- Email: [email protected]
Heterodyne frequency measurements of the 1-0 band of HF at 2.7 μm
JOURNAL OF MOLECULAR SPECTROSCOPY
Heterodyne
147,392-397 (1991)
Frequency Measurements of HF at 2.7 pm
of the 1-O Band
D. GODDON, A. GROH, H. J. HANSES,’ M. SCHNEIDER, AND W. URBAN Institut fir Angewandte Physik der Universitiit Bonn, Wegelerstr. 8, D-5300 Bonn 1. Federal Republic of Germany Absolute frequencies of live rotational-vibrational transitions of the D = I + 0 band of hydrogen fluoride around 3800 cm-’ were measured with sub-Doppler resolution. A beat frequency was measured between two Lamb-dip stabilized CO lasers and a tunable color center laser whose frequency was locked to the molecular transition by means of Doppler-free polarization saturation spectroscopy. The transition frequencies have been determined with an absolute accuracy of-t 1 MHz. This is an improvement of almost one order of magnitude to earlier Fourier-transform measurements by Guelachvili (Opt. Commun 19, 150-I 54 ( 1976)) which are systematically higher by about I5 MHZ. @1991Academic Press. 1nc.
INTRODUCTION
Secondary wavenumber standards are necessary for frequency calibration of broadband spectrometers like Fourier-transform spectrometers (FTS) or diode laser spectrometers. Although these spectrometers possess a very high reIative accuracy in the range of 10e4 to 10-5cm-‘, their precision in determining absolute frequencies may be lower by an order of magnitude. Calibration lines in the spectral region of interest make it possible to overcome systematic instrumental errors. The goal of the present experiment was to measure absolute frequencies of the HF molecule with sub-Doppler resolution. For this purpose a tunable CCL (color center laser) was used to detect and saturate the molecular transition. Two CO lasers were stabilized to the CO Lamb-dip and served as reference oscillators. The frequencies of the CO laser transitions are known to * 100 kHz due to the sub-Doppler heterodyne measurements done by Schneider et al. (I). A beat frequency between the CCL and the sum of the two CO lasers was genereated in a metal-insulator-metal point-contact diode and compared with a stable microwave oscillator.
EXPERIMENTAL
DETAILS
The experimental setup has been described previously by Groh et al. (2). In that earlier paper we reported sub-Doppler measurements on the CO2 molecule where the same experimental technique was used.
’ Present address: Quante AG, Uellendahler StraBe 353, D-5600 Wuppertal, Federal Republic of Germany. 0022-2852191 $3.00 Copyright 0 1991 by Academtc Press, Inc. All rights of reproduction in any form resewed
392
ABSOLUTE
FREQUENCIES
OF HF AT 2.7 pm
393
In the present paper measurements on the HF molecule are presented and additional information about the CCL and the detection of the saturated Lamb-dip signal is given. Two CO lasers served as secondary frequency standards. Their emission frequency was stabilized onto the Lamb-dip of vibrational-rotational transitions of the highly excited CO molecules by means of an optogalvanic detection technique. This leads to an absolute frequency accuracy of better than 200 kHz. These lasers were developed by Schneider et al. and are described in Ref. ( 1). The CCL used in the experiments was equipped with a lithium doped KC1 crystal. A reflection grating (450 grooves mm-’ ,2.8-grn blaze wavelength) in a Littrow mount served as a frequency selective end mirror and output coupler. The first-order reflectivity was approximately 80%. Single mode operation was achieved using an intracavity air spaced etalon with a finesse of 3.3. Under these conditions the laser was tunable between 3600 and 3950 cm-‘. With a pump power of 2 W at 647 nm the typical attainable single mode output power was in the range of 10 mW near the gain maximum. The experimental arrangement was the usual one for polarization saturation spectroscopy (3). The output of the CCL was split into two counter propagating beams, a strong, chopped pump beam and a weaker probe beam which crossed under a small angle (~7 mrad) within the 30-cm-long low-pressure absorption cell. Due to the sufficiently high pump power and circular polarization of the pump beam the gas sample becomes optically anisotropic. Therefore, the axis of polarization of the linear polarized probe beam is slightly rotated and the polarization itself becomes more elliptical. In resonance near the line center, the modulation of the pump beam is transferred to the probe beam. Phase sensitive detection yields a dispersion shaped profile of the Lamb-dip. In order to reduce noise components caused by changes of the laser intensity a differential detection scheme was used: A birefringent prism split the probe beam into two perpendicular polarization components which were monitored by two identical liquid-nitrogen-cooled indium arsenide photodetectors. A rotation of the axis of polarization of the probe beam increased one of the detector signals while the other one decreased. Amplified by a differential amplifier the signals were detected by means of a lock-in detector. Through the use of this detection scheme intensity fluctuations, which produce equal sign detector signals, are eliminated, whereas opposite sign signals due to the rotation of the axis of polarization are amplified. The main advantage of this method is that one gets a dispersion shaped signal with excellent signal-to-noise ratio (SNR) without the necessity of modulating the laser frequency. As an example the saturation signal of the HF P( 4)1_0 line is shown in Fig. 1, recorded at a HF pressure of 1.3 Pa ( 10 mTorr) and with 6 mW pump power focused to 145 mW cm-‘. The noise signal in Fig. 1 was monitored with the pump beam blocked and was magnified by a factor of 100, therefore a SNR of a few thousand was achieved. Although the stabilized CCL and the beat signal showed a linewidth of 10 MHz caused by intensity fluctuations of the krypton-ion pump laser (4), the frequency of the CCL could be stabilized to the center of the Lamb-dip signal with an accuracy better than 21 MHz.
394
GODDON
ET AL.
HF P(4), 1.3 Pa
I
I
I
I
0
50
100
150
MHz FIG. 1. Dispersion shaped Lamb-dip signal of the HF P(4),, factor of 100 and was obtained with the pump beam blocked.
line. The noise signal was amplified by a
RESULTS AND DISCUSSION
Five transitions of the P branch of the v = 1 + 0 band of HF were determined with sub-Doppler precision. Each of the P(2) to P(6) lines was measured several times. To ensure the independence of the individual measurements all three lasers were newly aligned and relocked before determining the frequency. Although the P( 1) and P( 7) lines fell into the tuning range of the CCL, we were unable to measure their frequencies because of lack of power. It was impossible to saturate the transitions and to get a beat signal at the same time. The frequency of the HF P(6),_. line was of special interest, because this line had been previously measured using two different methods which lead to results that do not agree with our measurement: Eng and Spears (5) used a HF laser which was heterodyned against the second harmonic of a CO laser. These authors determined the frequency of that transition to be 110 725 697.4 +-7 MHz. However, the lasers used in that experiment were only stabilized to their Doppler-limited gain profile. On the other hand, the FTS measurement of Guelachvili (6), Doppler-limited as well, yielded a frequency of 110 725 739f7.5 MHz. In our experiment, where all three lasers were sub-Doppler stabilized, we measured a frequency of 110 725 718.75kO.85 MHz. The uncertainty was taken as the square root of the sum of the squared individual errors, which were a720 kHz for the stabilization of the CCL (two times the standard deviation of 23 independent measurements) and k300 kHz maximum error for each CO laser.
ABSOLUTE
FREQUENCIES
OF
HF
395
AT 2.7 Frn
The comparison between the FTS measurements of Ref. (6) and the frequencies determined in the present work show that the FTS data are systematically higher in frequency by 10 to 20 MHz. A frequency shift in the same direction and of approximately the same magnitude has already been noticed by different authors ( 7, 8). As we wanted to take advantage of the numerous line positions measured by G. Guelachvili, we took them into account attributing a higher uncertainty (+30 MHz) than the reported one (+7.5 MHz). The uncertainties of our sub-Doppler measurements of the P( 2) to P( 6) lines were taken to be + 1 MHz. Along with these infrared transitions there exist highly accurate data of ground state rotational transitions of the HF molecule from Jennings et al. ( 9). Two of the lines given in Ref. (9) were remeasured with increased resolution yielding more accurate rotational constants for HF ( 10). It is worth noting that the fit program used in the present work led to the same results as in Ref. ( 9), whereas the drastic reduction of the errors of the molecular constants in Ref. (10)was not reproducible. The data and the estimated uncertainties of Refs. (9) and (10) were also included into our fit procedure. The data were fit to the equations for the energy levels of diatomic molecules: F(u, J) =
G(u)+ B,.J(J+
1) - O,.[J(J+
+H,.[J(J+
l)]’
1)]3-L,*[J(Jf
1)14+‘44,.[J(J+
v,& = F( 2“, J’) - F( 2)“, J”)
1,15
(I) (2)
and u. =
G(d) - G(d).
(3)
The lines were weighted according to their reciprocal squared estimated uncertainty. In Table I the observed (Refs. (6, 9, 10) and our measurements) and calculated frequencies and their differences are given. The uncertainties in the last digits ( 2~) of the calculated line positions were calculated with the variance-covariance matrix ( I I ) of the molecular constants and are given in parentheses. Table II shows the HF molecular constants and their 20 uncertainties as they are given in Refs. (6, 10) and those determined in the present work.
CONCLUSION
In this paper we have reported sub-Doppler measurements of the P branch of the ~1= 1 + 0 band of HF around 3800 cm-‘. Five absolute frequencies have been determined with an accuracy of + 1 MHz by heterodyning a CCL against two Lambdip stabilized CO lasers. A set of molecular constants for HF has been derived by using our data together with earlier infrared measurements (6) and measurements of ground state rotational transitions ( 9, 10). The absolute frequency of the band origin of the v = 1 + 0 system has been determined with an accuracy of + 1.1 MHz.
396
GODDON
ET AL.
TABLE I Measured v-
J"
v' J
and Calculated OBSERVEDa
[&‘I 41.1109832(30) 82.1711179(60) 123.1296703(90) 163.9361645(120) 204 54045(20) 244 89283(20) 284 94444(30)
Frequencies CALCULATEDb
[&‘I 4!.1109818(23) 82.1711169(36) 123.1296763(49) 163 936165(10) 204.540438(21) 244.892815(38) 284.944190(60) 324 646142187) 363.95104(12) 402 61214116) 441 16368(191 479.02100(24) 516 26058(28) 552 92015(33) 588 89678(39) 624.17690(44) 656.71641(501 692 46070(56) 725 43473(62) 757.54503(67) 788 77976(70) 613.10874(71) 848 50346168) 876 93706(61) 904 38440(51) 930 82201(37) 956 22809(27) 980 58251(35) 1003 86678(54) 1026 06404(71) 1047.15901(77) 1067.13802(59) 1065 98886(281 1103 7010(13) 1120 2651(34) 1135.6736(68)
00
01
01 02 03 04 05 06 07 08 0 9 010 0 11 0 12 0 13 0 14 0 15 0 16 0 17 0 18 0 19 0 20 0 21 0 22 0 23 0 24 0 25 0 26 0 27 0 28 0 29 030 0 31 0 32 0 33 0 34 0 35
02 03 04 05 06 07 08 09 010 011 0 12 0 13 0 14 0 15 0 16 0 17 0 18 0 19 0 20 0 21 0 22 0 23 0 24 0 25 0 26 0 27 Q 28 0 29 0 30 031 0 32 0 33 0 34 0 35 0 36
01 02 03 04 05 06 07 08 OS 010 0 11 0 12 0 13
10 I1 12 13 14 15 16 17 18 19 1 10 1 11 1 12
3920 3118(10) 3677.707068(33)’ 3833 661267(33)* 3766.227307(33)* 3741.459370(33)* 3693.412419(33)’ 3644.1427(10) 3593.7055(10) 3542.1590(10) 3489.5594(10) 3435.9660(10)
3920 311517137) 3877 707079(29) 3833.661272(20) 3788 227295120) 3741 459340122) 3693 412450(30) 3644 142399(73) 3593.70555115) 3542.15875124) 3489.55320(34) 3435 96435143) 3381 43184(60) 3326.01345(110)
00 01 02 03 04 05 06 07 08 0 9 0 10 0 11 0 12 0 13
11 12 13 14 15 16 17 18 19 I 10 1 11 I 12 I 13 1 14
4000.9892(10) 4038.9623(10) 4075.2936(10) 4109.9364(10) 4142.8462(10) 4173.9798(10) 4203.2961(10) 4230.7559(10) 4256 3222(10) 4279 9604(10) 4301.6366(10) 4321.3204(10)
4000 989178(30) 4036 962065(X) 4075.293137(26) 4109 935943(391 4142.845704[64) 4173.97940(11) 4203.29588(19) 4230 75593(28) 4256 32237136) 4279 96016(41) 4301 63652151) 4321.32103(93) 4338 98577(193) 4354 60551(377)
692 4842120) 725 4373120) 757.5486(20) 768 7776120) 819.1002(20)
956 22816(27) 980 5632(15) 1003 6672110) 1047.1570(25) 1067 1377(10) 1085 98903(27)
of Hydrogen
Fluoride
OES -CALC.
CALCULATEDb
WI
[MHz1
0.043 0.029 -0.180 -0.016 0.350 0.443 7.489
1232476.228(68) 2463428.11(11) 3691334.83(15) 4914662.59(30) 6131968.08(63) 7341701.9(11) 8542411.9(18) 9732646.5(26) 10910977.6(36) 12076QO4.0(47) 13226354.1(56) 14360688.3(71) 15477702.4(85) 16576129.2(10) 17654741.(12) 18712353.(13) 13747821.(15) 20760049. (17) 21747986.(19) 22710629.(20) 23647022.(21) 24556262.(21) 25437494.(20) 26289912. (18) 27112762.(15) 27905342.(11) 28666396.9(82) 29397124.(10) 30095169.(16) 30760626.(21) 31393037.123) 31991993.(16) 32557127.7(86) 33088123.(40) 33584703.(103) 34046637.(204)
104.841 77.088 107.129 -64.778 -256.134
2 159 20.790 12 679 -60.379 -9.467 4 392
8 490 -0.337 -0.136 Q 350 0.911 -0 939 9.031 -1.571 7.450 6.116 49.593
0.661 7.050 13.891 13.703 14.875 11.867 6.464 -0.935 -5.103 7.050 2.253 -18.857
117527982.6(11) 116250733.67(87) 114930273.58(61) 113568197.23(61) 112166129.19(67) 110725719.69(91) 109248640.7(22) 107736582.1(44) 106191247 S(72) 104614353.(10) 103007620.(13) 101372776.(18) 99711555 (33) 119946638 Ol(89) 121085036.52(65) 122174214.65(77) 123212779.9(12) 124199389.7(19) 125132754.5(34) 126011640.5(57) 126834872 O(841 127601335.(11) 128309978 (12) 128959819.(15) 129549945.(28) 130079521.(58) 130547789 (113)
a Rotational data taken from Refs. (9) and ( 10): Infrared data taken from Ref. (6) except *; * denotes our measurements; b The uncertainties in the last digits (20) are given in parentheses.
ABSOLUTE
FREQUENCIES
OF HF AT 2.7 Fm
397
TABLE II
Molecular Constants of Hydrogen Fluoride
Rlzf.(lO)
Ref.(6)
OO(l-0)
3961.42290(25)
This
work
3961.4224986(372)
90
20.559743(14)
20.55973002(33)
20.55973007(123)
DO. lo4
21.2045(28)
21.19880(13)
21.199162(642)
HO. 10’
16.8(2)
16.3380(67)
16.3441(213)
LO. 1012
24.0(50)
14.810(67)
14.876(267)
MO.1016
____
9.81(27)
10.05(100)
19.787478(14)
--__
19.78746571(556)
D1. lo4
20.6399(28)
----
20.6332(20)
HI. lo*
16.1(2)
___-
15.415(117)
Ll
----
Lo
1Votr. Values in cm-’ The uncertainties
in the
--__
last digits (20) are given in parentheses.
ACKNOWLEDGMENTS
We thank Dr. R. Beigang for many helpful discussions during the phase of construction of the CCL. This work was partly supported by the Deutsche Forschungsgemeinschaft and by the Land Nordrhein-Westfalen. RECEIVED:
January
14, 199
1 REFERENCES
1. M. SCHNEIDER, K. M. EVENSON, M. D. VANEK. D. A. JENNINGS,J. S. WELLS. A. STAHN. AND W. URBAN, J. Mol. Spectrosc. 135, 197-206 ( 1989). 2. A. GROH, D. GODDON, M. SCHNEIDER,W. ZIMMERMANN, AND W. URBAN, J. Mol. Spectrosc. 146,
161-168 (1991). 3. C. 4. 5. 6. 7.
WIEMAN AND T. W. HANSCH,Phys. Rev. Left. 36, 1170- 1173 ( 1976 1.
R. R. G. C.
BEIGANG,G. LITFIN, AND H. WELLING, Opt. Commun. 22.269-271 (1977). S. ENG AND D. L. SPEARS,Appl. Phys. Lett. 21,650-652 ( 1975 1. GUELACHVILI, Opt. Commun. 19, 150-154 (1976). R. POLLOCK, F. R. PETERSEN,D. A. JENNINGS,AND J. S. WELLS. J. Mol. Spectrosc. 99, 357-368 (1983). 8. L. R. BROWN AND R. A. TOTH, J. Opt. Sot. Am. B Opt. Phvs. 2,842-856 (1985). 9. D. A. JENNINGS, K. M. EVENSON, L. R. ZINK, C. DEMUYNCK, J. L. DESTOMBES, B. LEMOINE. AND J. W. C. JOHNS, J. Mol. Spectrosc. 122, 477-480 ( 1987).
10. D. A. JENNINGS AND J. S. WELLS, J. Mol. Spectrosc. 130, 267-268 (1988). Il. D. L. ALBRITTON, A. L. SCHMELTEKOPF, AND R. N. ZARE. in “Molecular Spectroscopy: Modern
Research II” (K. Narahari Rao, Ed.). p. 1. Academic Press. New York. 1976.
Heterodyne
147,392-397 (1991)
Frequency Measurements of HF at 2.7 pm
of the 1-O Band
D. GODDON, A. GROH, H. J. HANSES,’ M. SCHNEIDER, AND W. URBAN Institut fir Angewandte Physik der Universitiit Bonn, Wegelerstr. 8, D-5300 Bonn 1. Federal Republic of Germany Absolute frequencies of live rotational-vibrational transitions of the D = I + 0 band of hydrogen fluoride around 3800 cm-’ were measured with sub-Doppler resolution. A beat frequency was measured between two Lamb-dip stabilized CO lasers and a tunable color center laser whose frequency was locked to the molecular transition by means of Doppler-free polarization saturation spectroscopy. The transition frequencies have been determined with an absolute accuracy of-t 1 MHz. This is an improvement of almost one order of magnitude to earlier Fourier-transform measurements by Guelachvili (Opt. Commun 19, 150-I 54 ( 1976)) which are systematically higher by about I5 MHZ. @1991Academic Press. 1nc.
INTRODUCTION
Secondary wavenumber standards are necessary for frequency calibration of broadband spectrometers like Fourier-transform spectrometers (FTS) or diode laser spectrometers. Although these spectrometers possess a very high reIative accuracy in the range of 10e4 to 10-5cm-‘, their precision in determining absolute frequencies may be lower by an order of magnitude. Calibration lines in the spectral region of interest make it possible to overcome systematic instrumental errors. The goal of the present experiment was to measure absolute frequencies of the HF molecule with sub-Doppler resolution. For this purpose a tunable CCL (color center laser) was used to detect and saturate the molecular transition. Two CO lasers were stabilized to the CO Lamb-dip and served as reference oscillators. The frequencies of the CO laser transitions are known to * 100 kHz due to the sub-Doppler heterodyne measurements done by Schneider et al. (I). A beat frequency between the CCL and the sum of the two CO lasers was genereated in a metal-insulator-metal point-contact diode and compared with a stable microwave oscillator.
EXPERIMENTAL
DETAILS
The experimental setup has been described previously by Groh et al. (2). In that earlier paper we reported sub-Doppler measurements on the CO2 molecule where the same experimental technique was used.
’ Present address: Quante AG, Uellendahler StraBe 353, D-5600 Wuppertal, Federal Republic of Germany. 0022-2852191 $3.00 Copyright 0 1991 by Academtc Press, Inc. All rights of reproduction in any form resewed
392
ABSOLUTE
FREQUENCIES
OF HF AT 2.7 pm
393
In the present paper measurements on the HF molecule are presented and additional information about the CCL and the detection of the saturated Lamb-dip signal is given. Two CO lasers served as secondary frequency standards. Their emission frequency was stabilized onto the Lamb-dip of vibrational-rotational transitions of the highly excited CO molecules by means of an optogalvanic detection technique. This leads to an absolute frequency accuracy of better than 200 kHz. These lasers were developed by Schneider et al. and are described in Ref. ( 1). The CCL used in the experiments was equipped with a lithium doped KC1 crystal. A reflection grating (450 grooves mm-’ ,2.8-grn blaze wavelength) in a Littrow mount served as a frequency selective end mirror and output coupler. The first-order reflectivity was approximately 80%. Single mode operation was achieved using an intracavity air spaced etalon with a finesse of 3.3. Under these conditions the laser was tunable between 3600 and 3950 cm-‘. With a pump power of 2 W at 647 nm the typical attainable single mode output power was in the range of 10 mW near the gain maximum. The experimental arrangement was the usual one for polarization saturation spectroscopy (3). The output of the CCL was split into two counter propagating beams, a strong, chopped pump beam and a weaker probe beam which crossed under a small angle (~7 mrad) within the 30-cm-long low-pressure absorption cell. Due to the sufficiently high pump power and circular polarization of the pump beam the gas sample becomes optically anisotropic. Therefore, the axis of polarization of the linear polarized probe beam is slightly rotated and the polarization itself becomes more elliptical. In resonance near the line center, the modulation of the pump beam is transferred to the probe beam. Phase sensitive detection yields a dispersion shaped profile of the Lamb-dip. In order to reduce noise components caused by changes of the laser intensity a differential detection scheme was used: A birefringent prism split the probe beam into two perpendicular polarization components which were monitored by two identical liquid-nitrogen-cooled indium arsenide photodetectors. A rotation of the axis of polarization of the probe beam increased one of the detector signals while the other one decreased. Amplified by a differential amplifier the signals were detected by means of a lock-in detector. Through the use of this detection scheme intensity fluctuations, which produce equal sign detector signals, are eliminated, whereas opposite sign signals due to the rotation of the axis of polarization are amplified. The main advantage of this method is that one gets a dispersion shaped signal with excellent signal-to-noise ratio (SNR) without the necessity of modulating the laser frequency. As an example the saturation signal of the HF P( 4)1_0 line is shown in Fig. 1, recorded at a HF pressure of 1.3 Pa ( 10 mTorr) and with 6 mW pump power focused to 145 mW cm-‘. The noise signal in Fig. 1 was monitored with the pump beam blocked and was magnified by a factor of 100, therefore a SNR of a few thousand was achieved. Although the stabilized CCL and the beat signal showed a linewidth of 10 MHz caused by intensity fluctuations of the krypton-ion pump laser (4), the frequency of the CCL could be stabilized to the center of the Lamb-dip signal with an accuracy better than 21 MHz.
394
GODDON
ET AL.
HF P(4), 1.3 Pa
I
I
I
I
0
50
100
150
MHz FIG. 1. Dispersion shaped Lamb-dip signal of the HF P(4),, factor of 100 and was obtained with the pump beam blocked.
line. The noise signal was amplified by a
RESULTS AND DISCUSSION
Five transitions of the P branch of the v = 1 + 0 band of HF were determined with sub-Doppler precision. Each of the P(2) to P(6) lines was measured several times. To ensure the independence of the individual measurements all three lasers were newly aligned and relocked before determining the frequency. Although the P( 1) and P( 7) lines fell into the tuning range of the CCL, we were unable to measure their frequencies because of lack of power. It was impossible to saturate the transitions and to get a beat signal at the same time. The frequency of the HF P(6),_. line was of special interest, because this line had been previously measured using two different methods which lead to results that do not agree with our measurement: Eng and Spears (5) used a HF laser which was heterodyned against the second harmonic of a CO laser. These authors determined the frequency of that transition to be 110 725 697.4 +-7 MHz. However, the lasers used in that experiment were only stabilized to their Doppler-limited gain profile. On the other hand, the FTS measurement of Guelachvili (6), Doppler-limited as well, yielded a frequency of 110 725 739f7.5 MHz. In our experiment, where all three lasers were sub-Doppler stabilized, we measured a frequency of 110 725 718.75kO.85 MHz. The uncertainty was taken as the square root of the sum of the squared individual errors, which were a720 kHz for the stabilization of the CCL (two times the standard deviation of 23 independent measurements) and k300 kHz maximum error for each CO laser.
ABSOLUTE
FREQUENCIES
OF
HF
395
AT 2.7 Frn
The comparison between the FTS measurements of Ref. (6) and the frequencies determined in the present work show that the FTS data are systematically higher in frequency by 10 to 20 MHz. A frequency shift in the same direction and of approximately the same magnitude has already been noticed by different authors ( 7, 8). As we wanted to take advantage of the numerous line positions measured by G. Guelachvili, we took them into account attributing a higher uncertainty (+30 MHz) than the reported one (+7.5 MHz). The uncertainties of our sub-Doppler measurements of the P( 2) to P( 6) lines were taken to be + 1 MHz. Along with these infrared transitions there exist highly accurate data of ground state rotational transitions of the HF molecule from Jennings et al. ( 9). Two of the lines given in Ref. (9) were remeasured with increased resolution yielding more accurate rotational constants for HF ( 10). It is worth noting that the fit program used in the present work led to the same results as in Ref. ( 9), whereas the drastic reduction of the errors of the molecular constants in Ref. (10)was not reproducible. The data and the estimated uncertainties of Refs. (9) and (10) were also included into our fit procedure. The data were fit to the equations for the energy levels of diatomic molecules: F(u, J) =
G(u)+ B,.J(J+
1) - O,.[J(J+
+H,.[J(J+
l)]’
1)]3-L,*[J(Jf
1)14+‘44,.[J(J+
v,& = F( 2“, J’) - F( 2)“, J”)
1,15
(I) (2)
and u. =
G(d) - G(d).
(3)
The lines were weighted according to their reciprocal squared estimated uncertainty. In Table I the observed (Refs. (6, 9, 10) and our measurements) and calculated frequencies and their differences are given. The uncertainties in the last digits ( 2~) of the calculated line positions were calculated with the variance-covariance matrix ( I I ) of the molecular constants and are given in parentheses. Table II shows the HF molecular constants and their 20 uncertainties as they are given in Refs. (6, 10) and those determined in the present work.
CONCLUSION
In this paper we have reported sub-Doppler measurements of the P branch of the ~1= 1 + 0 band of HF around 3800 cm-‘. Five absolute frequencies have been determined with an accuracy of + 1 MHz by heterodyning a CCL against two Lambdip stabilized CO lasers. A set of molecular constants for HF has been derived by using our data together with earlier infrared measurements (6) and measurements of ground state rotational transitions ( 9, 10). The absolute frequency of the band origin of the v = 1 + 0 system has been determined with an accuracy of + 1.1 MHz.
396
GODDON
ET AL.
TABLE I Measured v-
J"
v' J
and Calculated OBSERVEDa
[&‘I 41.1109832(30) 82.1711179(60) 123.1296703(90) 163.9361645(120) 204 54045(20) 244 89283(20) 284 94444(30)
Frequencies CALCULATEDb
[&‘I 4!.1109818(23) 82.1711169(36) 123.1296763(49) 163 936165(10) 204.540438(21) 244.892815(38) 284.944190(60) 324 646142187) 363.95104(12) 402 61214116) 441 16368(191 479.02100(24) 516 26058(28) 552 92015(33) 588 89678(39) 624.17690(44) 656.71641(501 692 46070(56) 725 43473(62) 757.54503(67) 788 77976(70) 613.10874(71) 848 50346168) 876 93706(61) 904 38440(51) 930 82201(37) 956 22809(27) 980 58251(35) 1003 86678(54) 1026 06404(71) 1047.15901(77) 1067.13802(59) 1065 98886(281 1103 7010(13) 1120 2651(34) 1135.6736(68)
00
01
01 02 03 04 05 06 07 08 0 9 010 0 11 0 12 0 13 0 14 0 15 0 16 0 17 0 18 0 19 0 20 0 21 0 22 0 23 0 24 0 25 0 26 0 27 0 28 0 29 030 0 31 0 32 0 33 0 34 0 35
02 03 04 05 06 07 08 09 010 011 0 12 0 13 0 14 0 15 0 16 0 17 0 18 0 19 0 20 0 21 0 22 0 23 0 24 0 25 0 26 0 27 Q 28 0 29 0 30 031 0 32 0 33 0 34 0 35 0 36
01 02 03 04 05 06 07 08 OS 010 0 11 0 12 0 13
10 I1 12 13 14 15 16 17 18 19 1 10 1 11 1 12
3920 3118(10) 3677.707068(33)’ 3833 661267(33)* 3766.227307(33)* 3741.459370(33)* 3693.412419(33)’ 3644.1427(10) 3593.7055(10) 3542.1590(10) 3489.5594(10) 3435.9660(10)
3920 311517137) 3877 707079(29) 3833.661272(20) 3788 227295120) 3741 459340122) 3693 412450(30) 3644 142399(73) 3593.70555115) 3542.15875124) 3489.55320(34) 3435 96435143) 3381 43184(60) 3326.01345(110)
00 01 02 03 04 05 06 07 08 0 9 0 10 0 11 0 12 0 13
11 12 13 14 15 16 17 18 19 I 10 1 11 I 12 I 13 1 14
4000.9892(10) 4038.9623(10) 4075.2936(10) 4109.9364(10) 4142.8462(10) 4173.9798(10) 4203.2961(10) 4230.7559(10) 4256 3222(10) 4279 9604(10) 4301.6366(10) 4321.3204(10)
4000 989178(30) 4036 962065(X) 4075.293137(26) 4109 935943(391 4142.845704[64) 4173.97940(11) 4203.29588(19) 4230 75593(28) 4256 32237136) 4279 96016(41) 4301 63652151) 4321.32103(93) 4338 98577(193) 4354 60551(377)
692 4842120) 725 4373120) 757.5486(20) 768 7776120) 819.1002(20)
956 22816(27) 980 5632(15) 1003 6672110) 1047.1570(25) 1067 1377(10) 1085 98903(27)
of Hydrogen
Fluoride
OES -CALC.
CALCULATEDb
WI
[MHz1
0.043 0.029 -0.180 -0.016 0.350 0.443 7.489
1232476.228(68) 2463428.11(11) 3691334.83(15) 4914662.59(30) 6131968.08(63) 7341701.9(11) 8542411.9(18) 9732646.5(26) 10910977.6(36) 12076QO4.0(47) 13226354.1(56) 14360688.3(71) 15477702.4(85) 16576129.2(10) 17654741.(12) 18712353.(13) 13747821.(15) 20760049. (17) 21747986.(19) 22710629.(20) 23647022.(21) 24556262.(21) 25437494.(20) 26289912. (18) 27112762.(15) 27905342.(11) 28666396.9(82) 29397124.(10) 30095169.(16) 30760626.(21) 31393037.123) 31991993.(16) 32557127.7(86) 33088123.(40) 33584703.(103) 34046637.(204)
104.841 77.088 107.129 -64.778 -256.134
2 159 20.790 12 679 -60.379 -9.467 4 392
8 490 -0.337 -0.136 Q 350 0.911 -0 939 9.031 -1.571 7.450 6.116 49.593
0.661 7.050 13.891 13.703 14.875 11.867 6.464 -0.935 -5.103 7.050 2.253 -18.857
117527982.6(11) 116250733.67(87) 114930273.58(61) 113568197.23(61) 112166129.19(67) 110725719.69(91) 109248640.7(22) 107736582.1(44) 106191247 S(72) 104614353.(10) 103007620.(13) 101372776.(18) 99711555 (33) 119946638 Ol(89) 121085036.52(65) 122174214.65(77) 123212779.9(12) 124199389.7(19) 125132754.5(34) 126011640.5(57) 126834872 O(841 127601335.(11) 128309978 (12) 128959819.(15) 129549945.(28) 130079521.(58) 130547789 (113)
a Rotational data taken from Refs. (9) and ( 10): Infrared data taken from Ref. (6) except *; * denotes our measurements; b The uncertainties in the last digits (20) are given in parentheses.
ABSOLUTE
FREQUENCIES
OF HF AT 2.7 Fm
397
TABLE II
Molecular Constants of Hydrogen Fluoride
Rlzf.(lO)
Ref.(6)
OO(l-0)
3961.42290(25)
This
work
3961.4224986(372)
90
20.559743(14)
20.55973002(33)
20.55973007(123)
DO. lo4
21.2045(28)
21.19880(13)
21.199162(642)
HO. 10’
16.8(2)
16.3380(67)
16.3441(213)
LO. 1012
24.0(50)
14.810(67)
14.876(267)
MO.1016
____
9.81(27)
10.05(100)
19.787478(14)
--__
19.78746571(556)
D1. lo4
20.6399(28)
----
20.6332(20)
HI. lo*
16.1(2)
___-
15.415(117)
Ll
----
Lo
1Votr. Values in cm-’ The uncertainties
in the
--__
last digits (20) are given in parentheses.
ACKNOWLEDGMENTS
We thank Dr. R. Beigang for many helpful discussions during the phase of construction of the CCL. This work was partly supported by the Deutsche Forschungsgemeinschaft and by the Land Nordrhein-Westfalen. RECEIVED:
January
14, 199
1 REFERENCES
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161-168 (1991). 3. C. 4. 5. 6. 7.
WIEMAN AND T. W. HANSCH,Phys. Rev. Left. 36, 1170- 1173 ( 1976 1.
R. R. G. C.
BEIGANG,G. LITFIN, AND H. WELLING, Opt. Commun. 22.269-271 (1977). S. ENG AND D. L. SPEARS,Appl. Phys. Lett. 21,650-652 ( 1975 1. GUELACHVILI, Opt. Commun. 19, 150-154 (1976). R. POLLOCK, F. R. PETERSEN,D. A. JENNINGS,AND J. S. WELLS. J. Mol. Spectrosc. 99, 357-368 (1983). 8. L. R. BROWN AND R. A. TOTH, J. Opt. Sot. Am. B Opt. Phvs. 2,842-856 (1985). 9. D. A. JENNINGS, K. M. EVENSON, L. R. ZINK, C. DEMUYNCK, J. L. DESTOMBES, B. LEMOINE. AND J. W. C. JOHNS, J. Mol. Spectrosc. 122, 477-480 ( 1987).
10. D. A. JENNINGS AND J. S. WELLS, J. Mol. Spectrosc. 130, 267-268 (1988). Il. D. L. ALBRITTON, A. L. SCHMELTEKOPF, AND R. N. ZARE. in “Molecular Spectroscopy: Modern
Research II” (K. Narahari Rao, Ed.). p. 1. Academic Press. New York. 1976.