients for the two 13 CO2 laser bands are given in the last two columns in Tables 3 and 4. The air-induced shift coe+cients 0 (air) and N2 -induced shift coe+cients 0 (N2 ) in cm−1 =atm, measured for laser band I and II in 12 C16 O2 and 13 C16 O2 are plotted in Fig. 6(a) and (b), respectively. The self-shift coe+cients 0 (self ) in cm−1 =atm, for the 12 C16 O2 laser bands are displayed in Fig. 6(c). Except for a few data points, the measured shift coe+cients were negative. Under the experimental conditions used for recording air- and N2 -broadened spectra, the R(0) transition was very weak, and therefore the pressure-shift coe+cient for the R(0) line was more uncertain than most of the other lines [Tables 2–5 and Fig. 6(a) and (b)]. Variation of pressure-shift coe+cients with m (transition dependence) is clearly observed in these plots. The pressure shift coe+cients in the P-branch lines are diDerent than the pressure shifts in the R-branch lines. Also, the pressure-shift coe+cients in the R branch displayed a clearer m- (or J

) dependence than the P branch shift coe+cients. We Bnd that within our experimental uncertainties, the air- and N2 -induced shift coefBcients in 12 C16 O2 and 13 C16 O2 lines agreed fairly closely. Because the pressure shift coe+cients are much smaller than the broadening coe+cients, the precision achieved in the shift coe+cients is less than that of the broadening coe+cients. The present measurements and the results in Ref. [1] are the only studies revealing a J

dependence of pressure-induced shifts in the CO2 laser bands. Unlike the cases of air- and N2 -shift coe+cients, the self-shift coe+cients for transitions with |m| = ∼10–20 exhibit some peculiar behavior. In the P branch a “break” in the m-dependence of the shifts occurs between P(18) and P(20) in band I and between P(14) and P(16) in band II. In the R branch a similar “break” occurs between R(18) and R(20) in band I and between R(10) and R(12) in band II. Such large Vuctuations in the m-dependence of line shifts have been observed in cases of one polar molecule perturbed by another (see Ref. [28] and references therein). However, this type of m-dependence of shifts has not been previously observed for CO2 . A few examples from present measurements are shown below. 12

Transition

0 (self ) in cm−1 =atm

Transition

0 (self ) in cm−1 =atm

P(18) P(18) P(16) P(16)

−0:0007 ± 0:0001 −0:0031 ± 0:0002 −0:0006 ± 0:0001 −0:0034 ± 0:0002

R(16) R(16) R(18) R(18)

−0:0035 ± 0:0001 −0:0001 ± 0:0002 −0:0048 ± 0:0001 −0:0015 ± 0:0001

I II I II

I II I II

The diDerences in pressure shifts between pairs of transitions (listed above) are much larger than the measurement uncertainty (∼0:0001–0:0002 cm−1 =atm). However, we believe that these diDerences cannot be attributed to any measurement errors since self-broadening and N2 -broadening (or selfand air-broadening) were determined simultaneously using the same sets of data. The FTS phase errors we correct in our least-squares Bttings are the residual phase errors remaining from the phase correction that one normally applies while transforming the raw FTS data. On spectra

V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 411 – 434

429

Fig. 6. Measured pressure-shift coe+cients (in cm−1 =atm) plotted as a function of m for (a) 0 (air) in 12 C16 O2 and 13 C16 O2 laser bands (b) 0 (N2 ) in 12 C16 O2 and 13 C16 O2 laser bands and (c) 0 (self ) in 12 C16 O2 laser bands. The horizontal dashed line in each plot corresponds to zero pressure-shift coe+cients. The polynomial Bts for the P- and R-branches are shown in each panel with dashed and solid curves, respectively. Where error bars are not visible the uncertainties in the measured quantities are smaller than the size of the symbols used.

recorded with high pressure the determination of line position is more sensitive to this error than from low-pressure spectra. However, at high pressures, the induced asymmetry in the line proBles is su+cient to determine the residual phase errors quite well. In our least-squares Bttings we determined these phase errors to be very small indicating the (good) symmetry in the line shape. As a result the

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retrieved pressure shift coe+cients should be as good as it needs to be in order to determine positions to within the limits of other sources of error. Based upon the same uncertainty considerations as those for pressure broadening coe+cients, for strong well-measured transitions (4 6 J 6 40) we estimate the precision in the shift coe+cients to be about 5 –10% and the absolute uncertainty to be ∼10–30%. Similar to comparisons with broadening coe+cients, we also made comparisons of pressure shift coe+cients between the two laser bands, broadening gases and isotopomers. The results are listed in Table 5. We found that for pressure-induced shifts, it was more meaningful to calculate the pressure shift diDerences than their ratios. Within the experimental uncertainties and estimated errors, we did not Bnd any signiBcant diDerences in the shift coe+cients between the two laser bands, broadening gases or isotopomers. In Table 5, the mean and standard deviation of the pressure shift diDerences are listed. We have also listed the standard error estimate (SEE) associated with each mean and standard deviation. For the sake of completeness all the measured pressure shift coe+cients listed in Tables 1–4 were Bt to a cubic polynomial using nonlinear regression. The polynomial expression was similar to the one used for the broadening coe+cients [Eq. (4)]. However, since the |m|-dependence of the shifts is not symmetric [see Fig. 6(a) – (c)], the P- and R-branches were Bt separately. For each branch, all available measurements for both isotopomers (12 C16 O2 and 13 C16 O2 ) and both laser bands were Bt together, since the diDerences between bands and isotopomers were smaller than the uncertainties of the measurements. The coe+cients of the cubic polynomial determined from the measurements are listed in Table 7. The units of 0 are in cm−1 =atm at the corresponding temperature of the spectra. In the case of 0 (self ), in both branches of both laser bands, measured values are to be used rather than Btted values for 10 6 |m| 6 20 [see Fig. 6(c)]. For the polynomial Bts of the widths, all the constants are statistically determined. The c3 term for the self-broadened widths has the largest uncertainty. In contrast, for the Btting of the pressure shifts, only about one-third of the constants have values larger than the statistical uncertainty. Empirical expressions like these are most useful to interpolate missing values that cannot be directly measured; if the modeling is good, they can be used in the formation of databases such as HITRAN. However, for the pressure shifts, such expressions should be used sparingly, for as seen in Fig. 6, the expression deviates greatly for some of the measured values. The only other extensive self-induced pressure shift measurements in the 12 C16 O2 laser bands were reported by Kou and Guelachvili [7] who analyzed room temperature spectra recorded with the FTS of Laboratoire d’Infrarouge, Orsay, France. They measured shifts of 40 transitions in each of the two laser bands at four diDerent pressures (between 3 and 100 Torr). Their measurements were based upon a spectrum-by-spectrum analysis technique. Their self-shift coe+cients were negative and no evidence of J -dependence was found. Their average self-induced pressure shift coe+cient for the two laser bands was −0:0036 cm−1 =atm (−4:8 × 10−6 cm−1 =Torr) with a standard deviation of ∼0:002 cm−1 =atm. This is close to the lower bound of our present self-shift measurements. From studies conducted with small gas pressures (¡ 130 m Torr) SooHoo et al. [5,6] reported self-shift coe+cients of 63:1 ± 18:1 kHz=Torr [ + 0:0016 ± 0:0005 cm−1 =atm] and 62:1 ± 18:1 kHz=Torr [ + 0:0016 ± 0:0005 cm−1 =atm] as average values for the P and R branches in 12 16 C O2 laser bands. For the 13 C16 O2 laser bands they obtained 50:3 ± 16:8 kHz=Torr [ + 0:0013 ± 0:0004 cm−1 =atm] and 87:2 ± 37:8 kHz=Torr [ + 0:0022 ± 0:0010 cm−1 =atm] as the mean self-shift coe+cients for the P and R branches, respectively. Their measurements revealed very little J

de-

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431

pendence and no signiBcant diDerences between the P- and R-branch pressure shifts. In contrast, the self-shift coe+cients obtained in our present study clearly showed a J -dependence similar to air- and N2 -induced shift coe+cients, except for the “breaks” between J

= 10 and 20. The magnitudes of the self-shift coe+cients were found to be not much diDerent from the shifts produced by air or N2 . For all three broadening gases, the majority of the shift coe+cients were negative with values ranging between zero and −0:004 cm−1 =atm at the corresponding temperature of the spectra. In Fig. 7(a) and (b), we have compared the N2 -shift coe+cients measured in the 12 C16 O2 and 13 16 C O2 laser bands with the N2 shift coe+cients reported for the 3 band [26] and the 33 band [27]. Similarly, the self-shift coe+cients in the laser bands are compared [Fig. 7(c)] to those in the 33 band [27,30] and to the 21 + 202 + 3 band [29]. Similar to the measurements in the present work and the 3 study [26], the results in Refs. [27,29,30] also show clear J

dependence in the shift coe+cients. Arcas et al. [30] reported a self-shift coe+cient of −0:014 cm−1 =atm for the R(6) line in the 33 CO2 band. This value is nearly twice the magnitude of the shifts measured by Thibault [27] for the same transition. Although temperature dependence of self-broadening and foreign-gas broadening for several transitions in the 12 C16 O2 laser bands have been published in the literature (e.g. [8–11]), they are by no means exhaustive. Pressure-induced shifts were not determined in any of those studies. We have shown from the present study that the pressure-induced shifts due to self- and foreign gases are non-negligible and should be taken into account in the measurement of positions of CO2 laser transitions. As previously stated in Ref. [1] it will be highly useful for atmospheric applications to make a comprehensive study of the temperature dependence of both broadening and pressure-induced shift coe+cients for these transitions. 4. Conclusions The Brst extensive high-resolution experimental measurements of pressure broadening and pressureshift coe+cients of 13 CO2 laser bands using air and N2 as the broadening gases are presented here. This includes the Brst simultaneous analysis of both 12 C16 O2 and 13 C16 O2 spectra to obtain a consistent set of broadening and shift coe+cients involving air and N2 for the two laser bands. Self-broadening and self-shift coe+cients for the 12 C16 O2 laser bands and an observed J -dependence in the measured self-induced shift coe+cients have been determined. The self- and air-broadening coe+cients of the 12 C16 O2 laser bands agree to within 1% with the HITRAN database. No signiBcant vibrational dependence of broadening or pressure-shift coe+cients was evident between the two laser bands. No isotopic dependence greater than ∼1–2% in broadening measurements and in shift coe+cients (except in a few cases) greater than 0:001 cm−1 =atm was noticed when we compared measurements in the 12 C16 O2 and 13 C16 O2 laser bands perturbed by air or N2 . For both isotopomers the air-broadening coe+cients were 2– 4% smaller than the corresponding N2 -broadened values, but the air- and N2 -induced shifts were nearly the same. Some unexplained patterns in the self-induced shift coe+cients of 12 C16 O2 in both laser bands were observed. These pressure-shift coe+cients should be included in the future updates of the HITRAN line parameters compilation. The results should prove useful for the general understanding of the pressure broadening and pressure-shift parameters of the carbon dioxide molecule.

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Fig. 7. Measured pressure-induced shift coe+cients in cm−1 =atm of the CO2 bands as a function of m plotted for (a) N2 -induced shift coe+cients in the laser bands and the 3 band [26] of 13 C16 O2 (b) N2 -induced shift coe+cients in the laser bands, 3 band [24,26] and the 33 band [27] of 12 C16 O2 and (c) self-induced shift coe+cients in the laser bands, 33 band [27,30] and the 21 + 202 + 3 band [29] of 12 C16 O2 . The vibrational dependence of pressure-induced shifts is clearly distinguishable in these plots. Where error bars are not visible the uncertainties in the measured quantities are smaller than the size of the symbols used.

Line mixing and the temperature dependence of broadening and shift parameters could not be determined from the spectra recorded for this investigation. However, these additional parameters may be important for interpretation of atmospheric measurements and should be addressed in future laboratory investigations.

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Acknowledgements The authors thank Claude Plymate of the National Solar Observatory (NSO) for assistance in recording the spectra. Cooperative agreements and contracts with the National Aeronautics and Space Administration support the research at the College of William and Mary. The research at the Jet Propulsion Laboratory (JPL), California Institute of Technology was performed under contract with the National Aeronautics and Space Administration. The Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation operates NSO. We also gratefully acknowledge the additional Bnancial support of the McMath–Pierce FTS laboratory facility by the NASA Upper Atmosphere Research Program. References [1] Malathy Devi V, Benner DC, Smith MAH, Rinsland CP. Air- and N2 -broadening coe+cients and pressure-shift coe+cients in the 12 C16 O2 laser bands. JQSRT 1998;59(3–5):137–49. [2] Mandin J-Y, Dana V, Badaoui M, Guelachvili G, Morillon-Chapey M, Kou Q. Intensities and self-broadening coe+cients of 13 C16 O2 lines in the laser band region. J Mol Spectrosc 1992;155:393–402. [3] Freed C, Ross AHM, O’Donnell RG. Determination of laser line frequencies and vibrational-rotational constants of the 12 C18 O2 , 13 C16 O2 and 13 C18 O2 isotopes from measurements of CW beat frequencies with fast HgCdTe photodiodes and microwave frequency counters. J Mol Spectrosc 1974;49:439–53. [4] Woods PT, JolliDe BW. Stable single-frequency carbon dioxide lasers. J Phys E 1976;9:395–402. [5] SooHoo KL, Freed C, Thomas JE, Haus HA. Anomalous saturated absorption pressure shifts in CO2 . Phys Rev Lett 1984;53:1437–40. [6] SooHoo KL, Freed C, Thomas JE, Haus HA. Line center stabilized CO2 lasers as secondary frequency standards: determination of pressure shifts and other errors. IEEE J Quant Elec 1985;QE-21(8):1159–71. [7] Kou Q, Guelachvili G. Self-induced pressure shifts in the 9.4- and 10:4-m bands of CO2 by Fourier transform spectroscopy. J Mol Spectrosc 1991;148:324–8. [8] Bulanin MO, Bulychev VP, Khodos EB. Determination of the parameters of the vibrational-rotational lines in the 9.4 and 10:4 m bands of CO2 at diDerent temperatures. Opt Spectrosc (USSR) 1980;48(4):403–6. [9] Osipov VM. Temperature dependence of the P20 line halfwidth of the 10:6-m band of CO2 in the 500 –2100-K range. Opt Spectrosc (USSR) 1987;63(5):598–9. [10] Gross LA, Gri+ths PR. Pressure and temperature dependence of the self-broadened linewidths of the carbon dioxide laser bands. Appl Opt 1987;26(11):2250–5. [11] AriUe E, Lacome N, LUevy A. Measurement of CO2 line broadening in the 10:4-m laser transition at low temperatures. Appl Opt 1987;26(9):1636–40. [12] Malathy Devi V, Benner DC, Smith MAH, Rinsland CP, Brown LR, Dulick M. Absolute intensity measurements of the 12 C16 O2 laser bands near 10 m. JQSRT 2002;76(3–4):393–410. [13] Maki AG, Chou C-C, Evenson KM, Zink LR, Shy J-T. Improved molecular constants and frequencies for the CO2 laser from new high-J regular and hot-band frequency measurements. J Mol Spectrosc 1994;167:211–24. [14] Bradley LC, Soohoo KL, Freed C. Absolute frequencies of lasing transitions in nine CO2 isotopic species. IEEE J Quant Electron 1986;QE22(2):234–67. [15] Bernard V, Nogues G, Daussy Ch, Constantin L, Chardonnet Ch. CO2 laser stabilized on narrow saturated absorption resonances of CO2 ; improved absolute frequency measurements. Matrologia 1997;34:313–8. [16] Rothman LS, Rinsland CP, Goldman A, Massie ST, Edwards DP, Flaud J-M, Perrin A, Camy-Peyret C, Dana V, Mandin J-Y, Schroeder J, McCann A, Gamache RR, Wattson RB, Yoshino K, Chance KV, Jucks KW, Brown LR, Nemtchinov V, Varanasi P. The HITRAN molecular spectroscopic database and HAWKS (HITRAN Atmospheric Workstation): 1996 Edition. JQSRT 1998;60(5):665–710. [17] Rothman LS, Barbe A, Benner DC, Brown LR, Camy-Peyret C, Carleer MR, Chance KV, Clerbaux C, Dana V, Devi VM, Fayt A, Fisher J, Flaud J-M, Gamache RR, Goldman A, Jacquemart D, Jucks KW, LaDerty WJ, Maki

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