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Pressure broadening of deuterium hydride lines in the 5-0 vibrational band between 77 and 295 K
ICARUS91, 234--237(1991)
Pressure Broadening of Deuterium Hydride Lines in the 5 - 0 Vibrational Band between 77 and 295 K 1 WM. HAYDEN SMITH, CHARLES E. KEFFER, AND CHARLES P. CONNER Department of Earth and Planetary Sciences, Washington University, St. Louis, Missouri 63130
Received November 13, 1990; revised February 5, 1991
Self-broadening measurements have been made for the R(0) and R(1) lines of the 5-0 the vibration-rotation band o f d e u t e r i u m hydride. Pressure broadening coefficientsand temperature-dependence indices have been determined from measurements over the temperature range of 77 to 295 K. A temperature-dependent index, n, of 0.31 was derived for the HD lines studied. A provisional temperature-dependence index for H2 vibrational-rotational line broadening as small or smaller that the HD index is suggested. A small temperature-dependence index significantly reduces the derived H 2 abundances in the outer planets and correspondingly increases the D/H ratios. © 1991 Academic Press, Inc.
INTRODUCTION Line strength measurements and pressure broadening and pressure shift data for HD at room temperature have been reported by Trauger and Mickelson (1983). No lowtemperature data for vibration-rotation lines of HD have been reported although there is extensive literature for observations of pure rotational lines of H2 and HD in the Raman and for HD in far-infrared (Ulivi et al. 1989 and Van de Hout et al. 1980). Line strength and pressure shift measurements for H2 vibration-rotation quadrupole transitions were provided by Brault and Smith (1980), and Bragg et al. (1982). Smith et al. (1989c) have detailed additional results and reevaluated the 4-0 vibrational band data to use in modeling the atmosphere of Jupiter. Smith et al. (1989a,b) have derived a D/H ratio for Jupiter and upper limits for Uranus and Neptune, utilizing the above laboratory data and their high spectral resolution observations of HD and H2 lines. The degree of saturation of H 2 quadrupole absorption features depends sensitively upon the pressure broadening and pressure shift coefficients (Cochran and Smith 1983, McKellar 1974), resulting in as much as a twofold variation in the derived column abundance of H2 for Uranus and Neptune, with smaller, but detectable, effects for This researchwas supportedby the NSF underGrant AST 83-03108.
Saturn and Jupiter. The temperature dependence of the pressure-broadening and shift coefficients for the vibration-rotation spectrum of H2 also has an important effect on the interpretation of the abundances of H2 in the scattering atmospheres of the outer planets. H2 quadrupole line strengths, pressure shifts, and pressure-broadening data have been included in analyses of high spectral resolution observations of the atmospheres of the outer planets in studies of the structure of the dominantly H2-He atmospheres of the outer planets (e.g., Baines and Bergstralh (1986) and Baines and Smith (1990) give extensive baseline models for Uranus and Neptune); however, no H2 vibrational-rotation spectral measurements in the laboratory at temperature relevant to the atmospheres of the outer planets, i.e., 150 to 50 K, are available. Measuring pressure broadening coefficients for H2 vibrational overtones over an appropriate temperature range is a problem of very considerable experimental difficulty due to the extremely small absorption coefficients for the H 2quadrupole transitions. Since the HD 5-0 transitions are about 100 times stronger than the same vibrational levels in H2 and can be studied with our dye laser photoacoustic method, the temperature effect on collisions for HD molecules may be obtained. Then, the HD and H 2 pressurebroadening temperature dependence may be estimated and supported by the correlation among the various HD and H~ lab data.
EXPERIMENTATION AND ANALYSIS We report here pressure-broadening measurements of the 5-0 R(0) and R(1) deuterium hydride lines, performed using the dye laser photoacoustic spectrometer described in our earlier work (see Keffer et al. (1985, 1986) and Smith et al. (1990) for further experimental details). Briefly, a liquid nitrogen cooled photoacoustic detector was placed inside the cavity of a passively stabilized single frequency ring dye laser pumped by an amplitude-modulated argon ion laser. Interference fringes from a 15-GHz
234 0019-1035/91$3.00 Copyright© 1991by AcademicPress, Inc. All rightsof reproductionin any formreserved.
235
HD L O W - T E M P E R A T U R E S E L F - B R O A D E N I N G
ii
~4
-w
2
ii
n-
1
~
+ .x.
O -1
I 0
I
0.36
I
I
I
I
I
I
0.67
1.35
2.05
2.75
4.12
4.5
density [Amagsts] 004s 3
60;s 2
604's i
6045.0
6044
.9
6044.8
WAVELENGTH C~)
FIG. 1. Example HD vibrational-rotational line profile for the 5-0 R(1) line, fitted with the Galatry profile, as described in the text.
confocal etalon serve as relative frequency calibration and absolute wavelength measurements are made with a Michelson interferometer wavemeter. The HD used in all experiments was 98 at%, as certified by MSD Isotopes, Inc. Pressure measurements in the cell were accurate to --1.5%, using a capacitance manometer and temperature measurements were made using a silicon diode temperature sensor with an accuracy of -+ I K. The experimental line profiles were fit by Herbert's parameterization (Herbert 1974) of the Galatry line shape function using a nonlinear least squares curve fitting program. A spectral profile for the R(1) line is shown in Fig. 1 with the fitted profile superimposed. Pressure broadening coefficients were determined from linear regression analysis of Lorentzian half-width vs broadening gas pressure data. A power law dependence of pressure broadening coefficients on temperature is typically assumed in modeling planetary atmospheres. Accordingly, a temperature-dependence index has been derived from these pressure-broadening coefficients that assumes a power law dependence on the temperature, T, of the form: =
r(r0)(T0/T)",
where F is the pressure-broadening coefficient (cm-l/ atm), To is room temperature, and n is the temperaturedependence index. These data are summarized in Table I. Figure 2 plots the measured dependence of the line width of the 5-0 R(1) line of HD on the gas density. Collision narrowing is seen in the data and shows, for the R(0) line at I00 K, that the FWHM of the line is about 10-15% smaller at its minimum than the Doppler line width. At room temperature, the line width is narrowed
FIG. 2. HD line width vs density for the HD 5-0 R(0) line at a temperatures of 100 K. The points represent experimentally measured F W H M values using the parameters determined from least squares fits of the data to the Galatry function. The solid line is a least squares fit to the data and has no theoretical basis. All widths have been normalized to the Doppler F W H M .
by - 3 % below the Doppler width, in close agreement with the room temperature observations of Trauger and Mickelson (1983). The greater collision narrowing at low temperatures can be understood in terms of a smaller pressure broadening effect due to an expected line width reduction in the collision-induced reorientation. The density at which the minimum width occurs is constant throughout the observed temperature range. RESULTS AND DISCUSSION
The experimentally measured spectral line profiles for the 5-0 R(0) and R(1) lines have been fit to the Galatry line shape. The temperature-dependent self-broadening coefficients in Table I are presently unique since no lowtemperature pressure-broadening measurements have
TABLE I HD Pressure Broadening Coefficients and Temperature-Dependence Indices
Line Rs(0)
Rs(1)
Temperature (K)
F ( c m - 1/atm) Present data
F ( c m - l/atm) Previous b
294 100 84
0.0232 -+ 0.0032 0.0295 -+ 0.0013 0.0361 - 0.0009
0.025 -- 0.001
294 100 82
0.0262 -+ 0.0018 0.0315 --- 0.009 0.0437 + 0.0012
0.025 +- 0.001
na
0.31
0.32
a Where n is found from: F(T) = F(To)(To/T)", where Tis the temperature, F is the pressure-broadening coefficient (cm-Z/atm), To is room temperature, and n is the temperature-dependence index. b From Trauger et al. 1983.
236
SMITH, KEFFER, AND CONNER
been reported previously for lines in the 5-0 band. We also list in Table I the temperature-dependence indices (n) we have determined for the Rs(0) and Rs(1) lines. It is apparent from Table I that there is an observed rotational state dependence for the line widths. The pressure broadening coefficient f o r J = 1 is consistently larger than for J = 0. Typically, an initial rise in F for low J values, followed by a decreased width for higher J values is seen. Rabitz (1974) has given a plausible explanation by observing that this rising and falling behavior is characteristic of self-broadening where resonant collisions may occur. The pressure-broadening coefficient reaches a maximum near the Boltzmann distribution peak of the rotational states. The Anderson (1949) theory of pressure broadening predicts a temperature-dependence index, n, 0.5 for dispersion forces; however, the theory does not account for collision narrowing. The experimental temperaturedependence index is 0.31 and 0.32 for the HD 5-0 R(0) and R(1) lines, showing no dependence on rotational quantum number to within the precision of our determination. We estimate an accuracy of -10%; based on the agreement of the two independent measurements each of the two observed J values. This value of the temperature-dependence index is lower than that predicted for any pair-wise multipole interaction. We suggest that a weak temperature dependence is reasonable since KT becomes less than the rotational energy spacing of the lowest lying HD levels for temperatures below 130 K. This implies that state changing collisions become less likely at low temperatures, decreasing the contribution to the line broadening from reorientation effects. Similar behavior has been observed for H2 and HD self-broadening in pure rotational Spectra (e.g., Ulivi et al. 1989, Van den Hout et al. 1980). Although H2 is the major constituent of the atmospheres of all the major planets, the lack of a measured temperature-dependence index of its pressure broadening coefficient has required its entry into planetary atmospheric model computations as afixed parameter, usually taken equal to the predicted quadrupole value. In our most recent publications describing the structure of the atmOspheres of Jupiter and Neptune, we have instead used a provisional value ofn equal to that found for HD, as given below. A small " n " reduces the column density of H 2 derived from the observations and generally improves the consistency of model parameters, e.g., the level of unit optical cloud depth, with corresponding parameters found from other observational constraints. Note that the D/H ratio given by :Smith et al. (1989a) for Jupiter is not affected greatly for any plausible temperature-dependence coefficient, but is slightly increased by the provisional value for n and is already as small as the solar D/H. For detailed discussions, the referenced papers should be consulted.
The temperature dependence of line broadening that we have observed for HD may be larger than for H2 since the H2 molecule has a more coarsely spaced vibrational and rotational level structure than HD and exhibits a larger collisional narrowing. If inefficient state-changing collisions are a prime factor, then H2 may well have a temperature-dependence index that is even smaller than for HD since H2 lacks the angular dependent interaction terms in the intermolecular potential present for HD with its small, but nonzero, dipole moment. Our value of n = 0.3 for HD is consistent with the pure rotation data of Ulivi et al. and van den Hout et al. Until a direct measurement for the H2 vibrational transitions becomes available, a provisional value of n = 0.3 may be used for H2 rather than n = 0.75, as suggested for collisions controlled by the quadrupole moment for H2 (Trafton 1987). REFERENCES ANDERSON, P. W. 1949. Pressure broadening in the microwave and infra-red regions. Phys. Reo. 76, 647-661. BAINES, K. H., AND J. T. BERGSTRALH 1986. The structure of the uranian atmosphere: Constraints from the geometric albedo spectrum and H 2 and CH 4 line profiles. Icarus 65, 406-411. BAINES, K. H., AND W. H. SMITH 1990. The structure of the atmosphere of Neptune. Icarus 85, 65-108. BRAGG, S. L., J. B. BRAULT, AND W. H. SMITH 1982. Line positions and strengths in the H 2 quadrupole spectrum. Astrophys. 263, 9991004. BRAULT, J . B., AND W. H. SMITH 1980. Determination of the H2 4-0 S(1) quadrupole line strength and pressure shift. Astrophys. J. 235, L177-L178. COCHRAN, W. n . , AND W. H. SMITH 1983. Desaturation of H 2 quadrupole lines in the atmospheres of the outer planets. Astrophys. J. 271, 859-864.
HERBERT, F. 1974. Spectrum profiles, a generalized Voigt function including collision narrowing. J. Quant. Spectrosc. Radiat. Transfer 14, 943-951. KEFFER, C., C. CONNER, AND W. H. SMITH 1985. Gas phase cryogenic photoacoustic detector. Reo. Sci. Inst. 56, 2161. KEFFER, C., C. CONNER, AND W. H. SMITH 1986. Pressure broadening of methane in the 6190/~ and 6820/~ bands at low temperatures. J. Quant. Spectrosc Radiat Transfer 35, 495-501. MCKELLAR, A. R. W. 1974. The significance of pressure shifts for the interpretation of H 2 quadrupole lines in planetary spectra. Can. J. Phys. 52, 1144-1148. RABITZ, H. 1974. Advances in Chemical Physics. (H. Eyring, Ed.), Vol. 25, Annual Reviews Inc., Palo Alto. SMITH, W. H., K. H. BMNES AND W. V. SCHEMPP 1989a. The D/H ratio for Jupiter. Astrophys. J. 336, 962. SMITH, W. H., K. H. BAINES, W. V. SCHEMPP, AND J. SIMON 1989b. D/H for Uranus and Neptune. Astrophys. J. 336, 967. SMITH, W. H., J. SIMON, W. V. SCHEMPP, C. CONNER, AND W. MACY 1989c. Measurements of the H2 4-0 S(0, 1, and 2) features in Jupiter. Icarus 81, 429-440. SMITH, W. H., C. CONNER, AND K. H. BAINES 1990. Absorption coefficients for the 6190 A CHg band between 290 and 100 K with application to Uranus' atmosphere. Icarus 85, 58-64.
HD LOW-TEMPERATURE SELF-BROADENING TRAFTON, L. 1987. Uranus' 3-0 H 2 line profiles. Icarus 70, 13-30. TRAUGER, J. T., AND M. E. MICKELSON 1983. Laboratory absorption strengths and line shape parameters for the 4-0, 5-0, and 6-0 vibrational bands of HD, Icarus 56, 176. ULlvI, L., Lu, Z., AND G. C. TABISZ 1989. Temperature dependence
237
of collisional interference in the pure rotational far-ir spectrum of HD, Phys. Rev. A 40, 642-651. VAN DEN HOUT, K. D., P. W. HERMANS, MAZUR, E., ANO H. F. P. KNAAP 1980. The broadening and shift of rotational raman lines for H z isotopes at low temperatures. Physica 104A, 509-547.
Pressure Broadening of Deuterium Hydride Lines in the 5 - 0 Vibrational Band between 77 and 295 K 1 WM. HAYDEN SMITH, CHARLES E. KEFFER, AND CHARLES P. CONNER Department of Earth and Planetary Sciences, Washington University, St. Louis, Missouri 63130
Received November 13, 1990; revised February 5, 1991
Self-broadening measurements have been made for the R(0) and R(1) lines of the 5-0 the vibration-rotation band o f d e u t e r i u m hydride. Pressure broadening coefficientsand temperature-dependence indices have been determined from measurements over the temperature range of 77 to 295 K. A temperature-dependent index, n, of 0.31 was derived for the HD lines studied. A provisional temperature-dependence index for H2 vibrational-rotational line broadening as small or smaller that the HD index is suggested. A small temperature-dependence index significantly reduces the derived H 2 abundances in the outer planets and correspondingly increases the D/H ratios. © 1991 Academic Press, Inc.
INTRODUCTION Line strength measurements and pressure broadening and pressure shift data for HD at room temperature have been reported by Trauger and Mickelson (1983). No lowtemperature data for vibration-rotation lines of HD have been reported although there is extensive literature for observations of pure rotational lines of H2 and HD in the Raman and for HD in far-infrared (Ulivi et al. 1989 and Van de Hout et al. 1980). Line strength and pressure shift measurements for H2 vibration-rotation quadrupole transitions were provided by Brault and Smith (1980), and Bragg et al. (1982). Smith et al. (1989c) have detailed additional results and reevaluated the 4-0 vibrational band data to use in modeling the atmosphere of Jupiter. Smith et al. (1989a,b) have derived a D/H ratio for Jupiter and upper limits for Uranus and Neptune, utilizing the above laboratory data and their high spectral resolution observations of HD and H2 lines. The degree of saturation of H 2 quadrupole absorption features depends sensitively upon the pressure broadening and pressure shift coefficients (Cochran and Smith 1983, McKellar 1974), resulting in as much as a twofold variation in the derived column abundance of H2 for Uranus and Neptune, with smaller, but detectable, effects for This researchwas supportedby the NSF underGrant AST 83-03108.
Saturn and Jupiter. The temperature dependence of the pressure-broadening and shift coefficients for the vibration-rotation spectrum of H2 also has an important effect on the interpretation of the abundances of H2 in the scattering atmospheres of the outer planets. H2 quadrupole line strengths, pressure shifts, and pressure-broadening data have been included in analyses of high spectral resolution observations of the atmospheres of the outer planets in studies of the structure of the dominantly H2-He atmospheres of the outer planets (e.g., Baines and Bergstralh (1986) and Baines and Smith (1990) give extensive baseline models for Uranus and Neptune); however, no H2 vibrational-rotation spectral measurements in the laboratory at temperature relevant to the atmospheres of the outer planets, i.e., 150 to 50 K, are available. Measuring pressure broadening coefficients for H2 vibrational overtones over an appropriate temperature range is a problem of very considerable experimental difficulty due to the extremely small absorption coefficients for the H 2quadrupole transitions. Since the HD 5-0 transitions are about 100 times stronger than the same vibrational levels in H2 and can be studied with our dye laser photoacoustic method, the temperature effect on collisions for HD molecules may be obtained. Then, the HD and H 2 pressurebroadening temperature dependence may be estimated and supported by the correlation among the various HD and H~ lab data.
EXPERIMENTATION AND ANALYSIS We report here pressure-broadening measurements of the 5-0 R(0) and R(1) deuterium hydride lines, performed using the dye laser photoacoustic spectrometer described in our earlier work (see Keffer et al. (1985, 1986) and Smith et al. (1990) for further experimental details). Briefly, a liquid nitrogen cooled photoacoustic detector was placed inside the cavity of a passively stabilized single frequency ring dye laser pumped by an amplitude-modulated argon ion laser. Interference fringes from a 15-GHz
234 0019-1035/91$3.00 Copyright© 1991by AcademicPress, Inc. All rightsof reproductionin any formreserved.
235
HD L O W - T E M P E R A T U R E S E L F - B R O A D E N I N G
ii
~4
-w
2
ii
n-
1
~
+ .x.
O -1
I 0
I
0.36
I
I
I
I
I
I
0.67
1.35
2.05
2.75
4.12
4.5
density [Amagsts] 004s 3
60;s 2
604's i
6045.0
6044
.9
6044.8
WAVELENGTH C~)
FIG. 1. Example HD vibrational-rotational line profile for the 5-0 R(1) line, fitted with the Galatry profile, as described in the text.
confocal etalon serve as relative frequency calibration and absolute wavelength measurements are made with a Michelson interferometer wavemeter. The HD used in all experiments was 98 at%, as certified by MSD Isotopes, Inc. Pressure measurements in the cell were accurate to --1.5%, using a capacitance manometer and temperature measurements were made using a silicon diode temperature sensor with an accuracy of -+ I K. The experimental line profiles were fit by Herbert's parameterization (Herbert 1974) of the Galatry line shape function using a nonlinear least squares curve fitting program. A spectral profile for the R(1) line is shown in Fig. 1 with the fitted profile superimposed. Pressure broadening coefficients were determined from linear regression analysis of Lorentzian half-width vs broadening gas pressure data. A power law dependence of pressure broadening coefficients on temperature is typically assumed in modeling planetary atmospheres. Accordingly, a temperature-dependence index has been derived from these pressure-broadening coefficients that assumes a power law dependence on the temperature, T, of the form: =
r(r0)(T0/T)",
where F is the pressure-broadening coefficient (cm-l/ atm), To is room temperature, and n is the temperaturedependence index. These data are summarized in Table I. Figure 2 plots the measured dependence of the line width of the 5-0 R(1) line of HD on the gas density. Collision narrowing is seen in the data and shows, for the R(0) line at I00 K, that the FWHM of the line is about 10-15% smaller at its minimum than the Doppler line width. At room temperature, the line width is narrowed
FIG. 2. HD line width vs density for the HD 5-0 R(0) line at a temperatures of 100 K. The points represent experimentally measured F W H M values using the parameters determined from least squares fits of the data to the Galatry function. The solid line is a least squares fit to the data and has no theoretical basis. All widths have been normalized to the Doppler F W H M .
by - 3 % below the Doppler width, in close agreement with the room temperature observations of Trauger and Mickelson (1983). The greater collision narrowing at low temperatures can be understood in terms of a smaller pressure broadening effect due to an expected line width reduction in the collision-induced reorientation. The density at which the minimum width occurs is constant throughout the observed temperature range. RESULTS AND DISCUSSION
The experimentally measured spectral line profiles for the 5-0 R(0) and R(1) lines have been fit to the Galatry line shape. The temperature-dependent self-broadening coefficients in Table I are presently unique since no lowtemperature pressure-broadening measurements have
TABLE I HD Pressure Broadening Coefficients and Temperature-Dependence Indices
Line Rs(0)
Rs(1)
Temperature (K)
F ( c m - 1/atm) Present data
F ( c m - l/atm) Previous b
294 100 84
0.0232 -+ 0.0032 0.0295 -+ 0.0013 0.0361 - 0.0009
0.025 -- 0.001
294 100 82
0.0262 -+ 0.0018 0.0315 --- 0.009 0.0437 + 0.0012
0.025 +- 0.001
na
0.31
0.32
a Where n is found from: F(T) = F(To)(To/T)", where Tis the temperature, F is the pressure-broadening coefficient (cm-Z/atm), To is room temperature, and n is the temperature-dependence index. b From Trauger et al. 1983.
236
SMITH, KEFFER, AND CONNER
been reported previously for lines in the 5-0 band. We also list in Table I the temperature-dependence indices (n) we have determined for the Rs(0) and Rs(1) lines. It is apparent from Table I that there is an observed rotational state dependence for the line widths. The pressure broadening coefficient f o r J = 1 is consistently larger than for J = 0. Typically, an initial rise in F for low J values, followed by a decreased width for higher J values is seen. Rabitz (1974) has given a plausible explanation by observing that this rising and falling behavior is characteristic of self-broadening where resonant collisions may occur. The pressure-broadening coefficient reaches a maximum near the Boltzmann distribution peak of the rotational states. The Anderson (1949) theory of pressure broadening predicts a temperature-dependence index, n, 0.5 for dispersion forces; however, the theory does not account for collision narrowing. The experimental temperaturedependence index is 0.31 and 0.32 for the HD 5-0 R(0) and R(1) lines, showing no dependence on rotational quantum number to within the precision of our determination. We estimate an accuracy of -10%; based on the agreement of the two independent measurements each of the two observed J values. This value of the temperature-dependence index is lower than that predicted for any pair-wise multipole interaction. We suggest that a weak temperature dependence is reasonable since KT becomes less than the rotational energy spacing of the lowest lying HD levels for temperatures below 130 K. This implies that state changing collisions become less likely at low temperatures, decreasing the contribution to the line broadening from reorientation effects. Similar behavior has been observed for H2 and HD self-broadening in pure rotational Spectra (e.g., Ulivi et al. 1989, Van den Hout et al. 1980). Although H2 is the major constituent of the atmospheres of all the major planets, the lack of a measured temperature-dependence index of its pressure broadening coefficient has required its entry into planetary atmospheric model computations as afixed parameter, usually taken equal to the predicted quadrupole value. In our most recent publications describing the structure of the atmOspheres of Jupiter and Neptune, we have instead used a provisional value ofn equal to that found for HD, as given below. A small " n " reduces the column density of H 2 derived from the observations and generally improves the consistency of model parameters, e.g., the level of unit optical cloud depth, with corresponding parameters found from other observational constraints. Note that the D/H ratio given by :Smith et al. (1989a) for Jupiter is not affected greatly for any plausible temperature-dependence coefficient, but is slightly increased by the provisional value for n and is already as small as the solar D/H. For detailed discussions, the referenced papers should be consulted.
The temperature dependence of line broadening that we have observed for HD may be larger than for H2 since the H2 molecule has a more coarsely spaced vibrational and rotational level structure than HD and exhibits a larger collisional narrowing. If inefficient state-changing collisions are a prime factor, then H2 may well have a temperature-dependence index that is even smaller than for HD since H2 lacks the angular dependent interaction terms in the intermolecular potential present for HD with its small, but nonzero, dipole moment. Our value of n = 0.3 for HD is consistent with the pure rotation data of Ulivi et al. and van den Hout et al. Until a direct measurement for the H2 vibrational transitions becomes available, a provisional value of n = 0.3 may be used for H2 rather than n = 0.75, as suggested for collisions controlled by the quadrupole moment for H2 (Trafton 1987). REFERENCES ANDERSON, P. W. 1949. Pressure broadening in the microwave and infra-red regions. Phys. Reo. 76, 647-661. BAINES, K. H., AND J. T. BERGSTRALH 1986. The structure of the uranian atmosphere: Constraints from the geometric albedo spectrum and H 2 and CH 4 line profiles. Icarus 65, 406-411. BAINES, K. H., AND W. H. SMITH 1990. The structure of the atmosphere of Neptune. Icarus 85, 65-108. BRAGG, S. L., J. B. BRAULT, AND W. H. SMITH 1982. Line positions and strengths in the H 2 quadrupole spectrum. Astrophys. 263, 9991004. BRAULT, J . B., AND W. H. SMITH 1980. Determination of the H2 4-0 S(1) quadrupole line strength and pressure shift. Astrophys. J. 235, L177-L178. COCHRAN, W. n . , AND W. H. SMITH 1983. Desaturation of H 2 quadrupole lines in the atmospheres of the outer planets. Astrophys. J. 271, 859-864.
HERBERT, F. 1974. Spectrum profiles, a generalized Voigt function including collision narrowing. J. Quant. Spectrosc. Radiat. Transfer 14, 943-951. KEFFER, C., C. CONNER, AND W. H. SMITH 1985. Gas phase cryogenic photoacoustic detector. Reo. Sci. Inst. 56, 2161. KEFFER, C., C. CONNER, AND W. H. SMITH 1986. Pressure broadening of methane in the 6190/~ and 6820/~ bands at low temperatures. J. Quant. Spectrosc Radiat Transfer 35, 495-501. MCKELLAR, A. R. W. 1974. The significance of pressure shifts for the interpretation of H 2 quadrupole lines in planetary spectra. Can. J. Phys. 52, 1144-1148. RABITZ, H. 1974. Advances in Chemical Physics. (H. Eyring, Ed.), Vol. 25, Annual Reviews Inc., Palo Alto. SMITH, W. H., K. H. BMNES AND W. V. SCHEMPP 1989a. The D/H ratio for Jupiter. Astrophys. J. 336, 962. SMITH, W. H., K. H. BAINES, W. V. SCHEMPP, AND J. SIMON 1989b. D/H for Uranus and Neptune. Astrophys. J. 336, 967. SMITH, W. H., J. SIMON, W. V. SCHEMPP, C. CONNER, AND W. MACY 1989c. Measurements of the H2 4-0 S(0, 1, and 2) features in Jupiter. Icarus 81, 429-440. SMITH, W. H., C. CONNER, AND K. H. BAINES 1990. Absorption coefficients for the 6190 A CHg band between 290 and 100 K with application to Uranus' atmosphere. Icarus 85, 58-64.
HD LOW-TEMPERATURE SELF-BROADENING TRAFTON, L. 1987. Uranus' 3-0 H 2 line profiles. Icarus 70, 13-30. TRAUGER, J. T., AND M. E. MICKELSON 1983. Laboratory absorption strengths and line shape parameters for the 4-0, 5-0, and 6-0 vibrational bands of HD, Icarus 56, 176. ULlvI, L., Lu, Z., AND G. C. TABISZ 1989. Temperature dependence
237
of collisional interference in the pure rotational far-ir spectrum of HD, Phys. Rev. A 40, 642-651. VAN DEN HOUT, K. D., P. W. HERMANS, MAZUR, E., ANO H. F. P. KNAAP 1980. The broadening and shift of rotational raman lines for H z isotopes at low temperatures. Physica 104A, 509-547.