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Absolute intensity measurements of the 12C16O2 laser bands near 10μm
Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 393 – 410
Absolute intensity measurements of the laser bands near 10 m
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12
C16O2
V. Malathy Devia; ∗ , D. Chris Benner a , M.A.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 1 April 2002; received in revised form 14 May 2002
Abstract Line intensities of the two 12 C16 O2 laser bands (3 –1 and 3 –202 ) centered near 960.9 and 1063:7 cm−1 , respectively, were obtained from analysis of 30 room temperature long path laboratory absorption spectra recorded at 0.0028 and 0:0053 cm−1 resolution with the McMath–Pierce Fourier transform spectrometer at the National Solar Observatory (located on Kitt Peak). The spectra were analyzed simultaneously with the multispectrum nonlinear least-squares ?tting procedure. The measured line intensities were further analyzed to derive the vibrational band intensities and Herman–Wallis coeAcients. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: CO2 ; CO2 laser bands; Infrared spectra; Fourier transform infrared (FTIR) spectroscopy; Absolute intensity
1. Introduction Accurate line parameters (positions, intensities and line shape coeAcients) of carbon dioxide transitions are required in order to retrieve atmospheric pressure and temperature from terrestrial remote sensing spectra. The prominent 12 C16 O2 laser bands located near 10 m (00011–10001 or 3 –1 at 960:9 cm−1 ) and (00011–10002 or 3 –202 at 1063:7 cm−1 ) are particularly useful for tropospheric studies. As a result, high-resolution laboratory investigations of both their intensities and pressure broadening have been pursued ([1– 4] and the references therein). The line positions of these two ∗
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 7 - 5
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bands are so well known from heterodyne measurements [5] that they are commonly referred to as “the laser bands” and serve as secondary standards for infrared line positions. For intensities, the more recent measurements from Dana et al. [3] and Johns and NoMel [4] have been found to agree within 2.8%. Subsequently, the values of Dana et al. (rather an average of the two studies) have been adopted for the HITRAN database [6 –8]. In this paper, we report new absolute line intensity measurements of these two bands in order to con?rm the accuracies of the past results and provide guidance for future improvements to the database. Previously, the pressure-broadening coeAcients of the main isotopomer were investigated [1], and recently we undertook an extension of that work for 13 C16 O2 . A new analysis of self-broadened 12 16 C O2 was also performed, resulting in the retrieval of line intensities as well. The multispectrum nonlinear least-squares procedure was applied to analyze 30 spectra of natural CO2 and 13 C-enriched CO2 , in pure samples and in dilute mixtures with dry air and nitrogen. The broadening results are reported elsewhere [2], but this paper presents the corresponding intensity analysis by which the band intensities, Herman–Wallis coeAcients and the square of the rotationless transition dipole moments were determined for the two laser bands of 12 C16 O2 . 2. Experimental details and data retrievals All spectra analyzed in this investigation were obtained with the McMath–Pierce Fourier transform spectrometer (FTS). The experimental conditions are summarized in Table 1. The McMath–Pierce 1-m Fourier Transform Spectrometer is a folded Michelson interferometer; each mirror can travel up to 1m, for a maximum path diOerence of 2 m. The interferometer has a total internal path of approximately 12 m from inputs to outputs. In practice, only one input and both outputs are utilized. The two outputs have complementary phases so that the diOerence in the signals produced by two matched detectors is used to record the interferogram. The sum of the signals is almost unmodulated and can be used to ratio out small DC source Puctuations when appropriate. The source is focused onto the plane of a circular aperture (generally 8 mm in diameter) and is accepted at the collimator as an f=50 beam. After passing through the interferometer, the collimated beam is reimaged onto the detectors with about a 15% image scale reduction. The 12-m path within the FTS between the input port and the detector mounts is housed in a vacuum chamber evacuated by high-speed pumps. Vacuum within the tank during operation falls in the 0.1– 0.01 Torr range. Operating the FTS under vacuum has many advantages including reduced atmospheric absorption, vacuum wavenumber results without index of refraction corrections, improved acoustic decoupling of the interferometer, and the elimination of convective currents. Appropriate optical ?lters are used to reduce the eOect of shot noise from all photons incident on the detectors in order to optically isolate the regions of the spectrum of interest. The external path from the glower source to the FTS tank is purged with dry nitrogen to reduce atmospheric absorption. This external path in most of our experimental conditions was on the order of 0.5 –1 m, but it was about 4 m when the 6-m base path White cell was used to record some of the spectra (spectra 1–10; see Table 1). The source of dry nitrogen used for purging these atmospheric paths was blow-oO from a 50-l liquid N2 Dewar containing a 100 W heater. The pressures in the purged atmospheric paths as well as the “evacuated” interferometer tank and the corresponding
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395
Table 1 Summary of the experimental conditions of the CO2 spectra Serial no.
Temperature (K)
Principal isotopomer and broadening gas
CO2 volume mixing ratio
Path (m)
Pressure (Torr)a
Spectral resolution (cm−1 )
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
297.30 297.60 297.60 297.60 297.60 292.00 291.90 291.95 295.50 295.80 298.35 298.35 295.85 295.95 298.95 298.85 298.65 298.65 298.55 298.35 297.15 296.95 297.75 297.85 298.05 298.15 297.45 297.65 297.85 297.95
12
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.025 0.025 0.025 0.025 0.035 0.035 0.035 0.035 1.0 1.0 0.055 0.055 0.055 0.055 0.033 0.033 0.033 0.033
193.28 433.88 72.98 72.98 193.28 72.98 72.98 72.98 97.04 97.04 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85
18.07 24.95 3.08 24.96 24.96 125.1 251.1 400.6 151.2 300.3 3.70 1.40 500.3 375.15 250.35 125.30 401.5 300.4 200.25 100.40 1.9 3.8 400.35 300.35 200.55 100.50 402.20 300.35 200.65 101.35
0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028
a
CO2 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 + air 12 CO2 + air 12 CO2 + air 12 CO2 + air 12 CO2 + N2 12 CO2 + N2 12 CO2 + N2 12 CO2 + N2 13 CO2 13 CO2 13 CO2 + air 13 CO2 + air 13 CO2 + air 13 CO2 + air 13 CO2 + N2 13 CO2 + N2 13 CO2 + N2 13 CO2 + N2 12
760 Torr = 1 atm = 101:325 kPa = 1:01325 bar.
temperatures are also usually monitored during the course of recording the spectra with appropriate pressure gauges and thermometer=thermistor probes. For the present study, a water-cooled glower operating between 120 and 150 V was used as the source of radiation. A KCl beamsplitter (wedged) with GaP coating was installed in the FTS, and the instrument was con?gured so that asymmetric interferograms were obtained to achieve the maximum (single pass) resolution of 0:0053 cm−1 . Near zero path diOerence the interferogram was two-sided. Liquid-helium-cooled As : Si detectors and a room temperature InSb optical ?lter were used in collecting the data covering the region 500 –1450 cm−1 . However, while recording the last 20 spectra listed in Table 1, an additional cold CaF2 ?lter was also used to reduce the optical band
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pass to 750 –1450 cm−1 . The diameter of the input aperture was set to 8 mm. The double-pass mode described by Jennings et al. [9] was used in recording spectra 11–30 listed in Table 1 at 0:0028 cm−1 resolution. The sampling frequency was set to 2500 Hz. The 30 spectra listed in Table 1 were obtained at three diOerent times and with two diOerent absorption cells. One cell was a 1.37-m base path Pyrex-bodied multipass cell with a total path set to 84:85 m. The other cell was a 6-m base path White cell (available at the National Solar Observatory) with total path length adjusted to 73, 97, 193 and 434 m. Spectra 1–5 were obtained using the 6-m baselength White cell. Twelve interferograms were co-added in each spectrum. The second set (spectra 6 –10) was also obtained using the same 6-m base path White cell, with the same resolution (0:0053 cm−1 ), and 20 interferograms were co-added for each spectrum. The remaining 20 spectra were recorded using the 1.37-m base path multipass cell. For the last 20 spectra recorded with 0:0028 cm−1 resolution 8–12 interferograms were co-added in each spectrum. A single, full resolution scan in double-pass mode took approximately 5 min to complete and the total time taken to record each spectrum was between 40 min and 1 h. This was suAcient to obtain a signal-to-RMS noise ratio in the range of ∼300–700. The absorption path lengths inside the White cell and Pyrex multipass cell are believed to be known with an uncertainty of ∼0:1% so that this uncertainty will have only minimal eOects on the retrieved line intensities. The sample pressures were measured and monitored using Datametrics or Baratron capacitance manometers (absolute pressure gauges) with a 0 –10 or 0 –1000 Torr head as appropriate. The Datametrics gauges were calibrated within a year prior to making measurements. Two T-type thermocouples attached to the body of the 1.37-m base path multipass cell were used to determine the sample temperatures. Temperatures of the sample within the White cell were measured with a single thermistor probe suspended inside the cell at the center. For the ?rst 10 spectra (Table 1) recorded with the White cell the average uncertainties in temperature and pressure measurements are about ±1:5 K and ±0:5%, respectively. The pressures and temperatures of the gas samples in spectra 11–30 (Table 1) remained constant to within ∼0:2% and ∼0:5 K, respectively. The gas samples were 99.995% pure natural CO2 (predominantly 12 CO2 ) and 90% 13 C-enriched CO2 . Spectra 1–14 (Table 1) were recorded with only the natural CO2 sample in the absorption cell and spectra 21 and 22 were recorded with the 13 CO2 sample alone. For the pressure-broadened spectra lean CO2 –air (or CO2 –N2 ) mixtures were prepared by initially ?lling the cell with either natural CO2 or 13 CO2 (∼12–22 Torr) and then adding dry air (or dry nitrogen) to the sample until the total pressure reached about 400 –500 Torr. In each series of pressure-broadened spectra (Table 1) the spectrum with the highest total pressure was recorded ?rst, and the subsequent lower pressure spectra were obtained by pumping out some of the gas mixture. Appropriate phase corrections were applied to the raw interferograms to achieve a phase plot that is as Pat as possible across the useful band pass. We applied a strong apodization to all of the spectra that is described by a(X ) = [1 − (X=Xmax )2 ]2 ;
(1)
where X is the path diOerence, Xmax the maximum path diOerence and the interferogram is multiplied by the value of a(X ) at the corresponding value of X before transformation. In addition to this strong apodization, a weak apodization function given in Eq. (2) was applied to spectra 11–30 (Table 1).
V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 393 – 410
A(X ) = 1
397
for X 6 0:95Xmax
A(X ) = cos2 {10 [(X=Xmax ) − 0:95]} for 0:95Xmax 6 X 6 Xmax :
(2)
The exact apodization function was properly accounted for in each spectrum during the analysis. The volume mixing ratio of the CO2 sample in each spectrum (spectra 13–20 and 23–30) was determined prior to the multispectrum least-squares ?ts. Before starting the multispectrum ?tting, the enhancements of the various isotopomers present in both the natural sample as well as the 13 C-enriched CO2 samples were determined [10]. These determinations were achieved by least-squares ?tting the intensities of transitions belonging to various isotopomers in such a way that their intensities matched in all of the spectra used in the analysis. Additional experimental details and analysis techniques are given in Refs. [1,2,10,11]. 3. Analysis Intensity measurements were performed by simultaneously ?tting 22 of the 30 spectra (Table 1) at a time using the multispectrum ?tting technique [10]. The 22 spectra analyzed in each simultaneous ?t included either the ?rst 12 spectra, spectra 21 and 22, and the eight air-broadened spectra (four with 12 CO2 and four with 13 CO2 ) or the ?rst 12 spectra, spectra 21 and 22, and the eight N2 -broadened spectra (four with 12 CO2 and four with 13 CO2 ). The multispectrum ?tting technique included two broadening gases in each ?t, one being the absorbing gas itself. Hence, each set of data (self and air or self and N2 ) was analyzed to retrieve self-broadening and air-broadening or self-broadening and N2 -broadening coeAcients [2] in addition to intensities. The absolute intensities determined from the two sets of ?tted spectra agreed within 1%. No collisional narrowing eOect was evident in the residuals of the ?ts. Fig. 1 is an example of a multispectrum ?tted interval near 1078 cm−1 covering several R-branch transitions belonging to the 12 C16 O2 3 –202 laser band. Some of the weak features in this ?gure belong to the 12 + 3 –312 and 202 + 3 –402 ‘hot’ bands. R-branch transitions belonging to the laser bands of 16 O12 C18 O, 16 O12 C17 O and 16 O13 C18 O isotopomers also appear in this wavelength interval. Each of these weak lines was treated as an individual line with its parameters varied (unconstrained) in the least-squares solutions. In the upper panel (a) we show the 22 calculated spectra while the magni?ed residuals (observed minus calculated) resulting from the least-squares ?t to the observed spectra are shown in the lower panel (b). 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 is due to unwedged windows in the 1.37-m base path (84:85 m path length) multipass absorption cell. This channeling was successfully modeled in the spectral ?tting. For several of the spectra, the zero level was noticeably oOset. When strong saturated absorption lines are present in the spectrum, the program ?ts this oOset 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 oOsets less than 1.0%. The intensity error is much more sensitive to the zero level for the saturated lines, but the zero level is very well determined in our analysis, typically to ±0:002% of the continuum level. This causes only a negligible error in intensity determinations compared to errors resulting from other sources. In all cases a constant oOset for a given spectrum within a given ?tted interval was suAcient. Benner [12]
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Fig. 1. Twenty-two calculated spectra (upper panel) and the corresponding residuals (bottom panel; observed minus calculated on an expanded scale) from a multispectrum ?t near 1078 cm−1 . 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 ?t. The channeling appearing in some of these spectra can be clearly seen. In addition to the 12 C16 O2 and the 13 C16 O2 laser lines, lines belonging to laser band II of the 16 O12 C18 O, 16 O12 C17 O and 16 O13 C18 O isotopomers are also visible (not labeled in the ?gure). Several weak transitions belonging to the R branch of the (12 + 3 –312 and 202 + 3 –402 ) hot band lines of 12 C16 O2 also appear in this spectral region. Tick marks at the top of panel (a) indicate positions of spectral lines included in the least-squares calculations.
has discussed details regarding the error arising due to zero level oOsets. Phase errors were small (typically 6 0:01 rad), but measurable and also successfully modeled in our analysis. The positions and intensities of the lines were determined by ?tting a 5 –15 cm−1 wide segment from each of the spectra simultaneously. Each spectral line in the ?tted interval was modeled using
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399
the Voigt line shape function convolved with the instrument line shape function appropriate for the McMath–Pierce FTS. Initial values of the spectral line parameters were taken from the HITRAN database [7,8]. The self-broadened half-width coeAcients determined from our analysis are reported in Ref. [2]. Prior to performing multispectrum ?ttings, a relative calibration of the wavelength scales of all of the spectra included in the analysis was performed. Positions of a number of water vapor lines belonging to the 2 band were measured in one spectrum and the wavelength scales of all the remaining spectra were adjusted by matching the positions of the same water vapor lines relative to the ?rst spectrum. These lines appear in each spectrum due to residual atmospheric water in the optical path outside the sample cell. The derived zero-pressure line center positions of the laser band transitions after the multispectrum ?ts were then used to correct the scale to best match the positions obtained from laser heterodyne techniques [5]. The observed individual line intensities, Si , in natural abundance, were ?tted to the expression [13]: −C2 i i SV −C2 Ei 1 − exp × F: (3) Si = Li exp 0 Q r T T Here, i is the resonant (center position of the ith spectral line) frequency, 0 the band origin, SV the vibrational band intensity, Li the rotational line intensity or HMonl–London factor, Qr the lower state rotational partition function at the temperature T , Ei the lower state rotational energy, C2 the second radiation constant (hc=k; h is Planck’s constant, c is the speed of light and k is the Boltzmann constant), and F the non-rigid–rotor factor that is described below. The CO2 laser bands are parallel-type bands and the HMonl–London factor Li is given by [14] Li =
m2 − l2 |m|
for P and R branches;
(4)
where m = J + 1 for the R branch, and m = −J for the P branch, J is the lower-state rotational quantum number and l the lower-state vibrational angular momentum quantum number. SV , as given in Eq. (3), takes account only of the rotational partition function assuming that there is no vibrational contribution and in addition takes no account of the isotopic abundance. In order to obtain the dipole moment matrix element, it is necessary to take into account the vibrational population of the lower state and also of the isotopic abundance. The square of the dipole moment matrix element, |R|2 (in Debye2 ), is computed using the following equation that has been modi?ed from Ref. [15]: |R|2 =
1 Qv SV 3hc ; 8 3 × 10−36 0 exp(−C2 EV =T )
(5)
where Qv is the vibrational partition function, EV the lower-state vibrational energy, T the temperature of the gas sample in Kelvin, and is the mixing ratio of the 12 C16 O2 isotopomer in a natural sample. In our calculations, values of 263.90333 (at 296 K), 1.08456 (at 296 K) and 0.9842 were used for Qr , Qv and , respectively. The isotopic abundance of 0.9842 for 12 C16 O2 has been adopted from the HITRAN compilation [6 –8]. The F factor de?nes the departure of the line intensities from rigid-rotor behavior. For CO2 , non-rigid behavior arises from Coriolis- and Fermi-type interactions and centrifugal distortion
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eOects. Toth [16] has used ?rst-order non-degenerate perturbation theory to derive explicit F-factor expressions for application in the analysis of CO2 and N2 O line intensity measurements. For the parallel (Ul = 0) bands, the F factor is modeled as F = [1 + A1 m + A2 m2 + A3 m3 ]2
for P and R branches:
(6)
Because of these vibration–rotation interaction eOects, the integrated band intensity Sband will diOer from the vibrational band intensity SV (see Table 4). For the – bands (the bands measured in this work), the Q branch is forbidden, and the sum has been computed from the calculated P- and R-branch line intensities in each band through J = 94, according to [17] S(m): (7) Sband = m=0
A minimum spectral line intensity cut-oO of 1:0 × 10−28 cm−1 =(molecule cm−2 ) at 296 K was used in computing the Sband . The vibrational band intensity and the F-factor coeAcients as de?ned in Eqs. (3) and (6) were determined by a least-squares procedure that minimizes the weighted sum of the squares of the residuals between the ?tted and the calculated line intensities. The assigned weights were inversely proportional to the square of the estimated uncertainty obtained from the multispectrum ?t. Details about the weighting scheme are given in Ref. [11]. The measured line intensities for the laser bands are plotted in Fig. 2a. The unequal intensity distributions (small but noticeable) between the P and R branches due to Fermi interaction are observed in Fig. 2a. The percentage intensity residual Ri (%Res) listed in Tables 2 and 3 is expressed as Sobs − Scalc ; (8) Ri (%Res) = 100 Scalc where Sobs and Scalc represent the observed and calculated line intensity, respectively. Except for the high-J lines (J ¿60) in the P and R branches, the residuals as shown in Fig. 2b are typically about 2% for both laser bands. To indicate the quality of an individual line intensity measurement, the residual as a percentage of the calculated line intensity is also listed in Tables 2 and 3. 4. Results and discussion The measured absolute rovibrational intensities in a natural mix of isotopomers for the individual spectral lines of the CO2 laser bands are listed in Tables 2 and 3. In these two tables we have listed for each line the position, rotational assignment, measured line intensity with its uncertainty, calculated line intensity and the intensity residual (observed minus calculated) as a percentage of the calculated intensity. Because of lack of knowledge of exact isotopomer abundances in the 13 CO2 sample, the absolute intensities of the 13 CO2 laser band lines are not reported here. In addition to determining the band intensity SV , and the non-rigid rotor (F-factor=Herman–Wallis) coeAcients (shown in Table 4), the least-squares solution also gives , an estimate of the quality of the ?t for each measured band. The uncertainty of the multispectrum ?t is the formal uncertainty arising in the least-squares solution. This includes the uncertainty due to the noise in the spectrum
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401
Fig. 2. (a) Measured line intensities in cm−1 =(molecule cm−2 ) at 296 K as a function of the rotational quantum number index m for the laser bands I and II. The small A1 value for the Coriolis coeAcient obtained for these bands results in slightly diOerent intensities for the P and R branches. Uncertainties are smaller than the symbols. (b) The observed minus calculated line intensities as a percentage of the calculated intensity plotted as a function of m. The weak high-J lines have large percentage intensity errors.
and any residuals that may result from under?tting due to inadequacy of the input model. The quality of the ?t can be compared with the internal uncertainties reported by the multispectrum ?t. This is done by dividing the standard deviation of the ?t (for a given weight) by the uncertainty of the multispectrum ?t (for the same weight). This method provides a means for evaluating the level of some systematic errors in the multispectrum ?t. For the laser bands I and II whose intensities were measured in this study, this ratio was approximately 4 and 5, respectively, which indicates that the multispectrum ?t error analysis accounts for only about 20 –25% of the total uncertainty in the measured spectral line intensity. Further sources of systematic errors that are still not accounted in the analysis may include uncertainties in the
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Table 2 Line positions and intensities in the Position (cm−1 )
886.3752 891.3268 893.7595 896.1642 898.5406 900.8899 903.2118 905.5066 910.0159 912.2308 914.4193 916.5818 922.9143 924.9740 927.0083 929.0174 931.0014 932.9604 934.8945 936.8038 938.6882 940.5481 942.3833 944.1940 945.9802 947.7420 949.4793 951.1922 952.8808 954.5451 956.1850 957.8005 959.3918 961.7329 963.2631 964.7690 966.2504 967.7072 969.1395 970.5472 971.9303 973.2885 974.6220 975.9304 977.2139 978.4723
12
C16 O2 laser band I (3 –1 )
Assignment
P74 P70 P68 P66 P64 P62 P60 P58 P54 P52 P50 P48 P42 P40 P38 P36 P34 P32 P30 P28 P26 P24 P22 P20 P18 P16 P14 P12 P10 P8 P6 P4 P2 R0 R2 R4 R6 R8 R10 R12 R14 R16 R18 R20 R22 R24
Line intensitya
%Resb
Observed
Calculated
2.85(55)E-27 1.093(62)E-26 1.849(58)E-26 3.043(57)E-26 5.183(60)E-26 8.129(73)E-26 1.184(9)E-25 1.817(9)E-25 4.126(10)E-25 5.762(13)E-25 8.273(14)E-25 1.149(4)E-24 2.977(5)E-24 3.879(8)E-24 4.960(13)E-24 6.355(12)E-24 7.857(17)E-24 9.489(22)E-24 1.150(2)E-23 1.353(3)E-23 1.544(3)E-23 1.736(3)E-23 1.912(3)E-23 2.057(3)E-23 2.148(3)E-23 2.201(3)E-23 2.147(3)E-23 2.034(3)E-23 1.866(3)E-23 1.603(2)E-23 1.264(2)E-23 8.777(10)E-24 4.518(3)E-24 2.294(2)E-24 6.778(6)E-24 1.100(2)E-23 1.476(2)E-23 1.793(3)E-23 2.027(3)E-23 2.196(3)E-23 2.298(3)E-23 2.313(3)E-23 2.249(3)E-23 2.118(3)E-23 1.974(3)E-23 1.773(3)E-23
3.818E-27 1.105E-26 1.834E-26 2.996E-26 4.814E-26 7.611E-26 1.184E-25 1.811E-25 4.030E-25 5.864E-25 8.390E-25 1.180E-24 2.960E-24 3.883E-24 5.003E-24 6.331E-24 7.863E-24 9.583E-24 1.146E-23 1.343E-23 1.541E-23 1.732E-23 1.903E-23 2.042E-23 2.136E-23 2.173E-23 2.143E-23 2.038E-23 1.856E-23 1.597E-23 1.269E-23 8.823E-24 4.531E-24 2.291E-24 6.790E-24 1.101E-23 1.477E-23 1.791E-23 2.033E-23 2.198E-23 2.284E-23 2.295E-23 2.240E-23 2.128E-23 1.973E-23 1.788E-23
−25.4 − 1.1 0.8 1.6 7.7 6.8 0.0 0.4 2.4 − 1.7 − 1.4 − 2.7 0.6 − 0.1 − 0.9 0.4 − 0.1 − 1.0 0.4 0.8 0.1 0.3 0.5 0.7 0.6 1.3 0.2 − 0.2 0.6 0.3 − 0.4 − 0.5 − 0.3 0.1 − 0.2 − 0.1 0.0 0.1 − 0.3 − 0.1 0.6 0.8 0.4 − 0.5 0.0 − 0.8
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403
Table 2 (continued) 979.7054 980.9132 982.0955 983.2522 984.3832 985.4883 986.5674 987.6202 988.6467 989.6465 990.6197 991.5658 992.4848 993.3765 994.2405 995.0767 995.8846 996.6644 997.4155 998.1378 998.8309 999.4947 1000.1278 1000.7323 a b
R26 R28 R30 R32 R34 R36 R38 R40 R42 R44 R46 R48 R50 R52 R54 R56 R58 R60 R62 R64 R66 R68 R70 R72
1.577(2)E-23 1.361(2)E-23 1.162(2)E-23 9.708(15)E-24 7.942(11)E-24 6.403(8)E-24 5.058(5)E-24 3.921(31)E-24 2.991(21)E-24 2.231(15)E-24 1.637(13)E-24 1.173(11)E-24 8.405(10)E-25 5.823(8)E-25 4.028(7)E-25 2.684(7)E-25 1.803(6)E-25 1.189(5)E-25 7.325(42)E-26 4.708(41)E-26 2.786(41)E-26 1.763(39)E-26 1.108(38)E-26 5.84(39)E-27
1.585E-23 1.376E-23 1.170E-23 9.760E-24 7.986E-24 6.414E-24 5.057E-24 3.916E-24 2.978E-24 2.226E-24 1.635E-24 1.180E-24 8.374E-25 5.842E-25 4.007E-25 2.703E-25 1.793E-25 1.170E-25 7.509E-26 4.741E-26 2.944E-26 1.799E-26 1.081E-26 6.395E-27
− − − − − −
− − − − − − − −
0.5 1.1 0.7 0.5 0.6 0.2 0.0 0.1 0.4 0.2 0.1 0.6 0.4 0.3 0.5 0.7 0.5 1.6 2.5 0.7 5.4 2.0 2.4 8.7
Intensities are reported in units of cm−1 =(molecule cm−2 ) at 296 K (in natural abundance). ((Sobs − Scalc )=Scalc )100.
calibration of pressure gauge (¡1%) or thermometer (0.2%), lack of knowledge of exact isotopomer mixing ratios (∼0:05%), a consistent path length error (¡0:1%), channel spectrum correction (∼0:01%), lack of knowledge of zero level (∼0:3%), lack of knowledge of continuum (∼0:1%), purity of the sample (¡0:01%), phase error (∼0:1%) and the shape of the instrumental line pro?le. Based upon these estimates we believe that the absolute uncertainties in our intensities to be about 2%. In Fig. 3(a) and (b) we illustrate the ratio of each residual resulting from the band intensity ?t to the standard deviation of the same ?t as a function of m for laser bands I and II, respectively. The scatter in Fig. 3(a) and (b) is random. Our intensity measurements compare favorably (within 1%) with the results of Dana et al. [3] but are systematically lower [mean diOerence is −(5 ± 2)%] than measurements made by Johns and NoMel [4]. In both laser bands, for the lower quantum number transitions (|m| 6 20) intensity values reported in the HITRAN agree fairly closely to our measurements, but for higher quantum number transitions they diOer from our results by several percent. The source for this deviation is not precisely known especially since it has been reported that the SV and the F factor coef?cients adopted in the HITRAN database [6 –8] are stated to be the values of Dana et al. [3]. Apparently less accurate Herman–Wallis factors were applied while generating the HITRAN line list.
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Table 3 Line positions and intensities in Position (cm−1 )
986.3557 988.8171 991.2609 993.6829 996.0841 998.4647 1000.8239 1003.1616 1005.4775 1007.7713 1010.0429 1012.2918 1014.5179 1016.7210 1018.9007 1021.0569 1023.1894 1025.2979 1027.3822 1029.4421 1031.4774 1033.4880 1035.4736 1037.4341 1039.3693 1041.2790 1043.1632 1045.0217 1046.8542 1048.6608 1050.4413 1052.1955 1053.9235 1055.6250 1057.3002 1058.9487 1060.5706 1062.1660 1066.0373 1067.5391 1069.0141 1070.4623 1071.8838 1073.2784 1074.6464 1075.9878
12
C16 O2 laser band II (3 –202 )
Assignment
P76 P74 P72 P70 P68 P66 P64 P62 P60 P58 P56 P54 P52 P50 P48 P46 P44 P42 P40 P38 P36 P34 P32 P30 P28 P26 P24 P22 P20 P18 P16 P14 P12 P10 P8 P6 P4 P2 R2 R4 R6 R8 R10 R12 R14 R16
Line intensitya
%Resb
Observed
Calculated
5.3(4)E-27 6.7(4)E-27 1.32(4)E-27 2.32(4)E-26 3.54(4)E-26 5.53(4)E-26 8.65(4)E-26 1.361(6)E-25 2.102(6)E-25 3.193(7)E-25 4.810(8)E-25 7.011(8)E-25 1.016(1)E-24 1.429(1)E-24 1.982(2)E-24 2.723(2)E-24 3.651(3)E-24 4.816(6)E-24 6.237(9)E-24 7.975(14)E-24 1.001(2)E-23 1.228(2)E-23 1.501(3)E-23 1.778(3)E-23 2.066(3)E-23 2.389(3)E-23 2.662(3)E-23 2.910(4)E-23 3.106(4)E-23 3.251(4)E-23 3.324(4)E-23 3.251(4)E-23 3.068(4)E-23 2.830(4)E-23 2.427(4)E-23 1.905(3)E-23 1.320(2)E-23 6.763(6)E-24 1.019(2)E-23 1.686(3)E-23 2.272(4)E-23 2.751(4)E-23 3.112(4)E-23 3.376(4)E-23 3.539(4)E-23 3.578(4)E-23
4.382E-27 7.517E-27 1.270E-26 2.111E-26 3.456E-26 5.568E-26 8.831E-26 1.379E-25 2.118E-25 3.201E-25 4.762E-25 6.969E-25 1.003E-24 1.421E-24 1.980E-24 2.712E-24 3.653E-24 4.838E-24 6.297E-24 8.053E-24 1.012E-23 1.248E-23 1.512E-23 1.797E-23 2.095E-23 2.393E-23 2.677E-23 2.930E-23 3.132E-23 3.266E-23 3.312E-23 3.258E-23 3.092E-23 2.811E-23 2.416E-23 1.918E-23 1.333E-23 6.846E-24 1.028E-23 1.669E-23 2.243E-23 2.726E-23 3.103E-23 3.364E-23 3.508E-23 3.540E-23
19.9 −10.6 3.7 9.6 2.5 − 0.7 − 2.1 − 1.3 − 0.7 − 0.3 1.0 0.6 1.3 0.5 0.1 0.4 − 0.1 − 0.4 − 1.0 − 1.0 − 1.1 − 1.7 − 0.7 − 1.1 − 1.4 − 0.2 − 0.6 − 0.7 − 0.8 − 0.4 0.3 − 0.2 − 0.8 0.7 0.4 − 0.7 − 1.0 − 1.2 − 0.8 1.0 1.3 0.9 0.3 0.4 0.9 1.1
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Table 3 (continued) 1077.3025 1079.8522 1081.0874 1083.4788 1084.6351 1085.7654 1086.8698 1087.9483 1089.0011 1090.0284 1091.0302 1092.0068 1092.9582 1093.8847 1094.7865 1095.6636 1096.5164 1097.3449 1098.1495 1098.9303 1099.6874 1100.4208 1101.1316 1101.8192 1102.4843 1103.7457 1104.3446 a b
R18 R22 R24 R28 R30 R32 R34 R36 R38 R40 R42 R44 R46 R48 R50 R52 R54 R56 R58 R60 R62 R64 R66 R68 R70 R74 R76
3.464(4)E-23 3.118(4)E-23 2.832(4)E-23 2.185(4)E-23 1.928(3)E-23 1.564(3)E-23 1.292(3)E-23 1.039(2)E-23 8.373(15)E-24 6.528(12)E-24 5.045(6)E-24 3.811(4)E-24 2.837(2)E-24 2.066(2)E-24 1.487(1)E-24 1.018(2)E-24 7.094(13)E-25 4.860(8)E-25 3.282(7)E-25 2.144(6)E-25 1.434(5)E-25 9.28(41)E-26 5.52(4)E-26 3.40(4)E-26 2.01(3)E-26 7.30(3)E-27 5.4(3)E-27
3.469E-23 3.087E-23 2.813E-23 2.192E-23 1.878E-23 1.578E-23 1.301E-23 1.054E-23 8.382E-24 6.551E-24 5.031E-24 3.799E-24 2.820E-24 2.058E-24 1.478E-24 1.044E-24 7.249E-25 4.955E-25 3.332E-25 2.205E-25 1.436E-25 9.207E-26 5.809E-26 3.608E-26 2.206E-26 7.865E-27 4.588E-27
− 0.1 1.0 0.7 − 0.3 2.7 − 0.9 − 0.7 − 1.4 − 0.1 − 0.3 0.3 0.3 0.6 0.4 0.6 − 2.4 − 2.1 − 1.9 − 1.5 − 2.8 − 0.2 0.8 − 5.0 − 5.8 − 9.0 − 7.1 17.5
Intensities are reported in units of cm−1 =(molecule cm−2 ) at 296 K (in natural abundance). ((Sobs − Scalc )=Scalc )100.
Comparisons of present intensity measurements with other recent studies are shown in Fig. 4. In Fig. 4(a) we have re-plotted the measured intensities for laser bands I and II as a function of m and in Fig. 4(b) – (d) we have compared the present intensity measurements with values determined by Johns and NoMel [4], Dana et al. [3], and the HITRAN database [6 –8]. In Fig. 4(e) we have compared the measured results of Dana et al. [3] that are adopted in HITRAN [6 –8] with the actual values listed in the HITRAN [6 –8]. The small diOerences in Fig. 4(e) are attributed to intensity values calculated from the F-factor coeAcients of Dana et al. [3] rather than the observed intensities. In Table 4 we present the best-?t values for SV , the square of the rotationless transition dipole moment |R|2 and the F-factor coeAcients along with the calculated integrated band intensity Sband . The values for Sband listed in Refs. [3,4] were computed utilizing the F-factor coeAcients reported by the authors. The uncertainties given in parentheses are one standard deviation in units of the last quoted digit. The F-factor coeAcients were retained in the solution only if the standard deviation for that coeAcient was at least three times smaller than the value of the coeAcient itself. The Coriolis coeAcient A1 and the quadratic coeAcient A2 were determined for both laser bands while
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Table 4 Intensities and F-factor coeAcients derived for the
12
C16 O2 laser bands
Laser band
Present work
Dana et al. [3]
Johns and NoMel [4]
00011 ← 10001 (3 –1 ) |R|2a A1 A2 SV b (×10−21 ) Sband b (×10−21 )
0.0014251(14) −0.000493(14) −0.0000162(4) 0.60556(60) 0.5907
0.0014395(55) −0.000783(41) −0.0000106(13) 0.613 0.6011
0.0014932(22) −0.000641(16) −0.00000917(53) 0.62981(92) 0.6187
Correlation coeAcients SV and A2 A1 and A2 SV and A1
−0.610 −0.563 +0.023
00011 ← 10002 (3 –202 ) |R|2a A1 A2 A3 (×10−7 ) SV b (×10−21 ) Sband b (×10−21 )
0.0011748(18) −0.000114(36) 0.0000102(4) −0.83(15) 0.9109(14) 0.9176
0.0011774(24)
0.0012186(19) −0.000266(24) 0.00001499(78)
Correlation coeAcients A1 and A3 SV and A2 A2 and A3 A1 and A2 SV and A1 SV and A3
−0.940 −0.795 −0.045 +0.026 +0.021 −0.002
0.0000133(17) 0.915 0.9253
0.9412(15) 0.9528
a
Debye2 . SV is the vibrational band intensity and Sband is the integrated band intensity (sum of all computed intensities in the band through J = 94) in units of cm−1 =(molecule cm−2 ) at 296 K (in natural abundance). b
cubic distortion term A3 was determined for laser band II only. The correlation coeAcients among the determined parameters obtained for the two laser bands are also given in this table. From these coeAcients an estimate of the uncertainty in each of the calculated intensity could be made. For laser band II, the A1 and A3 coeAcients were not well determined, but were both essential for obtaining a good ?t. However, we were able to determine a linear combination of the two parameters well. Using the correlation coeAcients it was found that A1 + 2000A3 = −0:000280(13). This sum is determined to 20 times its uncertainty while A1 is determined to only three times its uncertainty and A3 is determined to only about ?ve and a half times its uncertainty. Our SV and |R|2 values compare reasonably well with the measurements of Dana et al. [3]. The values adopted in the HITRAN database [6 –8] are based upon the results obtained by Dana and co-workers [3]. We have compared our measurements with values listed in Refs. [3,4,6 –8]. The comparison of ratios of SV and |R|2 obtained from diOerent studies are made in Table 5. For a given band, the ratios of SV and |R|2 between any two studies should give the same values.
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407
Fig. 3. Ratio of residuals of individual spectral lines obtained from the band intensity ?t to the standard deviation of the ?t for (a) laser band I and (b) laser band II.
Since the values adopted in the HITRAN database [6 –8] for the SV and |R|2 are those of Dana et al. [3] comparisons with Refs. [6 –8] are not included in Table 5. The diOerences between present study and Dana et al. [3] are within 1% for laser band I and ¡0:5% for laser band II while the results between this study and Johns and NoMel [4] diOer by 4% and 3% for laser band I and II, respectively. We believe that this diOerence may be due to slightly diOerent partition functions employed in each analysis. We have adopted a value of 286.219 corresponding to 296 K as the total internal partition sum for the 12 C16 O2 isotopomer. This value has been taken from the HITRAN compilation [7,8] and from Gamache et al. [18].
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V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 393 – 410
Fig. 4. (a) Measured spectral line intensities as a function of the rotational quantum number index m for the two laser bands. (b) – (d) Percentage intensity diOerences between Refs. [3,4,6 –8] and present work. (b) Intensities from Johns and NoMel [4] are higher than present measured intensities by an average value of 4%. (c) Values determined by Dana et al. [3] agree with our present measurements within about 1%. (d) The diOerences in intensities between values from HITRAN [6 –8] and present measurements are in opposite directions for the two laser bands. (e) Percentage diOerences between the intensity measurements by Dana et al. [3] and the values in the HITRAN database [6 –8]. Mean value of the diOerences is ¡1%.
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Table 5 Comparisons of SV and |R|2 Laser band
Ratio
Dana et al. [3] to the present work
Johns and NoMel [4] to the present work
I
|R|2 SV
1:010 ± 0:004 1.012
1:048 ± 0:002 1:040 ± 0:002
II
|R|2 SV
1:002 ± 0:003 1.004
1:037 ± 0:002 1:033 ± 0:002
5. Conclusions In the present study we obtained absolute line intensities of the two 12 C16 O2 laser bands, (00011– 10001) and (00011–10002), located at 10 m. The 22 room temperature high-resolution (0.0028– 0:0053 cm−1 ) long path (73–434 m) laboratory absorption spectra recorded with a Fourier transform spectrometer were analyzed with a multispectrum nonlinear least-squares ?tting technique. These intensity measurements were modeled to an absolute accuracy of at least 98% by applying a three-term Herman–Wallis expression. The wide range of J values {P(74) –R(72) in laser band I and P(76) –R(76) in laser band II} reached in our investigation permitted the cubic distortion coeAcient to be determined for the ?rst time in the (00011–10002) band near 1064 cm−1 . Only two Herman–Wallis terms were required for the (00011–10001) band at 961 cm−1 . The present measurements con?rmed the intensity values determined by Dana and co-workers within about 1%. The present intensity values agreed with those by Dana et al. within ∼0:5% for the 1064 cm−1 band and were lower than the values of Dana et al. by ∼1:0% for the 961 cm−1 band. The intensity values determined in the present study for both laser bands are lower than the values of Johns and NoMel by ∼4%. Comparison with the corresponding entries in the HITRAN database revealed that the overall normalization on the absolute intensities from Dana et al. that was adopted by HITRAN database was consistent with the present values. However, less accurate Herman–Wallis factors had apparently been applied. Better accuracy for these CO2 intensities in the database can be achieved by the use of more accurate Herman–Wallis terms.
Acknowledgements The authors thank Claude Plymate of the National Solar Observatory (NSO) for assistance in recording some of the spectra. Cooperative agreements and contracts with 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 thank the NASA Upper Atmosphere Research Program for their support of the McMath–Pierce FTS laboratory facility.
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References [1] Malathy Devi V, Benner DC, Smith MAH, Rinsland CP. Air- and N2 -broadening coeAcients and pressure-shift coeAcients in the 12 C16 O2 laser bands. JQSRT 1998;59(3–5):137–49. [2] Malathy Devi V, Benner DC, Smith MAH, Brown LR, Dulick M. Multispectrum analysis of pressure broadening and pressure shift coeAcients in the 12 C16 O2 and 13 C16 O2 laser bands. JQSRT 2002;76(3–4):411–34. [3] Dana V, Mandin J-Y, Guelachvili G, Kou Q, Morillon-Chapey M, Wattson RB, Rothman LS. Intensities and self-broadening coeAcients of 12 C16 O2 lines in the laser band region. J Mol Spectrosc 1992;152:328–41. [4] Johns JWC, NoMel M. Absolute intensities in CO2 : The laser bands near 10 m. J Mol Spectrosc 1992;156:403–14. [5] Maki AG, Chou CC, 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. [6] Rothman LS, Gamache RR, Tipping RH, Rinsland CP, Smith MAH, Benner DC, Malathy Devi V, Flaud J-M, Camy-Peyret C, Perrin A, Goldman A, Massie ST, Brown LR, Toth RA. The HITRAN molecular database: Editions of 1991 and 1992. JQSRT 1992;48(5=6):469–507. [7] 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. [8] Rothman LS, Barbe A, Benner DC, Brown LR, Camy-Peyret C, Carleer MR, Chance KV, Clerbaux C, Dana V, Malathy Devi V, Fayt A, Fisher J, Flaud J-M, Gamache RR, Goldman A, Jacquemart D, Jucks KW, LaOerty WJ, Maki AG, Mandin J-Y, Massie ST, Newnham D, Perrin A, Rinsland CP, Schroeder J, Smith K, Smith MAH, Toth RA, Vander Auwera J, Varanasi P, Yoshino K. HITRAN molecular spectroscopic database: 2000 Edition, in preparation. [9] Jennings DE, Hubbard R, Brault JW. Double passing the Kitt Peak 1-meter Fourier transform spectrometer. Appl Opt 1985;24(21):3438–40. [10] Benner DC, Rinsland CP, Malathy Devi V, Smith MAH, Atkins D. A multispectrum nonlinear least squares ?tting technique. JQSRT 1995;53(6):705–21. [11] Malathy Devi V, Benner DC, Rinsland CP, Smith MAH. Absolute rovibrational intensities of 12 C16 O2 absorption bands in the 3090 –3850 cm−1 spectral region. JQSRT 1998;60(1):741–70. [12] Benner DC. A multispectrum nonlinear least squares ?tting technique: Zero level oOsets. JQSRT, submitted for publication. [13] Rothman LS, Young LDG. Infrared energy levels and intensities of carbon dioxide-II. JQSRT 1981;25:505–24. [14] Olson WB, Maki AG, LaOerty WJ. Tables of N2 O absorption lines for the calibration of tunable infrared lasers from 522–657 cm−1 to 657 cm−1 and from 1115 –1340 cm−1 to 1340 cm−1 . J Phys Chem Ref Data 1981;10(4):1065–84. [15] Johns JWC. Absolute intensity and pressure broadening measurements of CO2 in the 4:3 m region. J Mol Spectrosc 1987;125:442–64. [16] Toth RA. Line strengths of N2 O in the 1120 –1440 cm−1 region. Appl Opt 1984;23(11):1825–34. [17] Rinsland CP, Benner DC, Malathy Devi V, Ferry PS, Sutton CH, Richardson DJ. Atlas of high resolution infrared spectra of carbon dioxide. Appl Opt 1984;23(13):2051–2. [18] Gamache RR, Kennedy S, Hawkins R, Rothman LS. Total internal partition sums for molecules in the terrestrial atmosphere. J Mol Struct 2000;517=518:407–25.
Absolute intensity measurements of the laser bands near 10 m
www.elsevier.com/locate/jqsrt
12
C16O2
V. Malathy Devia; ∗ , D. Chris Benner a , M.A.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 1 April 2002; received in revised form 14 May 2002
Abstract Line intensities of the two 12 C16 O2 laser bands (3 –1 and 3 –202 ) centered near 960.9 and 1063:7 cm−1 , respectively, were obtained from analysis of 30 room temperature long path laboratory absorption spectra recorded at 0.0028 and 0:0053 cm−1 resolution with the McMath–Pierce Fourier transform spectrometer at the National Solar Observatory (located on Kitt Peak). The spectra were analyzed simultaneously with the multispectrum nonlinear least-squares ?tting procedure. The measured line intensities were further analyzed to derive the vibrational band intensities and Herman–Wallis coeAcients. ? 2002 Elsevier Science Ltd. All rights reserved. Keywords: CO2 ; CO2 laser bands; Infrared spectra; Fourier transform infrared (FTIR) spectroscopy; Absolute intensity
1. Introduction Accurate line parameters (positions, intensities and line shape coeAcients) of carbon dioxide transitions are required in order to retrieve atmospheric pressure and temperature from terrestrial remote sensing spectra. The prominent 12 C16 O2 laser bands located near 10 m (00011–10001 or 3 –1 at 960:9 cm−1 ) and (00011–10002 or 3 –202 at 1063:7 cm−1 ) are particularly useful for tropospheric studies. As a result, high-resolution laboratory investigations of both their intensities and pressure broadening have been pursued ([1– 4] and the references therein). The line positions of these two ∗
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 7 - 5
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bands are so well known from heterodyne measurements [5] that they are commonly referred to as “the laser bands” and serve as secondary standards for infrared line positions. For intensities, the more recent measurements from Dana et al. [3] and Johns and NoMel [4] have been found to agree within 2.8%. Subsequently, the values of Dana et al. (rather an average of the two studies) have been adopted for the HITRAN database [6 –8]. In this paper, we report new absolute line intensity measurements of these two bands in order to con?rm the accuracies of the past results and provide guidance for future improvements to the database. Previously, the pressure-broadening coeAcients of the main isotopomer were investigated [1], and recently we undertook an extension of that work for 13 C16 O2 . A new analysis of self-broadened 12 16 C O2 was also performed, resulting in the retrieval of line intensities as well. The multispectrum nonlinear least-squares procedure was applied to analyze 30 spectra of natural CO2 and 13 C-enriched CO2 , in pure samples and in dilute mixtures with dry air and nitrogen. The broadening results are reported elsewhere [2], but this paper presents the corresponding intensity analysis by which the band intensities, Herman–Wallis coeAcients and the square of the rotationless transition dipole moments were determined for the two laser bands of 12 C16 O2 . 2. Experimental details and data retrievals All spectra analyzed in this investigation were obtained with the McMath–Pierce Fourier transform spectrometer (FTS). The experimental conditions are summarized in Table 1. The McMath–Pierce 1-m Fourier Transform Spectrometer is a folded Michelson interferometer; each mirror can travel up to 1m, for a maximum path diOerence of 2 m. The interferometer has a total internal path of approximately 12 m from inputs to outputs. In practice, only one input and both outputs are utilized. The two outputs have complementary phases so that the diOerence in the signals produced by two matched detectors is used to record the interferogram. The sum of the signals is almost unmodulated and can be used to ratio out small DC source Puctuations when appropriate. The source is focused onto the plane of a circular aperture (generally 8 mm in diameter) and is accepted at the collimator as an f=50 beam. After passing through the interferometer, the collimated beam is reimaged onto the detectors with about a 15% image scale reduction. The 12-m path within the FTS between the input port and the detector mounts is housed in a vacuum chamber evacuated by high-speed pumps. Vacuum within the tank during operation falls in the 0.1– 0.01 Torr range. Operating the FTS under vacuum has many advantages including reduced atmospheric absorption, vacuum wavenumber results without index of refraction corrections, improved acoustic decoupling of the interferometer, and the elimination of convective currents. Appropriate optical ?lters are used to reduce the eOect of shot noise from all photons incident on the detectors in order to optically isolate the regions of the spectrum of interest. The external path from the glower source to the FTS tank is purged with dry nitrogen to reduce atmospheric absorption. This external path in most of our experimental conditions was on the order of 0.5 –1 m, but it was about 4 m when the 6-m base path White cell was used to record some of the spectra (spectra 1–10; see Table 1). The source of dry nitrogen used for purging these atmospheric paths was blow-oO from a 50-l liquid N2 Dewar containing a 100 W heater. The pressures in the purged atmospheric paths as well as the “evacuated” interferometer tank and the corresponding
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395
Table 1 Summary of the experimental conditions of the CO2 spectra Serial no.
Temperature (K)
Principal isotopomer and broadening gas
CO2 volume mixing ratio
Path (m)
Pressure (Torr)a
Spectral resolution (cm−1 )
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
297.30 297.60 297.60 297.60 297.60 292.00 291.90 291.95 295.50 295.80 298.35 298.35 295.85 295.95 298.95 298.85 298.65 298.65 298.55 298.35 297.15 296.95 297.75 297.85 298.05 298.15 297.45 297.65 297.85 297.95
12
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.025 0.025 0.025 0.025 0.035 0.035 0.035 0.035 1.0 1.0 0.055 0.055 0.055 0.055 0.033 0.033 0.033 0.033
193.28 433.88 72.98 72.98 193.28 72.98 72.98 72.98 97.04 97.04 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85 84.85
18.07 24.95 3.08 24.96 24.96 125.1 251.1 400.6 151.2 300.3 3.70 1.40 500.3 375.15 250.35 125.30 401.5 300.4 200.25 100.40 1.9 3.8 400.35 300.35 200.55 100.50 402.20 300.35 200.65 101.35
0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0053 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028 0.0028
a
CO2 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 12 CO2 + air 12 CO2 + air 12 CO2 + air 12 CO2 + air 12 CO2 + N2 12 CO2 + N2 12 CO2 + N2 12 CO2 + N2 13 CO2 13 CO2 13 CO2 + air 13 CO2 + air 13 CO2 + air 13 CO2 + air 13 CO2 + N2 13 CO2 + N2 13 CO2 + N2 13 CO2 + N2 12
760 Torr = 1 atm = 101:325 kPa = 1:01325 bar.
temperatures are also usually monitored during the course of recording the spectra with appropriate pressure gauges and thermometer=thermistor probes. For the present study, a water-cooled glower operating between 120 and 150 V was used as the source of radiation. A KCl beamsplitter (wedged) with GaP coating was installed in the FTS, and the instrument was con?gured so that asymmetric interferograms were obtained to achieve the maximum (single pass) resolution of 0:0053 cm−1 . Near zero path diOerence the interferogram was two-sided. Liquid-helium-cooled As : Si detectors and a room temperature InSb optical ?lter were used in collecting the data covering the region 500 –1450 cm−1 . However, while recording the last 20 spectra listed in Table 1, an additional cold CaF2 ?lter was also used to reduce the optical band
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pass to 750 –1450 cm−1 . The diameter of the input aperture was set to 8 mm. The double-pass mode described by Jennings et al. [9] was used in recording spectra 11–30 listed in Table 1 at 0:0028 cm−1 resolution. The sampling frequency was set to 2500 Hz. The 30 spectra listed in Table 1 were obtained at three diOerent times and with two diOerent absorption cells. One cell was a 1.37-m base path Pyrex-bodied multipass cell with a total path set to 84:85 m. The other cell was a 6-m base path White cell (available at the National Solar Observatory) with total path length adjusted to 73, 97, 193 and 434 m. Spectra 1–5 were obtained using the 6-m baselength White cell. Twelve interferograms were co-added in each spectrum. The second set (spectra 6 –10) was also obtained using the same 6-m base path White cell, with the same resolution (0:0053 cm−1 ), and 20 interferograms were co-added for each spectrum. The remaining 20 spectra were recorded using the 1.37-m base path multipass cell. For the last 20 spectra recorded with 0:0028 cm−1 resolution 8–12 interferograms were co-added in each spectrum. A single, full resolution scan in double-pass mode took approximately 5 min to complete and the total time taken to record each spectrum was between 40 min and 1 h. This was suAcient to obtain a signal-to-RMS noise ratio in the range of ∼300–700. The absorption path lengths inside the White cell and Pyrex multipass cell are believed to be known with an uncertainty of ∼0:1% so that this uncertainty will have only minimal eOects on the retrieved line intensities. The sample pressures were measured and monitored using Datametrics or Baratron capacitance manometers (absolute pressure gauges) with a 0 –10 or 0 –1000 Torr head as appropriate. The Datametrics gauges were calibrated within a year prior to making measurements. Two T-type thermocouples attached to the body of the 1.37-m base path multipass cell were used to determine the sample temperatures. Temperatures of the sample within the White cell were measured with a single thermistor probe suspended inside the cell at the center. For the ?rst 10 spectra (Table 1) recorded with the White cell the average uncertainties in temperature and pressure measurements are about ±1:5 K and ±0:5%, respectively. The pressures and temperatures of the gas samples in spectra 11–30 (Table 1) remained constant to within ∼0:2% and ∼0:5 K, respectively. The gas samples were 99.995% pure natural CO2 (predominantly 12 CO2 ) and 90% 13 C-enriched CO2 . Spectra 1–14 (Table 1) were recorded with only the natural CO2 sample in the absorption cell and spectra 21 and 22 were recorded with the 13 CO2 sample alone. For the pressure-broadened spectra lean CO2 –air (or CO2 –N2 ) mixtures were prepared by initially ?lling the cell with either natural CO2 or 13 CO2 (∼12–22 Torr) and then adding dry air (or dry nitrogen) to the sample until the total pressure reached about 400 –500 Torr. In each series of pressure-broadened spectra (Table 1) the spectrum with the highest total pressure was recorded ?rst, and the subsequent lower pressure spectra were obtained by pumping out some of the gas mixture. Appropriate phase corrections were applied to the raw interferograms to achieve a phase plot that is as Pat as possible across the useful band pass. We applied a strong apodization to all of the spectra that is described by a(X ) = [1 − (X=Xmax )2 ]2 ;
(1)
where X is the path diOerence, Xmax the maximum path diOerence and the interferogram is multiplied by the value of a(X ) at the corresponding value of X before transformation. In addition to this strong apodization, a weak apodization function given in Eq. (2) was applied to spectra 11–30 (Table 1).
V. Malathy Devi et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 76 (2003) 393 – 410
A(X ) = 1
397
for X 6 0:95Xmax
A(X ) = cos2 {10 [(X=Xmax ) − 0:95]} for 0:95Xmax 6 X 6 Xmax :
(2)
The exact apodization function was properly accounted for in each spectrum during the analysis. The volume mixing ratio of the CO2 sample in each spectrum (spectra 13–20 and 23–30) was determined prior to the multispectrum least-squares ?ts. Before starting the multispectrum ?tting, the enhancements of the various isotopomers present in both the natural sample as well as the 13 C-enriched CO2 samples were determined [10]. These determinations were achieved by least-squares ?tting the intensities of transitions belonging to various isotopomers in such a way that their intensities matched in all of the spectra used in the analysis. Additional experimental details and analysis techniques are given in Refs. [1,2,10,11]. 3. Analysis Intensity measurements were performed by simultaneously ?tting 22 of the 30 spectra (Table 1) at a time using the multispectrum ?tting technique [10]. The 22 spectra analyzed in each simultaneous ?t included either the ?rst 12 spectra, spectra 21 and 22, and the eight air-broadened spectra (four with 12 CO2 and four with 13 CO2 ) or the ?rst 12 spectra, spectra 21 and 22, and the eight N2 -broadened spectra (four with 12 CO2 and four with 13 CO2 ). The multispectrum ?tting technique included two broadening gases in each ?t, one being the absorbing gas itself. Hence, each set of data (self and air or self and N2 ) was analyzed to retrieve self-broadening and air-broadening or self-broadening and N2 -broadening coeAcients [2] in addition to intensities. The absolute intensities determined from the two sets of ?tted spectra agreed within 1%. No collisional narrowing eOect was evident in the residuals of the ?ts. Fig. 1 is an example of a multispectrum ?tted interval near 1078 cm−1 covering several R-branch transitions belonging to the 12 C16 O2 3 –202 laser band. Some of the weak features in this ?gure belong to the 12 + 3 –312 and 202 + 3 –402 ‘hot’ bands. R-branch transitions belonging to the laser bands of 16 O12 C18 O, 16 O12 C17 O and 16 O13 C18 O isotopomers also appear in this wavelength interval. Each of these weak lines was treated as an individual line with its parameters varied (unconstrained) in the least-squares solutions. In the upper panel (a) we show the 22 calculated spectra while the magni?ed residuals (observed minus calculated) resulting from the least-squares ?t to the observed spectra are shown in the lower panel (b). 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 is due to unwedged windows in the 1.37-m base path (84:85 m path length) multipass absorption cell. This channeling was successfully modeled in the spectral ?tting. For several of the spectra, the zero level was noticeably oOset. When strong saturated absorption lines are present in the spectrum, the program ?ts this oOset 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 oOsets less than 1.0%. The intensity error is much more sensitive to the zero level for the saturated lines, but the zero level is very well determined in our analysis, typically to ±0:002% of the continuum level. This causes only a negligible error in intensity determinations compared to errors resulting from other sources. In all cases a constant oOset for a given spectrum within a given ?tted interval was suAcient. Benner [12]
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Fig. 1. Twenty-two calculated spectra (upper panel) and the corresponding residuals (bottom panel; observed minus calculated on an expanded scale) from a multispectrum ?t near 1078 cm−1 . 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 ?t. The channeling appearing in some of these spectra can be clearly seen. In addition to the 12 C16 O2 and the 13 C16 O2 laser lines, lines belonging to laser band II of the 16 O12 C18 O, 16 O12 C17 O and 16 O13 C18 O isotopomers are also visible (not labeled in the ?gure). Several weak transitions belonging to the R branch of the (12 + 3 –312 and 202 + 3 –402 ) hot band lines of 12 C16 O2 also appear in this spectral region. Tick marks at the top of panel (a) indicate positions of spectral lines included in the least-squares calculations.
has discussed details regarding the error arising due to zero level oOsets. Phase errors were small (typically 6 0:01 rad), but measurable and also successfully modeled in our analysis. The positions and intensities of the lines were determined by ?tting a 5 –15 cm−1 wide segment from each of the spectra simultaneously. Each spectral line in the ?tted interval was modeled using
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399
the Voigt line shape function convolved with the instrument line shape function appropriate for the McMath–Pierce FTS. Initial values of the spectral line parameters were taken from the HITRAN database [7,8]. The self-broadened half-width coeAcients determined from our analysis are reported in Ref. [2]. Prior to performing multispectrum ?ttings, a relative calibration of the wavelength scales of all of the spectra included in the analysis was performed. Positions of a number of water vapor lines belonging to the 2 band were measured in one spectrum and the wavelength scales of all the remaining spectra were adjusted by matching the positions of the same water vapor lines relative to the ?rst spectrum. These lines appear in each spectrum due to residual atmospheric water in the optical path outside the sample cell. The derived zero-pressure line center positions of the laser band transitions after the multispectrum ?ts were then used to correct the scale to best match the positions obtained from laser heterodyne techniques [5]. The observed individual line intensities, Si , in natural abundance, were ?tted to the expression [13]: −C2 i i SV −C2 Ei 1 − exp × F: (3) Si = Li exp 0 Q r T T Here, i is the resonant (center position of the ith spectral line) frequency, 0 the band origin, SV the vibrational band intensity, Li the rotational line intensity or HMonl–London factor, Qr the lower state rotational partition function at the temperature T , Ei the lower state rotational energy, C2 the second radiation constant (hc=k; h is Planck’s constant, c is the speed of light and k is the Boltzmann constant), and F the non-rigid–rotor factor that is described below. The CO2 laser bands are parallel-type bands and the HMonl–London factor Li is given by [14] Li =
m2 − l2 |m|
for P and R branches;
(4)
where m = J + 1 for the R branch, and m = −J for the P branch, J is the lower-state rotational quantum number and l the lower-state vibrational angular momentum quantum number. SV , as given in Eq. (3), takes account only of the rotational partition function assuming that there is no vibrational contribution and in addition takes no account of the isotopic abundance. In order to obtain the dipole moment matrix element, it is necessary to take into account the vibrational population of the lower state and also of the isotopic abundance. The square of the dipole moment matrix element, |R|2 (in Debye2 ), is computed using the following equation that has been modi?ed from Ref. [15]: |R|2 =
1 Qv SV 3hc ; 8 3 × 10−36 0 exp(−C2 EV =T )
(5)
where Qv is the vibrational partition function, EV the lower-state vibrational energy, T the temperature of the gas sample in Kelvin, and is the mixing ratio of the 12 C16 O2 isotopomer in a natural sample. In our calculations, values of 263.90333 (at 296 K), 1.08456 (at 296 K) and 0.9842 were used for Qr , Qv and , respectively. The isotopic abundance of 0.9842 for 12 C16 O2 has been adopted from the HITRAN compilation [6 –8]. The F factor de?nes the departure of the line intensities from rigid-rotor behavior. For CO2 , non-rigid behavior arises from Coriolis- and Fermi-type interactions and centrifugal distortion
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eOects. Toth [16] has used ?rst-order non-degenerate perturbation theory to derive explicit F-factor expressions for application in the analysis of CO2 and N2 O line intensity measurements. For the parallel (Ul = 0) bands, the F factor is modeled as F = [1 + A1 m + A2 m2 + A3 m3 ]2
for P and R branches:
(6)
Because of these vibration–rotation interaction eOects, the integrated band intensity Sband will diOer from the vibrational band intensity SV (see Table 4). For the – bands (the bands measured in this work), the Q branch is forbidden, and the sum has been computed from the calculated P- and R-branch line intensities in each band through J = 94, according to [17] S(m): (7) Sband = m=0
A minimum spectral line intensity cut-oO of 1:0 × 10−28 cm−1 =(molecule cm−2 ) at 296 K was used in computing the Sband . The vibrational band intensity and the F-factor coeAcients as de?ned in Eqs. (3) and (6) were determined by a least-squares procedure that minimizes the weighted sum of the squares of the residuals between the ?tted and the calculated line intensities. The assigned weights were inversely proportional to the square of the estimated uncertainty obtained from the multispectrum ?t. Details about the weighting scheme are given in Ref. [11]. The measured line intensities for the laser bands are plotted in Fig. 2a. The unequal intensity distributions (small but noticeable) between the P and R branches due to Fermi interaction are observed in Fig. 2a. The percentage intensity residual Ri (%Res) listed in Tables 2 and 3 is expressed as Sobs − Scalc ; (8) Ri (%Res) = 100 Scalc where Sobs and Scalc represent the observed and calculated line intensity, respectively. Except for the high-J lines (J ¿60) in the P and R branches, the residuals as shown in Fig. 2b are typically about 2% for both laser bands. To indicate the quality of an individual line intensity measurement, the residual as a percentage of the calculated line intensity is also listed in Tables 2 and 3. 4. Results and discussion The measured absolute rovibrational intensities in a natural mix of isotopomers for the individual spectral lines of the CO2 laser bands are listed in Tables 2 and 3. In these two tables we have listed for each line the position, rotational assignment, measured line intensity with its uncertainty, calculated line intensity and the intensity residual (observed minus calculated) as a percentage of the calculated intensity. Because of lack of knowledge of exact isotopomer abundances in the 13 CO2 sample, the absolute intensities of the 13 CO2 laser band lines are not reported here. In addition to determining the band intensity SV , and the non-rigid rotor (F-factor=Herman–Wallis) coeAcients (shown in Table 4), the least-squares solution also gives , an estimate of the quality of the ?t for each measured band. The uncertainty of the multispectrum ?t is the formal uncertainty arising in the least-squares solution. This includes the uncertainty due to the noise in the spectrum
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401
Fig. 2. (a) Measured line intensities in cm−1 =(molecule cm−2 ) at 296 K as a function of the rotational quantum number index m for the laser bands I and II. The small A1 value for the Coriolis coeAcient obtained for these bands results in slightly diOerent intensities for the P and R branches. Uncertainties are smaller than the symbols. (b) The observed minus calculated line intensities as a percentage of the calculated intensity plotted as a function of m. The weak high-J lines have large percentage intensity errors.
and any residuals that may result from under?tting due to inadequacy of the input model. The quality of the ?t can be compared with the internal uncertainties reported by the multispectrum ?t. This is done by dividing the standard deviation of the ?t (for a given weight) by the uncertainty of the multispectrum ?t (for the same weight). This method provides a means for evaluating the level of some systematic errors in the multispectrum ?t. For the laser bands I and II whose intensities were measured in this study, this ratio was approximately 4 and 5, respectively, which indicates that the multispectrum ?t error analysis accounts for only about 20 –25% of the total uncertainty in the measured spectral line intensity. Further sources of systematic errors that are still not accounted in the analysis may include uncertainties in the
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Table 2 Line positions and intensities in the Position (cm−1 )
886.3752 891.3268 893.7595 896.1642 898.5406 900.8899 903.2118 905.5066 910.0159 912.2308 914.4193 916.5818 922.9143 924.9740 927.0083 929.0174 931.0014 932.9604 934.8945 936.8038 938.6882 940.5481 942.3833 944.1940 945.9802 947.7420 949.4793 951.1922 952.8808 954.5451 956.1850 957.8005 959.3918 961.7329 963.2631 964.7690 966.2504 967.7072 969.1395 970.5472 971.9303 973.2885 974.6220 975.9304 977.2139 978.4723
12
C16 O2 laser band I (3 –1 )
Assignment
P74 P70 P68 P66 P64 P62 P60 P58 P54 P52 P50 P48 P42 P40 P38 P36 P34 P32 P30 P28 P26 P24 P22 P20 P18 P16 P14 P12 P10 P8 P6 P4 P2 R0 R2 R4 R6 R8 R10 R12 R14 R16 R18 R20 R22 R24
Line intensitya
%Resb
Observed
Calculated
2.85(55)E-27 1.093(62)E-26 1.849(58)E-26 3.043(57)E-26 5.183(60)E-26 8.129(73)E-26 1.184(9)E-25 1.817(9)E-25 4.126(10)E-25 5.762(13)E-25 8.273(14)E-25 1.149(4)E-24 2.977(5)E-24 3.879(8)E-24 4.960(13)E-24 6.355(12)E-24 7.857(17)E-24 9.489(22)E-24 1.150(2)E-23 1.353(3)E-23 1.544(3)E-23 1.736(3)E-23 1.912(3)E-23 2.057(3)E-23 2.148(3)E-23 2.201(3)E-23 2.147(3)E-23 2.034(3)E-23 1.866(3)E-23 1.603(2)E-23 1.264(2)E-23 8.777(10)E-24 4.518(3)E-24 2.294(2)E-24 6.778(6)E-24 1.100(2)E-23 1.476(2)E-23 1.793(3)E-23 2.027(3)E-23 2.196(3)E-23 2.298(3)E-23 2.313(3)E-23 2.249(3)E-23 2.118(3)E-23 1.974(3)E-23 1.773(3)E-23
3.818E-27 1.105E-26 1.834E-26 2.996E-26 4.814E-26 7.611E-26 1.184E-25 1.811E-25 4.030E-25 5.864E-25 8.390E-25 1.180E-24 2.960E-24 3.883E-24 5.003E-24 6.331E-24 7.863E-24 9.583E-24 1.146E-23 1.343E-23 1.541E-23 1.732E-23 1.903E-23 2.042E-23 2.136E-23 2.173E-23 2.143E-23 2.038E-23 1.856E-23 1.597E-23 1.269E-23 8.823E-24 4.531E-24 2.291E-24 6.790E-24 1.101E-23 1.477E-23 1.791E-23 2.033E-23 2.198E-23 2.284E-23 2.295E-23 2.240E-23 2.128E-23 1.973E-23 1.788E-23
−25.4 − 1.1 0.8 1.6 7.7 6.8 0.0 0.4 2.4 − 1.7 − 1.4 − 2.7 0.6 − 0.1 − 0.9 0.4 − 0.1 − 1.0 0.4 0.8 0.1 0.3 0.5 0.7 0.6 1.3 0.2 − 0.2 0.6 0.3 − 0.4 − 0.5 − 0.3 0.1 − 0.2 − 0.1 0.0 0.1 − 0.3 − 0.1 0.6 0.8 0.4 − 0.5 0.0 − 0.8
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403
Table 2 (continued) 979.7054 980.9132 982.0955 983.2522 984.3832 985.4883 986.5674 987.6202 988.6467 989.6465 990.6197 991.5658 992.4848 993.3765 994.2405 995.0767 995.8846 996.6644 997.4155 998.1378 998.8309 999.4947 1000.1278 1000.7323 a b
R26 R28 R30 R32 R34 R36 R38 R40 R42 R44 R46 R48 R50 R52 R54 R56 R58 R60 R62 R64 R66 R68 R70 R72
1.577(2)E-23 1.361(2)E-23 1.162(2)E-23 9.708(15)E-24 7.942(11)E-24 6.403(8)E-24 5.058(5)E-24 3.921(31)E-24 2.991(21)E-24 2.231(15)E-24 1.637(13)E-24 1.173(11)E-24 8.405(10)E-25 5.823(8)E-25 4.028(7)E-25 2.684(7)E-25 1.803(6)E-25 1.189(5)E-25 7.325(42)E-26 4.708(41)E-26 2.786(41)E-26 1.763(39)E-26 1.108(38)E-26 5.84(39)E-27
1.585E-23 1.376E-23 1.170E-23 9.760E-24 7.986E-24 6.414E-24 5.057E-24 3.916E-24 2.978E-24 2.226E-24 1.635E-24 1.180E-24 8.374E-25 5.842E-25 4.007E-25 2.703E-25 1.793E-25 1.170E-25 7.509E-26 4.741E-26 2.944E-26 1.799E-26 1.081E-26 6.395E-27
− − − − − −
− − − − − − − −
0.5 1.1 0.7 0.5 0.6 0.2 0.0 0.1 0.4 0.2 0.1 0.6 0.4 0.3 0.5 0.7 0.5 1.6 2.5 0.7 5.4 2.0 2.4 8.7
Intensities are reported in units of cm−1 =(molecule cm−2 ) at 296 K (in natural abundance). ((Sobs − Scalc )=Scalc )100.
calibration of pressure gauge (¡1%) or thermometer (0.2%), lack of knowledge of exact isotopomer mixing ratios (∼0:05%), a consistent path length error (¡0:1%), channel spectrum correction (∼0:01%), lack of knowledge of zero level (∼0:3%), lack of knowledge of continuum (∼0:1%), purity of the sample (¡0:01%), phase error (∼0:1%) and the shape of the instrumental line pro?le. Based upon these estimates we believe that the absolute uncertainties in our intensities to be about 2%. In Fig. 3(a) and (b) we illustrate the ratio of each residual resulting from the band intensity ?t to the standard deviation of the same ?t as a function of m for laser bands I and II, respectively. The scatter in Fig. 3(a) and (b) is random. Our intensity measurements compare favorably (within 1%) with the results of Dana et al. [3] but are systematically lower [mean diOerence is −(5 ± 2)%] than measurements made by Johns and NoMel [4]. In both laser bands, for the lower quantum number transitions (|m| 6 20) intensity values reported in the HITRAN agree fairly closely to our measurements, but for higher quantum number transitions they diOer from our results by several percent. The source for this deviation is not precisely known especially since it has been reported that the SV and the F factor coef?cients adopted in the HITRAN database [6 –8] are stated to be the values of Dana et al. [3]. Apparently less accurate Herman–Wallis factors were applied while generating the HITRAN line list.
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Table 3 Line positions and intensities in Position (cm−1 )
986.3557 988.8171 991.2609 993.6829 996.0841 998.4647 1000.8239 1003.1616 1005.4775 1007.7713 1010.0429 1012.2918 1014.5179 1016.7210 1018.9007 1021.0569 1023.1894 1025.2979 1027.3822 1029.4421 1031.4774 1033.4880 1035.4736 1037.4341 1039.3693 1041.2790 1043.1632 1045.0217 1046.8542 1048.6608 1050.4413 1052.1955 1053.9235 1055.6250 1057.3002 1058.9487 1060.5706 1062.1660 1066.0373 1067.5391 1069.0141 1070.4623 1071.8838 1073.2784 1074.6464 1075.9878
12
C16 O2 laser band II (3 –202 )
Assignment
P76 P74 P72 P70 P68 P66 P64 P62 P60 P58 P56 P54 P52 P50 P48 P46 P44 P42 P40 P38 P36 P34 P32 P30 P28 P26 P24 P22 P20 P18 P16 P14 P12 P10 P8 P6 P4 P2 R2 R4 R6 R8 R10 R12 R14 R16
Line intensitya
%Resb
Observed
Calculated
5.3(4)E-27 6.7(4)E-27 1.32(4)E-27 2.32(4)E-26 3.54(4)E-26 5.53(4)E-26 8.65(4)E-26 1.361(6)E-25 2.102(6)E-25 3.193(7)E-25 4.810(8)E-25 7.011(8)E-25 1.016(1)E-24 1.429(1)E-24 1.982(2)E-24 2.723(2)E-24 3.651(3)E-24 4.816(6)E-24 6.237(9)E-24 7.975(14)E-24 1.001(2)E-23 1.228(2)E-23 1.501(3)E-23 1.778(3)E-23 2.066(3)E-23 2.389(3)E-23 2.662(3)E-23 2.910(4)E-23 3.106(4)E-23 3.251(4)E-23 3.324(4)E-23 3.251(4)E-23 3.068(4)E-23 2.830(4)E-23 2.427(4)E-23 1.905(3)E-23 1.320(2)E-23 6.763(6)E-24 1.019(2)E-23 1.686(3)E-23 2.272(4)E-23 2.751(4)E-23 3.112(4)E-23 3.376(4)E-23 3.539(4)E-23 3.578(4)E-23
4.382E-27 7.517E-27 1.270E-26 2.111E-26 3.456E-26 5.568E-26 8.831E-26 1.379E-25 2.118E-25 3.201E-25 4.762E-25 6.969E-25 1.003E-24 1.421E-24 1.980E-24 2.712E-24 3.653E-24 4.838E-24 6.297E-24 8.053E-24 1.012E-23 1.248E-23 1.512E-23 1.797E-23 2.095E-23 2.393E-23 2.677E-23 2.930E-23 3.132E-23 3.266E-23 3.312E-23 3.258E-23 3.092E-23 2.811E-23 2.416E-23 1.918E-23 1.333E-23 6.846E-24 1.028E-23 1.669E-23 2.243E-23 2.726E-23 3.103E-23 3.364E-23 3.508E-23 3.540E-23
19.9 −10.6 3.7 9.6 2.5 − 0.7 − 2.1 − 1.3 − 0.7 − 0.3 1.0 0.6 1.3 0.5 0.1 0.4 − 0.1 − 0.4 − 1.0 − 1.0 − 1.1 − 1.7 − 0.7 − 1.1 − 1.4 − 0.2 − 0.6 − 0.7 − 0.8 − 0.4 0.3 − 0.2 − 0.8 0.7 0.4 − 0.7 − 1.0 − 1.2 − 0.8 1.0 1.3 0.9 0.3 0.4 0.9 1.1
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Table 3 (continued) 1077.3025 1079.8522 1081.0874 1083.4788 1084.6351 1085.7654 1086.8698 1087.9483 1089.0011 1090.0284 1091.0302 1092.0068 1092.9582 1093.8847 1094.7865 1095.6636 1096.5164 1097.3449 1098.1495 1098.9303 1099.6874 1100.4208 1101.1316 1101.8192 1102.4843 1103.7457 1104.3446 a b
R18 R22 R24 R28 R30 R32 R34 R36 R38 R40 R42 R44 R46 R48 R50 R52 R54 R56 R58 R60 R62 R64 R66 R68 R70 R74 R76
3.464(4)E-23 3.118(4)E-23 2.832(4)E-23 2.185(4)E-23 1.928(3)E-23 1.564(3)E-23 1.292(3)E-23 1.039(2)E-23 8.373(15)E-24 6.528(12)E-24 5.045(6)E-24 3.811(4)E-24 2.837(2)E-24 2.066(2)E-24 1.487(1)E-24 1.018(2)E-24 7.094(13)E-25 4.860(8)E-25 3.282(7)E-25 2.144(6)E-25 1.434(5)E-25 9.28(41)E-26 5.52(4)E-26 3.40(4)E-26 2.01(3)E-26 7.30(3)E-27 5.4(3)E-27
3.469E-23 3.087E-23 2.813E-23 2.192E-23 1.878E-23 1.578E-23 1.301E-23 1.054E-23 8.382E-24 6.551E-24 5.031E-24 3.799E-24 2.820E-24 2.058E-24 1.478E-24 1.044E-24 7.249E-25 4.955E-25 3.332E-25 2.205E-25 1.436E-25 9.207E-26 5.809E-26 3.608E-26 2.206E-26 7.865E-27 4.588E-27
− 0.1 1.0 0.7 − 0.3 2.7 − 0.9 − 0.7 − 1.4 − 0.1 − 0.3 0.3 0.3 0.6 0.4 0.6 − 2.4 − 2.1 − 1.9 − 1.5 − 2.8 − 0.2 0.8 − 5.0 − 5.8 − 9.0 − 7.1 17.5
Intensities are reported in units of cm−1 =(molecule cm−2 ) at 296 K (in natural abundance). ((Sobs − Scalc )=Scalc )100.
Comparisons of present intensity measurements with other recent studies are shown in Fig. 4. In Fig. 4(a) we have re-plotted the measured intensities for laser bands I and II as a function of m and in Fig. 4(b) – (d) we have compared the present intensity measurements with values determined by Johns and NoMel [4], Dana et al. [3], and the HITRAN database [6 –8]. In Fig. 4(e) we have compared the measured results of Dana et al. [3] that are adopted in HITRAN [6 –8] with the actual values listed in the HITRAN [6 –8]. The small diOerences in Fig. 4(e) are attributed to intensity values calculated from the F-factor coeAcients of Dana et al. [3] rather than the observed intensities. In Table 4 we present the best-?t values for SV , the square of the rotationless transition dipole moment |R|2 and the F-factor coeAcients along with the calculated integrated band intensity Sband . The values for Sband listed in Refs. [3,4] were computed utilizing the F-factor coeAcients reported by the authors. The uncertainties given in parentheses are one standard deviation in units of the last quoted digit. The F-factor coeAcients were retained in the solution only if the standard deviation for that coeAcient was at least three times smaller than the value of the coeAcient itself. The Coriolis coeAcient A1 and the quadratic coeAcient A2 were determined for both laser bands while
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Table 4 Intensities and F-factor coeAcients derived for the
12
C16 O2 laser bands
Laser band
Present work
Dana et al. [3]
Johns and NoMel [4]
00011 ← 10001 (3 –1 ) |R|2a A1 A2 SV b (×10−21 ) Sband b (×10−21 )
0.0014251(14) −0.000493(14) −0.0000162(4) 0.60556(60) 0.5907
0.0014395(55) −0.000783(41) −0.0000106(13) 0.613 0.6011
0.0014932(22) −0.000641(16) −0.00000917(53) 0.62981(92) 0.6187
Correlation coeAcients SV and A2 A1 and A2 SV and A1
−0.610 −0.563 +0.023
00011 ← 10002 (3 –202 ) |R|2a A1 A2 A3 (×10−7 ) SV b (×10−21 ) Sband b (×10−21 )
0.0011748(18) −0.000114(36) 0.0000102(4) −0.83(15) 0.9109(14) 0.9176
0.0011774(24)
0.0012186(19) −0.000266(24) 0.00001499(78)
Correlation coeAcients A1 and A3 SV and A2 A2 and A3 A1 and A2 SV and A1 SV and A3
−0.940 −0.795 −0.045 +0.026 +0.021 −0.002
0.0000133(17) 0.915 0.9253
0.9412(15) 0.9528
a
Debye2 . SV is the vibrational band intensity and Sband is the integrated band intensity (sum of all computed intensities in the band through J = 94) in units of cm−1 =(molecule cm−2 ) at 296 K (in natural abundance). b
cubic distortion term A3 was determined for laser band II only. The correlation coeAcients among the determined parameters obtained for the two laser bands are also given in this table. From these coeAcients an estimate of the uncertainty in each of the calculated intensity could be made. For laser band II, the A1 and A3 coeAcients were not well determined, but were both essential for obtaining a good ?t. However, we were able to determine a linear combination of the two parameters well. Using the correlation coeAcients it was found that A1 + 2000A3 = −0:000280(13). This sum is determined to 20 times its uncertainty while A1 is determined to only three times its uncertainty and A3 is determined to only about ?ve and a half times its uncertainty. Our SV and |R|2 values compare reasonably well with the measurements of Dana et al. [3]. The values adopted in the HITRAN database [6 –8] are based upon the results obtained by Dana and co-workers [3]. We have compared our measurements with values listed in Refs. [3,4,6 –8]. The comparison of ratios of SV and |R|2 obtained from diOerent studies are made in Table 5. For a given band, the ratios of SV and |R|2 between any two studies should give the same values.
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Fig. 3. Ratio of residuals of individual spectral lines obtained from the band intensity ?t to the standard deviation of the ?t for (a) laser band I and (b) laser band II.
Since the values adopted in the HITRAN database [6 –8] for the SV and |R|2 are those of Dana et al. [3] comparisons with Refs. [6 –8] are not included in Table 5. The diOerences between present study and Dana et al. [3] are within 1% for laser band I and ¡0:5% for laser band II while the results between this study and Johns and NoMel [4] diOer by 4% and 3% for laser band I and II, respectively. We believe that this diOerence may be due to slightly diOerent partition functions employed in each analysis. We have adopted a value of 286.219 corresponding to 296 K as the total internal partition sum for the 12 C16 O2 isotopomer. This value has been taken from the HITRAN compilation [7,8] and from Gamache et al. [18].
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Fig. 4. (a) Measured spectral line intensities as a function of the rotational quantum number index m for the two laser bands. (b) – (d) Percentage intensity diOerences between Refs. [3,4,6 –8] and present work. (b) Intensities from Johns and NoMel [4] are higher than present measured intensities by an average value of 4%. (c) Values determined by Dana et al. [3] agree with our present measurements within about 1%. (d) The diOerences in intensities between values from HITRAN [6 –8] and present measurements are in opposite directions for the two laser bands. (e) Percentage diOerences between the intensity measurements by Dana et al. [3] and the values in the HITRAN database [6 –8]. Mean value of the diOerences is ¡1%.
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409
Table 5 Comparisons of SV and |R|2 Laser band
Ratio
Dana et al. [3] to the present work
Johns and NoMel [4] to the present work
I
|R|2 SV
1:010 ± 0:004 1.012
1:048 ± 0:002 1:040 ± 0:002
II
|R|2 SV
1:002 ± 0:003 1.004
1:037 ± 0:002 1:033 ± 0:002
5. Conclusions In the present study we obtained absolute line intensities of the two 12 C16 O2 laser bands, (00011– 10001) and (00011–10002), located at 10 m. The 22 room temperature high-resolution (0.0028– 0:0053 cm−1 ) long path (73–434 m) laboratory absorption spectra recorded with a Fourier transform spectrometer were analyzed with a multispectrum nonlinear least-squares ?tting technique. These intensity measurements were modeled to an absolute accuracy of at least 98% by applying a three-term Herman–Wallis expression. The wide range of J values {P(74) –R(72) in laser band I and P(76) –R(76) in laser band II} reached in our investigation permitted the cubic distortion coeAcient to be determined for the ?rst time in the (00011–10002) band near 1064 cm−1 . Only two Herman–Wallis terms were required for the (00011–10001) band at 961 cm−1 . The present measurements con?rmed the intensity values determined by Dana and co-workers within about 1%. The present intensity values agreed with those by Dana et al. within ∼0:5% for the 1064 cm−1 band and were lower than the values of Dana et al. by ∼1:0% for the 961 cm−1 band. The intensity values determined in the present study for both laser bands are lower than the values of Johns and NoMel by ∼4%. Comparison with the corresponding entries in the HITRAN database revealed that the overall normalization on the absolute intensities from Dana et al. that was adopted by HITRAN database was consistent with the present values. However, less accurate Herman–Wallis factors had apparently been applied. Better accuracy for these CO2 intensities in the database can be achieved by the use of more accurate Herman–Wallis terms.
Acknowledgements The authors thank Claude Plymate of the National Solar Observatory (NSO) for assistance in recording some of the spectra. Cooperative agreements and contracts with 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 thank the NASA Upper Atmosphere Research Program for their support of the McMath–Pierce FTS laboratory facility.
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