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Effects of intercollisional interference on measured line strengths in the 3-0 quadrupole band of H2
Chemical Physics Letters 428 (2006) 39–41 www.elsevier.com/locate/cplett
Effects of intercollisional interference on measured line strengths in the 3-0 quadrupole band of H2 Daniel C. Robie Department of Natural Sciences, York College, City University of New York, Jamaica, NY 11451, USA Received 22 June 2006 Available online 20 July 2006
Abstract Recent observations of the 3-0 quadrupole band of H2 by cavity ring-down spectroscopy confirm discrepancies with theoretical calculations of the quadrupole transition moment. They also supply enough data to suggest that the discrepancy comes from narrow intercollisional interference dips in the collision-induced absorption. 2006 Elsevier B.V. All rights reserved.
The 3-0 (second overtone) band in the absorption spectrum of H2 was first predicted and observed by Herzberg over 50 years ago [1–3]. Arising from the electric quadrupole moment of the molecule, this weak band is important in the study of the atmospheres of the outer planets [4–6] and of cool stars [7]. Bands with a low strength are especially suited to studying these environments because they do not saturate even after pathlengths of hundreds of kilometers through megapascal pressures. Furthermore, the overtone bands of H2 above the first are in the visible (the second is around 815 nm, the third around 655 nm), readily accessible to ground-based telescopes. On the other hand, weak bands are inherently difficult to observe in the laboratory. Therefore, there have been many theoretical calculations of the quadrupole transition moments [8–15] and other spectroscopic parameters (pressure shifts [16,17], pressure broadening coefficients [18], etc. [16]) by a variety of methods. However, there has been a persistent discrepancy between these theoretical calculations and observed line strengths. Direct measurements of the line strengths in the 3-0 band have been 6–33% smaller than predicted [19,20]. Recently analyzed measurements of line strengths for seven lines in the 3-0 band carried out for the first time by cavity ring-down spectroscopy (CRDS) [19] agree with E-mail address: [email protected] 0009-2614/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.07.035
previous measurements, and confirm the discrepancy with the theoretical calculations. I propose a resolution of the discrepancy based on the phenomenon of intercollisional interference (II). Assemblies of molecules can interact with light not only through electric and magnetic moments characteristic of an isolated molecule, but also through moments induced by interacting molecules. Moments induced by a collision with another atom or molecule can result in collision-induced absorption (CIA) [21]. CIA has been observed with CRDS at pressures from tens of megapascals down to around 0.1 MPa [19,22]. Since CIA is the result of a binary collision, in a pure gas it is proportional to the square of the molecular density. A complete set of absorption coefficients for CIA in H2 at temperatures from 60 K up to 7000 K has been calculated [23]. CIA is greatest in spectral regions near allowed transitions. (In H2, vibrational transitions are electric-quadrupole allowed.) The short life of the collision complex determines the width of these overtone CIA bands, so they are broad — at room temperature, the 3-0 CIA band is 1000 cm1 wide [24]. The calculated CIA at the S(1) line of the 3-0 band is consistent with observations of non-resonant extinction around that line [19]. At 0.1 MPa in this region of the spectrum of H2, CIA is comparable in magnitude to Rayleigh scattering. In scans over only a few cm1 both of these non-resonant extinctions simply contribute to a flat baseline.
40
D.C. Robie / Chemical Physics Letters 428 (2006) 39–41
The transition dipole induced by one collision is, on average, oriented opposite to that of the subsequent collision. This correlation between successive induced transition dipoles diminishes the CIA [25], and is called intercollisional interference (II). It has been observed repeatedly in CIA spectra [16,20,24,26]. Because the relevant time scale is that between collisions, an II ‘dip’ is (approximately) a relatively narrow Lorentzian of width determined by the collision frequency — which, in turn, is proportional to the molecular density. The induced dipole moments that produce CIA depend on the rovibrational state of the molecule, and on the intermolecular potential, which itself depends on the molecular states [21,27]. II is restricted by symmetry to only some of the induced moments. Therefore, the II dip cannot exceed in depth the magnitude of the CIA at the resonance, and is likely to be smaller. There are no calculations of II using realistic potentials for H2 in the second overtone band [27]. It is important to note that, since CIA can easily exceed the peak height of a resonance, the II dip can be deeper than the resonance peak height. The resulting line shape goes below the apparent baseline. Extinction around the S(1) line will then have four contributions: etotal ¼ AS1 þ eR þ ACIA þ eII
ð1Þ
where AS1 ¼ S S1 lngð~mÞ
ð2Þ
is the absorption due to the S(1) resonance itself. The density n is in amagats. (One amagat is the density of the gas at 273.15 K and 1 atm pressure. The conversion factor to density in molecules cm3 is Loschmidt’s number L, 2.68 · 1019 cm3 for H2) SS1, calculated from a quadrupole transition matrix element, is the line strength in cm1/cm amagat; l is the pathlength in the absorber; the area-normalized line shape function is gð~mÞ. The contribution from Rayleigh scattering, constant over a small spectral range of a few cm1, is given by eR. Known values used here are given in Table 1. Finally, CIA is given by ACIA ¼ aln2
Table 1 Constants used in predicting fit coefficients
a0 cn cos d þ ð~m ~m0 Þ sin d 2 2 p ð~m ~m0 Þ þ ðcnÞ
ð4Þ
Here cn is the half-width half-maximum of the II dip, which is proportional to n. The value of c from Ref. [16] is about 0.05 cm1/amagat, and this should be approximately the same for all bands and lines. When the phase shift is 0, the II line shape reduces to a Lorentzian. The phase shift from Ref. [16] for the 1-0 band was 0.09 rad. They conjecture that the phase shift should be proportional to the quantum number of the upper vibrational quantum state, so I take the phase shift to be 0.27 rad. The integrated strength of the II is a0 cos d Z eII d~m ¼ a0 cos d ð5Þ The maximum possible eII is ACIA. Denote the fraction of CIA extinguished by II as f: eII;peak ¼ fACIA ¼ f an2 l a0 cos d ¼ pcn a0 ¼
f acpln cos d
ð6Þ
3
(For convenience, f is positive; it must be between 0 and 1.) The resulting line shape function is shown in Fig. 1. In contrast to the situation in the 1-0 band, the II dip in the 3-0 band is much narrower than the quadrupole resonance. This is because the quadrupole resonance is mainly Doppler-broadened, for which the width is proportional to the resonance center frequency, while the dip width, determined mainly by collision frequency, is the same for each band. The asymmetry in the II line shape is apparent, but not substantial. To find SS1 from a CRDS spectrum at low densities, the spectrum was fit by nonlinear regression to the sum of a linear baseline and the line shape function S S1 nlg0 ð~mÞ, where g and g 0 have the same functional form. The analytical integral of the line shape was calculated using the resulting fit
ð3Þ
5
extinction/10-6 per pass
Line shape functions for II in H2 have been investigated previously by Kelley and Bragg [16]. To a first approximation, the II dip forms a negative-going Lorentzian centered on the S(1) resonance at ~m0 . Including the phase shift d arising from elastic collisions introduces an asymmetry in the line shape:
Cavity length Line strength CIA coefficient II dip half-width half-maximum Effective phase shift
eII ¼
CIA + Rayleigh scattering
Rayleigh scattering 0 -0.3
l SS1 a c
135.4 cm 0.001317 cm1/km amagat 3.74 · 109 cm1/amagat2 0.050 cm1/amagat
Ref. Ref. Ref. Ref.
[19] [13] [27] [16]
d
0.27 rad
Ref. [16]
-0.2
-0.1
0.0
0.1
0.2
0.3
frequency shift/cm -1 Fig. 1. Calculated extinction around S(1) quadrupole resonance. The upper line is the total extinction, including the baseline (CIA and Rayleigh scattering), the quadrupole resonance, and the intercollisional interference dip, assuming f = 1. Model parameters are given in Table 1.
D.C. Robie / Chemical Physics Letters 428 (2006) 39–41 Table 2 Comparison of fit results with predictions based on theoretical calculations and known parameters Fit Linear coefficient (106 per pass cm1/amagat) Cubic coefficient (106 per pass cm1/amagat3)
Predicted
1.73 ± 0.03 0.095 ± 0.015
1.78 ± 0.04 0.082
integrated extinction/(10-6 per pass)cm-1
4
41
In order to observe the II dip at 1 amagat, where its area is over 5% of that for the quadrupole resonance S(1) alone, it is necessary to have a system bandwidth less than 0.01 cm1. Pulsed dye lasers such as the one used in Ref. [19] do not have such a narrow bandwidth, so it is not surprising that the II dip was not observed in those experiments. Frequency-stabilized CRDS [28,29] using tunable diode lasers should be capable of observing such dips. Acknowledgements I acknowledge the assistance of J.T. Hodges and R.D. van Zee of the National Institute of Standards and Technology, Gaithersburg, Maryland, and J.P. Looney of Brookhaven National Laboratory, Upton, New York. I acknowledge financial support from the National Institute of Standards and Technology, and the PSC-CUNY Fund of the City University of New York. Acknowledgement is made to the Donors of The Petroleum Research Fund of the American Chemical Society, for partial support of this research.
predicted without II
3
predicted with II
2
fit
1
References
0 0
1
2
3
density/amagat Fig. 2. Dependence of integrated extinction, less the weakly wavenumberdependent Rayleigh scattering and CIA, on density. Integrated extinction is given in units of (106 per pass)cm1. The middle line represents the predicted dependence using the theoretical SS1 and a value for f of 1; the uppermost line, using only a linear coefficient with the theoretical SS1.
parameters, and the baseline subtracted. The baseline included eR and ACIA. The area of the spectral fit was Z f acp 3 ln ed~m ¼ S S1 ln ð7Þ cos d In the linear term, only SS1 is unknown; and in the cubic term, only f is unknown, though it ought to be somewhat less than 1. The values of parameters used to predict the values of the fit results are summarized in Table 1. I have used a multilinear regression to fit the data for the S(1) line from Ref. [19] to an equation of this form. The results of the fit are given in Table 2, and shown in Fig. 2. The linear coefficient from the fit, and the predicted value, are in good agreement, less than the discrepancy previously observed between measurements of the S(1) line strength and the theoretical calculations. This suggests that at least part of the discrepancy is due to neglect of II. The predicted value of the cubic coefficient (for f = 1) agrees with the fit value to within the precision of the fit. A calculation of this type is not precise enough to determine the value of f, but the agreement is reasonable.
[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]
G. Herzberg, Astrophys. J. 87 (1938) 428. G. Herzberg, Nature 163 (1949) 170. G. Herzberg, Can. J. Res. A 28 (1950) 144. W.H. Smith, K.H. Baines, Icarus 85 (1990) 109. A. Borysow, J. Borysow, Y. Fu, Icarus 145 (2000) 601. K.H. Baines, M.E. Mickelson, L.E. Larson, D.W. Ferguson, Icarus 114 (1995) 328. A. Borysow, U.G. Jørgenson, Y. Fu, J. Quant. Spectros. Rad. Transfer 68 (2001) 235. H.M. James, A.S. Coolidge, Astrophys. J. 87 (1938) 438. G. Karl, J.D. Poll, J. Chem. Phys. 46 (1967) 2944. A.D. Birnbaum, J.D. Poll, J. Atmos. Sci. 26 (1969) 943. A. Dalgarno, A.C. Allison, J.C. Browne, J. Atmos. Sci. 26 (1969) 946. J.D. Poll, L. Wolniewicz, J. Chem. Phys. 68 (1978) 3053. C. Schwartz, R.J. Le Roy, J. Mol. Spectrosc. 121 (1987) 420. A.P. Mishra, T.K. Balasubramanian, Mol. Phys. 90 (1997) 895. L. Wolniewicz, I. Simbotin, A. Dalgarno, Astrophys. J. Suppl. Ser. 115 (1998) 293. J.D. Kelley, S.L. Bragg, Phys. Rev. A 29 (1984) 1168. A.R.W. McKellar, Icarus 22 (1974) 212. J.D. Kelley, S.L. Bragg, Phys. Rev. A 34 (1986) 3003. D.C. Robie, J.T. Hodges, J. Chem. Phys. 124 (2006) 024307. S.L. Bragg, J.W. Brault, W.H. Smith, Astrophys. J. 263 (1982) 999. L. Frommhold, Collision-induced Absorption in Gases, Cambridge University Press, 1993. H. Naus, W. Ubachs, Appl. Opt. 38 (1999) 3423. A. Borysow, Astron. Astrophys. 390 (2002) 779. C. Brodbeck, J.-P. Bouanich, N. -van-Thanh, Y. Fu, A. Borysow, J. Chem. Phys. 110 (1999) 4750. J. Van Kranendonk, Can. J. Phys. 46 (1968) 1173. J.D. Poll, J.L. Hunt, J.W. Mactaggart, Can. J. Phys. 53 (1975) 954. Y. Fu, C. Zheng, A. Borysow, J. Quant. Spectrosc. Rad. Transfer 67 (2000) 303. J.T. Hodges, H.P. Layer, W.W. Miller, G.E. Scace, Rev. Sci. Instr. 75 (2004) 849. J.B. Dudek, P.B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, K.K. Lehmann, Anal. Chem. 75 (2003) 4599.
Effects of intercollisional interference on measured line strengths in the 3-0 quadrupole band of H2 Daniel C. Robie Department of Natural Sciences, York College, City University of New York, Jamaica, NY 11451, USA Received 22 June 2006 Available online 20 July 2006
Abstract Recent observations of the 3-0 quadrupole band of H2 by cavity ring-down spectroscopy confirm discrepancies with theoretical calculations of the quadrupole transition moment. They also supply enough data to suggest that the discrepancy comes from narrow intercollisional interference dips in the collision-induced absorption. 2006 Elsevier B.V. All rights reserved.
The 3-0 (second overtone) band in the absorption spectrum of H2 was first predicted and observed by Herzberg over 50 years ago [1–3]. Arising from the electric quadrupole moment of the molecule, this weak band is important in the study of the atmospheres of the outer planets [4–6] and of cool stars [7]. Bands with a low strength are especially suited to studying these environments because they do not saturate even after pathlengths of hundreds of kilometers through megapascal pressures. Furthermore, the overtone bands of H2 above the first are in the visible (the second is around 815 nm, the third around 655 nm), readily accessible to ground-based telescopes. On the other hand, weak bands are inherently difficult to observe in the laboratory. Therefore, there have been many theoretical calculations of the quadrupole transition moments [8–15] and other spectroscopic parameters (pressure shifts [16,17], pressure broadening coefficients [18], etc. [16]) by a variety of methods. However, there has been a persistent discrepancy between these theoretical calculations and observed line strengths. Direct measurements of the line strengths in the 3-0 band have been 6–33% smaller than predicted [19,20]. Recently analyzed measurements of line strengths for seven lines in the 3-0 band carried out for the first time by cavity ring-down spectroscopy (CRDS) [19] agree with E-mail address: [email protected] 0009-2614/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.07.035
previous measurements, and confirm the discrepancy with the theoretical calculations. I propose a resolution of the discrepancy based on the phenomenon of intercollisional interference (II). Assemblies of molecules can interact with light not only through electric and magnetic moments characteristic of an isolated molecule, but also through moments induced by interacting molecules. Moments induced by a collision with another atom or molecule can result in collision-induced absorption (CIA) [21]. CIA has been observed with CRDS at pressures from tens of megapascals down to around 0.1 MPa [19,22]. Since CIA is the result of a binary collision, in a pure gas it is proportional to the square of the molecular density. A complete set of absorption coefficients for CIA in H2 at temperatures from 60 K up to 7000 K has been calculated [23]. CIA is greatest in spectral regions near allowed transitions. (In H2, vibrational transitions are electric-quadrupole allowed.) The short life of the collision complex determines the width of these overtone CIA bands, so they are broad — at room temperature, the 3-0 CIA band is 1000 cm1 wide [24]. The calculated CIA at the S(1) line of the 3-0 band is consistent with observations of non-resonant extinction around that line [19]. At 0.1 MPa in this region of the spectrum of H2, CIA is comparable in magnitude to Rayleigh scattering. In scans over only a few cm1 both of these non-resonant extinctions simply contribute to a flat baseline.
40
D.C. Robie / Chemical Physics Letters 428 (2006) 39–41
The transition dipole induced by one collision is, on average, oriented opposite to that of the subsequent collision. This correlation between successive induced transition dipoles diminishes the CIA [25], and is called intercollisional interference (II). It has been observed repeatedly in CIA spectra [16,20,24,26]. Because the relevant time scale is that between collisions, an II ‘dip’ is (approximately) a relatively narrow Lorentzian of width determined by the collision frequency — which, in turn, is proportional to the molecular density. The induced dipole moments that produce CIA depend on the rovibrational state of the molecule, and on the intermolecular potential, which itself depends on the molecular states [21,27]. II is restricted by symmetry to only some of the induced moments. Therefore, the II dip cannot exceed in depth the magnitude of the CIA at the resonance, and is likely to be smaller. There are no calculations of II using realistic potentials for H2 in the second overtone band [27]. It is important to note that, since CIA can easily exceed the peak height of a resonance, the II dip can be deeper than the resonance peak height. The resulting line shape goes below the apparent baseline. Extinction around the S(1) line will then have four contributions: etotal ¼ AS1 þ eR þ ACIA þ eII
ð1Þ
where AS1 ¼ S S1 lngð~mÞ
ð2Þ
is the absorption due to the S(1) resonance itself. The density n is in amagats. (One amagat is the density of the gas at 273.15 K and 1 atm pressure. The conversion factor to density in molecules cm3 is Loschmidt’s number L, 2.68 · 1019 cm3 for H2) SS1, calculated from a quadrupole transition matrix element, is the line strength in cm1/cm amagat; l is the pathlength in the absorber; the area-normalized line shape function is gð~mÞ. The contribution from Rayleigh scattering, constant over a small spectral range of a few cm1, is given by eR. Known values used here are given in Table 1. Finally, CIA is given by ACIA ¼ aln2
Table 1 Constants used in predicting fit coefficients
a0 cn cos d þ ð~m ~m0 Þ sin d 2 2 p ð~m ~m0 Þ þ ðcnÞ
ð4Þ
Here cn is the half-width half-maximum of the II dip, which is proportional to n. The value of c from Ref. [16] is about 0.05 cm1/amagat, and this should be approximately the same for all bands and lines. When the phase shift is 0, the II line shape reduces to a Lorentzian. The phase shift from Ref. [16] for the 1-0 band was 0.09 rad. They conjecture that the phase shift should be proportional to the quantum number of the upper vibrational quantum state, so I take the phase shift to be 0.27 rad. The integrated strength of the II is a0 cos d Z eII d~m ¼ a0 cos d ð5Þ The maximum possible eII is ACIA. Denote the fraction of CIA extinguished by II as f: eII;peak ¼ fACIA ¼ f an2 l a0 cos d ¼ pcn a0 ¼
f acpln cos d
ð6Þ
3
(For convenience, f is positive; it must be between 0 and 1.) The resulting line shape function is shown in Fig. 1. In contrast to the situation in the 1-0 band, the II dip in the 3-0 band is much narrower than the quadrupole resonance. This is because the quadrupole resonance is mainly Doppler-broadened, for which the width is proportional to the resonance center frequency, while the dip width, determined mainly by collision frequency, is the same for each band. The asymmetry in the II line shape is apparent, but not substantial. To find SS1 from a CRDS spectrum at low densities, the spectrum was fit by nonlinear regression to the sum of a linear baseline and the line shape function S S1 nlg0 ð~mÞ, where g and g 0 have the same functional form. The analytical integral of the line shape was calculated using the resulting fit
ð3Þ
5
extinction/10-6 per pass
Line shape functions for II in H2 have been investigated previously by Kelley and Bragg [16]. To a first approximation, the II dip forms a negative-going Lorentzian centered on the S(1) resonance at ~m0 . Including the phase shift d arising from elastic collisions introduces an asymmetry in the line shape:
Cavity length Line strength CIA coefficient II dip half-width half-maximum Effective phase shift
eII ¼
CIA + Rayleigh scattering
Rayleigh scattering 0 -0.3
l SS1 a c
135.4 cm 0.001317 cm1/km amagat 3.74 · 109 cm1/amagat2 0.050 cm1/amagat
Ref. Ref. Ref. Ref.
[19] [13] [27] [16]
d
0.27 rad
Ref. [16]
-0.2
-0.1
0.0
0.1
0.2
0.3
frequency shift/cm -1 Fig. 1. Calculated extinction around S(1) quadrupole resonance. The upper line is the total extinction, including the baseline (CIA and Rayleigh scattering), the quadrupole resonance, and the intercollisional interference dip, assuming f = 1. Model parameters are given in Table 1.
D.C. Robie / Chemical Physics Letters 428 (2006) 39–41 Table 2 Comparison of fit results with predictions based on theoretical calculations and known parameters Fit Linear coefficient (106 per pass cm1/amagat) Cubic coefficient (106 per pass cm1/amagat3)
Predicted
1.73 ± 0.03 0.095 ± 0.015
1.78 ± 0.04 0.082
integrated extinction/(10-6 per pass)cm-1
4
41
In order to observe the II dip at 1 amagat, where its area is over 5% of that for the quadrupole resonance S(1) alone, it is necessary to have a system bandwidth less than 0.01 cm1. Pulsed dye lasers such as the one used in Ref. [19] do not have such a narrow bandwidth, so it is not surprising that the II dip was not observed in those experiments. Frequency-stabilized CRDS [28,29] using tunable diode lasers should be capable of observing such dips. Acknowledgements I acknowledge the assistance of J.T. Hodges and R.D. van Zee of the National Institute of Standards and Technology, Gaithersburg, Maryland, and J.P. Looney of Brookhaven National Laboratory, Upton, New York. I acknowledge financial support from the National Institute of Standards and Technology, and the PSC-CUNY Fund of the City University of New York. Acknowledgement is made to the Donors of The Petroleum Research Fund of the American Chemical Society, for partial support of this research.
predicted without II
3
predicted with II
2
fit
1
References
0 0
1
2
3
density/amagat Fig. 2. Dependence of integrated extinction, less the weakly wavenumberdependent Rayleigh scattering and CIA, on density. Integrated extinction is given in units of (106 per pass)cm1. The middle line represents the predicted dependence using the theoretical SS1 and a value for f of 1; the uppermost line, using only a linear coefficient with the theoretical SS1.
parameters, and the baseline subtracted. The baseline included eR and ACIA. The area of the spectral fit was Z f acp 3 ln ed~m ¼ S S1 ln ð7Þ cos d In the linear term, only SS1 is unknown; and in the cubic term, only f is unknown, though it ought to be somewhat less than 1. The values of parameters used to predict the values of the fit results are summarized in Table 1. I have used a multilinear regression to fit the data for the S(1) line from Ref. [19] to an equation of this form. The results of the fit are given in Table 2, and shown in Fig. 2. The linear coefficient from the fit, and the predicted value, are in good agreement, less than the discrepancy previously observed between measurements of the S(1) line strength and the theoretical calculations. This suggests that at least part of the discrepancy is due to neglect of II. The predicted value of the cubic coefficient (for f = 1) agrees with the fit value to within the precision of the fit. A calculation of this type is not precise enough to determine the value of f, but the agreement is reasonable.
[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]
G. Herzberg, Astrophys. J. 87 (1938) 428. G. Herzberg, Nature 163 (1949) 170. G. Herzberg, Can. J. Res. A 28 (1950) 144. W.H. Smith, K.H. Baines, Icarus 85 (1990) 109. A. Borysow, J. Borysow, Y. Fu, Icarus 145 (2000) 601. K.H. Baines, M.E. Mickelson, L.E. Larson, D.W. Ferguson, Icarus 114 (1995) 328. A. Borysow, U.G. Jørgenson, Y. Fu, J. Quant. Spectros. Rad. Transfer 68 (2001) 235. H.M. James, A.S. Coolidge, Astrophys. J. 87 (1938) 438. G. Karl, J.D. Poll, J. Chem. Phys. 46 (1967) 2944. A.D. Birnbaum, J.D. Poll, J. Atmos. Sci. 26 (1969) 943. A. Dalgarno, A.C. Allison, J.C. Browne, J. Atmos. Sci. 26 (1969) 946. J.D. Poll, L. Wolniewicz, J. Chem. Phys. 68 (1978) 3053. C. Schwartz, R.J. Le Roy, J. Mol. Spectrosc. 121 (1987) 420. A.P. Mishra, T.K. Balasubramanian, Mol. Phys. 90 (1997) 895. L. Wolniewicz, I. Simbotin, A. Dalgarno, Astrophys. J. Suppl. Ser. 115 (1998) 293. J.D. Kelley, S.L. Bragg, Phys. Rev. A 29 (1984) 1168. A.R.W. McKellar, Icarus 22 (1974) 212. J.D. Kelley, S.L. Bragg, Phys. Rev. A 34 (1986) 3003. D.C. Robie, J.T. Hodges, J. Chem. Phys. 124 (2006) 024307. S.L. Bragg, J.W. Brault, W.H. Smith, Astrophys. J. 263 (1982) 999. L. Frommhold, Collision-induced Absorption in Gases, Cambridge University Press, 1993. H. Naus, W. Ubachs, Appl. Opt. 38 (1999) 3423. A. Borysow, Astron. Astrophys. 390 (2002) 779. C. Brodbeck, J.-P. Bouanich, N. -van-Thanh, Y. Fu, A. Borysow, J. Chem. Phys. 110 (1999) 4750. J. Van Kranendonk, Can. J. Phys. 46 (1968) 1173. J.D. Poll, J.L. Hunt, J.W. Mactaggart, Can. J. Phys. 53 (1975) 954. Y. Fu, C. Zheng, A. Borysow, J. Quant. Spectrosc. Rad. Transfer 67 (2000) 303. J.T. Hodges, H.P. Layer, W.W. Miller, G.E. Scace, Rev. Sci. Instr. 75 (2004) 849. J.B. Dudek, P.B. Tarsa, A. Velasquez, M. Wladyslawski, P. Rabinowitz, K.K. Lehmann, Anal. Chem. 75 (2003) 4599.