Sub-Doppler spectroscopy of the C—O stretching fundamental band of methanol by use of microwave sidebands of CO2 laser lines

2068 J. Opt. Soc. Am. B/Vol. 17, No. 12 /December 2000 Sun et al.

Sub-Doppler spectroscopy of the C—O stretchingfundamental band of methanol by use

of microwave sidebands of CO2 laser lines

Zhen-Dong Sun, Fusakazu Matsushima, Shozo Tsunekawa, and Kojiro Takagi

Department of Physics, Toyama University, Toyama 930-8555, Japan

Received May 2, 2000; revised manuscript received August 15, 2000

Microwave sidebands of CO2 laser lines were used in a sub-Doppler spectrometer to observe sub-Doppler spec-trum of the C—O stretching fundamental band (vCO 5 1 ← 0) of methanol. Frequencies of more than 200vibration-rotation lines were measured with an accuracy of better than 0.20 MHz. Sixty-one blended spectrallines in the Fourier-transform spectrum were resolved with a resolution of 0.2 MHz. For transitions involvingA-species levels with K 5 2, 3, and 4 in the vt 5 0 state and K 5 2 in the vt 5 1 state, 64 doublet lines arisingfrom asymmetry splittings were observed. From these observed asymmetry splittings and calculated ground-state splittings the asymmetry splittings and asymmetry-splitting constants for the vCO 5 1 state were deter-mined. The R- and Q-branch transitions for the (vt , E, K) 5 (1, E, 2) and (1, E, 5) sequences were assignedby observation of their Stark effects and by use of the Ritz’s combination principle. Term values of the levelsin the vCO 5 1 state for these two sequences were given, and their Taylor-series expansion coefficients weredetermined. © 2000 Optical Society of America [S0740-3224(00)00512-9]

OCIS codes: 300.6390, 300.6340, 300.6360, 300.6320, 300.6190, 300.6460.

1. INTRODUCTIONMicrowave modulation sidebands of CO2 laser lines (here-after called CO2 laser sidebands) are infrared sources ofgood tunability, high power, high spectral purity, andhigh frequency accuracy in the 9–11-mm wavelengthregion.1 By using these sources, we observed more than50 infrared–microwave double-resonance signals of themethanol molecule with large signal-to-noise ratios, de-termined their rotational transition frequencies with aprecision of 10 kHz, and studied the pressure dependenceof the double-resonance signals.1 As the second applica-tion of the CO2 laser sidebands, the sub-Doppler spectrumof the C—O stretching fundamental band of methanol isstudied in the present paper.

The methanol molecule is one of the simplestasymmetric-top molecules with hindered internalrotation.2 Its rotational and vibration-rotational spectraare complicated by the internal rotation,2,3 and its analy-sis is of fundamental importance in quantum chemistry.The C—O stretching fundamental band has been exten-sively studied by infrared Fourier-transform (FT) spec-troscopy by Moruzzi et al.4,5 This band is important inpractical application for far-infrared laser lines pumpedby transitions in this band.6,7 In the FT spectrum of thisband, where spectral resolution is limited by the Dopplerwidth of 60 MHz (FWHM) and where frequency accuracyis several megahertz,1,5,8 there are still many blended fea-tures, unresolved asymmetry doublet lines,5,9 and uniden-tified lines, as is shown below.

The sub-Doppler spectroscopy with CO2 laser side-bands as infrared sources has been successfully applied toobserve hyperfine structures10 of NH3, A1A2 splittings11

of PH3, and the Stark effects of nonpolar molecules.12,13

In the present study we applied this technique to study

0740-3224/2000/122068-13$15.00 ©

the C—O stretching fundamental band of methanol.Frequencies of vibration-rotation lines were measuredwith an accuracy of better than 0.20 MHz. Sixty-oneblended lines in the infrared FT spectrum were resolvedwith a resolution of 0.2 MHz. Asymmetry splittings ofthe A-species levels with K 5 2, 3, and 4 for the vt 5 0state and K 5 2 for the vt 5 1 state were observed, andasymmetry-splitting constants S and T in the vCO 5 1state were determined.

We noted that the assignments of R- and P-branchlines for the (1, E, 2) sequence in the vCO 5 1 ← 0 bandreported by Lees et al.14 do not agree with those given inRef. 5. Also, the transitions for the (1, E, 5) sequence inthis band have been reported only for R(6), Q(7), andP(8).5,15 In the present study, transitions involvingthese two sequences were studied to obtain definite as-signments and precise term values for various J values.As a result, fourteen transitions for the (1, E, 2) se-quence, which are consistent with the results of Ref. 14,and nine transitions for the (1, E, 5) sequence were iden-tified by observation of their Stark effects and by use ofthe Ritz’s combination principle.

2. EXPERIMENTAL DETAILSOur experimental setup is shown in Fig. 1. The micro-wave sidebands of CO2 laser lines generated in awaveguide-type modulator16 has already been described.1

The infrared beam of 10–15 W from the main CO2 laser(Edinburgh PL3) and microwave power of ;20 W in the7–18-GHz frequency range are fed to the modulator. Theoutput beam of the modulator consisting of a carrier andtwo sidebands is filtered by a Fabry–Perot interferometerto select a desired sideband.

2000 Optical Society of America

Sun et al. Vol. 17, No. 12 /December 2000 /J. Opt. Soc. Am. B 2069

Fig. 1. Experimental setup of the sub-Doppler spectrometer with CO2 laser sidebands. B.S.1–B.S.5, beam splitters; L1–L3, ZnSelenses; M1–M9, mirrors; TWTAmp., traveling-wave tube amplifier; F.P., Fabry–Perot interferometer; PSD, phase-sensitive detector.

A reference CO2 laser, of the same design as the CO2lasers used in our tunable far-infrared spectrometer,17

was used to check the frequency accuracy of the main CO2laser. Frequency of the reference CO2 laser was stabi-lized to a Lamb dip in a 4.3-mm fluorescence signal in anexternal CO2 cell, where absolute frequency uncertaintyis less than 35 kHz. The frequency accuracy of the mainlaser, which can be locked to its maximum gain, is a fewmegahertz. In the present experiment we achieved anabsolute frequency accuracy of 0.1 MHz by the followingmethod. The main laser was operated in a free-runningstate without any stabilization feedback. The beat notebetween the main and the reference lasers produced on aHgCdTe photoconductive detector (VIGO R500-1) wasmonitored by a spectrum analyzer. Because the main la-ser had a frequency stability of 0.1 MHz or better for sev-eral minutes in a free-running state, we manually tunedthe frequency of the main laser to that of the reference la-ser before measuring the frequency of a spectral line andkept monitoring the beat note during the measurement tomake sure that the laser frequency did not change.

A multiple-reflection cell with Stark electrodes18 wasused to observe absorption lines and their Stark effects.A pair of Stark plates and three mirrors with a radius ofcurvature of 1.38 m and a diameter of 10 mm are con-tained in a Pyrex tube 1.5 m in length and 10 cm in di-ameter. The Stark electrodes, made of aluminum plates1.2 m in length, were separated by eight quartz spacers of8-mm nominal thickness, and the plate spacing was cali-brated to be 8.0067 6 0.0020 mm by observation of thelevel crossing signals A, B, C, and D in the n2 band19 ofCD3I and by use of the level crossing fields observed inour laboratory.20 A dc voltage for the Stark effect and asine-wave voltage at 30 kHz for Stark modulation were

applied to one of the plates. We also used square-waveStark modulation as is used in a conventional microwavespectrometer to determine the zero-field frequencies oftransitions and to observe their Stark effects.

The laser beam makes four round trips (eight traversalin total) in the cell. The mirror M4 was adjusted so thatthe reflected beam was collinear with the incident beam.The direction of the polarization of the reflected beam wasmade perpendicular to that of the incident beam by aFresnel rhomb after it came out of the cell; thus the in-terference of two beams could be reduced.18 However, atthe latter stage of our experiment, the Fresnel rhomb wasremoved because the disturbance from the reflected beamto the main laser was not observed. The sideband beam,which passed through the sample cell and returned to thebeam splitter B.S.5, was then detected by a HgCdTe de-tector and processed by a phase-sensitive detector to yieldinverse Lamb-dip signals. The pressure of methanol inthe absorption cell was typically ;5 mTorr, which wasmeasured with a Pirani gauge calibrated by an oil ma-nometer. The polarization of the sideband laser beamwas parallel to the Stark field, and the Stark patternsshown in this paper (Figs. 2–5, 8, and 9) were observedunder the selection rule of DM 5 0.

3. EXPERIMENTAL RESULTS ANDANALYSESA. General Observation

1. Comparison of Lamb-Dip Spectrum and Fourier-Transform SpectrumFigure 2 shows a comparison of the spectrum in the0.1-cm21 range (1032.988–1033.088 cm21) observed by


use of our sub-Doppler spectrometer [Fig. 2(b)] with thatobserved by use of a FT spectrometer shown in Ref. 5 [Fig.2(a)]. In Fig. 2(b), broad features are Doppler-broadenedlines, and sharp features are inverse Lamb dips. All theassigned lines in Ref. 5 were observed as inverse Lambdips, designated by 1–22. Besides these lines, 18 uniden-tified sharp features, including fairly strong features,were observed and designated by U. In this and otherobservations, some of the weakest assigned lines in Ref. 5were observed with good signal-to-noise ratios as inverseLamb dips by use of our spectrometer.

2. Assignment of Transition by Observation of the StarkEffectFigure 3 shows the observed Lamb-dip signals of the tran-sition (vt A/E K, J)vCO 5 (0 E 2, 3)1 ← (0 E 2, 2)0 by useof square-wave Stark modulation at various sample pres-sures with a lower sideband of the 9P(28) CO2 laser line.The signals above and below the baselines show zero-fieldsignals and Stark patterns at an electric field of 50 V/cm.The signals look similar to typical signals observed with aconventional Stark-modulation microwave spectrometer21

and are easily identified as arising from a transition ofJ, K 5 3, 2 ↔ 2, 2. The inner and outer Stark compo-

nents are those with uMu 5 1 and 2, respectively. A spec-tral width (FWHM) of ;0.3 MHz at a pressure of 4 mTorrcomes from the saturation broadening of the infraredtransition. The spectral line is strongest at a pressure of10 mTorr, when saturation broadening is comparablewith pressure broadening, and becomes broader andweaker at higher pressure, when pressure broadening be-comes dominant.

Figure 4 shows Lamb-dip signals observed with a sine-wave Stark-modulation method for a blended feature inthe FT spectrum at a wave number of 1033.25934 cm21

assigned to the transitions of (0 E 23, 4)1 ← (0 E23, 4)0 and (0 A 2, 4)1 ← (0 A 21, 4)0 in Ref. 5. Two re-solved lines a and b were observed at 1033.259010 and1033.259232 cm21, respectively, for a small dc Stark volt-age (Fig. 4, curve I). For the dc Stark voltage of 30 V(Fig. 4, curve II), line a shows splittings owing to thesecond-order Stark effect, whereas line b does not split be-cause its Stark effect is smaller (for higher voltages thisline also splits). Thus we can assign lines a and b totransitions of (0 A 22, 4)1 ← (0 A 21, 4)0 and(0 E 23, 4)1 ← (0 E 23, 4)0, respectively. In the follow-ing study we made full use of the Stark effect to assignobserved transitions.

Fig. 2. (a) Fourier-transform (FT) spectrum from 1032.988 to 1033.088 cm21 (Ref. 5) and (b) the sub-Doppler spectrum obtained by themicrowave (15–12-GHz) lower sideband of the 9P(34) CO2 laser line with square-wave Stark-modulation voltage of 40 V (present study).The numbers 1–22 designate assigned lines, and the symbol U designates unidentified lines in the FT spectrum.


3. Resolution and Frequency Accuracy of the PresentMeasurementFigure 5 shows two resolved lines a and b separatedby 0.4 MHz in frequency, where lines a and bare (0 A 42, 11)1 ← (0 A 42, 10)0 and (0 A 41, 11)1

← (0 A 41, 10)0, respectively. We can reduce the line-

Fig. 3. Stark patterns of the Lamb-dip signal for the transition(0 E 2, 3)1 ← (0 E 2, 2)0 for a lower sideband of the 9P(28) CO2laser line with a power of ;2 mW. The methanol pressures are(a) 4, (b) 10, and (c) 20 mTorr. The signals above and below thebaselines are zero-field signals and Stark patterns, respectively.The square-wave modulation voltage was 40 V, and the PSDtime constant was 1 s.

width to ;0.2 MHz (FWHM) by reducing the pressureand input laser power without a serious decrease of sen-sitivity. So we can resolve two lines separated by 0.2MHz without special efforts.

The frequency accuracy of the main laser, as is men-tioned in Section 2, is 0.1 MHz. The reading error for thecenter frequency of the spectral line is 0.05 MHz for an

Fig. 4. Stark patterns of two Lamb-dip signals (a) and (b) for ablended line at 1033.25934 cm21 in the FT spectrum.5 Thelower sideband of the 9P(34) CO2 laser line was used. Themethanol pressure was 8 mTorr; the PSD time constant was 1 s;the Stark-modulation voltage was 5Vpp ; and the dc Stark biaseswere (I) 6 V and (II) 30 V.

Fig. 5. Inverse Lamb dips a and b of the (0 A46, 11)1

← (0 A 46, 10)0 transitions observed with the upper sideband ofthe 9P(16) CO2 laser line. The square-wave modulation voltagewas 40 V, and the PSD time constant was 1 s. The methanolpressure was 2 mTorr.


E-species line when Stark shifts are symmetric to thezero-field line centers, and it is 0.1 MHz or worse for someA-species lines when Stark shifts are asymmetric to their

line centers. Therefore the frequency accuracy of thepresent measurement is estimated to be 0.20 MHz.

For some observed lines, frequency accuracies were

Fig. 6. Energy-level diagrams of methanol for (a) two observed infrared transitions and (b) four observed infrared transitions in thesub-Doppler spectroscopy. The measured wave numbers (cm21) are na 5 1033.927609, nb 5 1025.858555, nc 5 1050.771935, nd5 1050.772827, ne 5 1033.028845, and n f 5 1033.032638. The microwave transition frequencies of nmw , n1 , and n2 (in MHz), are241 904.152, 531 892.839, and 531 869.162, respectively.

Table 1. Observed Infrared Transitions of Methanol

TransitionCO2 Laser

Sideband (MHz)nobs

a

(cm21)nobs

FT b

(cm21)npred

c

(cm21)nobs 2 npred

(MHz)

(0 A 32, 16)1 ← (0 A 32, 15)0 9P(8) 18040.04 1057.568348 1057.56849 1057.56849 24.3(0 A 31, 16)1 ← (0 A 31, 15)0 17857.67 1057.562265 1057.56237 1057.56250 27.0

(1 E 4, 16)1 ← (1 E 4, 15)0 17520.47 1057.551017 1057.55117 1057.55128 27.9(0 A 32, 15)1 ← (0 A 32, 14)0 9P(10) 118 623.79 1056.246291 1056.24635 1056.24636 22.1(0 A 31, 15)1 ← (0 A 31, 14)0 118 492.21 1056.241902 1056.24205 1056.24209 25.6

(0 E 210, 15)1 ← (0 E 210, 14)0 117 095.84 1056.195324 1056.19539 1056.19546 24.1(0 A 9, 15)1 ← (0 A 9, 14)0 111 261.53 1056.000712 1056.00090 1056.00062 2.8

(0 A 41, 14)1 ← (0 A 41, 13)0 215 977.86 1055.092104 1055.09200 1055.09203 2.2(0 A 42, 14)1 ← (0 A 42, 13)0 215 980.14 1055.092028 1055.09200 1055.09203 20.1(0 A 21, 14)1 ← (0 A 21, 13)0 9P(12) 18542.63 1054.208454 1054.20856 1054.20854 22.6(0 A 22, 14)1 ← (0 A 22, 13)0 17231.87 1054.164732 1054.16473 1054.16479 21.7(1 A 22, 13)1 ← (1 A 22, 12)0 28748.22 1053.631694 1053.63199 1053.63193 27.1(1 A 21, 13)1 ← (1 A 21, 12)0 28799.58 1053.629980 1053.63048 1053.63035 211.0(0 A 32, 13)1 ← (0 A 32, 12)0 211 301.75 1053.546517 1053.54741 1053.54709 217.2(0 A 31, 13)1 ← (0 A 31, 12)0 211 365.17 1053.544402 1053.54371 1053.54390 15.0

(0 E 23, 13)1 ← (0 E 23, 12)0 9P(14) 117 733.50 1052.787071 1052.78716 1052.78720 23.9(0 A 8, 12)1 ← (0 A 8, 11)0 111 270.61 1052.571492 1052.57166 1052.57144 1.6

(1 E 26, 12)1 ← (1 E 26, 11)0 211 123.22 1051.824514 1051.82468 1051.82471 25.9(0 A 11, 12)1 ← (0 A 11, 11)0 9P(14) 216 018.63 1051.661221 1051.66125 1051.66138 24.8(0 A 41, 11)1 ← (0 A 41, 10)0 9P(16) 115 986.80 1050.974544 1050.97460 1050.97454 0.1(0 A 42, 11)1 ← (0 A 42, 10)0 115 986.40 1050.974531 1050.97460 1050.97454 20.3

(0 E 2, 11)1 ← (0 E 2, 10)0 113 338.51 1050.886207 1050.88551 1050.88590 9.2(0 E 3, 11)1 ← (0 E 3, 10)0 111 876.85 1050.837451 1050.83755 1050.83758 23.9

(0 A 32, 11)1 ← (0 A 32, 10)0 19939.47 1050.772827 1050.77225 1050.77287 21.3(0 A 31, 11)1 ← (0 A 31, 10)0 19912.72 1050.771935 1050.77360 1050.77362 250.5

(0 E 1, 11)1 ← (0 E 1, 10)0 29175.21 1050.135230 1050.13531 1050.13532 22.7(0 E 22, 10)1 ← (0 E 22, 9)0 9P(18) 118 288.04 1049.270833 1049.27090 1049.27098 24.4

(0 A 12, 10)1 ← (0 A 12, 9)0 116 762.62 1049.219950 1049.22007 1049.22007 23.6(Table continued)


Table 1. Continued

TransitionCO2 Laser

Sideband (MHz)nobs

a

(cm21)nobs

FT b

(cm21)npred

c

(cm21)nobs 2 npred

(MHz)

(0 A 6, 10)1 ← (0 A 6, 9)0 114 300.25 1049.137814 1049.13796 1049.13799 25.3(0 A 11, 10)1 ← (0 A 11, 9)0 16849.21 1048.889274 1048.88924 1048.88939 23.5

(2 A 4, 8)1 ← (2 A 4, 7)0 211 406.03 1048.280346 1048.28055 1048.28052 25.2(2 E 22, 8)1 ← (2 E 22, 7)0 211 414.22 1048.280072 1048.28055 1048.28072 219.4

(1 E 24, 10)1 ← (1 E 24, 9)0 215 214.39 1048.153312 1048.15349 1048.15345 24.1(1 A 22, 9)1 ← (1 A 22, 8)0 216 548.48 1048.108812 1048.10938 1048.10933 215.5(1 A 21, 9)1 ← (1 A 21, 8)0 216 566.77 1048.108202 1048.10865 1048.10839 25.6(1 A 12, 9)1 ← (1 A 12, 8)0 9P(20) 19966.89 1047.186694 1047.18683 1047.18695 27.7(0 A 21, 9)1 ← (0 A 21, 8)0 19709.68 1047.178114 1047.17806 1047.17814 20.8(1 A 11, 9)1 ← (1 A 11, 8)0 19701.05 1047.177826 1047.17806 1047.17820 211.2(1 E 3, 11)1 ← (1 E 3, 10)0 19676.81 1047.177018 1047.17806 1047.17716 24.3(0 A 22, 9)1 ← (0 A 22, 8)0 19382.61 1047.167204 1047.16728 1047.16715 1.6

(0 E 2, 8)1 ← (0 E 2, 7)0 9P(20) 28337.72 1046.576118 1046.57627 1046.57626 24.2(0 A 32, 8)1 ← (0 A 32, 7)0 211 382.90 1046.474541 1046.47446 1046.47457 20.9(0 A 31, 8)1 ← (0 A 31, 7)0 211 388.08 1046.474369 1046.47446 1046.47457 26.0(0 A 12, 8)1 ← (0 A 12, 7)0 216 596.09 1046.300648 1046.30078 1046.30075 23.0

(0 E 6, 7)1 ← (0 E 6, 6)0 9P(22) 19877.73 1045.351155 1045.35129 1045.35135 25.8(1 E 23, 7)1 ← (1 E 23, 6)0 17141.36 1045.259879 1045.26006 1045.26012 27.2

(0 A 11, 7)1 ← (0 A 11, 6)0 212 935.23 1044.590197 1044.59025 1044.59029 22.8(1 E 28, 10)1 ← (1 E 28, 9)0 212 960.34 1044.589359 1044.59025 1044.58987 226.7

(1 A 22, 6)1 ← (1 A 22, 5)0 9P(24) 117 778.63 1043.756270 1043.75631 1043.75632 21.5(1 A 21, 6)1 ← (1 A 21, 5)0 117 773.04 1043.756084 1043.75631 1043.75632 27.1

(0 E 21, 6)1 ← (0 E 21, 5)0 115 102.71 1043.667011 1043.66716 1043.66714 23.9(0 E 2, 6)1 ← (0 E 2, 5)0 113 488.60 1043.613170 1043.61251 1043.61308 2.7(0 E 3, 6)1 ← (0 E 3, 5)0 112 656.95 1043.585429 1043.58557 1043.58564 26.3

(0 A 32, 6)1 ← (0 A 32, 5)0 110 628.95 1043.517783 1043.51784 1043.51778 0.1(0 A 31, 6)1 ← (0 A 31, 5)0 110 627.95 1043.517749 1043.51784 1043.51778 20.9(0 A 21, 6)1 ← (0 A 21, 5)0 212 323.34 1042.752177 1042.75230 1042.75241 27.0(0 A 22, 6)1 ← (0 A 22, 5)0 212 414.67 1042.749130 1042.74934 1042.74955 212.6

(0 E 23, 6)1 ← (0 E 23, 5)0 212 515.45 1042.745768 1042.74595 1042.74573 1.1(0 A 12, 5)1 ← (0 A 12, 4)0 9P(26) 115 190.32 1041.785769 1041.78590 1041.78584 22.1(0 A 11, 5)1 ← (0 A 11, 4)0 110 542.14 1041.630722 1041.63079 1041.63056 4.9

(1 E 25, 8)1 ← (1 E 25, 7)0 110 503.95 1041.629448 1041.63079 1041.62953 22.5(2 E 1, 2)1 ← (2 E 1, 1)0 29170.96 1040.973164 1040.97358 1040.97274 12.7(1 A 4, 8)1 ← (1 A 4, 7)0 9P(28) 117 593.43 1039.956168 1039.95637 1039.95634 25.2(1 E 3, 6)1 ← (1 E 3, 5)0 113 936.55 1039.834188 1039.83434 1039.83437 25.5(0 E 1, 4)1 ← (0 E 1, 3)0 113 398.07 1039.816226 1039.81634 1039.81623 20.1

(1 A 12, 4)1 ← (1 A 12, 3)0 112 994.78 1039.802774 1039.80293 1039.80324 214.0(1 A 11, 4)1 ← (1 A 11, 3)0 112 744.82 1039.794436 1039.79458 1039.79447 21.0(0 A 21, 4)1 ← (0 A 21, 3)0 110 364.93 1039.715051 1039.71451 1039.71452 15.9(0 A 22, 4)1 ← (0 A 22, 3)0 110 339.67 1039.714209 1039.71451 1039.71484 218.9

(0 E 23, 4)1 ← (0 E 23, 3)0 110 313.40 1039.713333 1039.71348 1039.71329 1.3(1 E 21, 11)1 ← (1 E 21, 10)0 16637.14 1039.590706 1039.59088 1039.59102 29.4

(1 E 1, 3)1 ← (1 E 1, 2)0 27971.09 1039.103428 1039.10281 1039.10352 22.8(0 E 21, 3)1 ← (0 E 21, 2)0 28000.97 1039.102431 1039.10281 1039.10267 27.2

(0 E 2, 3)1 ← (0 E 2, 2)0 29968.74 1039.036793 1039.03697 1039.03706 28.0(1 E 22, 4)1 ← (1 E 22, 3)0 210 946.83 1039.004168 1039.00432 1039.00421 21.3(0 E 22, 3)1 ← (0 E 22, 2)0 215 873.22 1038.839841 1038.84001 1038.83992 22.4

(1 E 0, 3)1 ← (1 E 0, 2)0 216 092.14 1038.832539 1038.83269 1038.83270 24.8(2 E 1, 1)1 ← (2 E 1, 1)0 9P(30) 111 010.26 1037.801372 1037.80135 1037.80126 3.4(2 E 1, 2)1 ← (2 E 1, 2)0 19763.06 1037.759771 1037.75970 1037.75934 12.9(2 E 1, 3)1 ← (2 E 1, 3)0 17892.87 1037.697388 1037.69746 1037.69768 28.8

(0 A 12, 2)1 ← (0 A 12, 1)0 29678.97 1037.111254 1037.11142 1037.11138 23.8(0 A 11, 2)1 ← (0 A 11, 1)0 211 446.23 1037.052305 1037.05242 1037.05248 25.2

(2 E 3, 4)1 ← (2 E 3, 4)0 9P(32) 18608.16 1035.760753 1035.76096 1035.76075 0.1(1 A 22, 6)1 ← (1 A 21, 6)0 9P(34) 118 427.39 1034.102671 1034.10234 1034.10257 3.0

(Table continued)


Table 1. Continued

TransitionCO2 Laser

Sideband (MHz)nobs

a

(cm21)nobs

FT b

(cm21)npred

c

(cm21)nobs 2 npred

(MHz)

(1 A 21, 6)1 ← (1 A 22, 6)0 118 402.94 1034.101855 1034.10234 1034.10226 212.1(0 A 12, 5)1 ← (0 A 11, 5)0 117 356.25 1034.066941 1034.06688 1034.06701 22.1(0 A 6, 17)ri ← (0 A 7, 17)0 117 300.75 1034.065090 1034.06419 1034.06512 20.9

(0 E 6, 7)1 ← (0 E 6, 7)0 117 243.86 1034.063192 1034.06419 1034.06340 26.2(2 A 01, 0)1 ← (2 A 01, 1)0 117 208.47 1034.062012 1034.06215 1034.06215 24.1

(0 A 3, 4)1 ← (0 A 3, 4)0 116 399.50 1034.035027 1034.03547 1034.03526 27.0(0 A 12, 4)1 ← (0 A 11, 4)0 115 769.03 1034.013997 1034.01385 1034.01403 21.0

(0 E 3, 5)1 ← (0 E 3, 5)0 115 755.90 1034.013559 1034.01385 1034.01373 25.1(0 E 22, 3)1 ← (0 E 22, 3)0 115 317.80 1033.998946 1033.99888 1033.99903 22.5(1 E 23, 7)1 ← (1 E 23, 7)0 115 301.41 1033.998399 1033.99888 1033.99865 28.4(0 A 4, 10)ri ← (0 A 5, 10)0 115 233.05 1033.996119 1033.99694 1033.99624 23.6(0 A 4, 6)ri ← (0 A 5, 6)0 115 213.52 1033.995467 1033.99549 1033.99532 4.4

(0 E 21, 6)1 ← (0 E 21, 6)0 115 089.45 1033.991329 1033.99187 1033.99146 23.9(0 A 12, 3)1 ← (0 A 11, 3)0 114 497.25 1033.971575 1033.97172 1033.97172 24.3(1 A 22, 7)1 ← (1 A 21, 7)0 114 315.55 1033.965514 1033.96526 1033.96490 18.4(1 A 21, 7)1 ← (1 A 22, 7)0 114 271.72 1033.964052 1033.96418 1033.96435 28.9

(1 E 4, 7)1 ← (1 E 4, 7)0 114 251.78 1033.963387 1033.96366 1033.96387 214.5(0 A 4, 5)ri ← (0 A 5, 5)0 113 818.30 1033.948928 1033.94867 1033.94885 2.3

(0 A 32, 5)1 ← (0 A 31, 5)0 113 715.93 1033.945513 1033.94570 1033.94551 0.1(0 A 31, 5)1 ← (0 A 32, 5)0 113 714.83 1033.945476 1033.94570 1033.94551 21.0(0 A 12, 2)1 ← (0 A 11, 2)0 113 542.27 1033.939721 1033.93991 1033.93983 23.3

(0 E 2, 6)1 ← (0 E 2, 6)0 9P(34) 113 237.26 1033.929546 1033.92938 1033.92947 2.3(0 E 22, 4)1 ← (0 E 22, 4)0 113 179.19 1033.927609 1033.92676 1033.92780 25.7

(0 A 8, 8)1 ← (0 A 8, 8)0 113 148.90 1033.926599 1033.92676 1033.92676 24.8(0 E 24, 4)1 ← (0 E 24, 4)0 112 945.05 1033.919799 1033.91980 1033.91987 22.1

(0 A 12, 1)1 ← (0 A 11, 1)0 112 904.82 1033.918457 1033.91885 1033.91874 28.5(0 E 6, 8)1 ← (0 E 6, 8)0 112 515.19 1033.905461 1033.90534 1033.90556 23.0(0 E 3, 6)1 ← (0 E 3, 6)0 112 500.18 1033.904960 1033.90534 1033.90517 26.3

(0 A 11, 1)1 ← (0 A 12, 1)0 111 203.26 1033.861700 1033.86195 1033.86193 26.9(1 E 1, 7)1 ← (1 E 1, 7)0 110 761.70 1033.846971 1033.84679 1033.84676 6.3

(0 A 32, 6)1 ← (0 A 31, 6)0 110 496.34 1033.838119 1033.83800 1033.83809 0.9(0 A 31, 6)1 ← (0 A 32, 6)0 110 493.10 1033.838011 1033.83800 1033.83809 22.4(1 A 22, 8)1 ← (1 A 21, 8)0 19620.79 1033.808914 1033.80831 1033.80841 15.1(1 A 21, 8)1 ← (1 A 22, 8)0 19548.01 1033.806486 1033.80655 1033.80721 221.7

(1 E 4, 8)1 ← (1 E 4, 8)0 19532.83 1033.805980 1033.80619 1033.80623 27.5(0 E 2, 7)1 ← (0 E 2, 7)0 19501.79 1033.804945 1033.80491 1033.80489 1.6

(0 A 11, 2)1 ← (0 A 12, 2)0 18438.13 1033.769464 1033.76963 1033.76963 25.0(0 A 32, 7)1 ← (0 A 31, 7)0 16739.24 1033.712796 1033.71286 1033.71290 23.1(0 A 31, 7)1 ← (0 A 32, 7)0 16731.27 1033.712530 1033.71286 1033.71290 211.1(0 A 21, 4)1 ← (0 A 22, 4)0 26794.37 1033.261363 1033.26132 1033.26079 17.2

(0 E 23, 4)1 ← (0 E 23, 4)0 26858.24 1033.259232 1033.25934 1033.25919 1.3(0 A 22, 4)1 ← (0 A 21, 4)0 26864.91 1033.259010 1033.25934 1033.25970 220.7(0 A 8, 12)1 ← (0 A 8, 12)0 9P(34) 27613.61 1033.234036 1033.23383 1033.23397 2.0

(0 A 41, 11)1 ← (0 A 42, 11)0 27636.73 1033.233265 1033.23383 1033.23327 20.1(0 A 42, 11)1 ← (0 A 41, 11)0 27638.11 1033.233219 1033.23383 1033.23327 21.5(0 A 32, 10)1 ← (0 A 31, 10)0 27751.86 1033.229425 1033.22815 1033.22853 26.8(0 A 31, 10)1 ← (0 A 32, 10)0 27816.99 1033.227252 1033.22815 1033.22778 215.8(0 A 11, 5)1 ← (0 A 12, 5)0 28144.79 1033.216318 1033.21567 1033.21615 5.0(0 E 2, 11)1 ← (0 E 2, 11)0 210 881.20 1033.125041 1033.12459 1033.12476 8.4

(0 E 22, 10)1 ← (0 E 22, 10)0 210 914.25 1033.123939 1033.12459 1033.12410 24.8(0 A 9, 9)1 ← (0 A 9, 9)0 211 695.83 1033.097868 1033.09793 1033.09801 24.3

(0 E 3, 11)1 ← (0 E 3, 11)0 211 945.84 1033.089529 1033.08966 1033.08959 21.8(0 A 21, 6)1 ← (0 A 22, 6)0 212 372.28 1033.075304 1033.07556 1033.07555 27.4

(2 E 21, 1)1 ← (2 E 21, 2)0 212 547.15 1033.069471 1033.06885 1033.06948 20.3(0 E 23, 6)1 ← (0 E 23, 6)0 212 668.69 1033.065417 1033.06533 1033.06540 0.5

(0 A 22, 6)1 ← (0 A 21, 6)0 212 701.90 1033.064309 1033.06533 1033.06474 212.9(Table continued)


Table 1. Continued

TransitionCO2 Laser

Sideband (MHz)nobs

a

(cm21)nobs

FT b

(cm21)npred

c

(cm21)nobs 2 npred

(MHz)

(0 A 32, 11)1 ← (0 A 31, 11)0 213 651.38 1033.032638 1033.03296 1033.03252 3.5(0 A 31, 11)1 ← (0 A 32, 11)0 213 765.10 1033.028845 1033.02901 1033.03066 254.4

(0 A 6, 10)1 ← (0 A 6, 10)0 214 205.73 1033.014147 1033.01398 1033.01424 22.8(0 A 41, 12)1 ← (0 A 42, 12)0 214 253.00 1033.012570 1033.01212 1033.01238 5.7(0 A 42, 12)1 ← (0 A 41, 12)0 214 255.75 1033.012478 1033.01212 1033.01238 2.9

(0 E 9, 13)1 ← (0 E 9, 13)0 214 886.66 1032.991433 1032.99190 1032.99173 28.9(0 A 21, 7)1 ← (0 A 22, 7)0 9P(34) 215 873.61 1032.958512 1032.95886 1032.95872 26.2

(2 E 1, 2)1 ← (2 E 1, 3)0 216 435.06 1032.939784 1032.93883 1032.93929 14.8(0 A 22, 7)1 ← (0 A 21, 7)0 216 466.47 1032.938737 1032.93958 1032.93889 24.6

(0 E 24, 11)1 ← (0 E 24, 11)0 217 331.95 1032.909867 1032.91001 1032.91004 25.2(0 E 2, 12)1 ← (0 E 2, 12)0 217 354.75 1032.909107 1032.91001 1032.91020 232.7(0 E 1, 8)1 ← (0 E 1, 8)0 217 363.05 1032.908830 1032.91001 1032.90894 23.3

(0 A 32, 15)1 ← (0 A 31, 15)0 9P(36) 117 765.99 1032.070041 1032.07009 1032.07011 22.1(1 E 24, 10)1 ← (1 E 24, 10)0 117 614.80 1032.064996 1032.06517 1032.06522 26.7

(0 A 31, 15)1 ← (0 A 32, 15)0 117 066.73 1032.046716 1032.04757 1032.04687 24.6(0 E 210, 15)1 ← (0 E 210, 15)0 116 870.17 1032.040158 1032.04035 1032.04024 22.5

(0 A 9, 15)1 ← (0 A 9, 15)0 110 864.90 1031.839844 1031.84017 1031.84033 214.6(1 E 4, 16)1 ← (1 E 4, 16)0 110 861.77 1031.839740 1031.84017 1031.84003 28.7

(0 E 23, 13)1 ← (0 E 23, 13)0 110 401.63 1031.824392 1031.82460 1031.82455 24.7(0 A 32, 16)1 ← (0 A 31, 16)0 19267.35 1031.786556 1031.78676 1031.78675 25.8(0 A 31, 16)1 ← (0 A 32, 16)0 18247.45 1031.752535 1031.75296 1031.75277 27.0(0 E 21, 1)1 ← (0 E 21, 2)0 210 543.95 1031.125722 1031.12592 1031.12599 28.0

(0 A 11, 2)1 ← (0 A 11, 3)0 9P(38) 211 631.53 1029.054106 1029.05430 1029.05425 24.3(0 A 12, 2)1 ← (0 A 12, 3)0 214 035.54 1028.973916 1028.97392 1028.97403 23.4

(1 E 1, 3)1 ← (1 E 1, 4)0 9P(40) 113 688.14 1027.838758 1027.83896 1027.83884 22.5(0 E 21, 3)1 ← (0 E 21, 4)0 112 825.58 1027.809986 1027.81014 1027.81023 27.3

(0 E 2, 3)1 ← (0 E 2, 4)0 9P(40) 110 759.28 1027.741062 1027.74124 1027.74134 28.3(2 E 3, 4)1 ← (2 E 3, 5)0 110 235.28 1027.723583 1027.72303 1027.72359 20.2(0 E 3, 3)1 ← (0 E 3, 4)0 110 210.98 1027.722773 1027.72303 1027.72293 24.7

(1 E 21, 3)1 ← (1 E 21, 2)0 26870.22 1027.153005 1027.15314 1027.15342 212.4(1 A 4, 8)1 ← (1 A 4, 8)0 28992.99 1027.082197 1027.08237 1027.08239 25.8

(1 A 11, 3)1 ← (1 A 11, 4)0 211 225.49 1027.007729 1027.00787 1027.00797 27.2(1 A 12, 3)1 ← (1 A 12, 4)0 211 691.66 1026.992179 1026.99235 1026.99238 26.0

(0 E 1, 3)1 ← (0 E 1, 4)0 212 157.45 1026.976642 1026.97675 1026.97676 23.5(0 E 23, 3)1 ← (0 E 23, 4)0 215 189.61 1026.875500 1026.87623 1026.87564 24.2

(0 A 22, 3)1 ← (0 A 22, 4)0 215 195.17 1026.875315 1026.87521 1026.87551 25.9(0 A 21, 3)1 ← (0 A 21, 4)0 215 217.08 1026.874584 1026.87438 1026.87442 4.9(1 A 4, 10)1 ← (1 A 4, 10)0 215 300.81 1026.871791 1026.87190 1026.87184 21.5

(0 E 22, 4)1 ← (0 E 22, 5)0 9P(42) 116 809.08 1025.858555 1025.85871 1025.85875 25.9(0 E 24, 4)1 ← (0 E 24, 5)0 116 665.93 1025.853780 1025.85393 1025.85385 22.1

(0 A 11, 4)1 ← (0 A 11, 5)0 112 892.38 1025.727908 1025.72802 1025.72808 25.2(0 A 12, 4)1 ← (0 A 12, 5)0 19045.74 1025.599597 1025.59970 1025.59962 20.7

(1 E 21, 2)1 ← (1 E 21, 1)0 17970.28 1025.563724 1025.56372 1025.56389 25.0

a The observed wave numbers were calculated from the measured frequencies of CO2 laser sidebands by use of 299 792 458 m/s for the speed of light.Frequencies of the CO2 laser lines listed by Freed et al.24 were used.

b nobsFT refers to the observed wave number reported in Ref. 5.

c npred refers to the predicted wave number calculated from the term value of Ref. 5.

checked by use of the Ritz’s combination principle. Twoexamples are given. In Fig. 6(a) the difference of two in-frared transitions a and b observed with the 9P(34) and9P(42) laser CO2 lines, respectively, na 2 nb , agreeswith the observed microwave frequency22 with an error of0.01 MHz. In Fig. 6(b), when two transitions c and d andtwo transitions e and f were observed with the 9P(16)and 9P(34) CO2 laser lines, respectively, a composite of

observed frequencies, (nc 1 nd) 2 (ne 1 n f), agrees withthe sum n1 1 n2 with an error of 0.06 MHz, where n1 andn2 are the calculated microwave frequencies23 of the tran-sitions of (0 A 32, 11)0 ← (0 A 32, 10)0 and (0 A 31, 11)0

← (0 A 31, 10)0, respectively. For all other tests, mostof the errors are less than 0.15 MHz, and this value isconsistent with the estimated observed frequency uncer-tainty of 0.20 MHz.


B. Resolved Blended Lines and Asymmetry DoubletLines in the Fourier-Transform Spectrum

1. Measured Transitions of MethanolIn the FT spectral atlas of the C—O stretching fundamen-tal band of methanol5 the most crowded region is centerednear 1033.5 cm21, where many blended lines have beenobserved. In the present study we selected from Ref. 5the overlapped lines whose frequencies are within thetunable range of our spectrometer and tried to resolvethem. Based on the term values reported in Ref. 5, indi-vidual frequencies in overlapped lines were calculated aspredicted frequencies. The individual lines were ob-served within 10 MHz from the predicted frequencies inmost cases. Other spectral lines at the immediate vicini-ties of predicted lines were also measured. We observed

Fig. 7. Histogram of the deviations between the observed andpredicted frequencies appearing in Table 1.

inverse Lamb-dip signals for 206 infrared transitions,which are listed in Tables 1 and 4. Frequencies of theCO2 laser lines given by Freed et al.24 were used. Wealso observed many unidentified lines, which are notlisted here. The observed wave numbers given in Ref. 5are also listed in Table 1 for comparison. Each blendedline in Ref. 5 is resolved into two or three single lines.Twenty-eight unresolved asymmetry doublet lines givenin Ref. 5 (see also Table 2) are resolved into two compo-nents. Table 1 also includes four transitions in the in-plane rocking band, designated by ri.

Deviations of the observed frequencies from the pre-dicted frequencies given in Table 1 are shown in a histo-gram in Fig. 7. As was pointed out in Ref. 1, most of thedeviations are less than 5 MHz, but some of them come upto tens of megahertz. These deviations reflect the fre-quency accuracies of the infrared measurement given inRef. 5.

2. Observed Asymmetry Splittings and Asymmetry-Splitting Constants for the vco 5 1 StateThe asymmetry splittings for the A species in the vco5 1 state have been measured by various methods:those for levels with K 5 2 and 3 of higher J by FTspectrometer,5 those for J, K 5 3,2 by the multiple-resonance method,25 and those for J, K 5 11, 4 and 14, 4by the double-resonance method.1 The asymmetry split-tings were studied rather systematically in the presentstudy.

We observed frequencies of many resolved doublet linesresulting from the asymmetry splittings (one example isshown in Fig. 5) given in Table 1. From the observed fre-quencies, the double-resonance results1 and the calcu-lated ground-state splittings,23 asymmetry splittings inthe vCO 5 1 state for levels with K 5 2, 3, and 4 in thevt 5 0 state and K 5 2 in the vt 5 1 state were deter-mined as shown in Table 2.

Table 2. Asymmetry Splittings DE(K, J) (in MHz)a for the vCO Ä 1 State of Methanol

State J DE(2, J) Obs.-Calc.b J DE(3, J) Obs.-Calc.b J DE(4, J) Obs.-Calc.b

vt 5 03 12.14(0.20) c 20.09 5 0.58(0.03) 0.03 11 0.71(0.03) 04 36.66(0.20) 20.02 6 1.61(0.03) 20.04 12 1.42(0.03) 06 170.76(0.20) 20.16 7 4.10(0.03) 20.02 14 4.78(0.03) 07 307.13(0.20) 20.20 8 9.05(0.20) 09 803.03(0.20) 0.15 10 33.72(0.20) 0.20

14 4387.86(0.20) 20.01 11 58.40(0.20) 20.1312 97.31(0.20) 20.0513 155.51(0.20) 0.0615 358.60(0.20) 20.0316 522.77(0.20) 0.01

vt 5 16 11.85(0.20) 0.027 21.32(0.20) 0.048 35.27(0.20) 20.189 55.80(0.20) 0.10

13 229.91(0.20) 20.01

a Estimated experimental uncertainties are shown in parentheses.b Asymmetry splittings were calculated from the asymmetry-splitting constants in Table 3.c DE(2, 3) equals 12.23 MHz in Ref. 25 for the vt 5 0 state.


Fig. 8. Stark pattern of the (1 E 2, 3)1 ← (1 E 2, 2)0 transitionobserved with the upper sideband of the 9P(36) CO2 laser line.The Stark-modulation voltage was 5 Vpp , and the dc Stark biaswas 45 V. The methanol pressure was 6 mTorr. The inner andouter Stark components are those with uMu 5 1 and 2, respec-tively. The M 5 0 Stark component that was supposed to be atthe center of the pattern was not observed because of its smallmodulation effect. Four weak features between four strong sig-nals are collision-induced center dips.

Table 3. Asymmetry-Splitting Constants (in MHz)a

for the vCO Ä 1 State of Methanol

vt K S T

0 2 0.102062(31) 27.65(15) 3 1026

0 3 2.7367(35) 3 1025 22.23(10) 3 1029

0 4 2.804(0) 3 1029 0 (assumed)1 2 7.045(23) 3 1023 2147(129) 3 1029

a Quoted numbers are one standard deviation in units of the last quoteddigits.

The observed asymmetry splittings are used to deter-mine the asymmetry-splitting constants. The asymme-try splittings DE are approximately given by5

DE~vt , K, J !

5~J 1 K !!

~J 2 K !!@S~vt , K ! 1 J~J 1 1 !T~vt , K !#, (1)

where S(vt , K) and T(vt , K) are the asymmetry-splitting constants depending on the quantum numbersvt and K. The least-squares fit of observed asymmetrysplittings to Eq. (1) yields the constants S and T for thevCO 5 1 state as shown in Table 3. For vt 5 0 and K5 4, only S was determined by assuming T 5 0, sinceonly three asymmetry splittings were observed. The dif-ferences between the observed and the calculated split-tings are listed in Table 2.

C. Transitions for the (1, E, 2) and (1, E, 5) SequencesLees et al.14 observed vCO 5 1 ← 0 transitions of metha-nol using an FT spectrometer and assigned nine R-branchand ten P-branch transitions for the (1, E, 2) sequence.This assignment is not consistent with the assignmentand term values for this sequence given in Ref. 5. Forthe (1, E, 5) sequence, only transitions involving J 5 7in the vCO 5 1 state were reported in Refs. 5 and 15. Inthe present study the transitions for these two sequenceswere studied to give definite assignment and to determinetheir precise term values for various J values.

Table 4. Observed Transitions of the (1, E, 2) and (1, E, 5) Sequences of Methanol

Energy-LevelSequence Transition

CO2 LaserSideband (MHz)

nobs(cm21)

ncalca

(cm21)nobs 2 ncalc

(MHz)

(1, E, 2) Q(2) 9P(40) 26462.74 1027.166597 1027.167467 226.09Q(3) 26340.13 1027.170687 1027.170467 6.61Q(7) 26670.89 1027.159654 1027.159876 26.65Q(8) 27163.45 1027.143224 1027.143827 218.08Q(9) 27885.23 1027.119148 1027.119586 213.12Q(10) 28862.35 1027.086555 1027.086442 3.39Q(11) 210 117.16 1027.044699 1027.044045 19.59Q(12) 211 671.14 1026.992864 1026.993211 210.40R(2) 9P(36) 115 620.37 1031.998469 1031.998257 6.37R(4) 9P(32) 27617.49 1035.219524 1035.218612 27.35R(5) 9P(30) 218 284.58 1036.824202 1036.823777 12.74R(8) 9P(26) 19604.04 1041.599430 1041.599896 213.95R(10) 9P(22) 28422.39 1044.740728 1044.740045 20.46R(11) 9P(20) 216 725.93 1046.296317 1046.296591 28.22

(1, E, 5) Q(5) 9P(34) 17340.33 1033.732846 1033.734093 237.38Q(9)b 210 181.19 1033.148391 1033.137789 317.85Q(10)b 217 288.39 1032.911320 1032.937015 2770.32Q(14) 9P(36) 113 227.83 1031.918663 1031.918191 14.14R(6) 9P(22) 28356.01 1044.742943 1044.741041 57.01R(9)b 9P(18) 110 384.55 1049.007200 1049.032775 2766.72R(11) 9P(14) 212 176.97 1051.789365 1051.790792 242.77R(13) 9P(12) 116 200.13 1054.463881 1054.463441 13.18R(15) 9P(8) 27522.99 1057.049221 1057.049360 24.18

a The frequencies were calculated from the Taylor-series expansion coefficients in Table 6.b Not included in the fitting.


1. (1, E, 2) SequenceWe assigned the lines in Table 4 to those belonging to the(1, E, 2) sequence by observing their Stark effects. Asan example, Fig. 8 shows the R(2) transition for the(1, E, 2) sequence observed at the electric field of 56.3V/cm. This Stark pattern and the shifts of componentsshow that the transition is J, K 5 3, 2 ↔ 2, 2.

The assignment given in Table 4 is essentially thesame as that given in Ref. 14. The observed wave num-bers of R-branch transitions in Table 4 agree with most ofthose given in Ref. 14 within 0.0012 cm21. The assign-ment for the four pairs of transitions Q(3) and R(2),Q(9) and R(8), Q(11) and R(10), and Q(12) and R(11)can be checked by the combination rule, since each pairshares a common upper level. The loop defect for thefirst pair is 0.06 MHz, obtained by use of the observed fre-quency for the transition of E, vt 5 1, J, K 5 3, 2 ← 2, 2in the vCO 5 0 state.3 The loop defects for the second,third, and forth pairs are obtained as 0.11, 0.05, and 0.11MHz by use of the observed22 or calculated23 frequenciesfor the transitions of E, vt 5 1, J, K 5 9, 2 ← 8, 2, 11, 2← 10, 2, and 12, 2 ← 11, 2 in the vCO 5 0 state, respec-tively. Since all of these defects can be regarded as zerowithin experimental uncertainties of observed frequen-cies, the assignments for these four pairs are confirmed.

2. (1, E, 5) SequenceThe R(6) and Q(7) lines for the (1, E, 5) sequence havebeen reported in Refs. 5 and 15. Observed lines assignedto this sequence in the present study are listed in Table 4.All of these lines split into M components at some Starkfields, and their J values were determined without uncer-tainty. As an example, the Stark pattern of the R(15)line at the electric field of 1000 V/cm is shown in Fig. 9,where the outermost components are of M 5 615.

For the Q(5) line, two lines were observed at1033.732846 and 1033.741375 cm21 that showed theStark patterns peculiar to Q(5) and that showed compa-rable Stark shifts in magnitude. The former line was as-signed to the Q(5) line belonging to the (1, E, 5) se-quence because the corresponding P(6) line was observedin the FT spectrum.26 The R(6) line of the (1, E, 5) se-quence assigned by Ref. 5 was confirmed by observation ofits Stark effect. The line assigned to Q(9) is the only lineshowing the Stark effect expected for this sequence in thefrequency range between 500 MHz above and 900 MHzbelow the calculated frequency given in Table 4. The lineassigned to R(11) is the only line showing the Stark effectexpected for the (1, E, 5) sequence in the frequency rangeof 200 MHz centered at the observed frequency. The as-signment for the two pairs of transitions Q(10) and R(9)and Q(14) and R(13) was checked by the combinationrule. The loop defects for the first and the second pairsare 0.03 and 0.01 MHz by use of an observed frequency22

for the E, vt 5 1, J, K 5 10, 5 ← 9, 5 transition in thevCO 5 0 state and a calculated frequency23 for the E, vt5 1, J, K 5 14, 5 ← 13, 5 transition in the vCO 5 0state, respectively. These small loop defects have con-firmed the assignment of these two pairs of transitions.

3. Term Values and Their Taylor-Series ExpansionCoefficients of the (1, E, 2) and (1, E, 5) Sequences in thevCO 5 1 StateTerm values W for the (1, E, 2) and (1, E, 5) sequencesin the vCO 5 1 state are given in Table 5. In the determi-nation of term values for levels in the vCO 5 1 state fromthe wave numbers observed in the present study, theground-state (vCO 5 0) term values in Ref. 5 were used.The uncertainties of the ground-state term values can bechecked by use of observed microwave frequencies in lit-erature or infrared frequencies observed in this study,and it was found that they are a few megahertz for sev-eral levels in the vt 5 1 state. When two different termvalues resulted for a level in the vCO 5 1 state from theuncertainties of the ground-state term values, their aver-age value was given, as shown in Table 5.

Term values belonging to a sequence are expanded as aTaylor series in J(J 1 1) as5

W~J ! 5 (m50

am@J~J 1 1 !#m, (2)

Fig. 9. Stark pattern of the (1 E 5, 16)1 ← (1 E 5, 15)0 transi-tion observed with the lower sideband of the 9P(8) CO2 laserline. The Stark-modulation voltage was 30 Vpp , and the dcStark bias was 800 V. The methanol pressure was 4 mTorr.The outermost components are of uMu 5 15.

Table 5. Term Values W for the vCO Ä 1 State ofMethanol

Energy-LevelSequence J

Wobs(cm21)

Wobs 2 Wcalca

(MHz)

(1, E, 2) 2 1437.911211 220.353 1442.743083 9.355 1457.228854 25.196 1466.879432 9.427 1478.133174 29.718 1490.988788 219.029 1505.444994 212.32

10 1521.500610 6.3211 1539.154783 22.8612 1558.406401 211.75

(1, E, 5) 5 1484.102756 238.917 1504.766773 57.919 1531.795331 321.18

10 1547.654080 2764.1112 1584.239435 236.9514 1627.165687 19.2616 1676.454971 21.31

a The term values were calculated from the Taylor-series expansion co-efficients in Table 6.


Table 6. Taylor-Series Expansion Coefficients (in cm21)a for the vCO Ä 1 State of Methanol

Energy-LevelSequence a0 a1 a2 3 1010 a3 3 1012

(1, E, 2) 1433.07970(53) 0.805476(31) 218 7683(4711) 34 129(1947)(1, E, 5) 1460.26618(145) 0.794569(25) 8935(851)

a Quoted numbers are one standard deviation in units of the last quoted digits.

whose expansion coefficients are determined by a least-squares fit. The Taylor-series expansion coefficients ofthe (1, E, 2) and (1, E, 5) sequences in the vCO 5 1 statethus determined are shown in Table 6, and fitting resultsare shown in Tables 4 and 5.

In the fitting for the (1, E, 2) sequence, the fitting up toJ 5 12 shows the rms residual for transition frequenciesof 15.17 MHz. Even if we limit our analysis for J up to10, the residual is 9.41 MHz. When a4 is included in ad-dition to a0 –a3 in the analysis for J up to 12, the residualreduces to 3.63 MHz, but it is still much larger than theexperimental uncertainty or uncertainties of the ground-state term values used for the analysis.

In the fitting for the (1, E, 5) sequence it was foundthat the term values for the J 5 9 and 10 levels in thevCO 5 1 state deviate much in the opposite direction fromthe calculated values. Furthermore, the effective Kvalue for J 5 10 in the vCO 5 1 state, which was esti-mated from the Stark effect on the Q(10) line, deviatesmuch from K 5 5. So the existence of a local perturba-tion near J 5 9 and 10 in the vCO 5 1 state was as-sumed, and these two levels are excluded from the fitting.

4. DISCUSSION AND CONCLUSIONIn the present study a sub-Doppler spectrometer thatuses CO2 laser sidebands and its application to the sub-Doppler spectroscopy for the C—O stretching fundamen-tal band of methanol have been described, in which spec-tral lines were observed with a frequency precision of 0.20MHz and a spectral resolution of 0.2 MHz. Many over-lapped lines in previous FT works were resolved, andtheir frequencies were measured accurately. As one ap-plication for the high resolution of our spectrometer,asymmetry splittings in the A species of methanol wereobserved and analyzed.

Two advantages of the sub-Doppler spectroscopy overthe Doppler-limited spectroscopy are mentioned as to theassignment of infrared transitions. The first advantageis that the Stark effect of each line can be observed clearlyfor its identification. As is shown in Fig. 2, spectral linesof methanol are densely crowded near the band center,and fairly strong lines are spaced at every 100–200 MHz.For the observation of the laser Stark pattern of eachtransition, the Stark shift of each split component shouldbe much larger than the spectral linewidth. In theDoppler-limited spectroscopy, when large Stark shifts arerequired, it is difficult to observe clear Stark lobes be-cause of the interference from neighboring lines. Thesub-Doppler method is almost indispensable in observingclear Stark patterns of lines useful for their identifica-tions. The second advantage is that the combination ruleis applied usefully to the assignment of spectral lines

when their frequencies are known accurately. A set ofobserved lines used for the combination usually includesa microwave line, the frequency of which is known accu-rately. In this case, frequencies of the other lines in theset should be known as accurately as that of the micro-wave line for the useful application of the combinationrule. This advantage was also fully taken in the assign-ment of high-J lines in the vt 5 1, E, K 5 2 and 5 se-quences.

The microwave modulator used in the present studycovers a frequency range of 10 GHz for either side of aCO2 laser line. The 12C16O2 laser lines in the 10-mm re-gion are spaced at every 60 GHz. So the frequency cov-erage is one third of the whole range of CO2 laser frequen-cies. This coverage is increased by use of isotopic CO2lasers, such as 13C16O2,

12C18O2, and 13C18O2 lasers. Al-though the frequency coverage is not complete, the side-band laser is an excellent source for the sub-Doppler spec-troscopy.

ACKNOWLEDGMENTSWe are grateful to R. M. Lees for assignment of the Q(5)line in the (1, E, 5) sequence and valuable comments onthis study. We also thank S. Ishikuro for his help in thisexperiment. Z. D. Sun acknowledges the financial sup-port by the Japanese Government. This study was sup-ported in part by a Grant-in-Aid for Scientific Research(C) from the Ministry of Education, Science, Sports andCulture of Japan (11640390).

REFERENCES1. Z. D. Sun, F. Matsushima, S. Tsunekawa, and K. Takagi,

‘‘Infrared–microwave double-resonance spectroscopy ofCH3OH by use of sidebands of CO2 laser lines,’’ J. Opt. Soc.Am. B 16, 1447–1454 (1999).

2. C. C. Lin and J. D. Swalen, ‘‘Internal rotation and micro-wave spectroscopy,’’ Rev. Mod. Phys. 31, 841–892 (1959).

3. R. M. Lees and J. G. Baker, ‘‘Torsion-vibration-rotation in-teractions in methanol. I. Millimeter wave spectrum,’’ J.Chem. Phys. 48, 5299–5319 (1968).

4. G. Moruzzi, F. Strumia, P. Carnesecchi, R. M. Lees, I. Muk-hopadhyay, and J. W. C. Johns, ‘‘Fourier spectrum ofCH3OH between 950 and 1100 cm21,’’ Infrared Phys. 29,583–606 (1989).

5. G. Moruzzi, B. P. Winnewisser, M. Winnewisser, I. Mukho-padhyay, and F. Strumia, Microwave, Infrared and LaserTransitions of Methanol (CRC, Boca Raton, Fla., 1995).

6. T. Y. Chang, T. J. Bridges, and E. G. Burkhard, ‘‘CW sub-millimeter laser action in optically pumped methyl fluoride,methyl alcohol and vinyl chloride gases,’’ Appl. Phys. Lett.17, 249–251 (1970).

7. J. O. Henningsen, ‘‘Molecular spectroscopy by far infraredlaser emission,’’ Infrared and Millimeter Waves (Academic,New York, 1982), Vol. 5, Part I, pp. 29–128.

8. L. H. Xu and J. T. Hougen, ‘‘Global fit of rotational transi-


tions in the ground state of methanol,’’ J. Mol. Spectrosc.169, 396–409 (1995), and references therein.

9. G. Moruzzi and L. H. Xu, ‘‘Resolution of multiple overlap-ping lines in the analysis of molecular spectra,’’ J. Mol.Spectrosc. 165, 233–248 (1994).

10. G. Magerl, W. Schupita, J. M. Frye, W. A. Kreiner, and T.Oka, ‘‘Sub-Doppler spectroscopy of the v2 band of NH3 us-ing microwave modulation sidebands of CO2 laser lines,’’ J.Mol. Spectrosc. 107, 72–83 (1984).

11. A. Ainetschian, U. Haring, G. Spiegl, and W. A. Kreiner,‘‘The v2 /v4 diad of PH3,’’ J. Mol. Spectrosc. 181, 99–107(1996).

12. G. Magerl, J. M. Frye, W. A. Kreiner, and T. Oka, ‘‘InverseLamp dip spectroscopy using microwave modulation side-bands of CO2 laser lines,’’ Appl. Phys. Lett. 42, 656–658(1983).

13. W. Hohe, A. Ainetschian, W. A. Kreiner, and M. Loete,‘‘Double modulation sideband spectroscopy: m0 , m24 andm44 of 28SiH4,’’ J. Mol. Spectrosc. 153, 316–323 (1992).

14. R. M. Lees, I. Mukhopadhyay, and J. W. C. Johns, ‘‘Assign-ment of IR transitions and FIR laser lines from torsionallyexcited CH3OH,’’ Opt. Commun. 55, 127–130 (1985).

15. S. Petersen and J. O. Henningsen, ‘‘Saturated absorptionStark spectroscopy of CH3OH with CO2 lasers,’’ InfraredPhys. 26, 55–71 (1986).

16. P. K. Cheo, ‘‘Frequency synthesized and continuously tun-able IR laser sources in 9–11 mm,’’ IEEE J. Quantum Elec-tron. QE-20, 700–709 (1984).

17. F. Matsushima, H. Odashima, D. Wang, S. Tsunekawa, andK. Takagi, ‘‘Far-infrared spectroscopy of LiH using a tun-

able far infrared spectrometer,’’ Jpn. J. Appl. Phys. 33,315–318 (1994).

18. Y. T. Chen, J. M. Frye, and T. Oka, ‘‘Sub-Doppler spectros-copy using a multiple-reflection mirror system,’’ J. Opt. Soc.Am. B 3, 935–939 (1986).

19. J. Sakai and M. Katayama, ‘‘Observation of nonlinear mo-lecular hyperfine level crossing in CD3I,’’ Chem. Phys. Lett.35, 395–398 (1975).

20. K. Takagi, M. Kuse, T. Kido, and M. Furuta, ‘‘Infrared-radiofrequency double-resonance Stark spectroscopy ofCH3OH using a CO2 laser,’’ J. Mol. Spectrosc. 153, 291–302(1992).

21. H. W. Kroto, Molecular Rotation Spectra (Dover, New York,1992), Chap. 7, pp. 164–178.

22. T. Anderson, F. C. Delucia, and E. Herbst, ‘‘Additional mea-surements and a refined analysis of the millimeter- andsubmillimeter-wave spectrum of methanol,’’ Astrophys. J.Suppl. 72, 797–814 (1990).

23. Y. B. Duan, ‘‘Theoretical study of spectra for a moleculewith internal rotation,’’ Ph.D. dissertation (Kanazawa Uni-versity, Kanazawa, Japan, 1996).

24. C. Freed, L. C. Bradley, and R. G. O’Donnell, ‘‘Absolute fre-quencies of lasing transitions in seven CO2 isotopic spe-cies,’’ IEEE J. Quantum Electron. QE-16, 1195–1206(1980).

25. L. H. Xu, A. M. Andrews, and G. T. Fraser, ‘‘Study of theovertone C—O stretching band of methanol by multipleresonance spectroscopy,’’ J. Chem. Phys. 103, 14–19 (1995).

26. R. M. Lees, Department of Physics, University of NewBrunswick, Fredericton, New Brunswick, E3B 5A3, Canada(personal communication, 2000).

Documents

Sub-Doppler spectroscopy of the C—O stretching fundamental band of methanol by use of microwave sidebands of CO2 laser lines