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Water vapor line strengths in the 1-μm region
JOURN4L
OF MOL.ECULAR
SPECTROSCOPY
111,
173-178
(1985)
Water Vapor Line Strengths in the l-pm Region V. N. CHEREPANOV.V. P. KOCHANOV. Yu. S. MAKUSHKIN, L. N. SINITSA, A. M. SOLODOV, 0. N. SULAKSHINA, AND 0. K. VOITSEKHOVSKAYA The Instiiute yf .Iimospheric Oplics SB. USSR kademy yf Sciences, 1. .4kadetnicheskii Avenue. Torn& 634055. USSR The line strengths of Hz0 bands v, + vz + q and v2 + 2~ have been measured using a highresolution Nd-glass single-mode laser spectrophotometer. The parameters of 33 lines were found by fitting a Voigt contour to experimental line profile. The vibration-rotation interaction affecting the line strength was taken into account by using the F factor in the three-parametric form, and its constants for v, + v2 + s, and vz + 2~ bands were found. There is a good agreement between line intensities calculated using these constants and the experimental values. & 1985 Academc Press. Inc. I. INTRODUCTION
A wide range of problems in spectroscopy, atmospheric optics, and astrophysics require precise knowledge of the fine structure of the vibration-rotation spectra of water vapor. Until recently, only a few papers are known (1-4) in which the H20 absorption spectra in the 1-pm region were measured. In Ref. (I) weak lines of the water vapor bands v2 + 2v3, vl + v2 + v3, and 2vi + v2 were observed in the solar spectra due to absorption by the Earth’s atmosphere. The positions of the strongest Hz0 lines in the region 8050-9370 cm-’ were measured using the Fourier spectrometer with a spectral resolution of 5 - 10e3 cm-’ in Ref. (2). Several water vapor absorption lines in the range of 9241-9455 cm-’ were recorded using the intracavity laser spectrometer with an effective absorption length of 10 km in Ref. (3). It should be noted that. as distinct to line positions, absolute strength measurements were made only for a few of the absorption lines of the solar spectrum in the region 92209243 cm-’ (4). This paper presents the results of the absolute line strength measurements of the v2 + 2~3, vI + v2 + 5, and 2vi + v2H20 bands using the high-resolution laser spectrophotometer, which has been described earlier (5). The line strengths obtained were processed to find the dipole moment matrix element parameters for vibrationrotation interactions. II. EXPERIMENTAL
DETAILS
The high-resolution laser spectrophotometer was developed on the basis of the running-wave ring-cavity Nd-glass laser with frequency continuously tuned during a generation pulse (6). The instantaneous spectral line width of the laser was extremely narrow (less than 2 MHz) and was tuned during the generation pulse up 173
0022-2852185 Copyri~t All n&s
0
$3.00
1985 by Academic Press. Inc.
of reproduction in any form reserved.
174
CHEREPANOV
ET AL.
to 0.7 cm- ‘. The total spectral range of generation (9240-9500 cm-‘) was covered from pulse to pulse by turning a dispersion prism in the laser cavity. The line position of the laser generation was controlled using the grating spectrometer with an accuracy of 0.08 cm-‘, while the precise frequency measurements (0.001 cm-‘) were carried out using a thermostatic evacuated Fabry-Perot interferometer which has a base length of 103.5 mm. The laser generation strongly depends on absorption of atmospheric air inside its cavity: thus, such a laser should operate as an intracavity spectrometer (7). To eliminate this effect the laser cavity was evacuated; this enabled us to obtain smooth laser pulses even if strong atmospheric absorption lines were in the tuning frequency range of the laser. The spectra have been recorded using the gas sample contained in a 3-m-long “White-type” multipass absorption cell set for a 280-m pathlength. The temperature control was conducted with an accuracy of 0.5 K and the gas pressure was determined with a precision of 2%. The intensity of the light beam incident on the absorption cell was about 100 times lower than that of the output laser beam so that, as simple estimations showed, nonlinear absorption effects and gas sample heating certainly did not occur at the given experimental conditions. The line shape was assumed as a Voigt profile:
(1)
Here v is the running frequency, v. is the center of the absorption line, S is the line strength, P is the homogeneous (impact) halfwidth, KS is the Boltzmann constant, T is the gas temperature, and m. is the mass of the absorbing molecules. The values of the parameters S, P, and vo, as well as the confidence intervals AS, AP, and Avo for 95% probability level have been obtained by least-squares fitting. It was revealed that about 30 points for each experimental line shape were required to provide the accuracy of the line strength measurements AS/S N 10%; and two or three scans were used to obtain the actual values of the parameters. While processing the overlapping spectral lines, the number of experimental points Ki(Vi) was doubled and the absorption coefficient K(Y) was regarded as a sum of expressions (1) with independent parameters. The spectral line width of the laser was about two orders of magnitude less than the Doppler width of the investigated absorption lines; that enabled us to neglect the effect of instrumental function of the spectrometer on the measured data. High resolution of the spectrophotometer provided for reliable separation of the overlapping lines of the water vapor at wavenumbers 9343.6, 9325.1, and 9257.1 cm-‘, recorded at the water vapor pressures, PHzo of 17.1, 14.5, and 2.7 Torr, respectively (Fig. 1). The positions of the strongest lines of each doublet and their assignments were taken from Ref. (2). The positions of the weaker lines of doublets were measured using the Fabry-Perot interferometer with a 0.001 cm-’ accuracy relative to the stronger lines.
WATER VAPOR LINE STRENGTHS
175
\
5-
O-
5-
3, 9257.04
0 08 FREClUENCY
CM -’
FIG. 1. The experimental record of overlapping lines (0). The solid line represents the best-fitted sum of two contours (I); the dashed line corresponds to separated lines.
It should be noted that in the Fourier transform spectrometer measurements (2) only a doublet at 9343 cm-’ was resolved. The obtained wavenumber separation of the line in this doublet was Au = 0.0396 + 0.005 cm-‘: this differs somewhat from our measurements, Au = 0.0337 f 0.0020 cm-‘. III. DETERMINATION
OF INTRAMOLECULAR
PARAMETERS
In order to obtain a reliable interpretation of the experimental spectra one should take into account intramolecular interactions. At present, powerful theoretical methods of calculation of vibration-rotation molecular spectra are available, and they are based on the idea of constructing effective rotational Hamiltonians (8-12). These methods enabled one to simplify significantly the expression for a total vibration-rotation wave function and to describe precisely the spectra observed. In particular, due to these methods a good agreement between the experimental and theoretical line intensity values of the pure rotational spectrum, fundamental, and first overtone HZ0 bands was reached, using the conventional treatment of the perturbation theory both in the form of contact transformation (13-16) and in the projector form (8, 17. 18). One of the variants of the projector calculation technique was used in this paper for analyzing the measured Hz0 absorption line intensities (8, II). In this case, the matrix element of dipole moment in the first approximation of the perturbation theory in the absence of resonance interactions can be written as I( V’R’IMIVR)IZ = (CY’+ pm + rC(K)/C)? *L, where (Y’= CI+ ( Vl&.lLV);
(2)
CHEREPANOV
176
ET AL.
TABLE I
The Parametersof the MatrixElementof the Hz0 DipoleMoment* Band
oi
v, + 2 VI + v,
v,
(-2.48+_0.28).10
+ v,
(
is the
l
denotes a’=
(-1.88+0.15)'~O-4
/
number
(7 exp ’ ~CAC
,(-1.71+0.21)~10-5
3.2*0.71j*10-3 I ( 2.43 + ,.,,47
1
N
(-3.4+_0.46).10-5
are that
of the in
(v’(cg(v)
lines
used
1
in
experimental
parentheaea
18
6
10
( ,2
( ,0_25
1
1
1
I
,4
processing; and
the
% uexp,% CJrdc.
N
Y
P
-4
reproductional
standard
deviation
errcms, is
also
respectively; given.
+ CY.
V’R’ and VR are the vibration and rotation quantum numbers of the upper and lower energy levels, respectively; (Y, p, and y are the parameters of vibrationrotation interaction; m, C, and C(K) are functions which depend on rotational quantum numbers (17, 19). L is the line strength, and fig is the projection of dipole moment of molecule on the molecular axis g:
g=
X,
V’= 111
i Y,
V’ = 012.
The experimental values of H20 absorption line intensities (18 lines of the v2 + 2v3 band and 6 lines of the v1 + v2 + v3 band) obtained in this paper were used for determination of (Y, 0, and y parameters. Since six lines of the vI + v2 + v3 are insufficient for reliable statistical processing, additional line strengths of v, + v2 + v3 band from Ref. (4) were used. The results of fitting by the least-squares method are given in Table I. In spite of a relatively small number of lines used in the fitting, the parameters of vibrationrotation interaction were obtained with good accuracy. The representation (2) of the matrix element of the dipole moment can be regarded as satisfactory. Table II gives the intensities of Scale.using a’, 0, and y parameters in comparison with the experimental ones (Sex&, with the intensities s T,T,,and data from the 1982 version of the Air Force Geophysics Laboratory compilation and Ref. (20). The values of Scale.obtained using expression (2) are in good agreement with the experimental data, including the lines noted in Table II by (*), which were not used in the fitting. As may be noticed from Table II, the model of rigid rotator is not applicable with the investigated bands since it leads to errors in the line strengths up to 100%. This conclusion is in agreement with the theoretical estimations of the influence of regular vibration-rotation interaction on the line intensities made in Ref. (19). The parameters 01’, ,f3, and y can be used for determining the third
177
WATER VAPOR LINE STRENGTHS TABLE II Hz”0 Vibration-Rotation Line Intensities of the 000 - r’; v2V; Bands. (S, cm-’ mol-’ cm2. 102’; T = 296 K) -1 ?I cm v;v;v;
j@c-J’K&
5.r
s,p
S[x)l
9219.8520
012
414
523
14.5
i4I
25.5
9221.8964
111
134
853
7.96
141
14.4
15.3
9224.2410
111
634
753
11.29[4]
21.2
22.1
0.85
59.1
3.48
Scale. 14.21' 7.02 12.2 0.39+
9224.8013
012
716
743
9227.6997
012
431
542
9229.2919
012
432
541
52.1 [41
9229.6967
111
835
954
1.27 141
2.99
1.34
9237.8018
111
936
1055
2.67 141
4.18
4.49
2.03
9241.5674
111
918
1037
2.68 141
4.84
5.13
3.09
9242.8633
111
505
642
2.04[41
3.56
3.57
2.94
9243.06
012
524
633
6.51 L4]
12.6
24.8
7.72'
9251.2366
111
627
946
7.92+_0.28
10.2
10.8
7.22
642
10.85+_0.37
1.8
28.6
11.2
551
16.2&_2.08
28.2
49.1
17
53.1%_2.2
84.7
147
51.2
0.54 [41 19.6
141
35.6
52.7
107
164
2.79
20' 60.5'
9253.5810
012
533
9257.0521
012'
440
9257.0813
012
441
550
9260.9210
111
818
931
5.920.58
7.6
8
6.4
9263.4294
012
633
744
5.25iO.24
8.38
9.59
5.57 6.16
9272.2696
111
e36
955
4.74io.31
6.97
1.35
9274.6446
012
734
845
5.92+_0.21
10.3
9.09
92W.0295
012
634
743
15.5e1.43
23.8
40.9
16.4
9280.8090
012
541
652
33.15i1.55
45.2
75.3
30
9281.0820
012
542
651
9.55tO.27
15.1
25.3
10
9283.5903
012
625
734
4.1eo.47
12.8
33.8
9
9289.9265
210
625
752
4.23+_0.32
0.07
5.76
-
9303.1354
012
642
753
5.17iO.21
9304.4030
012
643
152
15.65iO.41
21.5
35
15.56
9305.4474
012
550
661
25.24+1.11
30.4
56
21.5
012
551
660
10.2
19
7.2
9319.8997
012
505
634
4.42iO.34
4.87
13.9
3.54
9323.1785
012
743
854
7.120.38
8.9
12.6
9325.0810
012
651
762
1.85+_0.32
4.85
9325.1145
012
652
761
5.1kO.33
9321.44
012
744
853
2.30+_0.33
3.18
9328.9895
012
615
725
3.16iO.52
3.9
9343.6449
111
651
710
1.13+_0.29
0.57
0.58
1.10
9343.6845
111
652
771
4.4eO.36
1.72
1.76
3.33
9346.95
012
836
945
2.lttO.35
2.83
6.89
2.43
Note
:
bone taken point Lines
positions from
from were
with
Ref.(21
4 numbers and with
Ref.(31,
not
u*ed
while
after
7.17
14.5
decimal
2 numbers they
in fitting.
are
after absent
11.2
5.11
6.95
8.66
3.73
26
11.1
4.0
2.50
14.6
3.03
point
are
decimal in &f.(2).
178
CHEREPANOV TABLE
012
661
770
012
660
771
9351.1444
012
045
954
9356.8332
111
10110
1139
9350.3939
ET AL.
II-Continued
6.2eO.26 2.83c_O.96 3.02to.41
8.3
16.5
6.77
2.8
5.51
2.28
3.19
5.43
2.74
1.04
1.11
1.98
1.91
4.54
1.5
1.64
1.69
3.46
1.29
2.28
1.14
3.9
6.79
3.44
9356.13520 012
514
643
9366.6107
111
752
071
9371.68
012
762
871
012
761
872
9391.94
012
862
973
9391.96
012
863
972
9409.1295
012
707
836
1.4420.44
1.37
5.41
1.29
9412.7789
012
716
845
1.3430.21
1.38
4.17
1.30
3.03+_0.35 2.3OtO.72
1.67~0.46
0.49
-
0.47
1.48
-
1.41
derivatives of dipole moment pk23and &33 when the data on the lowest derivatives, & and &, and proper force field constants are available. RECEIVED:
May
3 1, 1984. REFERENCES
SWENSON, W. S. BENEDICT, L. DELBOULLE, AND G. ROLAND, “The Solar Spectrum from A = 7498 to X = 12016. A Table of Measurements and Identification,” Liege. 1970. J. M. FLAUD, C. CAMY-PEYRET, K. NARAHARI RAO, et al.. J. Mol. Spectrosc. 75, 339-362 (1979). V. E. ZUEV, V. P. LOPASOV, AND L. N. SINITSA, Opt. Spectrosc. 45, 590-593, 1978. J. B. BRECIUNRIECE AND D. N. B. HALL, Solar Phys. 28, 15-21 (1973). V. P. KOCHANOV, L. N. SINITSA, AND A. M. SOLOWV, Opt. Commun., in press. M. M. MAK~G~N AND A. M. SOLODOV, JETP Left. 4, 309-3 12 (1978). V. E. ZUEV, V. P. LOPASOV, L. N. SINITSA. AND A. M. SOLODOV, J. Mol. Spectrosc. 94, 208-210 (1982). Yu. S. MAKUSHKIN, Opt. Spectrosk. 37, 662-667 (1974). C. BLOCH, Nucl. Phys. 6, 329-347 (1958). VL. G. TYUTEREV, (unpublished). F. JORGENSEN, Mol. Phys. 29, 1137-l 164 (1975). Yu. S. MAKUSHKIN AND VL. G. TYUTEREV, Sov. Phys. J. I, 75-90 (1977). J. M. FLAUD AND C. CAMY-PEYRET, J. Mol. Spectrosc. 55, 278-3 10 (1975). F. LEGAY, Cah. Phys. 12, 416-436 (1958). C. CAMY-PEYRET AND J. M. FLAUD, Mol. Phys. 32, 523-537 (1976). C. CAMY-PEYRET, J. M. FLAUD, AND R. A. TOTH, J. Mol. Spectrosc. 67, I 17-131 (1977). 0. K. VOITSEKHOVSKAYA, I. I. IPPOLITOV, AND Yu. S. MAKUSHKIN. Opt. Spektrosk. 35, 42-47 (1973). R. A. TOTH, J. Ql;ant. Spectrosc. Radiat. Transfer 13, 1127-I 142 (1973). I. I. IP~~LITOV AND Yu. S. MAKUSHKIN, Sov. Phys. J. 3, 101-107 (1970).
1. J. 2. 3. 4. 5. 6. 7. 8. 9. 10. Il. 12. 13. 14. 15. 16. 17.
18. 19. 20. L. S. ROTHMAN, R. R. CRAMACHE, A. BARBE, A. GOLDMAN, J. R. GILLIS. L. R. BROWN, R. A. TOTH, J. M. FLAUD, AND C. CAMY-PEYRET, App. Opt. 22, 2247-2256 (1983).
OF MOL.ECULAR
SPECTROSCOPY
111,
173-178
(1985)
Water Vapor Line Strengths in the l-pm Region V. N. CHEREPANOV.V. P. KOCHANOV. Yu. S. MAKUSHKIN, L. N. SINITSA, A. M. SOLODOV, 0. N. SULAKSHINA, AND 0. K. VOITSEKHOVSKAYA The Instiiute yf .Iimospheric Oplics SB. USSR kademy yf Sciences, 1. .4kadetnicheskii Avenue. Torn& 634055. USSR The line strengths of Hz0 bands v, + vz + q and v2 + 2~ have been measured using a highresolution Nd-glass single-mode laser spectrophotometer. The parameters of 33 lines were found by fitting a Voigt contour to experimental line profile. The vibration-rotation interaction affecting the line strength was taken into account by using the F factor in the three-parametric form, and its constants for v, + v2 + s, and vz + 2~ bands were found. There is a good agreement between line intensities calculated using these constants and the experimental values. & 1985 Academc Press. Inc. I. INTRODUCTION
A wide range of problems in spectroscopy, atmospheric optics, and astrophysics require precise knowledge of the fine structure of the vibration-rotation spectra of water vapor. Until recently, only a few papers are known (1-4) in which the H20 absorption spectra in the 1-pm region were measured. In Ref. (I) weak lines of the water vapor bands v2 + 2v3, vl + v2 + v3, and 2vi + v2 were observed in the solar spectra due to absorption by the Earth’s atmosphere. The positions of the strongest Hz0 lines in the region 8050-9370 cm-’ were measured using the Fourier spectrometer with a spectral resolution of 5 - 10e3 cm-’ in Ref. (2). Several water vapor absorption lines in the range of 9241-9455 cm-’ were recorded using the intracavity laser spectrometer with an effective absorption length of 10 km in Ref. (3). It should be noted that. as distinct to line positions, absolute strength measurements were made only for a few of the absorption lines of the solar spectrum in the region 92209243 cm-’ (4). This paper presents the results of the absolute line strength measurements of the v2 + 2~3, vI + v2 + 5, and 2vi + v2H20 bands using the high-resolution laser spectrophotometer, which has been described earlier (5). The line strengths obtained were processed to find the dipole moment matrix element parameters for vibrationrotation interactions. II. EXPERIMENTAL
DETAILS
The high-resolution laser spectrophotometer was developed on the basis of the running-wave ring-cavity Nd-glass laser with frequency continuously tuned during a generation pulse (6). The instantaneous spectral line width of the laser was extremely narrow (less than 2 MHz) and was tuned during the generation pulse up 173
0022-2852185 Copyri~t All n&s
0
$3.00
1985 by Academic Press. Inc.
of reproduction in any form reserved.
174
CHEREPANOV
ET AL.
to 0.7 cm- ‘. The total spectral range of generation (9240-9500 cm-‘) was covered from pulse to pulse by turning a dispersion prism in the laser cavity. The line position of the laser generation was controlled using the grating spectrometer with an accuracy of 0.08 cm-‘, while the precise frequency measurements (0.001 cm-‘) were carried out using a thermostatic evacuated Fabry-Perot interferometer which has a base length of 103.5 mm. The laser generation strongly depends on absorption of atmospheric air inside its cavity: thus, such a laser should operate as an intracavity spectrometer (7). To eliminate this effect the laser cavity was evacuated; this enabled us to obtain smooth laser pulses even if strong atmospheric absorption lines were in the tuning frequency range of the laser. The spectra have been recorded using the gas sample contained in a 3-m-long “White-type” multipass absorption cell set for a 280-m pathlength. The temperature control was conducted with an accuracy of 0.5 K and the gas pressure was determined with a precision of 2%. The intensity of the light beam incident on the absorption cell was about 100 times lower than that of the output laser beam so that, as simple estimations showed, nonlinear absorption effects and gas sample heating certainly did not occur at the given experimental conditions. The line shape was assumed as a Voigt profile:
(1)
Here v is the running frequency, v. is the center of the absorption line, S is the line strength, P is the homogeneous (impact) halfwidth, KS is the Boltzmann constant, T is the gas temperature, and m. is the mass of the absorbing molecules. The values of the parameters S, P, and vo, as well as the confidence intervals AS, AP, and Avo for 95% probability level have been obtained by least-squares fitting. It was revealed that about 30 points for each experimental line shape were required to provide the accuracy of the line strength measurements AS/S N 10%; and two or three scans were used to obtain the actual values of the parameters. While processing the overlapping spectral lines, the number of experimental points Ki(Vi) was doubled and the absorption coefficient K(Y) was regarded as a sum of expressions (1) with independent parameters. The spectral line width of the laser was about two orders of magnitude less than the Doppler width of the investigated absorption lines; that enabled us to neglect the effect of instrumental function of the spectrometer on the measured data. High resolution of the spectrophotometer provided for reliable separation of the overlapping lines of the water vapor at wavenumbers 9343.6, 9325.1, and 9257.1 cm-‘, recorded at the water vapor pressures, PHzo of 17.1, 14.5, and 2.7 Torr, respectively (Fig. 1). The positions of the strongest lines of each doublet and their assignments were taken from Ref. (2). The positions of the weaker lines of doublets were measured using the Fabry-Perot interferometer with a 0.001 cm-’ accuracy relative to the stronger lines.
WATER VAPOR LINE STRENGTHS
175
\
5-
O-
5-
3, 9257.04
0 08 FREClUENCY
CM -’
FIG. 1. The experimental record of overlapping lines (0). The solid line represents the best-fitted sum of two contours (I); the dashed line corresponds to separated lines.
It should be noted that in the Fourier transform spectrometer measurements (2) only a doublet at 9343 cm-’ was resolved. The obtained wavenumber separation of the line in this doublet was Au = 0.0396 + 0.005 cm-‘: this differs somewhat from our measurements, Au = 0.0337 f 0.0020 cm-‘. III. DETERMINATION
OF INTRAMOLECULAR
PARAMETERS
In order to obtain a reliable interpretation of the experimental spectra one should take into account intramolecular interactions. At present, powerful theoretical methods of calculation of vibration-rotation molecular spectra are available, and they are based on the idea of constructing effective rotational Hamiltonians (8-12). These methods enabled one to simplify significantly the expression for a total vibration-rotation wave function and to describe precisely the spectra observed. In particular, due to these methods a good agreement between the experimental and theoretical line intensity values of the pure rotational spectrum, fundamental, and first overtone HZ0 bands was reached, using the conventional treatment of the perturbation theory both in the form of contact transformation (13-16) and in the projector form (8, 17. 18). One of the variants of the projector calculation technique was used in this paper for analyzing the measured Hz0 absorption line intensities (8, II). In this case, the matrix element of dipole moment in the first approximation of the perturbation theory in the absence of resonance interactions can be written as I( V’R’IMIVR)IZ = (CY’+ pm + rC(K)/C)? *L, where (Y’= CI+ ( Vl&.lLV);
(2)
CHEREPANOV
176
ET AL.
TABLE I
The Parametersof the MatrixElementof the Hz0 DipoleMoment* Band
oi
v, + 2 VI + v,
v,
(-2.48+_0.28).10
+ v,
(
is the
l
denotes a’=
(-1.88+0.15)'~O-4
/
number
(7 exp ’ ~CAC
,(-1.71+0.21)~10-5
3.2*0.71j*10-3 I ( 2.43 + ,.,,47
1
N
(-3.4+_0.46).10-5
are that
of the in
(v’(cg(v)
lines
used
1
in
experimental
parentheaea
18
6
10
( ,2
( ,0_25
1
1
1
I
,4
processing; and
the
% uexp,% CJrdc.
N
Y
P
-4
reproductional
standard
deviation
errcms, is
also
respectively; given.
+ CY.
V’R’ and VR are the vibration and rotation quantum numbers of the upper and lower energy levels, respectively; (Y, p, and y are the parameters of vibrationrotation interaction; m, C, and C(K) are functions which depend on rotational quantum numbers (17, 19). L is the line strength, and fig is the projection of dipole moment of molecule on the molecular axis g:
g=
X,
V’= 111
i Y,
V’ = 012.
The experimental values of H20 absorption line intensities (18 lines of the v2 + 2v3 band and 6 lines of the v1 + v2 + v3 band) obtained in this paper were used for determination of (Y, 0, and y parameters. Since six lines of the vI + v2 + v3 are insufficient for reliable statistical processing, additional line strengths of v, + v2 + v3 band from Ref. (4) were used. The results of fitting by the least-squares method are given in Table I. In spite of a relatively small number of lines used in the fitting, the parameters of vibrationrotation interaction were obtained with good accuracy. The representation (2) of the matrix element of the dipole moment can be regarded as satisfactory. Table II gives the intensities of Scale.using a’, 0, and y parameters in comparison with the experimental ones (Sex&, with the intensities s T,T,,and data from the 1982 version of the Air Force Geophysics Laboratory compilation and Ref. (20). The values of Scale.obtained using expression (2) are in good agreement with the experimental data, including the lines noted in Table II by (*), which were not used in the fitting. As may be noticed from Table II, the model of rigid rotator is not applicable with the investigated bands since it leads to errors in the line strengths up to 100%. This conclusion is in agreement with the theoretical estimations of the influence of regular vibration-rotation interaction on the line intensities made in Ref. (19). The parameters 01’, ,f3, and y can be used for determining the third
177
WATER VAPOR LINE STRENGTHS TABLE II Hz”0 Vibration-Rotation Line Intensities of the 000 - r’; v2V; Bands. (S, cm-’ mol-’ cm2. 102’; T = 296 K) -1 ?I cm v;v;v;
j@c-J’K&
5.r
s,p
S[x)l
9219.8520
012
414
523
14.5
i4I
25.5
9221.8964
111
134
853
7.96
141
14.4
15.3
9224.2410
111
634
753
11.29[4]
21.2
22.1
0.85
59.1
3.48
Scale. 14.21' 7.02 12.2 0.39+
9224.8013
012
716
743
9227.6997
012
431
542
9229.2919
012
432
541
52.1 [41
9229.6967
111
835
954
1.27 141
2.99
1.34
9237.8018
111
936
1055
2.67 141
4.18
4.49
2.03
9241.5674
111
918
1037
2.68 141
4.84
5.13
3.09
9242.8633
111
505
642
2.04[41
3.56
3.57
2.94
9243.06
012
524
633
6.51 L4]
12.6
24.8
7.72'
9251.2366
111
627
946
7.92+_0.28
10.2
10.8
7.22
642
10.85+_0.37
1.8
28.6
11.2
551
16.2&_2.08
28.2
49.1
17
53.1%_2.2
84.7
147
51.2
0.54 [41 19.6
141
35.6
52.7
107
164
2.79
20' 60.5'
9253.5810
012
533
9257.0521
012'
440
9257.0813
012
441
550
9260.9210
111
818
931
5.920.58
7.6
8
6.4
9263.4294
012
633
744
5.25iO.24
8.38
9.59
5.57 6.16
9272.2696
111
e36
955
4.74io.31
6.97
1.35
9274.6446
012
734
845
5.92+_0.21
10.3
9.09
92W.0295
012
634
743
15.5e1.43
23.8
40.9
16.4
9280.8090
012
541
652
33.15i1.55
45.2
75.3
30
9281.0820
012
542
651
9.55tO.27
15.1
25.3
10
9283.5903
012
625
734
4.1eo.47
12.8
33.8
9
9289.9265
210
625
752
4.23+_0.32
0.07
5.76
-
9303.1354
012
642
753
5.17iO.21
9304.4030
012
643
152
15.65iO.41
21.5
35
15.56
9305.4474
012
550
661
25.24+1.11
30.4
56
21.5
012
551
660
10.2
19
7.2
9319.8997
012
505
634
4.42iO.34
4.87
13.9
3.54
9323.1785
012
743
854
7.120.38
8.9
12.6
9325.0810
012
651
762
1.85+_0.32
4.85
9325.1145
012
652
761
5.1kO.33
9321.44
012
744
853
2.30+_0.33
3.18
9328.9895
012
615
725
3.16iO.52
3.9
9343.6449
111
651
710
1.13+_0.29
0.57
0.58
1.10
9343.6845
111
652
771
4.4eO.36
1.72
1.76
3.33
9346.95
012
836
945
2.lttO.35
2.83
6.89
2.43
Note
:
bone taken point Lines
positions from
from were
with
Ref.(21
4 numbers and with
Ref.(31,
not
u*ed
while
after
7.17
14.5
decimal
2 numbers they
in fitting.
are
after absent
11.2
5.11
6.95
8.66
3.73
26
11.1
4.0
2.50
14.6
3.03
point
are
decimal in &f.(2).
178
CHEREPANOV TABLE
012
661
770
012
660
771
9351.1444
012
045
954
9356.8332
111
10110
1139
9350.3939
ET AL.
II-Continued
6.2eO.26 2.83c_O.96 3.02to.41
8.3
16.5
6.77
2.8
5.51
2.28
3.19
5.43
2.74
1.04
1.11
1.98
1.91
4.54
1.5
1.64
1.69
3.46
1.29
2.28
1.14
3.9
6.79
3.44
9356.13520 012
514
643
9366.6107
111
752
071
9371.68
012
762
871
012
761
872
9391.94
012
862
973
9391.96
012
863
972
9409.1295
012
707
836
1.4420.44
1.37
5.41
1.29
9412.7789
012
716
845
1.3430.21
1.38
4.17
1.30
3.03+_0.35 2.3OtO.72
1.67~0.46
0.49
-
0.47
1.48
-
1.41
derivatives of dipole moment pk23and &33 when the data on the lowest derivatives, & and &, and proper force field constants are available. RECEIVED:
May
3 1, 1984. REFERENCES
SWENSON, W. S. BENEDICT, L. DELBOULLE, AND G. ROLAND, “The Solar Spectrum from A = 7498 to X = 12016. A Table of Measurements and Identification,” Liege. 1970. J. M. FLAUD, C. CAMY-PEYRET, K. NARAHARI RAO, et al.. J. Mol. Spectrosc. 75, 339-362 (1979). V. E. ZUEV, V. P. LOPASOV, AND L. N. SINITSA, Opt. Spectrosc. 45, 590-593, 1978. J. B. BRECIUNRIECE AND D. N. B. HALL, Solar Phys. 28, 15-21 (1973). V. P. KOCHANOV, L. N. SINITSA, AND A. M. SOLOWV, Opt. Commun., in press. M. M. MAK~G~N AND A. M. SOLODOV, JETP Left. 4, 309-3 12 (1978). V. E. ZUEV, V. P. LOPASOV, L. N. SINITSA. AND A. M. SOLODOV, J. Mol. Spectrosc. 94, 208-210 (1982). Yu. S. MAKUSHKIN, Opt. Spectrosk. 37, 662-667 (1974). C. BLOCH, Nucl. Phys. 6, 329-347 (1958). VL. G. TYUTEREV, (unpublished). F. JORGENSEN, Mol. Phys. 29, 1137-l 164 (1975). Yu. S. MAKUSHKIN AND VL. G. TYUTEREV, Sov. Phys. J. I, 75-90 (1977). J. M. FLAUD AND C. CAMY-PEYRET, J. Mol. Spectrosc. 55, 278-3 10 (1975). F. LEGAY, Cah. Phys. 12, 416-436 (1958). C. CAMY-PEYRET AND J. M. FLAUD, Mol. Phys. 32, 523-537 (1976). C. CAMY-PEYRET, J. M. FLAUD, AND R. A. TOTH, J. Mol. Spectrosc. 67, I 17-131 (1977). 0. K. VOITSEKHOVSKAYA, I. I. IPPOLITOV, AND Yu. S. MAKUSHKIN. Opt. Spektrosk. 35, 42-47 (1973). R. A. TOTH, J. Ql;ant. Spectrosc. Radiat. Transfer 13, 1127-I 142 (1973). I. I. IP~~LITOV AND Yu. S. MAKUSHKIN, Sov. Phys. J. 3, 101-107 (1970).
1. J. 2. 3. 4. 5. 6. 7. 8. 9. 10. Il. 12. 13. 14. 15. 16. 17.
18. 19. 20. L. S. ROTHMAN, R. R. CRAMACHE, A. BARBE, A. GOLDMAN, J. R. GILLIS. L. R. BROWN, R. A. TOTH, J. M. FLAUD, AND C. CAMY-PEYRET, App. Opt. 22, 2247-2256 (1983).