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Pressure broadening of the J = 1 ← 0 transition of carbon monoxide
JOURNALOFhIOLECULARSPECTROSCOPY
Pressure Broadening
58,474-478
(1975)
of the I = 1 +-0 Transition
R. B. NERF, JR., Department of Physics,
Columbia
AND
M.
A.
of Carbon
Monoxide
SONNENBERG
University, New York, New York 10027, and New York, New York, 10025
Goddard Institute for Space Studies, 2880 Broadway,
The pressure broadening of the carbon monoxide line near 115 GHz was measured at liquid nitrogen, dry ice, and room temperature, with typical experimental uncertainties of about 10%. Broadening gases were carbon monoxide, hydrogen, deuterium, helium, neon, and argon. No significant lineshifts were observed. INTRODUCTION
Pressure broadening measurements can be used in conjunction with other experimental data to help elicit the form of the intermolecular potential (1). Such studies are of importance in the investigation of rotational excitation of molecules by collisions, a topic of particular interest for the understanding of the formation of microwave spectral lines in the interstellar medium. Carbon monoxide (CO) is one of the most important of the known interstellar molecules because of its widespread occurrence, strong millimeter spectrum, and the crucial role it plays in the energy balance of interstellar clouds (2). Happily, it has sufficient vapor pressure for temperatures in the upper range of the interstellar regime (about 10-80 K) to make microwave pressure broadening measurements possible. We have measured the pressure broadening of the J = 1 + 0 transition at three convenient temperatures: liquid nitrogen (77 K), dry ice (195 K), and room (294 K). The choice of broadening gases was determined by astrophysical interest (Hz, He, DJ and simplicity (He, Ne, A). (Deuterium, although not abundant in the interstellar medium, was used because it has the same molecular potential as Hz, but a different thermal distribution of velocities.) EXPERIMENTAL
APPARATUS
Two configurations of the spectrometer were used for this study; they differ principally in the choice of instrumentation for signal processing and for recording the spectra. Except for an absorption cell designed for cryogenic temperatures, the first version was essentially identical to the spectrometer used for previously reported measurements on formaldehyde (3,4). Although this instrument proved quite successful, it was not well suited to optically thin lines, and the reduction of the data from x-y plots was both tedious and time consuming. The second version resulted from modifications which attempted to alleviate these problems; the lock-in amplifier, chopper wheel, and x-y recorder were replaced 474 Copyright @ 1975 by Academic Press. Inc. AU rights of reproduction in any form reserved.
PRESSURE BROADENING
OF CO
475
with a 512-channel signal averager and a digital tape recorder. Instead of slowly sweeping through the line over a period of some tens of seconds, the line was scanned 20 times a second, and several hundred scans were averaged for each measurements. Scanning the klystron faster than its thermal time constant greatly reduced baseline shifts from thermal tuning, a major source of error for weak lines. It was hoped that recording the spectra on computer-compatible magnetic tape would increase both the ease and accuracy of the data analysis. Since the designs of the spectrometers are straightforward, and one has been described in some detail elsewhere, we will concentrate primarily on those facets of the instruments which differ from the original. In the second configuration, the frequency of the microwave signal was swept in synchronism with the signal averager; a sawtooth voltage derived from the channel number was used to control a frequency synthesizer, to which the klystron was phaselocked. Typical frequency excursions at 11.5 GHz were 3040 MHz, determined in large part by the maximum available correction voltage in the phase-lock circuits. Although the spectrum recorded by the newer version is in a more convenient form, it lacks information contained in the earlier x-y plots. Since the microwave power is not amplitude modulated, the coupling capacitor between detector and signal averager filters out not only the dc bias on the bolometer, but any steady component in detected power. The optical depth of the line, for instance, is not immediately available; it must be measured or inferred in some other way. Both versions of the spectrometer used stainless steel absorption cells capable of operation at cryogenic temperatures; path lengths of 12.5 and 200 cm were used, depending on the line strength. The cells were constructed from two concentric cylinders of equal length; the smaller (-10 cm ID) formed the absorption cell, while the space between it and the larger (-12 cm ID) served as a coolant jacket. The extremities of the cylinders were welded to two annular flanges, which formed the ends of the coolant jacket and held the teflon lenses used as windows. Thermal insulation was provided by enclosing the cells in boxes constructed of 10 cm thick polystyrene or polyurethane foam. As has been noted (3,4), free space cells can severely distort lineshapes through standing waves originating at the horns and lens surfaces; these problems are particularly severe with metal cells since off-axis reflections are not rapidly attenuated. Pressure measurements were made with capacitive manometers; these are particularly well suited to pressure broadening studies because accuracy is unaffected by gas composition. Preliminary linewidth measurements were made using a O-l Torr sensor (CGS-Datametrics type 523-15) that had been independently calibrated to an accuracy of 1% against a McLeod gauge (3). Most of the later measurements were made with a new O-100 Torr sensor (Type 523-H) so that the maximum linewidth would not be constrained by the range of the pressure gauge. This gauge was not independently calibrated since accuracy checks on the original sensor were in reasonably good agreement with the manufacturer’s calibration. All gases used in this experiment were obtained commercially (Matheson Co.) with specified purities exceeding 98%. No further purification or analysis was attempted. EXPERIMENTAL
PROCEDURES
The procedures used for linewidth measurements with the earlier version of the spectrometer have been discussed previously and need not be repeated here.
476
NERF AND SONNENBERG
With the newer version of the spectrometer, the pressure broadened spectra were usually taken in a series of 10 to 20 measurements. Each group of spectra were preceded and followed by baseline measurements and shared a common frequency calibration. For self-broadening, the CO pressure could be either increased or decreased for successive measurements. Foreign gas broadening allowed only an increase in the broadener since, under decreasing pressure, different components of a mixture will often outgas from the cell walls at different rates, which leads to an ambiguity in composition. Sufficient time was allowed between measurements to allow thermal equilibrium and complete mixing of gases to be obtained. Frequency calibrations were made by manually selecting 8 to 15 memory channels and measuring the klystron frequency for each. Intermediate values were obtained by five-point Lagrange interpolation. It was determined that no significant error was introduced in the linewidth by calibrating with a static, rather than a sweeping, klystron frequency. The linewidths were obtained from the digitized spectra by nonlinear least-squaresfitting methods (5). First, the baseline and line spectrum were corrected for the distortions introduced by the coupling capacitor. Then, a comparison spectrum was calculated, using initial guesses for the instrumental and spectral line parameters. From the differences between the observed and calculated spectra, corrections to the initial parameters were obtained from a linear least-squares fit. The improved parameters were substituted for the initial guesses and the least-squares fit iterated until the parameters converged on a set of values or until obvious numerical instability set in. The computer program used to fit the observed spectra assumed a general Voigt lineshape, i.e., including both Doppler and pressure broadening (6). When development was first begun on this program it was hoped that the data were of sufficient quality that the lineshape parameters (optical depth, Lorentz width, center frequency) and standing wave effects (VSWR, phase angle) could be determined from the least-squares fit. However, preliminary studies soon showed that attempts to fit all these parameters were often numerically unstable, and that the final solutions were influenced by the initial estimates of the parameters. These potentially treacherous problems were avoided by a simpler approach; only the linewidth and center frequency were obtained from the fit. The optical depth, when sufficiently large to affect the derived linewidth, was obtained from independent measurements. Standing wave distortions of the lineshape were eliminated from the fit, but allowed for by increasing the estimated error in the width. RESULTS
Pressure broadening coefficients for the 115 GHz carbon monoxide line are shown in Table I. They were derived from a linear least-squares fit of Lorentz half-width versus partial pressure of the broadening gas. Assigned errors-typically of the order of lO%were predominantly determined by estimates of the maximum effect of standing waves on the width. The only previous pressure broadening measurement on this line known to us was reported as a private communication from J. P. Rusk in Ref. (7) ; his value of 3.5 f 0.2 MHz/Torr for the room temperature self-broadening is in good agreement with our result.
PRESSURE
BROADENING
477
OF CO
TABLE I PRESSURR
BROADENING
J = 1-o
COEFFICIENTS* (?dES/TORR) FOR THE
TRANSITION OF CARBON
MONOXIDE
77 K
TEMPERXMIRE 195 K
294 K
9.3 kO.9
4.8 io.5
3.4 *0.3
II2 . . . . .
7.2 20.7
4.1 10.5
3-o to.3
D2
.e...
6.8 *O.J
3.1 k0.J
2.6 kO.3
He
.... .
3.9 f0.4
2.3 f0.3
1.9 f0.2
Ne
..e..
4.8 f0.5
2.4 f0.3
1.6 k0.2
7.3 kO.7
3.5 to.5
2.8 f0.3
BROADENER
co
.. ...
A . ....
*
Halfwidth
at half
maximum.
The integrated intensities of the observed spectral lines provide a convenient check on the internal agreement of the linewidth data. For pure CO spectra the observed values of the integrated intensities are consistent with intensities calculated from the measured CO dipole moment (8). Changes in the integrated intensity during a series of foreign broadening observations indicated absorption and evolution of small amounts of CO from the cell walls. The magnitude of the effect seemed to depend on the broadening gas, with hydrogen showing the largest range and neon the smallest. Correction of
00
200
T,OK---.
FIG. 1. Temperature
300
0
loo
200
300
T, lK-
dependence of the cross sections for foreign and self-broadening of carbon monoxide.
NERF
478
AND
SONNENBERG
the broadening coefficients for the indicated loss or gain of CO yielded improved agreement between different series of measurements. Pressure broadening cross sections derived from the linewidths are plotted versus temperature in Fig. 1. Over the range of temperature studied, there appears to be a general increase in cross section with decreasing temperature; the larger the room temperature cross section, the greater the increase in going to liquid-nitrogen temperatures. No significant lineshifts (>0.3 MHz/Torr) were observed for any of the broadeners studied. ACKNOWLEDGMENTS We are indebted to Professor Patrick Thaddeus for support and guidance of this work. Particular thanks are due Dr. Sheldon Green for aid, assistance, and encouragement throughout the progress of this experiment. RECEIVED:
March 5, 1975 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8.
S. GREEN ANDP. TBADDEUS,Astrophys. J. 191, 653 (1974). P. S. BERGERAND M. SIMON,Astrophys. J. 180, L43 (1973). R. B. NERF, JR., Thesis, Columbia University, 1974. R. B. NERF, JR., J. Mol. Spectrosc. 58, 451 (1975). B. R. MARTIN, “Statistics for Physicists,” Academic Press, New York, 1971. D. W. POSENER,Amtd. J. Phys. 12, 184 (1959). J. M. DOWLING,J. &ant. Spectrosc. Radiat. Transjer 9, 1613 (1969). J. S. MUENTER,J. Mol. Spectrosc. 55, 490 (1975).
Pressure Broadening
58,474-478
(1975)
of the I = 1 +-0 Transition
R. B. NERF, JR., Department of Physics,
Columbia
AND
M.
A.
of Carbon
Monoxide
SONNENBERG
University, New York, New York 10027, and New York, New York, 10025
Goddard Institute for Space Studies, 2880 Broadway,
The pressure broadening of the carbon monoxide line near 115 GHz was measured at liquid nitrogen, dry ice, and room temperature, with typical experimental uncertainties of about 10%. Broadening gases were carbon monoxide, hydrogen, deuterium, helium, neon, and argon. No significant lineshifts were observed. INTRODUCTION
Pressure broadening measurements can be used in conjunction with other experimental data to help elicit the form of the intermolecular potential (1). Such studies are of importance in the investigation of rotational excitation of molecules by collisions, a topic of particular interest for the understanding of the formation of microwave spectral lines in the interstellar medium. Carbon monoxide (CO) is one of the most important of the known interstellar molecules because of its widespread occurrence, strong millimeter spectrum, and the crucial role it plays in the energy balance of interstellar clouds (2). Happily, it has sufficient vapor pressure for temperatures in the upper range of the interstellar regime (about 10-80 K) to make microwave pressure broadening measurements possible. We have measured the pressure broadening of the J = 1 + 0 transition at three convenient temperatures: liquid nitrogen (77 K), dry ice (195 K), and room (294 K). The choice of broadening gases was determined by astrophysical interest (Hz, He, DJ and simplicity (He, Ne, A). (Deuterium, although not abundant in the interstellar medium, was used because it has the same molecular potential as Hz, but a different thermal distribution of velocities.) EXPERIMENTAL
APPARATUS
Two configurations of the spectrometer were used for this study; they differ principally in the choice of instrumentation for signal processing and for recording the spectra. Except for an absorption cell designed for cryogenic temperatures, the first version was essentially identical to the spectrometer used for previously reported measurements on formaldehyde (3,4). Although this instrument proved quite successful, it was not well suited to optically thin lines, and the reduction of the data from x-y plots was both tedious and time consuming. The second version resulted from modifications which attempted to alleviate these problems; the lock-in amplifier, chopper wheel, and x-y recorder were replaced 474 Copyright @ 1975 by Academic Press. Inc. AU rights of reproduction in any form reserved.
PRESSURE BROADENING
OF CO
475
with a 512-channel signal averager and a digital tape recorder. Instead of slowly sweeping through the line over a period of some tens of seconds, the line was scanned 20 times a second, and several hundred scans were averaged for each measurements. Scanning the klystron faster than its thermal time constant greatly reduced baseline shifts from thermal tuning, a major source of error for weak lines. It was hoped that recording the spectra on computer-compatible magnetic tape would increase both the ease and accuracy of the data analysis. Since the designs of the spectrometers are straightforward, and one has been described in some detail elsewhere, we will concentrate primarily on those facets of the instruments which differ from the original. In the second configuration, the frequency of the microwave signal was swept in synchronism with the signal averager; a sawtooth voltage derived from the channel number was used to control a frequency synthesizer, to which the klystron was phaselocked. Typical frequency excursions at 11.5 GHz were 3040 MHz, determined in large part by the maximum available correction voltage in the phase-lock circuits. Although the spectrum recorded by the newer version is in a more convenient form, it lacks information contained in the earlier x-y plots. Since the microwave power is not amplitude modulated, the coupling capacitor between detector and signal averager filters out not only the dc bias on the bolometer, but any steady component in detected power. The optical depth of the line, for instance, is not immediately available; it must be measured or inferred in some other way. Both versions of the spectrometer used stainless steel absorption cells capable of operation at cryogenic temperatures; path lengths of 12.5 and 200 cm were used, depending on the line strength. The cells were constructed from two concentric cylinders of equal length; the smaller (-10 cm ID) formed the absorption cell, while the space between it and the larger (-12 cm ID) served as a coolant jacket. The extremities of the cylinders were welded to two annular flanges, which formed the ends of the coolant jacket and held the teflon lenses used as windows. Thermal insulation was provided by enclosing the cells in boxes constructed of 10 cm thick polystyrene or polyurethane foam. As has been noted (3,4), free space cells can severely distort lineshapes through standing waves originating at the horns and lens surfaces; these problems are particularly severe with metal cells since off-axis reflections are not rapidly attenuated. Pressure measurements were made with capacitive manometers; these are particularly well suited to pressure broadening studies because accuracy is unaffected by gas composition. Preliminary linewidth measurements were made using a O-l Torr sensor (CGS-Datametrics type 523-15) that had been independently calibrated to an accuracy of 1% against a McLeod gauge (3). Most of the later measurements were made with a new O-100 Torr sensor (Type 523-H) so that the maximum linewidth would not be constrained by the range of the pressure gauge. This gauge was not independently calibrated since accuracy checks on the original sensor were in reasonably good agreement with the manufacturer’s calibration. All gases used in this experiment were obtained commercially (Matheson Co.) with specified purities exceeding 98%. No further purification or analysis was attempted. EXPERIMENTAL
PROCEDURES
The procedures used for linewidth measurements with the earlier version of the spectrometer have been discussed previously and need not be repeated here.
476
NERF AND SONNENBERG
With the newer version of the spectrometer, the pressure broadened spectra were usually taken in a series of 10 to 20 measurements. Each group of spectra were preceded and followed by baseline measurements and shared a common frequency calibration. For self-broadening, the CO pressure could be either increased or decreased for successive measurements. Foreign gas broadening allowed only an increase in the broadener since, under decreasing pressure, different components of a mixture will often outgas from the cell walls at different rates, which leads to an ambiguity in composition. Sufficient time was allowed between measurements to allow thermal equilibrium and complete mixing of gases to be obtained. Frequency calibrations were made by manually selecting 8 to 15 memory channels and measuring the klystron frequency for each. Intermediate values were obtained by five-point Lagrange interpolation. It was determined that no significant error was introduced in the linewidth by calibrating with a static, rather than a sweeping, klystron frequency. The linewidths were obtained from the digitized spectra by nonlinear least-squaresfitting methods (5). First, the baseline and line spectrum were corrected for the distortions introduced by the coupling capacitor. Then, a comparison spectrum was calculated, using initial guesses for the instrumental and spectral line parameters. From the differences between the observed and calculated spectra, corrections to the initial parameters were obtained from a linear least-squares fit. The improved parameters were substituted for the initial guesses and the least-squares fit iterated until the parameters converged on a set of values or until obvious numerical instability set in. The computer program used to fit the observed spectra assumed a general Voigt lineshape, i.e., including both Doppler and pressure broadening (6). When development was first begun on this program it was hoped that the data were of sufficient quality that the lineshape parameters (optical depth, Lorentz width, center frequency) and standing wave effects (VSWR, phase angle) could be determined from the least-squares fit. However, preliminary studies soon showed that attempts to fit all these parameters were often numerically unstable, and that the final solutions were influenced by the initial estimates of the parameters. These potentially treacherous problems were avoided by a simpler approach; only the linewidth and center frequency were obtained from the fit. The optical depth, when sufficiently large to affect the derived linewidth, was obtained from independent measurements. Standing wave distortions of the lineshape were eliminated from the fit, but allowed for by increasing the estimated error in the width. RESULTS
Pressure broadening coefficients for the 115 GHz carbon monoxide line are shown in Table I. They were derived from a linear least-squares fit of Lorentz half-width versus partial pressure of the broadening gas. Assigned errors-typically of the order of lO%were predominantly determined by estimates of the maximum effect of standing waves on the width. The only previous pressure broadening measurement on this line known to us was reported as a private communication from J. P. Rusk in Ref. (7) ; his value of 3.5 f 0.2 MHz/Torr for the room temperature self-broadening is in good agreement with our result.
PRESSURE
BROADENING
477
OF CO
TABLE I PRESSURR
BROADENING
J = 1-o
COEFFICIENTS* (?dES/TORR) FOR THE
TRANSITION OF CARBON
MONOXIDE
77 K
TEMPERXMIRE 195 K
294 K
9.3 kO.9
4.8 io.5
3.4 *0.3
II2 . . . . .
7.2 20.7
4.1 10.5
3-o to.3
D2
.e...
6.8 *O.J
3.1 k0.J
2.6 kO.3
He
.... .
3.9 f0.4
2.3 f0.3
1.9 f0.2
Ne
..e..
4.8 f0.5
2.4 f0.3
1.6 k0.2
7.3 kO.7
3.5 to.5
2.8 f0.3
BROADENER
co
.. ...
A . ....
*
Halfwidth
at half
maximum.
The integrated intensities of the observed spectral lines provide a convenient check on the internal agreement of the linewidth data. For pure CO spectra the observed values of the integrated intensities are consistent with intensities calculated from the measured CO dipole moment (8). Changes in the integrated intensity during a series of foreign broadening observations indicated absorption and evolution of small amounts of CO from the cell walls. The magnitude of the effect seemed to depend on the broadening gas, with hydrogen showing the largest range and neon the smallest. Correction of
00
200
T,OK---.
FIG. 1. Temperature
300
0
loo
200
300
T, lK-
dependence of the cross sections for foreign and self-broadening of carbon monoxide.
NERF
478
AND
SONNENBERG
the broadening coefficients for the indicated loss or gain of CO yielded improved agreement between different series of measurements. Pressure broadening cross sections derived from the linewidths are plotted versus temperature in Fig. 1. Over the range of temperature studied, there appears to be a general increase in cross section with decreasing temperature; the larger the room temperature cross section, the greater the increase in going to liquid-nitrogen temperatures. No significant lineshifts (>0.3 MHz/Torr) were observed for any of the broadeners studied. ACKNOWLEDGMENTS We are indebted to Professor Patrick Thaddeus for support and guidance of this work. Particular thanks are due Dr. Sheldon Green for aid, assistance, and encouragement throughout the progress of this experiment. RECEIVED:
March 5, 1975 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8.
S. GREEN ANDP. TBADDEUS,Astrophys. J. 191, 653 (1974). P. S. BERGERAND M. SIMON,Astrophys. J. 180, L43 (1973). R. B. NERF, JR., Thesis, Columbia University, 1974. R. B. NERF, JR., J. Mol. Spectrosc. 58, 451 (1975). B. R. MARTIN, “Statistics for Physicists,” Academic Press, New York, 1971. D. W. POSENER,Amtd. J. Phys. 12, 184 (1959). J. M. DOWLING,J. &ant. Spectrosc. Radiat. Transjer 9, 1613 (1969). J. S. MUENTER,J. Mol. Spectrosc. 55, 490 (1975).