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Pressure broadening and line shifts of Q-branch rotational transitions of methane by self- and air-collisions
JOURNAL
OF MOLECULAR
SPECTROSCOPY
139,337-342 (1990)
Pressure Broadening and Line Shifts of Q-Branch Rotational Transitions of Methane by Self- and Air-Collisions P. WOLF, J. HAEKEL, AND H. MADER Abteilung Chemische Physik im Institut jiir Physikalische Chemie der Universitiit Kiel. Federal Republic of Germany The transient emission technique in the time domain has been used to analyze the collisioninduced width and shift of microwave lines of methane for the pure gas and for mixtures with air. The pressure dependence of the relaxation rate 1 / Tz and the line frequency have been investigated at room temperature for the Q-branch transitions lOA:“-lOA:“, 13A:“-13Aj”, 10E’2’-IOE”‘, and IOF~Z’-lOF:” in the ground vibrational state. 0 1990 Academic Press. Inc.
INTRODUCTION Methane is an important absorber of radiation in many spectral regions in the atmosphere of the earth, and therefore contributes significantly to the greenhouse effect (I). Up to now the emphasis of investigations of methane in the microwave region was on centrifugal distortion analysis and on spin-rotation and spin-spin interaction (2, 3), which cause the hyperfine structure of F-type transitions. No pressure-broadening studies of microwave lines of methane have been reported so far, but a detailed knowledge of broadening and shift parameters for these transitions, especially in mixtures with air, is necessary for the analysis of atmospheric spectra. EXPERIMENTAL
DETAILS
For the pure gas and for mixtures of methane and air, the pressure dependence of the relaxation rate 1/ T2 and the resonance frequency were investigated for the Q-branch transitions 10A “‘-lo/4 13A”‘-13A”’ and I 2(‘) 3 2 I > loE’*‘-lOE”‘, 10F’*‘--10F”‘. The sampie of methane (stated purity of 99.995%) and the synthetic air (2 1% 02, 79% N2) were taken from lecture bottles supplied by Messer-Griesheim Co. The mixture compositions were established by gradually adding small amounts of the foreign gas to the sample cell, which was previously filled with a certain amount of methane. The gases were let slowly through needle valves out of a small volume, where they had been maintained at relatively high pressure (up to 10 atm). The pressure measurements were made with use of a capacitance manometer ( MKS Baratron 3 1OB). In order to stabilize the pressure and mixture compositions, a 20 liter ballast bulb was attached to the sample cell. The investigations of the pure gas were carried out in the pressure range from 3 to 90 mTorr ( 1 Torr = 133.32 Pa). For the mixtures, the partial pressure of methane was held fixed at 9 mTorr, and the partial 337
0022-2852190 $3.00 Copyright
0
1990 by Academic
All rights of reproduction
Press. Inc.
in any form resewed.
338
WOLF, HAEKEL, AND MADER
pressure of air was varied from 0 to 40 mTorr. All measurements were done at room temperature. The experiments were carried out with a microwave Fourier transform (MWFT) spectrometer in the J-Band. The instrument is described elsewhere (4). Pulse lengths of approximately 750 nsec and a pulse power up to 20 W were used for polarizing the sample. At a given pressure up to 3 - 10 7 experiments with sample intervals of 10 nsec and 1024 data points were averaged to obtain the final signal. RESULTS AND DISCUSSION
The pressure-broadening and lineshift coefficients of the investigated Q-branch transitions of methane for the pure gas and the mixtures with air were determined by analysis of the transient emission signal following pulse excitation of the sample gas. To obtain a value for the decay time T2 and the line center frequency u (or the angular beat frequency o) of the detected and averaged signal S(t) at a fixed pressure, the signal was compared with the theoretical expression S(t) = &.exp[-t2/4q2].exp[-t/T2]*cos(Wt
+ 4)
(1)
by a least-squares fit program (5) with &, , T2, w, and C$as fitting parameters. S(t) is the value of the signal at time t with reference to the offset of the MW pulse. The term exp( -t2/4q2) to account for Doppler dephasing of the transient signal was held fixed in the least-squares analysis, relating the constant q to the Doppler half-width Av, [ q = (In 2) “*/2nAvo]. Nonexponential decay behavior as predicted theoretically with consideration of absorber-speed-dependent relaxation rates (6) and wall collisional effects (6, 7) was not observed within the experimental accuracy of this investigation. In accordance with theoretical considerations (2) hyperhne splitting was not resolvable in the case of the F-type transition, and therefore is not considered in our analysis. From the fit results for I/ Tz and u, respectively, at different sample pressures, the coefficients for the linear pressure dependence of 1 / T2 and v were then obtained by means of a linear least-squares analysis, data points being weighted according to their standard deviations in the following expressions for the relaxation rate, l/T2
=
a
+PP,
(2)
and for the line frequency, v = Vo+ sp.
(3)
For the pure gas, p is the total sample pressure, Q is primarily due to wall collisions, and uo is the line frequency extrapolated to zero pressure. For the mixtures, p is the foreign gas partial pressure and 01contains a contribution from self-collisions of methane in a fixed amount. In this case v. is the line frequency corresponding to the partial pressure of methane. As an example for the linear pressure dependences, Figs. 1 and 2 show the results from the investigation on the transition 1OA ! ’ )- 1OA1” for the pure gas. Figure 1 shows the pressure dependence of I/ T2, Fig. 2 those of the line frequency, respectively, both together with the fitted straight lines.
PRESSURE
BROADENING
339
OF CH,
0.075 t
I ) p [mTorr:
,
3.3
78.2
FIG. 1. Experimental results for the pressure dependence of 1 /T2 for the transition J = 10, AI”-Ail’ of “CH., in the pure gas together with the fitted straight line. The error bars denote twice the standard deviations from fit results of transient emission signals.
V
[MHZ]
A 5014.098
-
5014.085t
, 3.3
I ) p [mTorr] 78.2
FIG. 2. Experimental results for the pressure dependence of the line frequency v0 for the transition J = 10. A j”-A:” of ‘%H4 in the pure gas together with the fitted straight line. The error bars denote twice the standard deviations from fit results of transient emission signals.
WOLF, HAEKEL, AND MADER
340
The resulting rate coefficients /3 for the investigated systems may be converted to the more familiar pressure-broadening parameters Au&p ( =P/~P) to characterize the pressure dependence of the halfwidth of the lines. The coefficients Au&p are given in Table I together with the lineshift coefficients 6 and the resonance frequencies of the investigated transitions. The quoted errors are the single standard deviations from the linear least-squares fit and do not reflect systematic deviations from pressure inaccuracies ( ~0.1 mTorr) and shifts in temperature ( -C 1 K). No attempt has been made here to relate the experimental results to a theoretical treatment of the binary collision event. As far as the long-range interaction is concerned, the studied systems exhibit a much sharper decrease of the intermolecular interaction with respect to the intermolecular distance r as compared to the interaction of polar molecules. In the latter case, the long-range dipole-dipole interaction shows a 1/r3 dependence for the attractive part of the interaction potential (8) which dominantly contributes to the pressure broadening of rotational lines. In such a case, a perturbative approach to collision theory such as the treatment of Anderson (9) may lead to satisfactory predictions of experimental linewidth data.
TABLE I Experimental Values of the Linewidth Au,,~/P and Lineshift Parameters 6 for Q-Branch Rotational Transitions of ‘*CH4 Due to Self and Air ( N2, 9) Collisions at Temperature T = 295 K (Errors in Parentheses Are Single Standard Deviations in Units of the Last Digit)
system
Transition
v0 M-l21
[MHzmrrll
Qb-cn4
CILI-Air
***:
b
CM/ZIP
[kHzTorTi
J=lO,~(“-&(I’
5014.099
2.82(8)
-173 (6)
J=l3,~“‘-&‘I’
6934.095
2.67110)
-189 (7)
J=lO,E’2’-E(”
6614.902
3.28(70)
-441(78)
J=10,R’2’-F2”’
6209.569
3.0408)
-227 (15)
J=l(),&"'-&(I)
5014.099
2.27(11)
-158 (12)
J=13,&"'-AI"'
6934.095
1.9908)
- 45(7)
J=lO,E’2’-E”’
6614.902
3.07(68)
***
J=~O,FI’~‘-F~“’
6209.569
2.50(56)
-156
Data not good enough for
analysis.
(44)
341
PRESSURE BROADENING OF CH.,
These approximations become questionable for the systems described here, which are characterized by a sharper decrease of the long-range, attractive part of the intermolecular potential energy. In the case of CH4-CH4 collisions the long-range forces are dominated by the dispersion interaction, with an r dependence as 1/r6, whereas the electrostatic interaction due to the permanent octopole moments behaves as 1 / r7 (8). Induction interaction, e.g., octopole-induced dipole interaction ( - 1/ r lo), is believed to be of minor importance in contributing to the broadening of lines. For the mixtures with the foreign gases N2 and 02 (air), contributions from the interaction of permanent electric moments, e.g., the octopole-quadrupole interaction ( - 1/ r6), are thought to be more effective. These contributions show an r dependence similar to the pure gas, so the pressure dependence of the relaxation rates in both systems should be of the same magnitude. The qualitative arguments given here to rationalize for the investigated systems that the intermolecular potential is of shorter range in comparison to polar molecules may be illustrated somewhat more quantitatively with calculation of effective collision diameters beff (or cross sections (T,~= a!&) from the experimental results for the pressure coefficients /3 of 1 / T2. The values for b,~ and aeff, given in Table II, were obtained with reference to gas kinetic considerations for a hard sphere collisional model according to b,r = (P)“2(kTp/8a)“4,
(4)
where P is the reduced mass of the collision partners, T is the temperature, the Boltzmann constant.
and k is
TABLE II Effective Collision Diameters be= and Cross Sections oen for T2-Relaxation of ‘?H4 for the Pure Gas and Mixtures with Air ( 02/N2)
System
Transition
beff
CH4 -CHs
J=lO,Al”‘-AZ”’
0.442(l)
0.613(3)
J=13,Az”‘-AI(‘)
0.431(l)
0.584(3)
J=lO,E(a)-E(l)
0.477 (5)
0.715(15)
J=~O,FI(~)-FZ”’
0.459(2)
0.662(6)
J=lO,Al(‘)-AZ”’
0.423 (1)
0.562(3)
J=13,Az”‘-Al(‘)
0.395(l)
0.490(3)
J=lO,E’2’-E(l)
0.412(5)
0.533 (15)
J=~O,FI(~)-FZ”’
0.444(4)
0.612(12)
CH4 -Air
[nml
Qeff
[rim21
342
WOLF,
HAEKEL,
AND
MADER
For polar molecules, effective collision diameters to describe pressure broadening of lines are usually found to be larger, as for example in case of the CH3CN-CH3CN system (be, = 2.5-3.0 n/m) (10). The smaller magnitude of berrfor the investigated systems with CH4 as absorber molecule clearly indicates the shorter-range nature of the intermolecular interaction potential, which possibly makes common line-broadening theories no longer applicable. Our results on pressure broadening are in good agreement with the values from studies of collision-induced widths and shifts of rovibrational transitions of methane and methane-air mixtures. Using the pressure-broadening coefficients for some v3 lines of CH4 for the pure gas (II ) and some v4 lines (air-broadening and lineshift) ( 12), mean values for be, of about 0.4 nm for self and air broadening are obtained. In the case of the shift coefficients of the air-broadened lines a mean value of - 110 kHz/Torr can be evaluated. With the exception of the sign, the accordance with our values for the shifts is rather poor. It is interesting to compare the results from Table II with corresponding values from our studies of collision-induced widths of rotational transitions of germane, which yielded a value for bef of about 0.68 nm for the pure gas. Both diameters are similar to the values of two colliding hard spheres, calculated from the bond lengths of the molecules methane and germane, respectively, and illustrate the short-range nature of the intermolecular potentials of spherical top molecules. To our knowledge, no theoretical calculations of the frequency-shifts of these molecules have been reported yet. ACKNOWLEDGMENTS
We thank all members of our group, especially Professor Dr. H. Dreizler, Dr. U. Andresen, and Dr. W. Stahl for help and discussions. This work was supported by funds from the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. RECEIVED:
September 18, 1989 REFERENCES
R. A. HOUGHTON AND G. M. WOODWELL,Sci. Amer. 4, 18-29 ( 1989). M. OLDANI, M. ANDRIST,A. BAUDERAND A. G. ROBIETTE,.I Mol. Spectrosc. 110,93-105 ( 1985 ). P. WOLF AND W. STAHL, Z. Naturjimch. A 44,651-654 ( 1989). G. BESTMANN,H. DREIZLER,E. FLIEGE,AND W. STAHL, J. Mol. Strut. 97,215-219 ( 1980). J. HAEKELAND H. MICDER,Z. Nuturforsch. A 43,203-206 ( 1988). S. L. COY, J. Chem. Phys. 73,5531-5555 (1980). H. MWDER,J. Quunt. Spectrosc. Radiut. Transfer, 32, 129-140 ( 1984). T. OKA, Adv. At. Mol. Phys. 9, 127-205 (1973). P. W. ANDERSON,Phys. Rev., 76,647-661 ( 1949). H. MKDER,H. B~MSDORF,AND U. ANDRESEN,Z. Nuturjbrsch. A 34,850-857 (1979). V. MALATHY DEVI, M. FIRDOVICH,D. G. JONES,AND D. G. S. SNYDER, J. Mol. Spectrosc. 97,333342 (1983). 12. C. P. RINSLAND,V. MALATHY DEVI, M. A. H. SMITH,AND D. C. BENNER,Appl. Optics 27,631-651 (1988).
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
OF MOLECULAR
SPECTROSCOPY
139,337-342 (1990)
Pressure Broadening and Line Shifts of Q-Branch Rotational Transitions of Methane by Self- and Air-Collisions P. WOLF, J. HAEKEL, AND H. MADER Abteilung Chemische Physik im Institut jiir Physikalische Chemie der Universitiit Kiel. Federal Republic of Germany The transient emission technique in the time domain has been used to analyze the collisioninduced width and shift of microwave lines of methane for the pure gas and for mixtures with air. The pressure dependence of the relaxation rate 1 / Tz and the line frequency have been investigated at room temperature for the Q-branch transitions lOA:“-lOA:“, 13A:“-13Aj”, 10E’2’-IOE”‘, and IOF~Z’-lOF:” in the ground vibrational state. 0 1990 Academic Press. Inc.
INTRODUCTION Methane is an important absorber of radiation in many spectral regions in the atmosphere of the earth, and therefore contributes significantly to the greenhouse effect (I). Up to now the emphasis of investigations of methane in the microwave region was on centrifugal distortion analysis and on spin-rotation and spin-spin interaction (2, 3), which cause the hyperfine structure of F-type transitions. No pressure-broadening studies of microwave lines of methane have been reported so far, but a detailed knowledge of broadening and shift parameters for these transitions, especially in mixtures with air, is necessary for the analysis of atmospheric spectra. EXPERIMENTAL
DETAILS
For the pure gas and for mixtures of methane and air, the pressure dependence of the relaxation rate 1/ T2 and the resonance frequency were investigated for the Q-branch transitions 10A “‘-lo/4 13A”‘-13A”’ and I 2(‘) 3 2 I > loE’*‘-lOE”‘, 10F’*‘--10F”‘. The sampie of methane (stated purity of 99.995%) and the synthetic air (2 1% 02, 79% N2) were taken from lecture bottles supplied by Messer-Griesheim Co. The mixture compositions were established by gradually adding small amounts of the foreign gas to the sample cell, which was previously filled with a certain amount of methane. The gases were let slowly through needle valves out of a small volume, where they had been maintained at relatively high pressure (up to 10 atm). The pressure measurements were made with use of a capacitance manometer ( MKS Baratron 3 1OB). In order to stabilize the pressure and mixture compositions, a 20 liter ballast bulb was attached to the sample cell. The investigations of the pure gas were carried out in the pressure range from 3 to 90 mTorr ( 1 Torr = 133.32 Pa). For the mixtures, the partial pressure of methane was held fixed at 9 mTorr, and the partial 337
0022-2852190 $3.00 Copyright
0
1990 by Academic
All rights of reproduction
Press. Inc.
in any form resewed.
338
WOLF, HAEKEL, AND MADER
pressure of air was varied from 0 to 40 mTorr. All measurements were done at room temperature. The experiments were carried out with a microwave Fourier transform (MWFT) spectrometer in the J-Band. The instrument is described elsewhere (4). Pulse lengths of approximately 750 nsec and a pulse power up to 20 W were used for polarizing the sample. At a given pressure up to 3 - 10 7 experiments with sample intervals of 10 nsec and 1024 data points were averaged to obtain the final signal. RESULTS AND DISCUSSION
The pressure-broadening and lineshift coefficients of the investigated Q-branch transitions of methane for the pure gas and the mixtures with air were determined by analysis of the transient emission signal following pulse excitation of the sample gas. To obtain a value for the decay time T2 and the line center frequency u (or the angular beat frequency o) of the detected and averaged signal S(t) at a fixed pressure, the signal was compared with the theoretical expression S(t) = &.exp[-t2/4q2].exp[-t/T2]*cos(Wt
+ 4)
(1)
by a least-squares fit program (5) with &, , T2, w, and C$as fitting parameters. S(t) is the value of the signal at time t with reference to the offset of the MW pulse. The term exp( -t2/4q2) to account for Doppler dephasing of the transient signal was held fixed in the least-squares analysis, relating the constant q to the Doppler half-width Av, [ q = (In 2) “*/2nAvo]. Nonexponential decay behavior as predicted theoretically with consideration of absorber-speed-dependent relaxation rates (6) and wall collisional effects (6, 7) was not observed within the experimental accuracy of this investigation. In accordance with theoretical considerations (2) hyperhne splitting was not resolvable in the case of the F-type transition, and therefore is not considered in our analysis. From the fit results for I/ Tz and u, respectively, at different sample pressures, the coefficients for the linear pressure dependence of 1 / T2 and v were then obtained by means of a linear least-squares analysis, data points being weighted according to their standard deviations in the following expressions for the relaxation rate, l/T2
=
a
+PP,
(2)
and for the line frequency, v = Vo+ sp.
(3)
For the pure gas, p is the total sample pressure, Q is primarily due to wall collisions, and uo is the line frequency extrapolated to zero pressure. For the mixtures, p is the foreign gas partial pressure and 01contains a contribution from self-collisions of methane in a fixed amount. In this case v. is the line frequency corresponding to the partial pressure of methane. As an example for the linear pressure dependences, Figs. 1 and 2 show the results from the investigation on the transition 1OA ! ’ )- 1OA1” for the pure gas. Figure 1 shows the pressure dependence of I/ T2, Fig. 2 those of the line frequency, respectively, both together with the fitted straight lines.
PRESSURE
BROADENING
339
OF CH,
0.075 t
I ) p [mTorr:
,
3.3
78.2
FIG. 1. Experimental results for the pressure dependence of 1 /T2 for the transition J = 10, AI”-Ail’ of “CH., in the pure gas together with the fitted straight line. The error bars denote twice the standard deviations from fit results of transient emission signals.
V
[MHZ]
A 5014.098
-
5014.085t
, 3.3
I ) p [mTorr] 78.2
FIG. 2. Experimental results for the pressure dependence of the line frequency v0 for the transition J = 10. A j”-A:” of ‘%H4 in the pure gas together with the fitted straight line. The error bars denote twice the standard deviations from fit results of transient emission signals.
WOLF, HAEKEL, AND MADER
340
The resulting rate coefficients /3 for the investigated systems may be converted to the more familiar pressure-broadening parameters Au&p ( =P/~P) to characterize the pressure dependence of the halfwidth of the lines. The coefficients Au&p are given in Table I together with the lineshift coefficients 6 and the resonance frequencies of the investigated transitions. The quoted errors are the single standard deviations from the linear least-squares fit and do not reflect systematic deviations from pressure inaccuracies ( ~0.1 mTorr) and shifts in temperature ( -C 1 K). No attempt has been made here to relate the experimental results to a theoretical treatment of the binary collision event. As far as the long-range interaction is concerned, the studied systems exhibit a much sharper decrease of the intermolecular interaction with respect to the intermolecular distance r as compared to the interaction of polar molecules. In the latter case, the long-range dipole-dipole interaction shows a 1/r3 dependence for the attractive part of the interaction potential (8) which dominantly contributes to the pressure broadening of rotational lines. In such a case, a perturbative approach to collision theory such as the treatment of Anderson (9) may lead to satisfactory predictions of experimental linewidth data.
TABLE I Experimental Values of the Linewidth Au,,~/P and Lineshift Parameters 6 for Q-Branch Rotational Transitions of ‘*CH4 Due to Self and Air ( N2, 9) Collisions at Temperature T = 295 K (Errors in Parentheses Are Single Standard Deviations in Units of the Last Digit)
system
Transition
v0 M-l21
[MHzmrrll
Qb-cn4
CILI-Air
***:
b
CM/ZIP
[kHzTorTi
J=lO,~(“-&(I’
5014.099
2.82(8)
-173 (6)
J=l3,~“‘-&‘I’
6934.095
2.67110)
-189 (7)
J=lO,E’2’-E(”
6614.902
3.28(70)
-441(78)
J=10,R’2’-F2”’
6209.569
3.0408)
-227 (15)
J=l(),&"'-&(I)
5014.099
2.27(11)
-158 (12)
J=13,&"'-AI"'
6934.095
1.9908)
- 45(7)
J=lO,E’2’-E”’
6614.902
3.07(68)
***
J=~O,FI’~‘-F~“’
6209.569
2.50(56)
-156
Data not good enough for
analysis.
(44)
341
PRESSURE BROADENING OF CH.,
These approximations become questionable for the systems described here, which are characterized by a sharper decrease of the long-range, attractive part of the intermolecular potential energy. In the case of CH4-CH4 collisions the long-range forces are dominated by the dispersion interaction, with an r dependence as 1/r6, whereas the electrostatic interaction due to the permanent octopole moments behaves as 1 / r7 (8). Induction interaction, e.g., octopole-induced dipole interaction ( - 1/ r lo), is believed to be of minor importance in contributing to the broadening of lines. For the mixtures with the foreign gases N2 and 02 (air), contributions from the interaction of permanent electric moments, e.g., the octopole-quadrupole interaction ( - 1/ r6), are thought to be more effective. These contributions show an r dependence similar to the pure gas, so the pressure dependence of the relaxation rates in both systems should be of the same magnitude. The qualitative arguments given here to rationalize for the investigated systems that the intermolecular potential is of shorter range in comparison to polar molecules may be illustrated somewhat more quantitatively with calculation of effective collision diameters beff (or cross sections (T,~= a!&) from the experimental results for the pressure coefficients /3 of 1 / T2. The values for b,~ and aeff, given in Table II, were obtained with reference to gas kinetic considerations for a hard sphere collisional model according to b,r = (P)“2(kTp/8a)“4,
(4)
where P is the reduced mass of the collision partners, T is the temperature, the Boltzmann constant.
and k is
TABLE II Effective Collision Diameters be= and Cross Sections oen for T2-Relaxation of ‘?H4 for the Pure Gas and Mixtures with Air ( 02/N2)
System
Transition
beff
CH4 -CHs
J=lO,Al”‘-AZ”’
0.442(l)
0.613(3)
J=13,Az”‘-AI(‘)
0.431(l)
0.584(3)
J=lO,E(a)-E(l)
0.477 (5)
0.715(15)
J=~O,FI(~)-FZ”’
0.459(2)
0.662(6)
J=lO,Al(‘)-AZ”’
0.423 (1)
0.562(3)
J=13,Az”‘-Al(‘)
0.395(l)
0.490(3)
J=lO,E’2’-E(l)
0.412(5)
0.533 (15)
J=~O,FI(~)-FZ”’
0.444(4)
0.612(12)
CH4 -Air
[nml
Qeff
[rim21
342
WOLF,
HAEKEL,
AND
MADER
For polar molecules, effective collision diameters to describe pressure broadening of lines are usually found to be larger, as for example in case of the CH3CN-CH3CN system (be, = 2.5-3.0 n/m) (10). The smaller magnitude of berrfor the investigated systems with CH4 as absorber molecule clearly indicates the shorter-range nature of the intermolecular interaction potential, which possibly makes common line-broadening theories no longer applicable. Our results on pressure broadening are in good agreement with the values from studies of collision-induced widths and shifts of rovibrational transitions of methane and methane-air mixtures. Using the pressure-broadening coefficients for some v3 lines of CH4 for the pure gas (II ) and some v4 lines (air-broadening and lineshift) ( 12), mean values for be, of about 0.4 nm for self and air broadening are obtained. In the case of the shift coefficients of the air-broadened lines a mean value of - 110 kHz/Torr can be evaluated. With the exception of the sign, the accordance with our values for the shifts is rather poor. It is interesting to compare the results from Table II with corresponding values from our studies of collision-induced widths of rotational transitions of germane, which yielded a value for bef of about 0.68 nm for the pure gas. Both diameters are similar to the values of two colliding hard spheres, calculated from the bond lengths of the molecules methane and germane, respectively, and illustrate the short-range nature of the intermolecular potentials of spherical top molecules. To our knowledge, no theoretical calculations of the frequency-shifts of these molecules have been reported yet. ACKNOWLEDGMENTS
We thank all members of our group, especially Professor Dr. H. Dreizler, Dr. U. Andresen, and Dr. W. Stahl for help and discussions. This work was supported by funds from the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie. RECEIVED:
September 18, 1989 REFERENCES
R. A. HOUGHTON AND G. M. WOODWELL,Sci. Amer. 4, 18-29 ( 1989). M. OLDANI, M. ANDRIST,A. BAUDERAND A. G. ROBIETTE,.I Mol. Spectrosc. 110,93-105 ( 1985 ). P. WOLF AND W. STAHL, Z. Naturjimch. A 44,651-654 ( 1989). G. BESTMANN,H. DREIZLER,E. FLIEGE,AND W. STAHL, J. Mol. Strut. 97,215-219 ( 1980). J. HAEKELAND H. MICDER,Z. Nuturforsch. A 43,203-206 ( 1988). S. L. COY, J. Chem. Phys. 73,5531-5555 (1980). H. MWDER,J. Quunt. Spectrosc. Radiut. Transfer, 32, 129-140 ( 1984). T. OKA, Adv. At. Mol. Phys. 9, 127-205 (1973). P. W. ANDERSON,Phys. Rev., 76,647-661 ( 1949). H. MKDER,H. B~MSDORF,AND U. ANDRESEN,Z. Nuturjbrsch. A 34,850-857 (1979). V. MALATHY DEVI, M. FIRDOVICH,D. G. JONES,AND D. G. S. SNYDER, J. Mol. Spectrosc. 97,333342 (1983). 12. C. P. RINSLAND,V. MALATHY DEVI, M. A. H. SMITH,AND D. C. BENNER,Appl. Optics 27,631-651 (1988).
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.