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Intensities and broadening coefficients for the Q branch of the 4v2↔v1 + v2 (471.511 cm-1) band of CO2
J. Quant. Spertrosc. Radiat. Transfer Vol. 50, No. 2, pp. 193-198, 1993
0022~4073/93 $6.00 + 0.00
Printedin GreatBritain.All rightsreserved
Copyright0 1993PergamonPressLtd
INTENSITIES AND BROADENING COEFFICIENTS FOR THE Q BRANCH OF THE 4V2 t, Vt i- V2 (471.511 Cm-‘) BAND OF CO, J. MARCOS SIROTA,~DENNISC. RELJTER, and M. J. MUMMA Planetary Systems Branch, NASA Goddard Space Flight Center, Code 693, Greenbelt, MD 20771, U.S.A. (Received
17 December
1992)
intensities for the Q-branch of the 4v, +B v, + vi (20003-l 1101) band in CO2 have been measured for the first time. Measurements were performed for lines Q 10 to Q28, at temperatures ranging from 385 to 426 K, for pressures from 3 to 40 torr, using our long wavelength tunable diode laser spectrometer. The combination of tunable diode lasers, a White cell, and a blocked impurity band detector enabled us to obtain signal to noise ratios > 1000 in the 471 cm-’ spectral region, with -3 x 10-4cm-’ spectral resolution. The band strength was found to be 8.6(2) x lO-25 cm molec-’ @296 K, and the Hermann-Wallis factor
Abstract-Absolute
was determined. Comparison with the values listed in the HITRAN 92 database are presented. Self-, N,- and O,-broadening coefficients were also measured.
INTRODUCTION We report here our experimental measurements of absolute intensities and broadening coefficients for the Q-branch of the 4v, c) v, + vi band in COZ, with origin at 471.5 11 cm-‘. To our knowledge, no previous measurements of this band have been made. The measurements were made using the Goddard tunable diode laser spectrometer, which is able to operate at wavelengths greater than 20 pm.’ This instrument provides very high signal to noise ratios compared to that achievable with a Fourier transform instrument. Fourier instruments yield relatively low signal to noise ratios in this region due to the weakness of available sources. CO2 is an important constituent of planetary atmospheres, having been observed for example on Mars, Venus, and Saturn’s moon Titan. The transitions measured here may be used, for instance, as a temperature probe for the low atmosphere of Venus. * Since the lower state of these transitions is highly excited (-2000 cm-‘) this band would allow deeper sounding than that achievable with shorter wavelength, more intense bands of CO*. The terrestrial atmospheric transmission at this wavelength is relatively high (75% at the IRTF in Hawaii) which would allow ground based observations. Our measurements also serve for verification of existing databases, where intensities for most transitions in this wavelength region have been obtained only by numerical methods. For example, in the HITRAN 92 database the band intensity was obtained by direct numerical diagonalization (DND), as described in Ref. 3. EXPERIMENTAL
SYSTEM
A detailed description of the diode laser spectrometer can be found in Ref. 1, so only a brief description will be given here. The infrared beam was generated by a lead salt semiconductor laser operating at about 36 K, whose temperature was stabilized to better than 0.005 K. The laser current was modulated with a ramp waveform at 200 Hz, generating a periodic laser frequency sweep 0.2 cm-’ wide. The beam is sent through a grating monochromator, to spectrally select a single laser mode. A chopper, synchronized with the laser scan, provided the zero signal reference. The gas was contained in a White cell (Laser Analytics LO-3) which was heated by electrical heating tape wrapped uniformly around the cylindrical cell. A layer of aluminium foil was installed around the cell, in order to further smooth any temperature gradients along the strainless steel wall. The temperature was measured at 20 points along the 1 m cell, and the heating rate of individual fNASA/National
Research Council Research Associate; to whom all correspondence should be addressed. 193
194
J. MARCOSSIROTA et al
heaters adjusted until the maximum temperature variation was less than 5 K. The average of these temperatures was considered the gas temperature. This gas temperature measurement was spectroscopically verified by using well known N,O transitions at 7.9 pm, as described in the Appendix. After passing through the cell the beam was focused onto a blocked impurity band extrinsic silicon detector, working at about 6 K. A cold bandpass filter and f-stop in front of the detector limited the background radiation received. Nevertheless, the detector operated background limited. This detector provided high signal to noise ratios, allowing short integration times, which minimized diode laser frequency drift. The signal was sent to a signal averager, where averages of about 300 scans were obtained. The data averaged for each run was automatically transferred to a computer for analysis. An example of the experimental data is shown in Fig. 1. DATA
ANALYSIS
Each raw data set, such as the one shown in Fig. 1, was divided by its corresponding background to obtain true transmittances. The logarithm of this ratio was then least squares fitted to a Voigt profile, using the program DECOMP, which is an interactive analysis program commonly used for the reduction of FTS data obtained at Kitt Peak National Observatory. The measured lines and their fit, for the data of Fig. 1, are shown in Fig. 2. The depth of each line, its width, and the ratio of Lore& component to the total width are the outputs of the program. The frequency axis was calibrated using etalon fringes, and corroborated with the measured line separations. We used the line positions which appear in HITRAN 92,4 in our analysis. These frequencies have been calculated as differences between upper and lower states energies, both of which have been obtained with high accuracy for CO2 using combination-differences of transitions at shorter wavelengths. Line identification was straightforward, since the Q28 line is separated by only 4.7 x 10-3cm-’ from a Hz0 line,4 which could be seen clearly by allowing a few torrs of air into the cell. The line intensities were obtained by a direct method,’ from the outputs of DECOMP. Using the line depth, width, gas pressure, temperature, and pathlength, the line intensity for each line was calculated as: S, = ln[l/r(v,)]P’xK(O,
a),
(1)
where ln[l/r(v,)] is the line depth, P’ = (l/b,)[(ln 2)/7r]“’ is the normalization factor, 6, is the Gaussian half width, and x =pf is the optical density, where p is the gas pressure in atmospheres, and I the path length. K(0, a) is the value of the Voigt function at the line center, where a = (bJbn)(ln 2)‘j2, and bL is the collisional half-width.
T = 405 K = 3 Torr e = 3600 cm Scans = 250 Averaging Time = 2 sec. Fig. I. Output from the signal averager for lines Q22-Q6, for the conditions shown.
Intensities and broadening cc&cients for the CO, Q branch
195
Q20 Fig. 2. Lines after background removal, for part of the trace shown in Fig. I. The least squares fitting to a Voigt profile is also shown.
The line intensity is related to the vibrational band intensity, Sv, as follows S _S y~g exp(-E,IkT) Iv J e,
(2)
[I-‘=+#$!JF,
VI3
and the band intensity can be expressed as function of the vibrational transition dipole moment r y”,y,, as:
=ELoToYi
s
’
3hcp,+
exp(-WkT) Q”
1V”.V’ r2
(3)
The terms defined in these two equations are: v, the transition frequency, v,, the band center frequency, QV and Qr the vibrational and rotational partition functions, E, and Ev the rotational and vibrational energy of the lower state, respectively, yi the isotopic abundance of the ith isotope and Lo the Loscmidth number at To = 273.15 K and p. = 1 atm. L$, is the square of the rotational transition moment or Holn-London factor, (4) for these Q branch, A1 = - 1 transitions, and FJ,, is the Hermann-Wallis
factor,
F’,o = [ 1 + Id*]*, for the AJ = 0 case. SJ was obtained from each measured line using Eq. (1). The Gaussian linewidth was calculated by means of a standard expression, from the measured linewidth and broadening coefficient determined in this study.5 Combining Eqs. (2)-(5), the two remaining unknowns are the transition dipole moment rP,V and the Hermann-Wallis coefficient b. These two numbers were obtained by means of a two parameter least squares fit of the data. Intensity values Figure 3 presents a summary of the measured data. The line is the result of the least squares fitting. The abscissa is a function only of J and T, which results from combining factors in Eqs. (2)-(5) in such a manner that the square of the transition dipole moment is the slope of the plot.
196
J. MARCO~SIROTA et al
cz 2-16-6
0
I /. 2,-
a_
.A
I _
J>
X(T
__.
6'10"
I_
4'IU_.
I”-
8'10
Fig. 3. Measured line intensities. The abscissa represents a grouping of factors from Eqs. (2) to (5) such that the slope of the plot is the square of the vibrational transition dipole moment. The line is the result of a two parameter least squares fit to the data (see text).
A large contributing factor to the experimental error is the uncertainty in gas temperature, since this hot band transition has an intensity sensitivity to temperature variations of N 2%/K at 400 K. Figure 4 shows measured rotational line intensities, and calculated values using the least squares fit parameters previously determined, for a particular dataset. The differences between the data and the calculated values are due mainly to noise and data processing uncertainties (e.g. background 4.10-25
h Y
I
I
I
I
I
I
20
22 24
@ yd
3’ lo-=
h 3 a, z
I
2*10-=
E C
L
cis l*lo-25
0 -
8
10
12
14
16
18
J Fig. 4. Line intensities for T = 390 K. [I= measured data points. The error bars correspond to the standard deviation of the data with respect to the fit, shown in Fig. 3. 0 = calculated line intensities using the values for TVy and 6 derived from Fig. 3, X = HITRAN 92 database values.
197
Intensities and broadening coefficients for the CO, Q branch Table 1. Summary of results. HlTRAN 92
Tbiawork Vibmtional dipole moment
rv:v*
Band intensity:
SV
Hexmann-Walliscoefficient (see a0 Collisional broadetig:(HWHM)
b
1.13(2) x 10-2 Debye O.%(2) x l(r24 cm mok-1
Q 2% K
1.15 x 10-24cm molec.-l (Ref. 3) 0.0
2.9(S) x lo-4
rCO2
0.%8(6) cm-l/ arm 0 390 K
m2
0.056(5) cm-l/ atm 8 390 K
7oZ 0.045(4) cm-l/ atm @ 390 K
determination). The HITRAN 92 database values are also shown, where the values for temperatures other than 296 K were calculated using HITRANPC.4 The database values for line intensities are, on the average, a factor of about 1.2 higher than our measured values. This ratio is not constant with J since in the database the Hermann-Wallis factor was taken as unity. The intensity results for the band are summarized in Table 1. Collisional
broadening
values
Self-, O,- and N,-broadening were measured for the lines Q22-26 of this band. These lines were chosen since their separation permits broadening without severe line overlapping. All broadening measurements were performed at 390 K. For CO*, pressures from 3 to 40 torr were used, and 20 measurements carried out. The differences in broadening among these three lines fall within the measurement uncertainty; thus a single coefficient equal to the average of the three is given in Table 1. For O2 and N, up to 20 torr of the foreign gas was added to 10 torr of CO*, in order to maintain good signal to noise ratio on the lines. The foreign gas broadening was then determined assuming that the total broadening was produced by the sum of the foreign- and self-broadening components. The measured broadening coefficients are summarized in Table 1. DISCUSSION The measured line intensities allowed us to determine the vibrational band intensity [Sv = 0.86(2) x lo-” cm molec-‘a296 K] and the second order Hermann-Wallis coefficient [b = 2.9(5) x 10e4] for this Q-branch. It should be pointed out that if we set the Hermann-Wallis coefficient b equal to zero in our data reduction, the resulting intensity is 1.05 x 1O-24cm molec- ‘, which differs by about 10% from the value obtained by direct numerical diagonalization by Rothman et a1,3 where b is equal to zero. However, for the lines measured here, the fitting error is twice as large if b is assumed to be zero than if it is a free parameter, indicating that the fitted value of b is statistically significant. Therefore, our measured band strength, including HermannWallis effects, is 25% lower than the value currently listed in Ref. 3. REFERENCES 1. J. M. Sirota, D. C. Reuter, and M. J. Mumma, Appf. Opt., 32, 2117 (1993). 2. V. G. Kunde, R. A. Hanel, and L. W. Herath, Icarus 32, 210 (1977). 3. L. S. Rothman, R. L. Hawkins, R. B. Wattson, and R. R. Gamache, JQSRT 48, 537 (1992). 4. L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. Chris Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, JQSRT 48, 469 (1992); D. K. Killinger and W. E. Wilcox, USF HITRAN-PC, University of South Florida (1992). 5. M. A. H. Smith, B. Fridovich, and K. N. Rao, Molecular Spectroscopy: Modern Research, Vol. III, Chap. 3, K. N. Rao Ed., Academic Press, New York, NY (1985). 6. R. A. Toth, Appl. Opt. 23, 1825 (1984). APPENDIX Gas Temperature
Vertjication
The temperature of the cell was measured with thermocouples at 20 points along its length, and the average of these temperatures was used as the gas temperature. In order to verify this assumption, we used two lines of N,O whose intensity ratio is highly sensitive to temperature
J. MMCXXSIROTAet al
198
variations in the 400 K range.6 The selected lines were P30 of the 00%lo”0 band for the “N’5N’60 isotope, and P44 of the 02°0-12”0 band for the “Niti isotope. These lines are separated by 36.4 x 10e3 cm-‘, therefore they were measured simultaneously in the same frequency scan. Their intensity ratio varies 1.5% per K, yielding a good spectral thermometer. The isotopic ratio was determined from natural abundance. An example of the measured and synthesized spectrum is shown in Fig. Al. The agreement between the thermocouple and the N,O-derived temperature was found to be rf:2 K.
1
.8
P30 1000-0000
P44 1200-0200
10253.6 1253.61 1253.62 1253.63 1253.84 1253.65 1253.66 1253.67 1253.68 wavemmber (an-l) Fig. Al. Cell temperature verification. The solid line corresponds to the measured spectrum (shifted in frequency for clarity), and the dotted lines correspond to synthesized spectra for five successive temperatures with AT = 5 K. The measured thermocouple temperature was 390 K. Here, 456 means “NlSN160 and 446 means “Niti.
0022~4073/93 $6.00 + 0.00
Printedin GreatBritain.All rightsreserved
Copyright0 1993PergamonPressLtd
INTENSITIES AND BROADENING COEFFICIENTS FOR THE Q BRANCH OF THE 4V2 t, Vt i- V2 (471.511 Cm-‘) BAND OF CO, J. MARCOS SIROTA,~DENNISC. RELJTER, and M. J. MUMMA Planetary Systems Branch, NASA Goddard Space Flight Center, Code 693, Greenbelt, MD 20771, U.S.A. (Received
17 December
1992)
intensities for the Q-branch of the 4v, +B v, + vi (20003-l 1101) band in CO2 have been measured for the first time. Measurements were performed for lines Q 10 to Q28, at temperatures ranging from 385 to 426 K, for pressures from 3 to 40 torr, using our long wavelength tunable diode laser spectrometer. The combination of tunable diode lasers, a White cell, and a blocked impurity band detector enabled us to obtain signal to noise ratios > 1000 in the 471 cm-’ spectral region, with -3 x 10-4cm-’ spectral resolution. The band strength was found to be 8.6(2) x lO-25 cm molec-’ @296 K, and the Hermann-Wallis factor
Abstract-Absolute
was determined. Comparison with the values listed in the HITRAN 92 database are presented. Self-, N,- and O,-broadening coefficients were also measured.
INTRODUCTION We report here our experimental measurements of absolute intensities and broadening coefficients for the Q-branch of the 4v, c) v, + vi band in COZ, with origin at 471.5 11 cm-‘. To our knowledge, no previous measurements of this band have been made. The measurements were made using the Goddard tunable diode laser spectrometer, which is able to operate at wavelengths greater than 20 pm.’ This instrument provides very high signal to noise ratios compared to that achievable with a Fourier transform instrument. Fourier instruments yield relatively low signal to noise ratios in this region due to the weakness of available sources. CO2 is an important constituent of planetary atmospheres, having been observed for example on Mars, Venus, and Saturn’s moon Titan. The transitions measured here may be used, for instance, as a temperature probe for the low atmosphere of Venus. * Since the lower state of these transitions is highly excited (-2000 cm-‘) this band would allow deeper sounding than that achievable with shorter wavelength, more intense bands of CO*. The terrestrial atmospheric transmission at this wavelength is relatively high (75% at the IRTF in Hawaii) which would allow ground based observations. Our measurements also serve for verification of existing databases, where intensities for most transitions in this wavelength region have been obtained only by numerical methods. For example, in the HITRAN 92 database the band intensity was obtained by direct numerical diagonalization (DND), as described in Ref. 3. EXPERIMENTAL
SYSTEM
A detailed description of the diode laser spectrometer can be found in Ref. 1, so only a brief description will be given here. The infrared beam was generated by a lead salt semiconductor laser operating at about 36 K, whose temperature was stabilized to better than 0.005 K. The laser current was modulated with a ramp waveform at 200 Hz, generating a periodic laser frequency sweep 0.2 cm-’ wide. The beam is sent through a grating monochromator, to spectrally select a single laser mode. A chopper, synchronized with the laser scan, provided the zero signal reference. The gas was contained in a White cell (Laser Analytics LO-3) which was heated by electrical heating tape wrapped uniformly around the cylindrical cell. A layer of aluminium foil was installed around the cell, in order to further smooth any temperature gradients along the strainless steel wall. The temperature was measured at 20 points along the 1 m cell, and the heating rate of individual fNASA/National
Research Council Research Associate; to whom all correspondence should be addressed. 193
194
J. MARCOSSIROTA et al
heaters adjusted until the maximum temperature variation was less than 5 K. The average of these temperatures was considered the gas temperature. This gas temperature measurement was spectroscopically verified by using well known N,O transitions at 7.9 pm, as described in the Appendix. After passing through the cell the beam was focused onto a blocked impurity band extrinsic silicon detector, working at about 6 K. A cold bandpass filter and f-stop in front of the detector limited the background radiation received. Nevertheless, the detector operated background limited. This detector provided high signal to noise ratios, allowing short integration times, which minimized diode laser frequency drift. The signal was sent to a signal averager, where averages of about 300 scans were obtained. The data averaged for each run was automatically transferred to a computer for analysis. An example of the experimental data is shown in Fig. 1. DATA
ANALYSIS
Each raw data set, such as the one shown in Fig. 1, was divided by its corresponding background to obtain true transmittances. The logarithm of this ratio was then least squares fitted to a Voigt profile, using the program DECOMP, which is an interactive analysis program commonly used for the reduction of FTS data obtained at Kitt Peak National Observatory. The measured lines and their fit, for the data of Fig. 1, are shown in Fig. 2. The depth of each line, its width, and the ratio of Lore& component to the total width are the outputs of the program. The frequency axis was calibrated using etalon fringes, and corroborated with the measured line separations. We used the line positions which appear in HITRAN 92,4 in our analysis. These frequencies have been calculated as differences between upper and lower states energies, both of which have been obtained with high accuracy for CO2 using combination-differences of transitions at shorter wavelengths. Line identification was straightforward, since the Q28 line is separated by only 4.7 x 10-3cm-’ from a Hz0 line,4 which could be seen clearly by allowing a few torrs of air into the cell. The line intensities were obtained by a direct method,’ from the outputs of DECOMP. Using the line depth, width, gas pressure, temperature, and pathlength, the line intensity for each line was calculated as: S, = ln[l/r(v,)]P’xK(O,
a),
(1)
where ln[l/r(v,)] is the line depth, P’ = (l/b,)[(ln 2)/7r]“’ is the normalization factor, 6, is the Gaussian half width, and x =pf is the optical density, where p is the gas pressure in atmospheres, and I the path length. K(0, a) is the value of the Voigt function at the line center, where a = (bJbn)(ln 2)‘j2, and bL is the collisional half-width.
T = 405 K = 3 Torr e = 3600 cm Scans = 250 Averaging Time = 2 sec. Fig. I. Output from the signal averager for lines Q22-Q6, for the conditions shown.
Intensities and broadening cc&cients for the CO, Q branch
195
Q20 Fig. 2. Lines after background removal, for part of the trace shown in Fig. I. The least squares fitting to a Voigt profile is also shown.
The line intensity is related to the vibrational band intensity, Sv, as follows S _S y~g exp(-E,IkT) Iv J e,
(2)
[I-‘=+#$!JF,
VI3
and the band intensity can be expressed as function of the vibrational transition dipole moment r y”,y,, as:
=ELoToYi
s
’
3hcp,+
exp(-WkT) Q”
1V”.V’ r2
(3)
The terms defined in these two equations are: v, the transition frequency, v,, the band center frequency, QV and Qr the vibrational and rotational partition functions, E, and Ev the rotational and vibrational energy of the lower state, respectively, yi the isotopic abundance of the ith isotope and Lo the Loscmidth number at To = 273.15 K and p. = 1 atm. L$, is the square of the rotational transition moment or Holn-London factor, (4) for these Q branch, A1 = - 1 transitions, and FJ,, is the Hermann-Wallis
factor,
F’,o = [ 1 + Id*]*, for the AJ = 0 case. SJ was obtained from each measured line using Eq. (1). The Gaussian linewidth was calculated by means of a standard expression, from the measured linewidth and broadening coefficient determined in this study.5 Combining Eqs. (2)-(5), the two remaining unknowns are the transition dipole moment rP,V and the Hermann-Wallis coefficient b. These two numbers were obtained by means of a two parameter least squares fit of the data. Intensity values Figure 3 presents a summary of the measured data. The line is the result of the least squares fitting. The abscissa is a function only of J and T, which results from combining factors in Eqs. (2)-(5) in such a manner that the square of the transition dipole moment is the slope of the plot.
196
J. MARCO~SIROTA et al
cz 2-16-6
0
I /. 2,-
a_
.A
I _
J>
X(T
__.
6'10"
I_
4'IU_.
I”-
8'10
Fig. 3. Measured line intensities. The abscissa represents a grouping of factors from Eqs. (2) to (5) such that the slope of the plot is the square of the vibrational transition dipole moment. The line is the result of a two parameter least squares fit to the data (see text).
A large contributing factor to the experimental error is the uncertainty in gas temperature, since this hot band transition has an intensity sensitivity to temperature variations of N 2%/K at 400 K. Figure 4 shows measured rotational line intensities, and calculated values using the least squares fit parameters previously determined, for a particular dataset. The differences between the data and the calculated values are due mainly to noise and data processing uncertainties (e.g. background 4.10-25
h Y
I
I
I
I
I
I
20
22 24
@ yd
3’ lo-=
h 3 a, z
I
2*10-=
E C
L
cis l*lo-25
0 -
8
10
12
14
16
18
J Fig. 4. Line intensities for T = 390 K. [I= measured data points. The error bars correspond to the standard deviation of the data with respect to the fit, shown in Fig. 3. 0 = calculated line intensities using the values for TVy and 6 derived from Fig. 3, X = HITRAN 92 database values.
197
Intensities and broadening coefficients for the CO, Q branch Table 1. Summary of results. HlTRAN 92
Tbiawork Vibmtional dipole moment
rv:v*
Band intensity:
SV
Hexmann-Walliscoefficient (see a0 Collisional broadetig:(HWHM)
b
1.13(2) x 10-2 Debye O.%(2) x l(r24 cm mok-1
Q 2% K
1.15 x 10-24cm molec.-l (Ref. 3) 0.0
2.9(S) x lo-4
rCO2
0.%8(6) cm-l/ arm 0 390 K
m2
0.056(5) cm-l/ atm 8 390 K
7oZ 0.045(4) cm-l/ atm @ 390 K
determination). The HITRAN 92 database values are also shown, where the values for temperatures other than 296 K were calculated using HITRANPC.4 The database values for line intensities are, on the average, a factor of about 1.2 higher than our measured values. This ratio is not constant with J since in the database the Hermann-Wallis factor was taken as unity. The intensity results for the band are summarized in Table 1. Collisional
broadening
values
Self-, O,- and N,-broadening were measured for the lines Q22-26 of this band. These lines were chosen since their separation permits broadening without severe line overlapping. All broadening measurements were performed at 390 K. For CO*, pressures from 3 to 40 torr were used, and 20 measurements carried out. The differences in broadening among these three lines fall within the measurement uncertainty; thus a single coefficient equal to the average of the three is given in Table 1. For O2 and N, up to 20 torr of the foreign gas was added to 10 torr of CO*, in order to maintain good signal to noise ratio on the lines. The foreign gas broadening was then determined assuming that the total broadening was produced by the sum of the foreign- and self-broadening components. The measured broadening coefficients are summarized in Table 1. DISCUSSION The measured line intensities allowed us to determine the vibrational band intensity [Sv = 0.86(2) x lo-” cm molec-‘a296 K] and the second order Hermann-Wallis coefficient [b = 2.9(5) x 10e4] for this Q-branch. It should be pointed out that if we set the Hermann-Wallis coefficient b equal to zero in our data reduction, the resulting intensity is 1.05 x 1O-24cm molec- ‘, which differs by about 10% from the value obtained by direct numerical diagonalization by Rothman et a1,3 where b is equal to zero. However, for the lines measured here, the fitting error is twice as large if b is assumed to be zero than if it is a free parameter, indicating that the fitted value of b is statistically significant. Therefore, our measured band strength, including HermannWallis effects, is 25% lower than the value currently listed in Ref. 3. REFERENCES 1. J. M. Sirota, D. C. Reuter, and M. J. Mumma, Appf. Opt., 32, 2117 (1993). 2. V. G. Kunde, R. A. Hanel, and L. W. Herath, Icarus 32, 210 (1977). 3. L. S. Rothman, R. L. Hawkins, R. B. Wattson, and R. R. Gamache, JQSRT 48, 537 (1992). 4. L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. Chris Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, and R. A. Toth, JQSRT 48, 469 (1992); D. K. Killinger and W. E. Wilcox, USF HITRAN-PC, University of South Florida (1992). 5. M. A. H. Smith, B. Fridovich, and K. N. Rao, Molecular Spectroscopy: Modern Research, Vol. III, Chap. 3, K. N. Rao Ed., Academic Press, New York, NY (1985). 6. R. A. Toth, Appl. Opt. 23, 1825 (1984). APPENDIX Gas Temperature
Vertjication
The temperature of the cell was measured with thermocouples at 20 points along its length, and the average of these temperatures was used as the gas temperature. In order to verify this assumption, we used two lines of N,O whose intensity ratio is highly sensitive to temperature
J. MMCXXSIROTAet al
198
variations in the 400 K range.6 The selected lines were P30 of the 00%lo”0 band for the “N’5N’60 isotope, and P44 of the 02°0-12”0 band for the “Niti isotope. These lines are separated by 36.4 x 10e3 cm-‘, therefore they were measured simultaneously in the same frequency scan. Their intensity ratio varies 1.5% per K, yielding a good spectral thermometer. The isotopic ratio was determined from natural abundance. An example of the measured and synthesized spectrum is shown in Fig. Al. The agreement between the thermocouple and the N,O-derived temperature was found to be rf:2 K.
1
.8
P30 1000-0000
P44 1200-0200
10253.6 1253.61 1253.62 1253.63 1253.84 1253.65 1253.66 1253.67 1253.68 wavemmber (an-l) Fig. Al. Cell temperature verification. The solid line corresponds to the measured spectrum (shifted in frequency for clarity), and the dotted lines correspond to synthesized spectra for five successive temperatures with AT = 5 K. The measured thermocouple temperature was 390 K. Here, 456 means “NlSN160 and 446 means “Niti.