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Pure rotational far-infrared transitions of 16O2 in its electronic and vibrational ground state
JOURNAL OF MOLECULAR SPECTROSCOPY
125, 154-158 (1987)
Pure Rotational Far-Infrared Transitions of 1602 in Its Electronic and Vibrational Ground State* LYNDON R. ZINK Department of Physics. Universityof Colorado,Boulder, Colorado 80309, and NationalBureau of Standards, Boulder, Colorado 80303
AND MASATAKA MIZUSHIMA Department of Physics, Universityof Colorado, Boulder, Colorado80309
Five lines in the far-infraredregion,due to N + 2 + N (AJ = 0) transitionsof the 160zmolecule in its (X32;, u = 0) state, are measured at 773.839691, 1466.807133, 1812.405539,2157.577773, and 2502.323923 GHz, using a tunable PTR spectrometer. The spectral lineshape of the 2.50THz line is analyzed and the pressure self-broadening parameter of 18.2(32) kHz/Pa (=2.43(43) MHz/Torr) is obtained. Q 1987 Academic Press.hc. INTRODUCTION
Since the electronic ground state, X3&, of the oxygen molecule O2 has the spin quantum number S = 1, each rotational level with given quantum number N is a triplet: J = N, N f 1, where J = N + S is the total angular momentum. The spinflip transitions, AN = 0, AJ = -t 1, are observed in the microwave region near 60 GHz (I-5). The magnetic dipole rotational transitions N + 2 * N are in the far-infrared (FIR) region. The laser magnetic resonance (LMR) technique has been applied to observe the N = 5 + 3 (6, 7), 15 + 13 (8), 17 + 15 (P), 21 + 19 (P), and 23 + 21 (8) transitions, but these observations were indirect in that the molecule had to be under external magnetic fields to produce resonances with given laser lines. Direct measurements of these transitions except for the lowest one have not been possible until now simply because no appropriate tunable radiation source was available. A new tunable far-infrared (FIR) source was developed by Evenson and others (IO, II) that mixes two COz laser lines using the metal-insulator-metal (MIM) diode as a nonlinear device. We measured five rotational lines of the r602 molecule in its (X3& 21= 0) state up to 2.502 THz (N = 15 + 13). The spectral lineshapes of these FIR lines are given by the Voigt profile, a superposition of Doppler and Lorentzian lineshapes. The lineshape of the 2.502-THz line is analyzed to extract the pressure self-broadening parameter in the linewidth of the Lorentzian lineshape. * This is a contribution of the National Bureau of Standards and is not subject to copyright. Work supported in part by NASA under Contract W 1S-042. 0022-2852187 $3.00 Copyright8 1987 by Academic R-s, Inc. All rightsof reproductionin any form reserved.
154
FIR TRANSITIONS
155
OF 160z
EXPERIMENTAL
The tunable FIR spectrometer is described in detail elsewhere (IO, II). Briefly, tunable cw FIR radiation is generated by nonlinear mixing of radiation from two CO* lasers in a MIM diode. The radiation is tuned by varying the output of one of the lasers over its pressure-broadened gain profile. The FIR radiation is emitted from the diode with a long-wire antenna and collected with a section of a parabolic mirror. This mirror reflects a collimated beam through an absorption cell. After passing through the cell, the radiation is detected by a liquid He-cooled Ge bolometer. The transitions were observed in a 3.6-m-long, single-pass cell, which was cooled with a flowing dry ice bath to about 200 K. The lower temperature improved the signal strength for the N = 5 + 3 transition by a factor of 3. Zeeman broadening of the signal by the earth’s magnetic field was observed, so the cell was shielded from the earth’s magnetic field with a steel trough. This shielding reduced the linewidth, which improved our signal-to-noise ratio and hence the accuracy of our measurements. Figure 1 shows a trace of the N = 15 + 13 transition taken with a 400-msec time constant. O2 pressure used in the frequency measurements ranged from 67 to 133 Pa. Pressure-broadening measurements were performed on the 2.5-THz line. The dry ice bath gave no significant increase in signal strength for this transition, so to simplify the experiment the broadening studies were performed at room temperature. Pressure ranged from 13 to 733 Pa for 02 self-broadening. Decreasing signal strength prevented measurements at higher pressures. TRANSITION
The Hamiltonian
FREQUENCIES
AND MOLECULAR
of the rotational states of 3L:molecules is given by (7)
Ej= Bfi’ - Dni4 + 3 {X(39: - s2) + X,(fi2(3$ + hm,(fi4(3$
PARAMETERS
- 3’) + (33: - s2)fi2)/2
- s2) + (3s: - g2)fi4)/2 I+ yN . S + y&‘N.
S + y,,#N
*S,
( 1)
where N and S are the rotational and spin angular momenta, and the subscript r indicates their components along the molecular axis.
FIG. 1. The recorder trace of N = 15 + 13, J = 14 t- 14 transitions of Oz. The total scan width was 65 MHz, the pressure was 67 Pa, and the cell was cooled to 200 K. Since we frequency modulate the signal, we are recording da/du against Y the frequency. We define 2x as the frequency difference between the maximum and minimum of the trace.
156
ZINK AND MIZLJSHIMA
All previously measured transition frequencies and the new ones obtained in the present work are summarized in Table I. A new set of values of the molecular parameters are determined in the least-squares fit to these data. The calculated frequencies are shown in Table I and the values of the molecular parameters are given in Table II. The present work improves the values of B,D, and XDDconsiderably. LMR data were not included in Table I because the zero-field frequencies obtained by extrapolating these data had uncertainties of much more than 1 MHz. They were not included in the least-squares fitting.
TABLE I Calculated and Observed Microwave and Far-Infrared Lines of 1602(X3&, D = 0) N’
Transition .J’+
N
.I
this
33
2
5 7
4 6
1 3 5
2 4 6
9 11
8 10
7 9
13 15 17 1 3
12 14 16 1 3
5 7 9 11 13 15 17
5 7 9 11 13 15 17
19 21 23 25 27 29 31
19 21 23 25 27 29 31
33 35 37 39 41 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
33 35 37 39 41 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
observed work
(GHz) others
Calculated ref.
talc-obs. (kHz) -86. -15.
773.839691(64)
773.839675 1120.715054
8 10
1466.807133(60) 1812.405539(112)
1466.807173 1812.405464
40. -75.
11 13
12 14
2157.577773(52) 2502.323923(92)
2157.577846 2502.323894
77. -29.
15 1 3 5 7 9 11 13 15 17 19 21
16 0 2 4 6 8 10 12 14 16 18 20
23 25 27 29 31
22 24 26 28 30
33 35 37 39
32 34 36 38
41 1 3 5 7 9 11 13 15 17
40 2 4 6 8 10 12 14 16 18
19 21 23 25 27
20 22 24 26 28
29 31 33 35 37 39 41
30 32 34 36 38 40 42
118.750343(10)3 62.486255( 60.306057(20)’ 59.164204(20)’ 58.323874(2O)l
2846.616330 118.750343 62.486260
3
lo)‘,
60.306061 59.164207 58.323877 57.612484
56.968180(20)2 56.363393(20j2 55.783819(20j2 55.221372(2012 54.671145(20j2
52.021423(9)
5
51.503348(18)’ 50.987760(19)5 50.474223(27j5
56.264772(10)‘,’ 58.446600(10)1,3 59.590978(20)1 60.434776(20)’ 61.150570(20)’ 61.800169(20)2 62.411223(20j1 63.568520(20j1 64.127777(2012
65.764744(20)’
67.900867(11)’ 68.431005(17)5 68.960312(12j5 69.489030(
15j5
0. 5. 17. 8. 7.
56.968206 56.363389 55.783802
26. -4. -17.
55.221367 54.671159 54.130000 53.595749
-5. 14.
53.066907 52.542394 52.021410 51.503350 50.987749 50.474238 49.962527 49.452379 56.264775 58.446590 59.590983 60.434776 61.150560 61 .a00154 62.411215 62.997977 63.568518 64.127767 64.670903 65.224071 65.764772 66.302091 66.836830 67.369598 67.900867 68.431005 68.960311 69.489026 70.017346
-13. 2. -11. 15.
3. 10. 5. 0. -10. -15. -8. -2. -10.
28.
0. 0. -1. -4.
FIR TRANSITIONS
157
OF 1602
TABLE II Values of Molecular Parameters for 1602 (X’Z, present
B
ref
work
ifI
5.83O9(61)x1O-5 3.34(146)x10-lo
1.452x10-’
59.501349
59.501346(21)
‘DD
9
43.100461
1.436~10-~
1.4514(78)x10-4
h
ref
5
43.100430
43.1004519(23)
D
, u = 0, in GHz)
5.8305~10-5 3.39x10-10
Y
-0.2525867(21)
-0.2525875
YD
-2.45296(175)x10-’
-2.4544x10-’
YDD
-1.44(30)x10-‘*
PRESSURE-BROADENING
ANALYSIS
In the FIR spectral lines the Doppler and pressure broadenings can be of comparable magnitude for pressures of several hundred pascals. Therefore, the lineshape of the absorption line is a convolution of the Doppler-broadened (Gaussian) and pressurebroadened (Lorentzian) lineshapes. This is described by the Voigt profile
where u. is the resonance frequency and
(3) is the Doppler width. At v. = 2.50 THz and T = 300 K we obtain yn = 3.28 MHz for the O2 molecule. The Lorentzian width yL is expected to be proportional to pressure P: YL
=
w.
(4)
Expression (2) gives a peak intensity which is pressure dependent while the integrated attenuation coefficient is proportional to the pressure. A in Eq. (2) is a constant independent of the pressure. We measure the first derivative da(v)/dv by frequency-modulating FIR radiation. As the typical recorder trace (Fig. 1) shows, the first derivative of a spectral line has a maximum and a minimum. Let the frequency difference between them be 2x. When we calculate x as a function of y&n using (3) we obtain Fig. 2, and we can fit the xmeasurement with the theoretical curve to find yL and yD simultaneously. The theoretical x-curve can be reproduced with sufficient accuracy by X/‘~D
=
0.0390(~L/yD)2
+
0.248(yJyD)
+ 0.593.
(3
By least-squares fitting our measured values of x to this formula, taking yn and a of Eq. (4) as adjustable parameters, we obtain
158
ZINK
AND
MIZUSHIMA
5~~~~~~~ ,_*_* -.-._._. -._._.-.* ._.-*-.-l-.-.-.-*-.-.-.
L
P
1
5
torr
FIG. 2. The theoretical curve of x against pressure and experimental values fitted by adjusting y. and the pressure-broadening parameter a.
yD = 3.13 f 0.50 MHz
(6a)
a = (0.74 _+0.13)~~ = 17.4 +-3.6 kHz/Pa (=2.32 + 0.48 MHz/Tot-r)
(6b) and Fig. 2 shows the fit. The value obtained in (6a) agrees with 3.28 MHz, the value calculated using Eq. (2) with T = 300 K, showing the validity of our theoretical interpretation. If we take the theoretical value of yn, namely, 3.28 MHz, we obtain a = 18.2 + 3.2 kHz/Pa (=2.43 f 0.43 MHz/Tot-r).
(7)
Liebe (12) measured the pressure-broadening parameter a of the 60-GHz lines of this molecule and obtained about 12.4 kHz/Pa (1.65 MHz/Ton-). Pickett and others (13, 14) measured u for 119- and 425-GHz lines and obtained 14.9 f .5 kHz/Pa (1.98 + 0.07 MHz/Tot-r) and 12.1 & 1.2 kHz/Pa (1.6 1 + 0.16 MHz/Ton), respectively. These values are not far from our present result given in Eq. (6b). ACKNOWLEDGMENTS We thank Dm. Kenneth Evenson and Donald Jennings for their advice and help in completing this work. RECEIVED:
January 12, 1987 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13. 14.
R. W. ZIMMERERAND M. MIZUSHIMA,Phys. Rev. 121, 152-155 (1961). B. G. WEST AND M. MIZUSHIMA,Phys. Rev. 143,31-32 (1966). J. S. M&NIGHT AND W. GORDY, Phys. Rev. Left. 21, 1787-1789 (1968). W. STEIBACHAND W. GORDY, Phys. Rev. A 8, 1753-1758 (1973). Y. ENLX AND M. MIZUSHIMA,Japan, J. Appl. Phys. 21, L379-L380 (1982). K. M. EVENSON,H. P. BROIDA,J. S. WELLS, R. J. MAHLER, AND M. MIZUSHIMA,Phys. Rev. Left. 21, 1038-1040 (1968). M. MIZUSHIMA, J. S. WELLS, K. M. EVENSON,AND W. M. WELCH, Phys. Rev. Lett. 29, 831-833 ( 1972). K. M. EVENSONAND M. MIZUSHIMA,Phys. Rev. A 6,2 197-2204 ( 1972). L. TOMUTA, M. MIZUSHIMA,C. J. HOWARD, AND K. M. EVENSON,Phys. Rev. A 12,974-979 (1975). K. M. EVENSON,D. M. JENNINGS? AND F. R. PETERSON,Appl. Phys. Lett. 44,576-578 (1984). K. M. EVENSON,D. A. JENNINGS,K. R. LEOPOLD,AND L. R. ZINK, in “Laser Spectroscopy VII” (T. D. Hansch and Y. R. Shen, Ed%), pp. 366-370, Springer-Verlag, Berlin 1985. H. J. LIEBE,IEEE Trans. Microwave Theory Tech. MlT-23, 380-386 (1975). B. J. SETZERAND H. M. PICKETT,J. Chem. Phys. 67,340-343 (1977). H. M. PICKETT,E. A. COHEN, AND D. E. BRINZA, Astrophys. J. 248, L49-L51 (1981).
125, 154-158 (1987)
Pure Rotational Far-Infrared Transitions of 1602 in Its Electronic and Vibrational Ground State* LYNDON R. ZINK Department of Physics. Universityof Colorado,Boulder, Colorado 80309, and NationalBureau of Standards, Boulder, Colorado 80303
AND MASATAKA MIZUSHIMA Department of Physics, Universityof Colorado, Boulder, Colorado80309
Five lines in the far-infraredregion,due to N + 2 + N (AJ = 0) transitionsof the 160zmolecule in its (X32;, u = 0) state, are measured at 773.839691, 1466.807133, 1812.405539,2157.577773, and 2502.323923 GHz, using a tunable PTR spectrometer. The spectral lineshape of the 2.50THz line is analyzed and the pressure self-broadening parameter of 18.2(32) kHz/Pa (=2.43(43) MHz/Torr) is obtained. Q 1987 Academic Press.hc. INTRODUCTION
Since the electronic ground state, X3&, of the oxygen molecule O2 has the spin quantum number S = 1, each rotational level with given quantum number N is a triplet: J = N, N f 1, where J = N + S is the total angular momentum. The spinflip transitions, AN = 0, AJ = -t 1, are observed in the microwave region near 60 GHz (I-5). The magnetic dipole rotational transitions N + 2 * N are in the far-infrared (FIR) region. The laser magnetic resonance (LMR) technique has been applied to observe the N = 5 + 3 (6, 7), 15 + 13 (8), 17 + 15 (P), 21 + 19 (P), and 23 + 21 (8) transitions, but these observations were indirect in that the molecule had to be under external magnetic fields to produce resonances with given laser lines. Direct measurements of these transitions except for the lowest one have not been possible until now simply because no appropriate tunable radiation source was available. A new tunable far-infrared (FIR) source was developed by Evenson and others (IO, II) that mixes two COz laser lines using the metal-insulator-metal (MIM) diode as a nonlinear device. We measured five rotational lines of the r602 molecule in its (X3& 21= 0) state up to 2.502 THz (N = 15 + 13). The spectral lineshapes of these FIR lines are given by the Voigt profile, a superposition of Doppler and Lorentzian lineshapes. The lineshape of the 2.502-THz line is analyzed to extract the pressure self-broadening parameter in the linewidth of the Lorentzian lineshape. * This is a contribution of the National Bureau of Standards and is not subject to copyright. Work supported in part by NASA under Contract W 1S-042. 0022-2852187 $3.00 Copyright8 1987 by Academic R-s, Inc. All rightsof reproductionin any form reserved.
154
FIR TRANSITIONS
155
OF 160z
EXPERIMENTAL
The tunable FIR spectrometer is described in detail elsewhere (IO, II). Briefly, tunable cw FIR radiation is generated by nonlinear mixing of radiation from two CO* lasers in a MIM diode. The radiation is tuned by varying the output of one of the lasers over its pressure-broadened gain profile. The FIR radiation is emitted from the diode with a long-wire antenna and collected with a section of a parabolic mirror. This mirror reflects a collimated beam through an absorption cell. After passing through the cell, the radiation is detected by a liquid He-cooled Ge bolometer. The transitions were observed in a 3.6-m-long, single-pass cell, which was cooled with a flowing dry ice bath to about 200 K. The lower temperature improved the signal strength for the N = 5 + 3 transition by a factor of 3. Zeeman broadening of the signal by the earth’s magnetic field was observed, so the cell was shielded from the earth’s magnetic field with a steel trough. This shielding reduced the linewidth, which improved our signal-to-noise ratio and hence the accuracy of our measurements. Figure 1 shows a trace of the N = 15 + 13 transition taken with a 400-msec time constant. O2 pressure used in the frequency measurements ranged from 67 to 133 Pa. Pressure-broadening measurements were performed on the 2.5-THz line. The dry ice bath gave no significant increase in signal strength for this transition, so to simplify the experiment the broadening studies were performed at room temperature. Pressure ranged from 13 to 733 Pa for 02 self-broadening. Decreasing signal strength prevented measurements at higher pressures. TRANSITION
The Hamiltonian
FREQUENCIES
AND MOLECULAR
of the rotational states of 3L:molecules is given by (7)
Ej= Bfi’ - Dni4 + 3 {X(39: - s2) + X,(fi2(3$ + hm,(fi4(3$
PARAMETERS
- 3’) + (33: - s2)fi2)/2
- s2) + (3s: - g2)fi4)/2 I+ yN . S + y&‘N.
S + y,,#N
*S,
( 1)
where N and S are the rotational and spin angular momenta, and the subscript r indicates their components along the molecular axis.
FIG. 1. The recorder trace of N = 15 + 13, J = 14 t- 14 transitions of Oz. The total scan width was 65 MHz, the pressure was 67 Pa, and the cell was cooled to 200 K. Since we frequency modulate the signal, we are recording da/du against Y the frequency. We define 2x as the frequency difference between the maximum and minimum of the trace.
156
ZINK AND MIZLJSHIMA
All previously measured transition frequencies and the new ones obtained in the present work are summarized in Table I. A new set of values of the molecular parameters are determined in the least-squares fit to these data. The calculated frequencies are shown in Table I and the values of the molecular parameters are given in Table II. The present work improves the values of B,D, and XDDconsiderably. LMR data were not included in Table I because the zero-field frequencies obtained by extrapolating these data had uncertainties of much more than 1 MHz. They were not included in the least-squares fitting.
TABLE I Calculated and Observed Microwave and Far-Infrared Lines of 1602(X3&, D = 0) N’
Transition .J’+
N
.I
this
33
2
5 7
4 6
1 3 5
2 4 6
9 11
8 10
7 9
13 15 17 1 3
12 14 16 1 3
5 7 9 11 13 15 17
5 7 9 11 13 15 17
19 21 23 25 27 29 31
19 21 23 25 27 29 31
33 35 37 39 41 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
33 35 37 39 41 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41
observed work
(GHz) others
Calculated ref.
talc-obs. (kHz) -86. -15.
773.839691(64)
773.839675 1120.715054
8 10
1466.807133(60) 1812.405539(112)
1466.807173 1812.405464
40. -75.
11 13
12 14
2157.577773(52) 2502.323923(92)
2157.577846 2502.323894
77. -29.
15 1 3 5 7 9 11 13 15 17 19 21
16 0 2 4 6 8 10 12 14 16 18 20
23 25 27 29 31
22 24 26 28 30
33 35 37 39
32 34 36 38
41 1 3 5 7 9 11 13 15 17
40 2 4 6 8 10 12 14 16 18
19 21 23 25 27
20 22 24 26 28
29 31 33 35 37 39 41
30 32 34 36 38 40 42
118.750343(10)3 62.486255( 60.306057(20)’ 59.164204(20)’ 58.323874(2O)l
2846.616330 118.750343 62.486260
3
lo)‘,
60.306061 59.164207 58.323877 57.612484
56.968180(20)2 56.363393(20j2 55.783819(20j2 55.221372(2012 54.671145(20j2
52.021423(9)
5
51.503348(18)’ 50.987760(19)5 50.474223(27j5
56.264772(10)‘,’ 58.446600(10)1,3 59.590978(20)1 60.434776(20)’ 61.150570(20)’ 61.800169(20)2 62.411223(20j1 63.568520(20j1 64.127777(2012
65.764744(20)’
67.900867(11)’ 68.431005(17)5 68.960312(12j5 69.489030(
15j5
0. 5. 17. 8. 7.
56.968206 56.363389 55.783802
26. -4. -17.
55.221367 54.671159 54.130000 53.595749
-5. 14.
53.066907 52.542394 52.021410 51.503350 50.987749 50.474238 49.962527 49.452379 56.264775 58.446590 59.590983 60.434776 61.150560 61 .a00154 62.411215 62.997977 63.568518 64.127767 64.670903 65.224071 65.764772 66.302091 66.836830 67.369598 67.900867 68.431005 68.960311 69.489026 70.017346
-13. 2. -11. 15.
3. 10. 5. 0. -10. -15. -8. -2. -10.
28.
0. 0. -1. -4.
FIR TRANSITIONS
157
OF 1602
TABLE II Values of Molecular Parameters for 1602 (X’Z, present
B
ref
work
ifI
5.83O9(61)x1O-5 3.34(146)x10-lo
1.452x10-’
59.501349
59.501346(21)
‘DD
9
43.100461
1.436~10-~
1.4514(78)x10-4
h
ref
5
43.100430
43.1004519(23)
D
, u = 0, in GHz)
5.8305~10-5 3.39x10-10
Y
-0.2525867(21)
-0.2525875
YD
-2.45296(175)x10-’
-2.4544x10-’
YDD
-1.44(30)x10-‘*
PRESSURE-BROADENING
ANALYSIS
In the FIR spectral lines the Doppler and pressure broadenings can be of comparable magnitude for pressures of several hundred pascals. Therefore, the lineshape of the absorption line is a convolution of the Doppler-broadened (Gaussian) and pressurebroadened (Lorentzian) lineshapes. This is described by the Voigt profile
where u. is the resonance frequency and
(3) is the Doppler width. At v. = 2.50 THz and T = 300 K we obtain yn = 3.28 MHz for the O2 molecule. The Lorentzian width yL is expected to be proportional to pressure P: YL
=
w.
(4)
Expression (2) gives a peak intensity which is pressure dependent while the integrated attenuation coefficient is proportional to the pressure. A in Eq. (2) is a constant independent of the pressure. We measure the first derivative da(v)/dv by frequency-modulating FIR radiation. As the typical recorder trace (Fig. 1) shows, the first derivative of a spectral line has a maximum and a minimum. Let the frequency difference between them be 2x. When we calculate x as a function of y&n using (3) we obtain Fig. 2, and we can fit the xmeasurement with the theoretical curve to find yL and yD simultaneously. The theoretical x-curve can be reproduced with sufficient accuracy by X/‘~D
=
0.0390(~L/yD)2
+
0.248(yJyD)
+ 0.593.
(3
By least-squares fitting our measured values of x to this formula, taking yn and a of Eq. (4) as adjustable parameters, we obtain
158
ZINK
AND
MIZUSHIMA
5~~~~~~~ ,_*_* -.-._._. -._._.-.* ._.-*-.-l-.-.-.-*-.-.-.
L
P
1
5
torr
FIG. 2. The theoretical curve of x against pressure and experimental values fitted by adjusting y. and the pressure-broadening parameter a.
yD = 3.13 f 0.50 MHz
(6a)
a = (0.74 _+0.13)~~ = 17.4 +-3.6 kHz/Pa (=2.32 + 0.48 MHz/Tot-r)
(6b) and Fig. 2 shows the fit. The value obtained in (6a) agrees with 3.28 MHz, the value calculated using Eq. (2) with T = 300 K, showing the validity of our theoretical interpretation. If we take the theoretical value of yn, namely, 3.28 MHz, we obtain a = 18.2 + 3.2 kHz/Pa (=2.43 f 0.43 MHz/Tot-r).
(7)
Liebe (12) measured the pressure-broadening parameter a of the 60-GHz lines of this molecule and obtained about 12.4 kHz/Pa (1.65 MHz/Ton-). Pickett and others (13, 14) measured u for 119- and 425-GHz lines and obtained 14.9 f .5 kHz/Pa (1.98 + 0.07 MHz/Tot-r) and 12.1 & 1.2 kHz/Pa (1.6 1 + 0.16 MHz/Ton), respectively. These values are not far from our present result given in Eq. (6b). ACKNOWLEDGMENTS We thank Dm. Kenneth Evenson and Donald Jennings for their advice and help in completing this work. RECEIVED:
January 12, 1987 REFERENCES
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. II. 12. 13. 14.
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